Kind: captions
Language: en
the following is a conversation with
Steven Wolfram his second time in the
podcast he's a computer scientist
mathematician theoretical physicist and
the founder and CEO of Wolfram research
a company behind Mathematica wol from
alpha Wolfram language and the new wolf
from physics project he's the author of
several books including a new kind of
Science and the new book a project to
find the fundamental Theory of physics
this second round of our conversation is
primarily focused on this latter
Endeavor of searching for the physics of
our universe in simple rules that do
their work on hypergraphs and eventually
generate the infrastructure from which
space time and all of modern physics can
emerge quick summary of the sponsors
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me say that to me the idea that
seemingly infinite complexity can arise
from very simple rules and initial
conditions is one of the most beautiful
and important mathematical and
philosophical Mysteries and science I
find that both cellular aoma and the
hypography working on to be the kind of
simple clear mathematical playground
within which fundamental ideas about
intelligence Consciousness and the
fundamental laws of physics could be
further developed in totally new ways in
fact I think I'll try to make a video or
two about the most beautiful aspects of
these models in the coming weeks
especially I think trying to describe
how fellow curious minds like myself can
jump in and explore them either just for
fun or potentially for publication of
new Innovative Research In Math computer
science and physics but honestly I think
the emerging complexity in these
hypergraphs can capture the imagination
of everyone even if you're someone who
never really connected with mathematics
that's my hope at least to have these
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finally here's my conversation with
Stephen
wlfr you said that there are moments in
history of physics it may be
mathematical physics or even mathematics
where breakthroughs happen and then a
flurry of progress follows so if you
look back through the history of physics
are what moments stand out to you as
important such breakthroughs where a
flurry of progress follows so the big
famous one is 1920s the invention of
quantum mechanics where you know in
about 5 or 10 years lots of stuff got
figured out that's now quantum mechanics
can you mention the people involved yeah
that kind of the shener Heisenberg you
know Einstein had been a key figure
originally plank then dur was a little
bit later that was something that
happened at that time that's sort of
before my time right in my time was in
the
1970s uh there was this sort of
realization that Quantum field theory
was actually going to be useful in
physics and uh qcd Quantum
thermodynamics theory of ques and gluons
and so on was really getting started and
uh there was again sort of big flurry of
things happened then I happened to be a
teenager at that time and happened to be
uh really involved in physics and so I
got to be part of that which was really
cool who were the key figures aside from
your young selves at that time you know
who won the Nobel Prize for qcd okay
people David Gross Frank wilchek you
know um David poiter the people who are
the sort of the slightly older
generation dick feineman Murray Gman
people like that uh uh who were Steve
Weinberg GED Hof he's younger he's he's
in the younger group actually but um
these are these are all you know
characters who are involved I mean it
was uh you know it's funny because those
are all people who are kind of in my
time and I know them and they don't seem
like sort of uh historical uh you know
iconic figures they seem more like uh
everyday characters so to speak um and
uh uh so it's always you know when you
look at history from long afterwards it
always seems like everything happened
instantly um and that's usually not the
case there was usually a long buildup
but usually there's you know there's
some method iCal thing happens and then
there's a whole bunch of low hanging
fruit to be picked and that usually
lasts 5 or 10 years you know we see it
today with machine learning and you know
deep learning neural Nets and so on you
know methodological Advance things
actually started working in you know
2011 2012 and so on and uh you know
there's been this sort of Rapid uh
picking of loow hanging fruit which is
probably you know some significant
fraction of the way way done so to speak
do you think there's a key moment like
if I had to really introspect like what
was the key moment for the Deep learning
quote unquote
Revolution I mean it's probably the Alex
net business Alex net with imag net so
is there something like that with
physics
where so deep learning neural networks
have been around for a long time there's
a bunch of 1940s yeah there's a bunch of
little pieces that came together and
then all of a sudden everybody's eyes
lit up like wow there's something here
like even just looking at your own work
just you're thinking about the universe
that there's Simple Rules can create
complexity you know at which point was
there a thing where your eyes light up
it's like wait a minute there's
something here is it the very first idea
or is it some moment along the line of
implementations and experiments and so
on there's there's a couple of different
stages to this I mean one is the think
about the world computationally you know
can we use programs instead of equations
to make models of the world that's
something that I got interested in in
the at the beginning of the 1980s you
know I did a bunch of computer
experiments uh you know when I first did
them I didn't really I I could see some
significance to them but took me a few
years to really say wow there's a big
important phenomenon here that lets sort
of complex things arise from very simple
programs um that kind of happened back
in 198 4 or so then you know bunch of
other years go by then I start actually
doing a lot of much more systematic
computer experiments and things and find
out that the you know this phenomenon
that I could only have said occurs in
one particular case is actually
something incredibly General and then
that led me to this thing called
principle of computational equivalence
and that was a a long story and then you
know as part of that process I was like
okay you can make simple programs can
make models of complicated things what
about the whole universe that's our sort
of ultimate example of a complicated
thing yeah and so I got to thinking you
know could we use these ideas to to
study fundamental physics uh you know I
happen to know a lot about you know
traditional fundamental physics my um uh
my first you know I I had a bunch of
ideas about how to do this in the early
1990s I made a bunch of technical
progress I figured out a bunch of things
I thought were pretty interesting you
know I wrote about them back in 2002
with the new kind of Science and the
cellular ainal world
there's echo in the cellular aomin world
with your new wol from physics project
World we'll get to all that allow me to
sort of romanticize a little more on the
philosophy of
science uh so Thomas philosopher of
science
describes that you know the progress in
science is made with uh these Paradigm
shifts and so to linger on the sort of
original line of discussion do you agree
with this view that there is
Revolutions in science that just kind of
flip the table what happens is it's a
different way of thinking about things
it's a different methodology for
studying things and that opens stuff up
this is this idea of
uh he's a famous biographer but I think
it's called the
innovators the biographer of Steve Jobs
of Albert Einstein he also wrote a book
I think it's called an evaders where he
discusses uh how a lot of uh the
Innovations in the history of computing
has been done by groups there's a
complicated group dynamic going on but
there's also a romanticized notion that
the individual is at the core of the
Revolution like where does your sense
fall is is uh ultimately like one person
responsible for these revolutions that
that creates the spark or one or two
whatever but or is it just the big mush
and mess and Chaos of of people
interacting the personalities
interacting I think it ends up being
like many things there's leadership and
there ends up being it's a lot easier
for one person to have a crisp new idea
than it is for a big committee to have a
crisp new idea and um I think you know
but I think it it can happen that you
know you have a great idea but the world
isn't ready for you for it and um you
know you can you can I mean this has
happened to me plenty right it's you
know you have an idea it's actually a
pretty good idea but things aren't ready
either either you're not really ready
for it or the ambient world isn't ready
for it and it's hard to get the thing to
to get traction it's kind of interesting
I mean when I look at a new kind of
science you're now living inside history
so you can't tell the story of these
decades but it seems like the new kind
of science has
not had the Revolutionary impact I would
think it uh might like it feels like at
some point of course it might be but it
feels at some point people will return
to that book and say there was something
special here this was incredible what
happened or do you think that's already
happened oh yeah it's happened except
that people aren't you know the the sort
of the heroism of it may not be there
but the what's happened is for 300 years
people basically said if you want to
make a model of things in the world
mathematical equations are the best
place to go
last 15 years doesn't happen you know
new models that get made of things most
often are made with programs not with
equations mhm now you know was that sort
of going to happen anyway was that a
consequence of you know my particular
work in my particular book it's hard to
know for sure I mean I am always amazed
at the amount of feedback that I get
from people where they say oh by the way
you know I started doing this whole line
of research because I read your book
blah blah blah blah blah it's like well
can you tell that from the academic
literature you know were was there a
chain of you know academic references
probably not one of the interesting side
effects of publishing in the way you did
this toome is it serves as an education
tool and an inspiration
to hundreds of thousands millions of
people but because it's not a single
it's not a chain of papers with piffy
titles it doesn't create a splash of
citations like it's had it's had plenty
of citations but it's it's you know I
think that the IT people think of it as
probably more you know conceptual
inspiration than uh than kind of a you
know this is a line from here to here to
here in our particular field right I
think that the you know the thing which
I am disappointed by and which will
eventually happen is this kind of study
of the this sort of pure
computationalism this kind of study of
the abstract behavior of the
reputational universe that should be a
big thing that lots of people do you
mean in mathematics purely almost like
it's still mathematics but it isn't
mathematics but it isn't it isn't it's a
new kind of mathematics it's atitle the
book yeah right that's why the book is
called that right that's not
coincidental yeah it's interesting that
I haven't seen really rigorous
investigation by thousands of people of
this idea I mean you look at your
competition around rule 30 I mean that's
fascinating if if you can say
something right is there some aspect of
this thing that could be predicted
that's a fundamental question of science
that's the core that has been a question
of science I think that's a that is a
some people's view of what science is
about and it's not clear that's the
right view in fact as we as we live
through this pandemic full of
predictions and so on it's an
interesting moment to be pondering what
what science's actual role in those
kinds of things is oh you think it's
possible that in
science clean beautiful simple
prediction may not even be possible in
real systems that's the open right
question I don't think it's open I think
that question is answered and the answer
is no well no no the answer could be
just humans are not smart enough yet
like we don't have the tools no that's
that's the whole point I mean that's
that's sort of the big discovery of this
principle of computational equivalence
of mine and um the uh you know this is
something which is kind of a follow on
to girdle's theorem to turing's work on
the halting problem all these kinds of
things that there is this fundamental
limitation built into science this idea
of computational irreducibility that
says that you know even though you may
know the rules by which something
operates that does not mean that you can
uh readily sort of be smarter than it
and jump ahead and figure out what it's
going to do yes but do you think there's
a hope for pockets of computational
reducibility computational re
reducibility
reducibility that's so and then and then
a set of tools and Mathematics that help
you discover such pockets that's where
we live is in the pockets of
reducibility right that's why you know
and this is one of the things that sort
of come out of this physics project and
actually something that again I should
have realized many years ago but didn't
um is uh you know the it it could very
well be that everything about the world
is computationally irreducible and
completely unpredictable but you know in
our experience of the world there is at
least some amount of prediction we can
make and that's because we have sort of
chosen a slice of um probably talk about
this in in much more detail but I mean
we've kind of chosen a slice of how to
think about the universe in which we can
kind of sample a certain amount of
computational reducibility and that's
that's sort of where we where we exist
um and uh it may not be the whole story
of how the universe is but it is the
part of the universe that we care about
and we sort of operate in and um that's
you know in science that's been sort of
a very special case of that that is
science has chosen to talk a lot about
places where there is this computational
reducibility that it can find you know
the motion of the planets can be more or
less predicted you know the uh uh
something about the weather is much
harder to predict something about you
know other kinds of things the the um
are much harder to predict and it it's
um uh these are but science has tended
to you know concentrate itself on places
where its methods have allowed
successful prediction so you think rule
30 if it could Linger on it because it's
just such a beautiful simple formulation
of the essential concept underlying all
the things we're talking about do you
think there's pockets of reducibility
inside rule 30 yes but it's a question
of how big are they what will they allow
you to say and so on and that's and
figuring out where those pockets are I
mean in a sense that's the that's sort
of a uh uh you know that is an essential
thing that one would like to do in
science um but it's it's also the the
important thing to realize that that has
not been you know is is that science if
you just pick an arbitrary thing you say
what's the answer to this question that
question may not be one that has a
computationally reducible answer that
question if you if you choose you know
if you walk along the series of
questions and you've got one that's
reducible and you get to another one
that's nearby and it's reducible too if
you stick to that kind of stick to the
land so to speak yeah then you can go
down this chain of sort of reducible
answerable things but if you just say
I'm just pick a question at random I'm
going to have my computer pick a
question at random yeah uh most likely
it's going to be irreducible most likely
it will be irreducible and and what
we're throwing in the world so to speak
uh we you know when we engineer things
we tend to engineer things to sort of
keep in the zone of reducibility when
we're thrown things by the natural world
for example not not at all certain that
we will be kept in this kind of zone of
reducibility can we talk about this
pandemic
then for a second is so how do we
there's obviously huge amount of
economic pain that people are feeling
there's a huge incentive and medical
pain uh Health just all kind
psychological there's a huge incentive
to figure this out to walk along the
trajectory of reducible of
reducibility there's there's a a lot of
disperate data you know people
understand generally how virus is spread
but it's very complicated because
there's a lot of uncertainty there's
a there could be a lot of variability
like so many obviously a nearly infinite
number of variables that uh that
represent human interaction and so you
have to figure out in ter from the
perspective of reducibility figure out
which
variables are really important in this
kind of uh from an epidemiological
perspective so why aren't we you kind of
said that we're clearly failing well I I
think it's a complicated thing so so I
mean you know when this pandemic started
up you know I happen to be in in the
middle of being about to release this
whole physics project thing but I
thought you know the timing is just uh
cosmically
but but um but you know but I thought
you know I I should do the public
service thing of you know trying to
understand what I could about the
pandemic and you know we've been
curating data about it and all that kind
of thing but but you know so I started
looking at the data and started looking
at modeling and I decided it's just
really hard you need to know a lot of
stuff that we don't know about human
interactions it's actually clear now
that there's a lot of stuff we didn't
know about viruses um and about the way
immunity works and so on and um it's you
know I think what will come out in in
the end is there's a certain amount of
of what happens that way you just kind
of have to trace each step and see what
happens there's a certain amount of
stuff where there's going to be a big
narrative about this happened because
you know of te- cell immunity this
happened because there's this whole
giant sort of field of of of
asymptomatic viral stuff out there you
know there will be a narrative and that
narrative whenever there's a narrative
that's kind of a sign of reducibility
but when you just say let's from first
principles figure out what's going on
then you can potentially be stuck in
this kind of uh mess of irreducibility
where you just have to simulate each
step and you can't do that unless you
know details about you know human
interaction networks and so on and so on
and so on the thing that has has been
very sort of frustrating to see is the
mismatch between people's expectations
about what science can deliver and what
science can actually deliver so to speak
um because people have this idea that
you know it's science so there must be a
definite answer and we must be able to
know that answer and you know this is it
is both uh uh you know that when you
after you've played around with sort of
little programs in the computational
universe you don't have that intuition
anymore you know it's it's I always I'm
always fond of saying you know the the
the the computational animals are always
smarter than you are that is you know
you look at one of these things and it's
like it can't possibly do such and such
a thing then you run it and it's like
wait a minute it's doing that thing how
does that work okay now I can go back
can understand it but that's the brave
thing about science is that in the chaos
of the irreducible universe we
nevertheless persist to find those
pockets that's kind of the whole point
that's like you say that the limits of
science but that you know yes it's
highly limited but there there's a hope
there and like there there's so many
questions I want to ask here so one you
said narrative which is really
interesting so obviously from uh at
every level of society you look at
Twitter everybody's constructing
narratives about the pandemic about not
just the pandemic but all the cultural
tension that we're going through so
there's narratives but they're not
necessarily connected to the
underlying reality of these systems so
our human narratives I don't even know
if
they're I don't like those pockets of
reducibility Cu we're uh it's like
constructing things that are not
actually representative of
reality well and thereby not giving us
like good solutions to how to predict
the system look it it gets complicated
because you know people want to say
explain the pandemic to me explain
what's going to happen in the future
like yes but but also can you explain it
is there a story to tell what already
happened in the past yeah what's going
to happen but I mean in you know it's
similar to sort of explaining things in
AI or in any computational system it's
like like you know explain what happened
well it could just be this happened
because of this detail and this detail
and this detail and a million details
and there isn't a big story to tell
there's no kind of Big Arc of the story
that says oh it's because you know
there's a viral field that has these
properties and people start showing
symptoms you know when when the seasons
change people will show symptoms and
people don't even understand you know
seasonal variation of flu for example
it's a it's a um uh it's something where
where you know that that could be a big
story or it could be just a zillion
little details that that mount up see
but okay let's let's uh pretend that
this pandemic like the Corona virus
resembles something like the
1D rule 30 cellular aoma okay so I mean
that's how
epidemiologists model virus spread
indeed yes sometimes use cellometer yes
yes and okay so you can say it's
simplistic but okay let's say it it is
it's representative of actually what
happens uh you know the the dynamic of
you have a graph it probably is closer
to the hypergraph uh model is yes it's
it's actually that's another funny thing
as as we were getting ready to release
this physics project we realized that a
bunch of things we'd worked out about
about foliations of causal graphs and
things were directly relevant to
thinking about contact tracing and
interaction of cell phones and so on
which is really weird but like it just
feels like uh it feels like we should be
able to get some beautiful core insight
about the spread of this particular
virus on the hypergraph of human
civilization right they I tried I didn't
I didn't manage to figure it out but
you're one person yeah but I mean I
think actually it's a funny thing
because it turns out the um the main
model you know this sir model I I only
realized recently was invented by the
the grandfather of a good friend of mine
from high school so that was just a you
know it's a weird thing right the
question is you know okay so you know
you know on this graph of how humans are
connected you know something about what
happens if this happens and that happens
that graph is made in complicated ways
that depends on on all sorts of issues
that where we don't have the data about
how Human Society works well enough to
be able to make that graph there's
actually um uh one of my kids did a
study of sort of what happens on
different kinds of graphs and how robust
are the results okay his basic answer is
there are few General results that you
can get that are quite robust like you
know a small number of big gatherings is
worse than a large number of small
Gatherings okay that's quite robust but
when you ask more detailed questions it
seemed like it just depends it depends
on details in other words it's kind of
telling you in that case you know the
irreducibility matters so to speak it's
not there's not going to be this kind of
one sort of Master theorem that says and
therefore this is how things are going
to work yeah but the there's a certain
kind of from a graph
perspective the certain kind of dynamic
to human
interaction so like large groups and
small groups I think it matters who the
groups are for example you could imagine
large depends how you define large but
you can imagine groups of 30
people as long like as long as they are
uh cleaks or whatever like right as as
long as the outgoing degree of that
graph is small or something like like
that like you can imagine some beautiful
underlying rule of human Dynamic
interaction where I can still be happy
where I can have a conversation with you
and a bunch of other people that mean a
lot to me in my life and then stay away
from the bigger I don't know not going
to Miley Cyrus concert or something like
that and and figuring out mathematically
some nice see this is an interesting
thing so I mean in you know this is the
question of what you're describing as
kind of uh the problem of
many situations where you would like to
get away from computational
irreducibility a classic one in physics
is thermodynamics the you know the
second law of Thermodynamics the law
that says you know entropy tends to
increase things that you know start
orderly tend to get more disordered or
which is also the thing that says given
that you have a bunch of heat it's hard
heat is you know the microscopic motion
of molecules it's hard to turn that heat
into systematic mechanical work it's
hard to you know just take something
being hot and turn that into oh the the
you know the all the atoms are going to
line up in the bar of metal and the
piece of metal is going to shoot in some
Direction that's essentially the same
problem as how do you go from this this
computationally irreducible mess of
things happening and get something you
want out of it right it's kind of mining
you know you're kind of now you know
actually I've I've understood in recent
years that that the story of of
thermodynamics is actually precisely a
story of computational irreducibility
but it is a um it is already an analogy
you know you can you can kind of see
that is can you take the um you know
what you're asking to do there is you're
asking to go from the um uh the kind of
um the mess of all these complicated
human interactions and all this kind of
computational processes going on and you
say I want to achieve this particular
thing out of it I want to kind of
extract from the heat of what's
happening I want to kind of extract this
useful piece of sort of mechanical work
that I find helpful I mean do you have a
hope for the pandemic so we'll talk
about physics but for the pandemic can
that be extracted do you think what's
your intuition the good news is the
curves basically you know for reasons we
don't understand the curves you know the
the the clearly measurable mortality
curves and so on for the Northern
Hemisphere have gone down yeah but the
bad news is that it could be a lot worse
for future viruses and what this
pandemic revealed is we're highly
unprepared for the dis discovery of the
pockets of reducibility within a
pandemic that's much more dangerous well
my my guess is the specific risk of you
know viral pandemics you know that the
pure virology and you know Immunology of
the thing this will cause that to
advance to the point where this
particular risk is probably considerably
mitigated but you know it's uh you know
does is is the structure of modern
society robust to all kinds of risks
well the answer is clearly no and you
know it's it's surprising to me the
extent to which people uh you know as I
say it's it's a it's kind of scary
actually how much people believe in
science that is people say oh you know
because the science does this that and
the other we'll do this and this and
this even though from a sort of Common
Sense point of view it's a little bit
crazy and and people are not prepared
and it doesn't really work in in society
as it is for people to say well actually
we don't really know how the science
Works people say well tell us what to do
yeah because then yeah what's the
alternative the for the masses it's
difficult to sit it's difficult to
meditate on computational reducibility
it's difficult to sit it's difficult to
enjoy a good dinner meal while while
knowing that you know nothing about the
world I think this is a this is a place
where you know this is this is what
politicians you know and political
leaders do for a living so to speak
because you got to make some decision
about what to do and it's um tell some
narrative that uh
while amidst the mystery and knowing not
much about the the past or the future
still telling a narrative that somehow
gives people hope that we know what the
heck we're doing yeah get Society
through the issue you know even even
though you know the idea that we're just
going to you know sort of be able to get
the definitive answer from science and
it's going to tell us exactly what to do
unfortunately you know uh that it's
interesting because let me point out
that if that was possible if science
could always tell us what to do then in
a sense our you know that would be a big
Downer for our lives if science could
always tell us what the answer is going
to be it's like well you know it's kind
of fun to live one's life and just sort
of see what happens if one could always
just say Let me let me check my science
oh I know you know the result of
everything is going to be 42 I don't
need to live my life and do what I do
it's just we already know the answer
it's actually good news in a sense that
there is this phenomenon of
computational irreducibility that
doesn't allow you to just sort of jump
through time and say this is the answer
so to speak um and that's so that's a
good thing the bad thing is it doesn't
allow you to jump through time and know
what the answer is it's scary do you
think we're going to be okay as a human
civilization you said we don't know
absolutely do you think it's do you
think we'll Prosper or destroy ourselves
as a in general in general I'm an
optimist the no I think that that you
know it'll be interesting to see for
example with this you know pandemic I
you know to
me you know when you look at like
organizations for example you know
having some kind of pertubation some
kick to the system usually the end
result of that is actually quite good
you know unless it kills the system it's
actually quite good usually and I think
in this case you know people I mean my
impression you know it's it's a little
weird for me because you know I've been
a remote Tech CEO for 30 years it
doesn't you know this is bizarrely uh
you know in the fact that you know like
this coming to see you here is is one of
the rare moments the first time in six
months that I've been like you know in a
building other than my house okay so so
so you know it's I'm I'm a kind of
ridiculous outlier in these kinds of
things but overall your sense is when
you shake up the system and throw in
chaos that you you uh challenge the
system we humans emerge better seems to
be that way who's to know but I think
that you know people you know my my sort
of vague impression is that people are
sort of you know oh what's actually
important you know what's uh what what
is worth caring about and so on and that
seems to be something that perhaps is is
more you know emergent in this kind of
situation it's so fascinating that on
the individual level we have our own
complex cognition we have Consciousness
we have intelligence we're trying to
figure out little puzzles and then that
somehow creates this graph of collective
intelligence where we figure out and
then you throw in these viruses of which
there's Millions different you know this
entire taxonomy and the viruses are
thrown into the system of collective
human intelligence and we little humans
figure out what to do about it we get
like we Tweet stuff about information
there's doctors as conspiracy theorists
and then we play with different
information I mean the whole of it is
fascinating um I I like you also very
optimistic but uh there's a fe just you
said uh the computational
reducibility there's always a fear of
the darkness of the uncertainty be
before us yeah it's scary I mean the
thing is if you knew everything it will
be
boring and and it would be and and then
um uh and worse than boring so to speak
it would be you it would reveal the
pointlessness so to speak and in a sense
the the fact that there is this
computational ability it's like as we
live our lives so to speak something is
being achieved we're Computing what our
lives you know uh you know what happens
in our lives that's funny so the
computation reducibility is kind of like
it gives the meaning to life it is the
meaning of life computation reducibility
is the meaning of life there you go it
it gives it meaning yes I mean it it it
it it's what it's what causes it to not
be something where you can just say uh
you know you went through all those
steps to live your life but we already
knew what the answer was was right hold
on one second I'm going to use my handy
wol from alfha sunburn computation thing
so long as I can get network here there
we
go oh actually you know what it says
sunburn unlikely this is a QA
moment this is a good moment okay okay
well let me just check what it thinks
see why it thinks that it doesn't seem
like my intuition this is one of these
cases where we can the question is do we
do we trust the science or do we um use
common sense the UV thing is cool the
yeah yeah well we'll see this is a QA
moment as I say it's
uh do we trust the product yes we trust
the product so and then there'll be a
data point either way if if I'm
desperately sunburned I will send in a
angry feedback because we mention the
concept so much and a lot of people know
it but can you say what competition
reducibility is yeah right so I mean the
question is if you think about things
that happen as being computations you
think about the uh some process in
physics something that you compute in
mathematics whatever else it's a
computation in the sense it has definite
rules you follow those rules you uh
follow them many steps and you get some
result so then the issue is if you look
at all these different kinds of
computations that can happen whether
they're computations that are happening
in the natural world whether they're
happening in our brains whether they're
happening in our mathematics whatever
else the big question is how do these
computations compare is are there dumb
computations and smart computations or
are they somehow all equivalent and the
thing that I kind of uh was sort of
surprised to realize from a bunch of
experiments that I did in the early 90s
and now we have tons more evidence for
it this thing I call the principle of
computational equivalence which
basically says when one of these
computations one of these processes that
follows rules doesn't seem like it's
doing something obviously simple then it
has reached the sort of equivalent level
of sophistic of computational
sophistication of everything so what
does that mean that means that you know
you might say gosh I'm I'm studying this
little tiny you know tiny program on my
computer I'm studying this little thing
in in nature but I have my brain and my
brain is surely much smarter than that
thing I'm going to be able to
systematically outrun the computation
that it does because I have a more
sophisticated computation that I can do
but what the principle of computational
equivalence say say is that doesn't work
our our brains are doing computations
that are exactly equivalent to the kinds
of computations that are being done in
all these other sorts of systems and so
what consequences that have well it
means that we can't systematically
outrun these systems these systems are
computationally irreducible in the sense
that there's no sort of shortcut that we
can make that jumps to the answer now in
a general case right right but but the
so what has happened you know what
science has become used to doing is
using the little sort of pockets of
computational reducibility which by the
way are an inevitable consequence of
computational irreducibility that there
have to be these Pockets scattered
around of computational reducibility to
be able to find those particular cases
where you can jump ahead I mean one one
thing sort of a little bit of a parable
type thing that I think is is fun to
tell you know if you look at ancient
Babylon they were trying to predict
three kinds of things they tried to
predict you know where the planets would
be what the weather would be like and
who would win or lose a certain battle
and they had no idea which of these
things would be more predictable than
the other that's funny and and you know
it turns out you know where the planets
are is a is a piece of computational
reducibility that you know 300 years ago
or so we pretty much cracked I mean it's
been technically difficult to get all
the details right but it's basically we
we got that you know who's going to win
or lose the battle no we didn't crack
that one that one that one right
game theorist are trying and then the
weather kind of halfway on that halfway
yeah I think we we're doing okay at that
one I you know longterm climate
different story but but the weather you
know we're we're much closer on that but
do you think eventually we'll figure out
the weather so do you think eventually
most thing will figure out the local
pockets in everything essentially the
local pockets of reducibility no I think
that the it's a it's an interesting
question but I think that the you know
there is an infinite collection of these
local Pockets we'll never run out of
local pockets and by the way those local
pockets are where we build engineering
for example that's how we you know when
we if we want to have a predictable life
so to speak then you know we have to
build in these sort of pockets of
reducibility otherwise you know if we
were if we were sort of existing in this
kind of irreducible world we'd never be
able to you know have definite things to
know what's going to happen you know I I
have to say I think one of the features
you know when we look at uh sort of
today from the future so to speak I
suspect one of the things where people
will say I can't believe they didn't see
that is stuff to do with the following
kind of thing so so you know if we
describe oh I don't know something like
um heat for instance we say oh you know
the air and in here it's you know it's
this temperature this pressure that's as
much as we can say otherwise just a
bunch of random molecules bouncing
around people will say I just can't
believe they didn't realize that there
was all this detail and how all these
molecules were bouncing around and they
could make use of that I mean actually I
realized there's a thing I realized last
week actually was um was a thing that
people say you know one of the scenarios
for the very long-term history of our
universe is a so-called heat death of
the universe where basically everything
just becomes thermodynamically boring
everything is just this big kind of gas
and thermal equilibrium people say
that's a really bad outcome but actually
it's not a really bad outcome it's an
outcome where there's all this comp
computation going on and all those
individual gas molecules are all
bouncing around in very complicated ways
doing this very elaborate computation it
just happens to be a computation that
right now we haven't found ways to
understand we haven't found ways you
know our brains haven't you know and our
mathematics and our science and so on
haven't found ways to tell an
interesting story about that it just
looks boring to us there's a there
you're saying there's a hopeful view of
the he death quote unquote of the
universe where there's actual beautiful
complexity going on similar to the kind
of complexity we think of that creates
Rich experience in human life and life
on Earth yes so those little molecules
interact in complex ways that there
could be intelligence in that there
could be absolutely I mean this this is
this is what you learn from this hopeful
message right I mean this is what you
kind of learned from this principle of
computational equivalence you learn it's
both a a message of of sort of Hope and
a message of kind of you know there
you're not as special as you think you
are so to speak I mean because you know
we we imagine that with sort of all the
things we do with with human
intelligence and all that kind of thing
and all of the stuff we've constructed
in science it's like we're very special
but actually it turns out well no we're
not we're just doing computations like
things in nature do computations like
those gas molecules do computations like
the weather does computations the only
the only thing about the computations
that we do that's really special is that
we understand what they are so to speak
in other words we have a you know to us
they're special because kind of they're
connected to our purposes our ways of
thinking about things and so on and
that's um but so so that's very human
Centric that's we're just attached to
this kind of thing so let's talk a
little bit of
physics maybe let's ask the uh the
biggest question what is a theory of
everything in general what does that
mean yeah so I mean the question is can
we kind of reduce what has been physics
as a something where we have to sort of
pick away and say do we roughly know
what how the world Works to something
where we have a complete formal Theory
where we say if we were to run this
program for long enough we would
reproduce everything you know down to
the fact that we're having this
conversation at this moment etc etc etc
any physical phenomena any phenomena in
this world any phenomenon in the
universe but the you know because of
computational irreducibility it's not
you know that's not something where you
say okay you've got the fundamental
Theory of Everything then you know tell
me whether you know uh lions are going
to eat tigers or something you know
that's a no you have to run this thing
for you know 10 to the 500 steps or
something to know something like that
okay so at some moment potentially you
say this is a rule and run this rule
enough times and you will get the whole
universe right that's that's what it
means to kind of have a fundamental
Theory of physics as far as I'm
concerned is you've got this rule it's
potentially quite simple we don't know
for sure it's simple but we have various
reasons to believe it might be simple
and then you say okay I'm showing you
this rule you just run it only 10 500
times and you'll get everything in other
words you you've kind of reduced the
problem of physics to a problem of
mathematics so to speak it's like it's a
if you know you like you generate the
digits of pi there's a definite
procedure you just generate them and it'
be the same thing if you have a a
fundamental Theory physics of the kind
that that I'm imagining you you know you
get a this Rule and you just run it out
and you get everything that happens in
the
universe so a Theory of
Everything is a
mathematical framework within which you
can explain everything that happens in
the universe it's kind of in a unified
way it's not there's a bunch of
disparate modules
of does it feel like if you create a
rule and we'll talk about the wol from
physics model which is fascinating but
if if you if you have a simple set of
rules with a with a data structure like
a
hypergraph does that feel like a
satisfying Theory of Everything because
then you really run up against the uh
irreducibility computational
reducibility right so that's a really
interesting question so I I I you know
what I thought was going to happen is I
thought we you know I thought we had a
pretty good I had a pretty good idea for
what the structure of this sort of
theory that's sort of underneath space
and time and so on might be like and I
thought gosh you know in my lifetime so
to speak we might be able to figure out
what happens in the first 10us 100 of
the universe MH and that would be cool
but it's pretty far away from anything
that we can see today and it will be
hard to test whether that's right and so
on and so on and so on to my huge
surprise although it should have been
obvious and it's embarrassing that it
wasn't obvious to me but but um to my
huge surprise we managed to get
unbelievably much further than that and
basically what happened is that it turns
out that even though there's this kind
of bed of computational
irreducibility that sort of uh these all
these Simple Rules run into there is a
there are certain pieces of
computational
reducibility that quite generically
occur for large classes of these rules
and and this is the really exciting
thing as far as I'm concerned the the
the big pieces of computational
reducibility are basically the pillars
of 20th century physics that's the
amazing thing that general relativity
and Quantum field Theory the sort of the
pillars of 20th century physics turn out
to be precisely the stuff you can say
there's a lot you can't say there's a
lot that's kind of at this irreducible
level where you kind of don't know
what's going to happen you have to run
it you know you can't run it within our
universe etc etc etc etc etc um but the
thing is there are things you can say
and the things you can say turn out to
be very beautifully exactly the
structure that was found in 20th century
physics namely general relativity and
quantum mechanics and general relativity
and quantum mechanics are these pockets
of reducibility that we think of
as that that you know 20th century
physics is essentially pockets of
reducibility and then it's it is
incredibly surprising that any kind of
model that's
generative from Simple Rules would have
would have such Pockets yeah well I
think what what's surprising uh is we
didn't know where those things came from
it's like general relativity it's a very
nice mathematically elegant Theory why
is it true you know quantum mechanics
why is it true what we realized is that
from this that they are these theories
are generic to a huge class of systems
that have these particular very
unstructured underlying rules and that's
the that's the thing that is sort of uh
remarkable and that's the thing to me
that's just it's really beautiful I mean
it's and the thing that's even more
beautiful is that it turns out that you
know people have been struggling for a
long time you know how does general
relativity theory of gravity relate to
Quantum Mechanics they seem to have all
kinds of incompatibilities it turns out
what we realized is at some level they
are the same Theory and that's just it's
it's just great as far as I'm concerned
so maybe like taking a little step back
from your
perspective not from the low not from
the beautiful hypog graph well from
physics model perspective but from the
perspective of 20th century physics what
is general relativity what is quantum
mechanics how do you think about these
two theories from the context of the
theory of everything like just even
definitions yeah yeah yeah right so so I
mean you know little bit of history of
physics right so so I mean the the you
know okay very very quick history of
right so so I mean you know physics you
know in ancient Greek times people
basically said we can just figure out
how the world works as you know we're
philosophers we're going to figure out
how the world works you know some
philosophers thought there were atoms
some philosophers thought there were you
know continuous flows of things people
had different ideas about how the world
works and they tried to just say we're
going to construct this idea of how how
the world Works they didn't really have
sort of Notions of doing experiments and
so on quite the same way as developed
later so that was sort of an early
tradition for thinking about sort of
models of the world then by the time of
1600s time of Galileo and then Newton um
sort of the big the big idea there was
you know you know title of Newton's book
you know Pria Mathematica mathematical
principles of natural philosophy we can
use mathematics to understand natural
philosophy to understand things about
the way the world works and so that then
led to this kind of idea that you know
we can write down a mathematical
equation and have that represent how the
world works so Newton's one of his most
famous ones is his universal law of
gravity inverse Square law of gravity
that allowed him to compute all sorts of
features of of the planets and so on
although some of them he got wrong and
it was took another hundred years for
people to actually be able to do the
math uh to the level that was needed but
but um but so that that had been this
sort of tradition was we write down
these mathematical equations we don't
really know where these equations come
from we write them down then we figure
out we work out their consequences and
we say yes that agrees with what we
actually observe in astronomy or
something like this so that tradition
continued and um then the first of these
two sort of great 20th century uh
Innovations was uh well the history is a
little bit more complicated but let's
let's say the the the um the the the
there were two quantum mechanics and
general relativity quantum mechanics
kind of 1900 was kind of the very early
uh stuff done by plank that led to the
idea of photons particles of light um
but let's let's take general relativity
first one one feature of the story is
that special relativity thing Einstein
invented in 1905 was something which
surprisingly was a kind of logically
invented Theory Theory it was not a
theory where it was something where
given these ideas that were sort of
axiomatically thought to be true about
the world it followed that such and such
a thing would be the case it was a
little bit different from the the kind
of methodological structure of some of
some existing theories in more in the
more recent times or it just been we
write down an equation and we find out
that it works so what happened there so
there's some reasoning about the light
the basic idea was you know the speed of
light is appears to be constant uh you
know even if you're traveling very fast
you shine a flashlight the light will
come out even if you're going at half
the speed of light the light doesn't
come out of your flashlight at one and a
half times the speed of light um it's
still just the speed of light and to
make that work you have to change your
view of how space and time work um to be
able to account for the fact that when
you're going faster it appears that you
know uh length is foreshortened and time
is dilated and things like this that's
special relativity that's special
relativity so then Einstein went on with
sort of vaguely similar kinds of
thinking 1915 invented general
relativity which is a theory of gravity
and the basic point of general
relativity is is it's a theory that says
when there is mass in space space is
curved and what is that mean you know
you usually you think of what's the
shortest distance between two points
like in in a ordinarily in on a plane in
space it's a straight line you know
photons light goes in straight lines
well then the question is is if if you
have a curved surface a straight line is
no longer straight on the surface of the
Earth the shortest distance between two
points is a great circle it's a circle
um it's uh so you know Einstein's
observation was maybe the physical uh
structure of space is such that space is
curved D so the shortest distance
between two points the the path the
straight line in quotes won't be
straight anymore and in particular if a
if a photon is is you know traveling
near near the Sun or something or if a
particle is going something is traveling
near the sun maybe the shortest path
will be one that is is uh is is
something which looks curved to us
because it seems curved to us because
space has been deformed by the presence
of mass associated with that that
massive object so so the kind of the
idea uh there is um think of the
structure of space as being a dynamical
changing kind of thing but then what
Einstein did was he wrote down these
differential equations that basically
represented the curvature of space and
its response to the presence of mass and
energy and that
ultimately is connected to the force of
gravity which is one of the forces that
seems to based on it strength operate on
a different scale than some of the other
forces so it operates at a scale as very
large what happens there is is just this
this curvature of space which causes you
know the paths of objects to be
deflected that's what gravity does it
causes the paths of objects to be
deflected and this is an explanation for
Gravity so to speak and the surprise is
that from 1915 until today everything
that we measured about gravity precisely
agrees with General and that's um uh and
that you know it wasn't clear black
holes were sort of predict well actually
the expansion of the universe was an
early potential prediction although
Einstein tried to sort of patch up his
equations to make it not cause the
universe to expand because it was kind
of so obvious the universe wasn't
expanding and um uh you know turns out
it was expanding and he should have just
trusted the equations and that's a
lesson for for those of us um interested
in making fundamental theories of
physics is you should trust your theory
and not try and Patch it because of
something that you think might be the
case that um uh that that might turn out
not to be the case even if the theory
says something crazy is happening yeah
right like the universe the universe is
expanding right which is but but um but
you know then it took until the 1940s
probably even really until the 1960s
until people understood that black holes
were a consequence of of general
relativity and so on but that's um you
know the big surprise has been that so
far this theory of gravity has perfectly
agreed with you know these collisions of
black holes seen by their gravitational
waves you know it all just works so
that's that's been kind of one pillar of
the story of physics it's mathematically
complicated to work out the consequences
of general relativity but it's not
there's there's no I mean and and and
some things are kind of squiggly and
complicated like people believe you know
energy is conserved okay well energy
conservation doesn't really work in
general activity in the same way as it
ordinarily does and it's all a big
mathematical story of how you actually
nail down something that is definitive
that you can talk about it and not
specific to the you know reference
frames you're operating in and so on and
so on and so on but fundamentally
general relativity is a straight shot in
the sense that you have this Theory you
work out its
consequences and and that that theory is
useful in terms of basic science and
trying to understand the way black holes
work the way the creation of Galaxy's
work s of all these kind of cosmological
thing understanding what happened like
you said at the Big Bang Yeah like all
those kinds of well no not not at the
Big Bang actually right but the well
features of the expansion of the
universe yes and and there are there are
lots of details where we don't quite
know how it's working you know is there
you know where's the dark matter is
there Dark Energy you know etc etc etc
but but fundamentally the the you know
the testable features of general
relativity it all works very beautifully
and it's it's in a sense it is
mathematically sophisticated but is not
conceptually hard to understand in some
sense okay so that's general relativity
and what's its friendly neighbor like
you said two theories quantum mechanics
right so quantum mechanics the the the
sort of the way that that originated was
one question was is the world continuous
or is it discret you know in ancient
Greek times people have been debating
this people debated it you you know
throughout history as light made of
waves is it continuous as it discrete as
it made of particles cor pusles whatever
um you know what had become clear in the
1800s is that
atoms that you know materials are made
of discrete atoms you know when you take
some water the water is not a continuous
fluid even though seems like a
continuous fluid to us at our scale but
if you say let's look at it smaller and
smaller and smaller and smaller scale
eventually you get down to these you
know these molecules and then atoms it's
made of discrete things the question is
sort of how important is this
discreetness just what's discret what's
not discret is energy discrete is you
know is what's discrete what's not and
so does it have mass those kinds of
questions yeah yeah right well there's
question I for example is mass discreet
is an interesting question which is now
something we can address but but um you
know what what happened in um uh the in
in the coming up to the 1920s there was
this kind of mathematical theory
developed that could explain certain
kinds of discreetness in in particularly
and in features of atoms and so on and
uh you know what developed was this
mathematical theory that was a theory
the theory of quantum mechanics theory
of wave functions sh's equation things
like this that's a mathematical theory
that allows you to calculate lots of
features of the microscopic World lots
of things about how atoms work etc etc
etc now the calculations all work just
great the um uh the question of what
does it really mean is a complicated
question now I mean to to just explain a
little bit historically the you know the
early calculations of things like atoms
worked great 1920s 1930s and so on there
was always a problem there were uh in
Quantum field Theory which is a theory
of uh uh in quantum mechanics you're
dealing with a certain number of at a
certain number of electrons and you fix
the number of electrons you say I'm
dealing with a two electron thing um in
Quantum field Theory you allow for
particles being created and destroyed so
you can emit a photon that didn't exist
before you can absorb a photon things
like that that's a more complicated
mathematically complicated Theory and it
had all kinds of mathematical issues and
all kinds of Infinities that cropped up
and it was finally figured out more or
less how to get rid of those but there
were only certain ways of doing the
calculations and those didn't work for
Atomic nuclei among other things um and
that led to a lot of development up
until the 1960s of alternative ideas for
how how one could understand what was
happening in atomic nuclei etc etc etc
end result in the end the kind of most
quotes obvious mathematical structure of
quantum field Theory seems to work
although it's mathematically difficult
to deal with but you can calculate all
kinds of things you can calculate to you
know a dozen decimal plac places certain
certain things you can measure them it
all works it's all beautiful now you way
the underlying fabric is the model of
that particular theory is Fields like
you keep saying
Fields those are quantum Fields those
are different from classical Fields uh a
field is something like you say um
there's like you say the temperature
field in this room it's like there is a
value of temperature at every Point
around the room that's um or or you can
say the wind field would be the the
vector Direction of the wind at every
point it's continuous yes and it's a
that's a classical field a Quantum field
is a much more mathematically elaborate
kind of thing um and I should explain
that that one of the pictures of quantum
mechanics that's really important is you
know in classical physics one believes
that sort of definite things happen in
the world you pick up a ball you throw
it the ball goes in a definite
trajectory that's has certain equations
of motion it goes in a parabola whatever
else in quantum mechanics the picture is
definitely things don't happen instead
sort of what happens is this whole sort
of structure of of all you know many
different paths being followed and um we
can calculate certain aspects of what
happens certain probabilities of
different outcomes and so on and you say
well what really happened what's really
going on what's the sort of uh what's
the underlying you know what's the
underlying story what how do we how do
we turn this this mathematical theory
that we can calculate things with into
something that we can really understand
and have a narrative about out and
that's been really really hard for
quantum mechanics my my friend dick
feeman always used to say nobody
understands quantum mechanics even
though he'd made his you know whole
career out of calculating things about
quantum mechanics um and uh you know so
so it's nevertheless it's uh what the
quantum field theory is very uh very
accurate at predicting a lot of the
physical phenomena so it works yeah and
but there are things about it you know
it has certain when we apply it the
standard model of particle physics for
example we uh you know which we apply to
calculate all kinds of things it works
really well and you say Well it has
certain parameters it has a whole bunch
of parameters actually you say why is
the you know why does the muon particle
exist why is it 206 times the mass of
the electron we don't know no idea but
so the standard model physics is is is
one of the models that's very accurate
for describing three three of the
fundamental forces of physics and look
looking at the the world of the very
small right and then there's back to the
neighbor of uh gravity general
relativity so and in the context of a
Theory of
Everything what's
traditionally the task of the
unification of these theories and why
the issue is you try to use the methods
of quantum field Theory to talk about
gravity and it doesn't work just like
there are photons of light so there are
gravitons which are sort of the
particles of gravity and when you try
and compute sort of the properties of
the of the particles of gravity the kind
of mathematical tricks that get used um
in working things out in Quantum field
Theory don't work and um that's um so
that's been a sort of fundamental issue
and when you think about black holes
which are a place where uh sort of the
the the structure of space is um uh you
know has has sort of Rapid variation and
you get kind of quantum effects mixed in
with effects from general relativity
things get very complicated and there
are apparent paradoxes and things like
that and people have you know there been
a bunch of mathematical developments in
in physics over the last I don't know 30
years or so which have kind of picked
away at those kinds of issues and got
hints about how things might work um and
but it hasn't been uh you know and the
other thing to realize is as far as
physics is concerned it's just like his
general relativity his Quantum field
Theory you know be happy yeah so do you
think there's a quantization of gravity
so quantum gravity what do you think of
efforts that people have tried to yeah
what do you think in general of the
efforts of the physics Community to try
to unify these laws so I think what's
it's interesting I mean I would have
said something very different before
what's happened with our physics project
um I mean you know the remarkable thing
is what we've been able to do is to make
from this very simple structurally
simple underlying set of ideas we've
been able to build this this you know
very elaborate structure that's both
very abstract and very sort of
mathematically rich and the big surprise
as far as I'm concerned is that it
touches many of the ideas that people
have had so in other words things like
string theory and so on uh twister
Theory it's like the you know we might
have thought I had thought we're out on
a prong we're building something that's
computational it's completely different
from what other people have done but
actually it seems like what we've done
is to provide essentially the machine
code that you know these things are are
various features of domain specific
languages so to speak that talk about
various aspects of this machine code and
I think there's a this is something that
to me is is is very exciting because it
allows one both for us to provide sort
of a new foundation for what's been
thought about there and for the all the
work that's been done in those areas to
you know to give us you know more more
momentum to be able to figure out what's
going on now you know people have sort
of hoped oh we're just going to be able
to get you know String Theory to just
answer everything that hasn't worked out
and I think we now kind of can see a
little bit about just sort of how far
away certain kinds of things are from
being able to explain things some things
one of the big surprises to me actually
I literally just got a message about one
aspect of this is um uh the uh uh you
know it's turning out to be easier I
mean this project has been so much
easier than I could ever imagine it
would be that is I thought we would be
you know just about able to understand
the first 10us 100 seconds of the
universe and um you know it would be 100
years before we get much further than
that it's just turned out it actually
wasn't that hard I me we're not finished
but you know so you're you're you're
seeing Echoes of all the disperate
theories of physics in this framework
yes I mean it's a very interesting you
know sort of History of Science likee
phenomenon I mean the best analogy that
I can see
is what happened with the early early
days of of computability and computation
Theory you know touring machines were
invented in 1936 people sort of
understand computation in terms of
touring machines but actually there had
been pre-existing theories of
computation combinators General
recursive functions Lambda calculus
things like this but people hadn't those
hadn't been concrete enough that people
could really wrap their arms around them
and understand what was going on and I
think what we're going to see in this
case is that a bunch of these
mathematical theories
um including some very I one of the
things that's really interesting is one
of the most abstract things that's come
out of of sort of uh
mathematics higher category Theory
things about Infinity groupoids things
like this which to me always just seemed
like they were floating off into the
stratosphere ionosphere of mathematics
um turn out to be things which our sort
of theory anchors down to something
fairly definite and says our super
relevant to the way that we can
understand how physics Works give me a
sec by the way I just threw a hat on
you've said that
um with this metaphor analogy that
Theory of Everything is a big
mountain and you have a sense
that however far we are up the
mountain that the the wolf from physics
model a
view of the universe is at least the
right Mountain we're the right Mountain
yes without question which aspect of it
is the right Mountain so for example I
mean so there's so many aspects to Just
The Way of the wol from physics project
the way it approaches the world that's
um that's clean
crisp uh and uh unique and Powerful so
you know there's a there's discreet
nature to it there's a hypergraph
there's a computational nature there's a
generative aspect you start from nothing
you generate
everything which do you think the actual
model is actually a really good one or
do you think this General principle of
from Simplicity generating complexity is
the right like what aspect of the
mountain yeah right I mean I I think
that the the kind of the meta idea about
using simple computational systems to do
things that's you know that's the
ultimate big Paradigm that is you know
sort of super important the details of
the particular model are very nice and
clean and allow one to actually
understand what's going on they are not
unique and in fact we know that we know
that there's a there's a large number of
different ways to describe essentially
the same thing I mean I can describe
things in terms of hypergraphs I can
describe them in terms of higher
category Theory I can describe them in a
bunch of different ways they are in some
sense all the same thing but our sort of
story about what's going on and and the
kind of kind of cultural mathematical
resonances are a bit different I think
it's it's it's perhaps worth sort of
saying a little bit about kind of the
the you know foundational ideas of of uh
of uh uh you know of these of these
models and things great so can you maybe
uh can we like rewind we've talked about
a little bit but can you say like what
the central idea is of the Wolfram
physics project right so so the question
is we're interested in finding a sort of
simple computational rule that describes
our whole universe can we just pause on
that I just so be that's such a
beautiful that's such a beautiful idea
that we can generate our universe from a
from a uh from a data structure a simple
structure simple set of rules and we can
generate our entire universe yes that's
all inspiring
right but but so so you know the
question is how do you actualize that
what might this rule be like and so one
thing you quickly realize is if you're
going to pack everything about our
universe into this tiny rule not much
that we are familiar with in our
universe will be obvious in that
rule so you don't get to fit all these
parameters of the universe all these
features of you know this is how space
works this is how time works etc etc etc
you don't get to fit that all it all has
to be sort of packed in to this this
thing something much smaller much more
basic much lower level machine code so
to speak than that and all the stuff
that we're familiar with has to kind of
emerge from the operation of so the rule
in itself because of the computational
reducibility is not going to tell you
the story it's not going to give you the
answer to uh it's not going to let you
predict what you're going to have for
lunch tomorrow and it's not going to let
you predict basically anything about
your life about the universe right but
and you're not going to be able to see
in that rule oh there's the three for
the number of dimensions of space and so
on that's not going to be there so space
time is not going to be obviously right
so the question is then what what is the
universe made of that's that's a it's a
basic question and we've had some
assumptions about what the universe is
made of for the last few thousand years
that I think in some cases I just turn
out not to be right and you know the
most important assumption is that space
is a continuous thing that is that you
can if you say let's pick a point in
space we're going to do geometry we're
going to pick a point we can pick a
point absolutely anywhere in space
precisely numbers we can specify of
where that point is in fact you know
uclid who kind of wrote down the
original kind of atiz of geometry back
in 300 BC or so um you know his his very
first definition he says a point is that
which has no part a point is this is
this you know uh this indivisible you
know infinitesimal thing okay so we
might have said that about material
objects we might have said that about
water for example we might have said
water is a continuous thing that we can
just uh you know pick any point we want
in in in some water but actually we know
it isn't true we know that water is made
of molecules that are discrete and so
the question one fundamental question is
what is space made of and so one of the
things that's sort of a starting point
for what I've done is to think of space
as a discrete thing to think of there
being sort of atoms of space just as
there are atoms of material things
although very different kinds of atoms
and by the way I mean this idea you know
there were ancient Greek philosophers
who had this idea there were you know
Einstein actually thought this is
probably how things would work out I
mean he said you know repeatedly he
thought that is way it would work out we
don't have the mathematical Tools in our
time which was 1940s 1950s and so on to
explore this like the way he thought you
mean that there is something very very
small and discreete that's underlying
space space yes and that that means that
so you know the mathematical Theory
mathematical theories in physics assume
that space can be described just as a
continuous thing you can just pick
coordinates and the coordinates can have
any values and that's how you define
space space is this just sort of
background uh sort of theater on which
the universe operates but can we draw a
distinction
between space as a thing that could be
described by uh three values coordinates
and how you're are you are you using the
word space more generally when you say
no I'm I'm just talking about space as
in what we experience in in in the
universe so you think this 3D aspect of
it is fundamental no I don't think that
3D is fundamental at all actually I
think that the what's the the the thing
that has been assumed is that space is
this continuous thing where you can just
describe it by let's say three numbers
for instance but most important thing
about that is that you can describe it
by PR prise numbers because you can pick
any point in space and you can talk
about motions any infinitesimal Motion
in space and that's what continuous
means that's what continuous means
that's what you know Newton invented
calculus to describe these kind of
continuous small variations and so on
that was that's kind of a fundamental
idea from uclid on that's been a
fundamental idea about space and so is
that right or wrong uh it's it's not
right it's not right it's it's it's it's
right at the level of our experience
most of of the time it's not right at
the level of the machine code so to
speak and so machine code yeah of the
simulation that's right that's right
they're the very lowest level of the
fabric of the universe at least under
the the the will from physics model is
your sense is as discreet right so so
now what does that mean so it means what
what is space then so in in um models
the basic idea is you say there are
these sort of atoms of space they're
these points that represent you know
represent places in space but they're
just discrete points and the only thing
we know about them is how they're
connected to each other we don't know
where they are they don't have
coordinates we don't get to say this is
a position such and such it's just
here's a big bag of points like in our
universe there might be 10 to the 100 of
these points and all we know is this
point is connected to this other point
so it's like you know all we have is the
friend nwor so to speak we don't we
don't have you know people's you know
physical addresses all we have is the
friend network of these points yeah the
underlying nature of reality is kind of
like a Facebook uh we don't know their
location but we have the friends yeah
yeah right we we we know which point is
connected to which other points and and
that's all we know and so you might say
well how on Earth can you get something
which is like our experience of of you
know what seems like continuous space
well the answer is by the time you have
10 to the 100 of these things there they
those connections can work in such a way
that on a large scale it will seem to be
like continuous space in let's say three
dimensions or some other number of
Dimensions or 2.6 Dimensions or whatever
else because they're much much much much
larger so like the uh the number of
relationships here we're talking about
is just a humongous amount so the the
kind of thing you're talking about is
very very very small relative to our
experience of daily life right so I mean
you know we don't know exactly the size
but maybe maybe uh uh 10 Theus uh maybe
around 10 Theus 100 m so you know the
size of to give a comparison you know
the size of a of a proton is 10us 15 M
and so this is something incredibly tiny
compared to that um and and the the idea
that from that would emerge the
experience of continuous space is
mindblowing what's your intuition why
that's possible like first of all I mean
we'll get in into it but I don't know if
we will through the medium of
conversation but the construct of
hypergraphs is just beautiful right
cellometer beautiful we'll talk about it
but okay but but but this thing about
you know continuity arising from
discrete systems is in today's world is
actually not so surprising I mean you
know your average computer screen right
every computer screen is made of
discrete pixels yet we have the you know
we have the idea that we're seeing these
continuous pictures I mean it's you know
the fact that on a large scale
continuity can arise from lots of
discrete elements this is at some level
unsurprising now but wait but the pixels
have uh a very definitive structure of
Neighbors on on a computer screen right
there is no concept of spatial of space
inherent in the underly fabric of
reality right right right so so the the
the point is but there are cases where
there are so for example let's just
imagine you have a square grid okay and
at every point on the grid you have one
of these atoms of space and it's
connected to four other four other atoms
of space on the you know Northeast
southwest corners right um there you
have something where if you zoom out
from that it's like a computer screen
yeah so the relationship creates the the
spatial like the relationship creates a
constraint which then in an emerging
sense creates a like yeah like a uh
basically a spatial coordinate for that
thing yeah right even though the
individual point doesn't have a space
even though the individual point doesn't
know anything it just knows what it's
you know what its neighbors are the on a
large scale it can be described by
saying oh it looks like it's a you know
this grid zoomed out grid you can say
well you can describe these different
points by saying they have certain
positions coordinates Etc now in the in
the sort of real setup it's more
complicated than that it isn't just a
square Grid or something it's something
much more Dynamic and complicated which
we'll talk about but um uh so you know
first the first idea the first key idea
is you know what's the universe made of
it's made of atoms of space basically
with these connections between them what
kind of connections do they have well so
a the simplest kind of thing you might
say is we've got something like a graph
where every uh every atom of space uh
where we have these edges that go
between atom these connections that go
between atoms of space we're not saying
how long these edges are we're just
saying there is a connection from from
this place to the from this atom to this
atom just a quick pause because there's
a lot of very people that listen to this
just to clarify because I did a poll
actually what do you think a graph is a
long time ago and it's kind of funny how
few people know the term graph uh
outside of computer science it's let's
call it a network I think that's that's
call a network is better so but every
time I like the word graph though so
let's define let's just say that graph
we'll use terms nodes and edges maybe
and it's just uh nodes
represent some abstract entity and then
the edges represent relationships
between those entities right exactly so
that's what graph say sorry so so there
you go so that's the basic structure
that is that is the simplest case of a
basic structure actually uh it tends to
be better to think about hypergraphs so
a hypergraph is just instead of saying
uh there are connections between Pairs
of things we say there are connections
between any number of things so there
might be Turner edges so instead of
instead of just having uh two points are
connected by an edge you say three
points are all associated with a
hyperedge are all connected by hyper
Edge that's just at some level that's at
some level that's a detail it's a detail
that happens to make the um for me you
know sort of in the history of this
project the realization that you could
do things that way broke out of certain
kinds of arbitrariness that I felt that
there was in the model before I had seen
how this worked I mean all a hypergraph
can be mapped to a graph it's just a
convenient representation mathematically
speaking right that's correct that's
correct but so then so okay so the the
first question the first idea of these
models of ours is spaces made of these
know connected sort of atoms of space
the next idea is space is all there is
there's nothing except for this space So
In traditional ideas in physics people
have said there's space it's kind of a
background and then there's matter all
these particles electrons all these
other things which exist in space right
but in this model one of the key ideas
is there's nothing except space so in
other words everything that has that
exists in the universe is a feature of
this hypergraph so how can that possibly
be well the way that works is that there
are certain uh structures in this
hypergraph where you say that little
twisty knotted thing we don't know
exactly how this works yet but but we we
have sort of idea about how it works
mathematically this sort of Twisted
knotted thing that's the core of an
electron this thing over there that has
this different form that's something
else so the different peculiarities of
the structure of this graph are the very
things
that uh we think of as the particles
inside the space but in fact it's just a
property of of space mindblowing first
of all that it's mind-blowing and we'll
probably talk in its Simplicity and
Beauty yes I think it's very beautiful I
this is I'm but okay so but that's space
and then there's another concept we
didn't really kind of mention but you
thinking of computation as a like a
transformation let's talk about time in
a second let's let's just let's just I
mean on the subject oface
that you know there's this question of
kind of what you know there's this idea
there is this hypergraph it represents
space and it represents everything
that's in Space the features of that
hypergraph you can say certain features
in this part we do know certain features
of the hypergraph represent the presence
of energy for example or the presence of
mass or momentum and we know what the
features of the hypergraph that
represent those things are but it's all
just the same hypergraph so one thing
you might ask is you know if you just
look at this hypergraph and you say and
we're going to talk about sort of what
the hypergraph does but if you say you
know how much of what's going on in this
hypergraph is things we know and care
about like particles and atoms of
electrons and all this kind of thing and
how much is just the background of space
so it turns out so far as in one rough
estimate of this all everything that we
care about in the universe is only one
part in 10 to 120 of what's actually
going on the vast majority of what's
Happening is purely things that maintain
the structure of space that in other
words that the things that are the
features of space that are the things
that we consider notable like the
presence of particles and so on that's a
tiny little piece of froth on the top of
all this activity that mostly is just
intended to you know mostly I can't say
intended there's no intention here that
just maintains the structure of
space let me let me load that in it's uh
it just makes me feel so good as a human
being well to be the froth on the one
and the 10 to the 120 or something of
well and also just humbling um how in
this mathematical framework how much
work needs to be done on the
infrastructure right of our universe
right to maintain the infrastructure of
our universe is a lot of work we are we
are merely writing a little tiny things
on top of that infrastructure but but
you know you you were just starting to
to talk a little bit about what I you
know we talked about you know space that
represents all the stuff that's in the
universe the question is what does that
stuff do and for that we have to start
talking about time and what is time and
so on and you know one of the the basic
idea of this model is time is the
progression of computation so in other
words we have a a structure of space and
there is a rule that says how that
structure of space will change and it's
the application the repeated application
of that rule that defines the progress
of time um and what does the rule look
like in in the space of hyperg grass
right so what the rule says is something
like if you have a little tiny piece of
hypergraph that looks like this then it
will be transformed into a piece of
hypergraph that looks like this so
that's all it says it says you pick up
these elements of space and the you can
think of these these uh edges these
hyper edges as being relations between
elements in space you might pick up uh
these two relations between elements in
space and we're not saying where those
elements are or what they are but every
time there's a certain arrangement of
elements in space then arrangement in
the sense of the way they're connected
then we transform it into some other
Arrangement so there's a little tiny
pattern and you transform it into
another little pattern that's right and
then because of this I mean again it's
kind of similar to Cellular atomine that
like yes on paper the rule looks like
super simple it's like uh yeah
okay yeah like yeah right from this the
universe can be born uh but like once
you start applying it beautiful
structure starts being potentially can
be created and what you're doing is
you're applying that rule to different
parts like to anytime you match it
within the hypergraph exactly and then
one of the like incredibly beautiful and
interesting things to think about is the
order in which you apply that rule yes
because that pattern appears all over
the place right so this is a big
complicated thing very hard to wrap
one's brain around okay so so you you
say the rule is every time you see this
little pattern transform it in this way
but yet you know as you look around the
space that represents the universe there
may be zillions of places where that
little pattern occurs yeah so so what
what what it says is just do this apply
this rule wherever you feel like and
what what is extremely non-trivial is
well okay so so this is happening sort
of in in computer science terms sort of
asynchronously you're just doing it
wherever wherever you feel like doing it
and the only constraint is that if
you're going to apply the rule somewhere
the the things to which you apply the
rule the the little you know elements to
which you apply the rule if they if they
have to be okay well you can think of
each application of the rule as being
kind of an event that happens in the
universe Y and these the input to an
event has to be ready for the event to
occur that is if one event occurred if
one transformation occurred and It
produced a particular atom of space then
that atom of space has to already exist
before another uh transformation that's
going to apply to that atom of space can
occur so like the prerequisite for the
event that's exist that's right so it it
that defines a kind of uh this sort of
set of causal relationships between
events it says this event Happ has to
have happened before this event but that
is um but that's that's not a very
limiting constraint no it's not and
what's still you still get the zillion
uh that's a technical term options
that's correct but but okay so this is
where things get a little bit more
elaborate but they're mindblowing so
right but so so what what what happens
is so the first thing you might say is
you know let's well okay so so this
question about the freedom of which
which event you do when well let me let
me sort of State an answer and then
explain it okay the the um the validity
of special relativity is a consequence
of the fact that in some sense it
doesn't matter in what order you do
these underlying things so long as they
respect this kind of set of causal
relationship
ship so and that's that's uh in a the
the part that's in a certain sense is a
really important one but the fact that
it it sometimes doesn't matter that's a
I don't know what that's another like
beautiful thing okay so so there's this
idea of what I call causal invariance
causal invariance exactly that's so
really really powerful powerful idea a
powerful idea which has actually Arisen
in different forms many times in the
history of mathematics mathematical
logic even computer science has many
different names um I mean our particular
version of it is a little bit tighter
than other versions but it's basically
the same idea here's here's how to think
about that idea so imagine that well
let's talk about it in terms of math for
a second let's say you're doing algebra
and you're told you know multiply out
this series of polinomial that are that
are multiplied together okay you say
well which order should I do that in so
well do I multiply the third one by the
fourth one and then do it by the first
one or do I do the fifth one by the
sixth one and then do that well it turns
out it doesn't matter you can you can
multiply them out in any order you'll
always get the same answer that's a
that's a a property if you think about
kind of making a kind of network that
represents in what order you do things
you'll get different orders for
different ways of multiplying things out
but you'll always get the same answer
same thing if you let's say you're
sorting you've got a bunch of A's and
B's they're in random some random order
you know baa BBB AA whatever and you you
have a little rule that says every time
you see ba flip it around to AB okay
eventually you apply that rule enough
times you'll have sorted the string so
that it's all the A's first and then all
the
B's again you there are many different
orders in which you can do that that
many different sort of places where you
can apply that update in the end you'll
always get the string sorted the same
way I know I know with sorting a string
it's it sounds obvious that's to me
surprising
that that there is in complicated
systems obviously with a with a string
but in in a hypergraph that the
application of the rule a asynchronous
rule can lead to the same results
sometimes yes yes that is it is not
obvious and it was something that um you
know I I sort of discovered that idea
for these kinds of systems in back in
the 1990s and for various reasons I I I
was not I was not satisfied by how sort
of fragile finding that particular
property was was and let me let me just
make another point which is that that it
turns out that even if the underlying
rule does not have this property of
causal invariance it can turn out that
every observation made by observers of
the rule can they can impose what
amounts to causal invariance on the rule
we can explain that it's a little bit
more complicated I mean technically that
has to do with this idea of completions
which is something that comes up in term
re writing systems automated theorem
proving systems and so on
but that let's let's ignore that for a
second we can come to that later but is
it useful to talk about observation not
yet not yet so so great so there's some
concept of causal invariance as uh you
apply these rules in an asynchronous way
you can think of those Transformations
as events so there's this hypergraph
that represents space and all of these
events happening in the space and the
graph grows in interesting complicated
ways and eventually the froth arises to
of a what we experience as human
existence so that's that's the that's
some version of the picture but but
let's explain a little bit more exactly
what's a little a little more detailed
like right well so so one thing that is
sort of surprising in this in this
theory is one of the sort of
achievements of 20th century physics was
kind of bringing space and time together
that was you know special relativity
people talk about SpaceTime this sort of
unified thing where space and time kind
of are mixed and there's a nice
mathematical formula M um that uh in
which you know space and time sort of
appear as part of the SpaceTime
Continuum the SpaceTime you know four
vectors and things like this um you know
we talk about spe time as the fourth
dimension and all these kinds of things
it's you know that and it seems like the
theory of relativity sort of says space
and time are fundamentally the same kind
of thing so one of the things that took
a while to understand in in this
approach of mine is that uh in in in my
kind of approach space and time are
really not fundamentally the same kind
of thing space is the extension of this
hypergraph time is the kind of progress
of this inexorable computation of these
rules getting applied to the hypergraph
so it's they seem like very different
kinds of things and and so that at first
seems like how can that possibly be
right how can that possibly be lorensen
variant that's the term for things being
you know following the the rules of
special artivity well it turns out that
when you have causal
invariance that and let's see we can
it's worth it's worth explaining a
little bit how this works it's a little
bit little bit elaborate but but the
basic point is that um uh the even
though space and time sort of come from
very different places it turns out that
the rules of sort of space time that
special relativity talks about um come
out of this model when you're looking at
large enough systems MH so so a way to
think about this you know in terms of
the when you're looking at large enough
systems um the U part of that story is
when you look at some fluid Like Water
for example there are equations that
govern the flow of water um those
equations are things that apply on a
large scale if you look at the
individual molecules they don't know
anything about those equations it's just
the the the sort of the large scale
effect of those molecules turns out to
follow those equations and it's the same
kind of thing happening in our
models I know this might be a a small
point but it might be a very big one
we've been talking about space and time
at the lowest level of the model which
is space the hypergraph time is the
evolution of this hypergraph but there's
also SpaceTime that we think about in
general relativity for special
relativity like what how does how do you
go from the uh lowest source code of
space and time we're talking about to
the more traditional terminology of
space and time right so so the the key
thing is this thing we call the causal
graph so the causal graph is the graph
of causal relationships between events
so every one of these little updating
events every one of these little
transformations of the hypergraph
happens somewhere in the hypergraph
happens at some stage in the
computation that's an event that event
is has a causal relationship to other
events in the sense that if the if
another event needs as its input the
output from the first event there will
be a causal relationship of the the the
future event will depend on the past
event so you can say it's it has a
causal connection and so you can make
this graph of causal relationships
between events that graph of causal
relationships causal invariance implies
that that graph is unique it doesn't
matter even though you think oh I'm I'm
you know let's say we were sorting a
string for example I did that particular
transposition of of characters at this
time and then I did that one then I did
this one turns out if you look at the
network of of connections between those
updating events that network is the same
it's it's the if if you were to see the
the the structure so in other words if
you were to draw that that if you were
to put that Network on a picture of
where you're doing all the updating the
places where you put the the nodes of
the network will be different but the
way the nodes are connected will always
be the same so but the causal graph is a
is I don't want it's kind of an observ
it's not uh enforced it's just emergent
from set of events well it's a it's a
feature of of okay so what it is
characteristic I guess of the way events
happen right it's an event can't happen
until its input is ready right and so
that creates this this network of causal
relationships and that's that's the
causal graph and the thing the next
thing to realize is okay we when you're
going to observe what happens in the
universe you have to sort of make sense
of this causal graph so and you are an
observer who yourself is part of this
causal graph and so that means so let me
give you an example of of how that works
so so imagine we have a really weird
Theory of physics of the world where it
says this updating process there's only
going to be one update at every moment
in time and it's just going to be like a
touring machine it has a little head
that runs around and just is always just
updating one thing at a time so you say
you know I have a theory of physics and
The Theory of physics says there's just
this one little place where things get
updated you say that's completely crazy
because you know it's plainly obvious
that things are being updated sort of
you know at the same syn yeah at the
same time but but the fact is that the
thing is that if I'm you know talking to
you and you seem to be being updated as
I'm being updated but but if there's
just this one little head that's running
around updating things I will not know
whether you've been updated or not until
I'm updated so in other words when you
draw this causal graph of the causal
relationship between the updatings and
you and the updatings in me it'll still
be the same causal graph whether even
though the underlying sort of story of
what happens is oh there's just this one
little thing and it goes and updates in
different places in the universe so is
that is that clear or is that a
hypothesis is that is that clear that
there's a unique causal graph uh if
there's causal invariance there's unique
coal growth that's so so it's okay to
think of what we're talking about as a
hypergraph and the operations on it as a
kind of touring machine with a single
head like a single guy running around
updating stuff um is that safe to
intuitively think of it this way um let
me think about that for a second yes I
think so I think that I think there's
nothing it doesn't matter I mean you you
can you can say okay there is one the
reason I'm pausing for a second is that
um I'm wondering well well when you say
running around depends how far it jumps
every time it runs around yeah yeah
that's right but I mean like one
operation at yeah you can think of it
one operation it's easier for the human
brain to think of it that way as opposed
to uh simultaneous it's not okay but the
thing is that's not how we experience
the world what we experience is we look
around everything seems to be happening
at successive moments in time everywhere
in space yes that is the um and that's
partly a feature of our particular
construction I mean that is the speed of
light is really fast compared to you
know we look around you know I can see
maybe 100 feet away right now um you
know it's uh the my brain does not
process very much in the time it takes
light to C 100 ft the brain operates at
a scale of hundreds of milliseconds or
something like that I don't know and and
speed of light is much faster right you
know light goes in a billionth of a
second light has gone a foot so it goes
a billion feet every second
there's certain moments through this
conversation where I I I uh imagine the
absurdity of the fact that there's two
descendants of Apes modeled by
hypergraph that are communicating with
each other and experiencing this whole
thing as a real time simultaneous update
with uh I'm taking in photons from you
right now but there's something much
much deeper going on right here it it
does have a it's paralyzing sometimes
just yes to remember that right no I
mean you know but so you know yes yes as
a small little tangent I I just
remembered that we're talking about I
mean this the about the fabric of
reality right so we we've got this
causal graph that represents the sort of
causal relationships between all these
events in the universe yeah that causal
graph kind of is a representation of
space time but our experience of it
requires that we pick reference frames
this is kind of a key idea Einstein had
this idea that what that means is we
have to say what are we going to pick as
being the uh sort of what we Define as
simultaneous moments in time so for
example we can say um you know we we set
how do we set our clocks you know if
we've got a a spacecraft landing on Mars
you know do we say that it you know what
what time is it landing at was it you
know even though there's a 20 minute
speed of light delay or something thing
you know what time do we say it landed
at how do we how do we set up sort of
time coordinates for for the world and
that turns out to be that there's kind
of this arbitrariness to how we set
these reference frames that Define sort
of what cils simultaneous and what is
the the essence of special relativity is
to think about reference frames going at
different speeds and to think about sort
of how they assign what counts as space
what counts as time and so on um that's
all well a bit technical but the basic
bottom line is that the this causal
invariance property that means that it's
always the same causal graph independent
of how you slice it with these reference
frames you'll always sort of see the
same physical processes go on and that's
basically why special relativity works
so there's something like special
relativity uh like everything around
space and time that uh that fits this
idea of the causal graph right well you
know one way to think about it is given
that you have a a basic structure that
just involves updating things in in
these you know connected updates and
looking at the causal relationships
between connected updates that's enough
when you unravel the consequences of
that that together with the fact that
there are lots of these things and that
you can take a Continuum limit and so on
implies special RS of a day and um so
that it's kind of a not a big deal
because it's kind of it's kind of a you
it was completely unobvious when you
started off with saying we've got this
graph it's being updated in time etc etc
etc that just looks like nothing to do
with special arts every day and yet you
get that and and what I mean then the
thing I mean this was stuff that I
figured out back in the 1990s the um the
the next big thing you get is General
Arts of day um and so the in this
hypergraph the this sort of limiting
structure when you have a very big
hypergraph you can think of as being
just like you know water seems
continuous on a large scale so this
hypergraph seems continuous on a large
scale one question is you know how many
dimensions of space does it correspond
to so one question you can ask is if you
just got a bunch of points and they're
connected together how do you deduce
what effective dimension of space that
bundle of points corresponds to and
that's that's pretty easy to explain so
basically if you say you got a point and
you look at how many neighbors does that
point have okay imagine it's on a square
grid then it'll have four neighbors go
another level out how many neighbors do
you get then what you realize is as you
go more and more levels out as you go
more and more distance on the graph out
you're you're capturing something which
is essentially a circle in two
Dimensions so that you know the the
number of the area of a circle is p pi r
squ so the it's the number of points
that you get to goes up like the
distance you've gone squared and in
general in D dimensional space it's R to
the^ D it's the the number of points you
get to if you go R steps on the graph
grows like the number of steps you go to
the power of the dimension and that's a
that's a way that you can estimate the
effective dimension of one of these
graphs so what does that grow to so how
does the dimension grow because uh I
mean obviously the visual aspect of
these hypergraphs they're often
visualized in three dimensions right and
then there's a certain kind of structure
uh like you said there's the I mean a
circle a sphere uh there there's a
planer aspect to
it to this graph to where it kind of it
almost starts creating a surface like a
complicated surface but a surface so how
does that connect to affected Dimension
okay so if you can lay out the graph in
such a way that the that the points in
the graph that uh you know the the
points that are neighbors on the graph
are neighbors as you lay them out out MH
and you can do that in two dimensions
then it's going to approximate a two-
dimensional thing if you can't do that
in two Dimensions if everything would
have to fold over a lot in two
dimensions then it's not an
approximating a two- dimensional thing
maybe you can lay it out in three
dimensions maybe you have to lay it out
in five Dimensions to have it be the
case that it sort of smoothly lays out
like that well but okay so uh and I
apologize for the different tangent
questions but you know there's an
Infinity number of possible
rules so we have to look for
rules that
uh that create the kind of structures
that that're reminiscent for uh that
have Echoes of the different physics
theories in them so what kind of rules
is there something simple to be said
about the kind of rules that you have
found beautiful that you have found
powerful right so so I mean what you
know one of the features of
computational ir reducibility is it's
very you you can't say in advance what's
going to happen happen with any
particular you can't say I'm going to
pick these rules from this part of rule
space so to speak because they're going
to be the ones that are going to work
that's you can make some statements
along those lines but you can't
generally say that now you know the
state of what we've been able to do is
you know different properties of the
universe like
dimensionality you know integer
dimensionality features of of other
features of of quantum mechanics things
like that at this point what we've got
is we've got rules that that uh any one
of those features we can get a rule that
has that feature yeah so we don't have
the the sort of the final here's a rule
which has all of these features we do
not have that yet so so if I were to try
to summarize the wolf from physics
project
which is uh you know something that's
been in your brain for a long time but
really has just exploded in activity you
know only just months ago yes uh so it's
an evolving thing and next week I'll try
to publish this conversation as quickly
as possible because by the time it's
published already new things will
probably have come out so uh so if I
were to summarize it we've talked about
the basics of there's a hypergraph that
represents space there is uh
Transformations and that hypergraph that
represents um time progress of time the
progress of time there's a cause a graph
that's a characteristic of this and the
basic process of science of yeah of
science within the wol from physics
model is to try different rules and see
which properties of physics that we know
of known physical theories are appear
within the graphs that emerg from that
rule that's what I thought it was going
to be uh oh okay so
what so what is it turns out we can do a
lot better than that it turns out that
using kind of mathematical ideas we can
say and computational ideas we can we
can make General statements and those
General statements turn out to
correspond to things that we know from
20th century physics in other words the
idea of you just try a bunch of rules
and see what they do that's what I
thought we were going to have to do um
but in in fact we can say given causal
invariance and computational
irreducibility we can derive and this is
where it gets really pretty interesting
we can derive special relativity we can
derive general relativity
we can derive quantum mechanics and
that's where things really start to get
exciting is you know it wasn't at all
obvious to me that even if we were
completely correct and even if we had
you know this is the rule you know even
if we found the rule to be able to say
yes it corresponds to things we already
know I did not expect that to be the
case and so for somebody who is uh
simple mind and definitely not a
physicist not even close what does
derivation mean in this case
okay so so let me this is interesting
question okay so there's so one one
thing in the context of computational
reducibility yeah yeah right right so
what you have to do let me give let me
go back to again the mundane example of
fluids and water and things like that
right so so you have a bunch of
molecules bouncing around you can say uh
just as a piece of mathematics I happen
to do this from cellular autometer back
in the mid 1980s you can say just as a
matter of mathematics you can say the
Continuum limit of these little
molecules bouncing around is the Navia
Stokes equations that's just a piece of
mathematics it's not it doesn't rely on
uh you have to make certain assumptions
that you have to say there's enough
Randomness in the way the molecules
bounce around that certain statistical
averages work etc etc etc okay it is a
very similar derivation to derive for
example the Einstein equations okay so
the way that Works roughly the einin
equations are about curvature of space
uh curvature of space I talked about
sort of how you can figure out dimension
of space there's a similar kind of way
of figuring out if you if you just sort
of say um uh you know you're making a
larger larger ball or larger and larger
if you draw a circle on the surface of
the Earth for example you might think
the area of a circle is pi r squ but on
the surface of the Earth because it's a
sphere it's not flat the the area of a
circle isn't precisely P pi r s as the
circle gets bigger the area is slightly
smaller than you would expect from the
formula P Pi R square has a little
correction term that depends on the the
ratio of the size of the circle to the
radius of the Earth okay so it's the
same basic thing allows you to measure
from one of these hyper graphs what is
its effective
curvature and that's oh so um the little
piece of mathematics that uh explains
special general
relativity is uh can map nicely to
describe fundamental property of the
hyps the curvature of H so special
relativity is about the relationship of
time to space general relativity is
about curvature in in this space
represented by this hypergraph so what
is the curvature of a hypergraph okay so
first I have to explain what was
explaining is first thing you have to
have is a notional Dimension you don't
get to talk about curvature of things if
you say oh it's a curved line but I
don't what a line is yet so yeah what is
the dimension of a
hypography hypergraph it's got a
trillion nodes in it yeah what is it
roughly like is it roughly like a grid a
two-dimensional grid is it roughly like
all those all those nodes are arranged
on line what's it roughly like and
there's a pretty simple mathematical way
to estimate that by just looking at the
the the this thing I was describing this
sort of the size of a ball that you
construct in the hypergraph that's a you
just measure that you can just you know
comput it on a computer for a given
hypergraph and you can say oh this thing
is wiggling around but it's it's roughly
corresponds to two or something like
that it roughly corresponds to 2.6 or
whatever so that's how you that's how
you have a notion of dimension in these
hypergraphs curvature is something a
little bit beyond that it's if you look
at the how the size of this ball
increases as you increase its radius
curvature is a correction to the SI size
increased associated with Dimension it's
a sort of a second order term in in the
in determining the size just like the
area of a circle is roughly P pi r s so
it goes up like R squar the two is
because it's in two Dimensions but when
that circle is drawn on a big sphere the
the actual formula is pi r 2 * 1
minus uh R 2 over a 2 and some
coefficient
so in other words there's a correction
to and that correction term that gives
you coverture and that correction term
is what makes this hypergraph correspond
have the potential to correspond to
curved space now the next question is is
that curvature is the way that curvature
works the way that Einstein's equations
of general relativity you know is it the
way they say it should work and the
answer is uh yes and the and so how does
that work the I mean you the the
calculation of the curvature of this
hypergraph for for some some set of
rules no it doesn't matter what the
rules are it doesn't so long as they
have causal invariance and computational
irreducibility and and they lead to
finite dimensional space f non infinite
dimensional space nonin dimensional it
can grow infinitely but it can't be
infinite dimensional so what ises a
infinitely dimensional hypog graph look
like so that mean for example so in a
you start from one root of the tree it
Doubles Doubles again doubles again
doubles again and that means if you ask
the question starting from a given point
how many points do you get to remember
in like a circle you get to r squ with a
two there on a tree you get to for
example 2 to the r it's exponential
dimensional so to speak or infinite
dimensional do you have a sense of in
the space of all possible rules how many
uh lead to uh infinitely dimensional
hypog grass is that U no okay is that an
important thing to know yes it's an
important thing to know I would love to
know the answer to that and but but you
know it gets a little bit more
complicated because for example it's
very possibly the case that in our
physical universe that the Universe
started infinite dimensional and it only
uh it as it as the you know at the big
bang it was very likely infinite
dimensional and as um as the universe
sort of expanded and cooled its
Dimension gradually went down and so one
of the bizarre possibilities which
actually there are experiments you can
do to try and look at this the universe
can have Dimension fluctuations so in
other words we think we live in a
three-dimensional universe but actually
there may be places where it's actually
3.01 dimensional or where it's you know
2.99 dimensional and it may be that in
the in the very early Universe it was
actually infinite dimensional and it's
only a late stage phenomenon that we end
up getting three-dimensional space but
from your perspective of the hypergraph
the one of the underlying assumptions
you kind of implied but you have a sense
a hope um set of assumptions that the
the rules that underly our universe or
the rule that underlies our universe is
static is that the one of the
assumptions you're currently operating
under uh yes but there's a there's a
footnote to that which we should get to
because it requires a few more steps
okay well actually then let's backtrack
to the curvature because we're talking
about as long as it's finite
dimensional uh finite dimensional
computational irreducibility and causal
invariance then it follows that uh the
uh that the large scale structure will
follow Einstein's equations and now let
me again qualify that a little bit more
there's a little bit more complexity to
it the um uh okay so Einstein's
equations in their simplest form apply
to the vacuum no matter just the vacuum
and they say in particular what they say
is if you have um uh so there's this
term jisc that's a term that means
shortest path comes from measuring
shortest paths on the earth so you you
look at a bunch of a bundle of jd6 a
bunch of shortest paths it's like the
paths that photons would take between
two points then the statement of
Einstein's equations is basically a
statement about a certain the that as
you look at a bundle of gd6 the
structure of space has to be such that
although the the cross-sectional area of
this bundle May although the actual
shape of the cross-section may change
the cross-sectional area does not that's
a version that's a that's the most
simple-minded version of amuu minus a
half r g mu new equals z which is the
the more mathematical version of
Einstein's equations it's a statement
it's a statement of thing called the
Richie tensor is equal to zero um that's
that's Einstein's equations for the
vacuum okay so we get that
in um as a result of this model but
footnote big you know big footnote
because all the matter in the universe
is the stuff we actually care about the
vacuum is not stuff we care about so the
question is how does matter come into
this and for that you have to understand
what energy is in these models and um
one of the things that we realized um
you know last late last year was um that
there's a very simple interpretation of
energy in these models
okay and
energy is basically well intuitively
it's the amount of activity in these
hypergraphs and the way that that
remains over time so a little bit more
formally you can think about this causal
graph as having these edges that
represent causal relationships you can
think about oh boy there's one more
concept that we didn't get to is that
the the notion of space-like
hypersurfaces
so this is this is a is not as scary as
it sounds the the um it's a it's a
common notion in general it's a the
notion is you are you're defining what
is a possibly what is what um where in
SpaceTime might be a particular moment
in time so in other words what what is a
consistent set of places where you can
say this is happening now so to speak
and you make this series of of of sort
of slices through the SpaceTime uh
through this causal graph to rep
represent sort of what we consider to be
successive moments in time okay it's
somewhat arbitrary because you can you
can deform that if you're going at a
different speed and special relativity
you tip those things if you're you can
you know there there are different kinds
of defamations but only certain
defamations are allowed by the structure
of the causal graph anyway be there as
it may the the the basic point is there
is a way of figuring out you know you
say what is the energy associated with
what's going on in this in this
hypergraph and the answer is there is a
precise definition of that and it is the
formal way to say it is it's the Flux Of
causal edges through space likee
hypersurfaces the slightly less formal
way to say it it's basically the amount
of activity the the see the reason it
gets tricky is you might say it's the
amount of activity per unit volume in in
this hyper graph but you haven't defined
what volume is so it's it's it's a
little bit that you have to but this
hypersurface gives some more formalism
to that yeah it gives a way to connect
that to but intuitive we should think
about is the just the amount of activity
right so so the amount of activity that
kind of remains in one place in the
hypergraph corresponds to energy the
amount of activity that is kind of where
an activity here affects an activity
somewhere else C corresponds to momentum
and um and so one of the things that's
kind of cool is that I'm trying to think
about how to say this intuitively the
mathematics is easy but the the
intuitive version I'm not sure but
basically the way that things sort of
stay in the same place and have activity
is associated with rest mass and so one
of the things that you get to derive
isal
mc^2 um that is a consequence of this
interpretation of energy in terms of the
way the causal graph Works which is a
the whole thing is sort of a consequence
of this whole story about updates and
hypergraphs and so on so can you Linger
on that a little bit how do we get eals
mc² so where does the mask come from so
okay okay I mean without is there an
intuitive so okay F first of all you're
pretty deep in the mathematical
explorations of this thing right now
we're in a very we're in a
flux uh currently so maybe you haven't
even had time to think about intuitive
explanations uh but yeah I mean this one
this one is is look roughly what's
happening that derivation is actually
rather easy and everybody and I've been
saying we should pay more attention to
this derivation because it's such you
know because people care about this one
and everybody says it's just easy it's
it's easy so there's some concept of
energy that's uh can be intuitively
thought of as the activity the the flux
the level the level of uh changes that
occurring based on the Transformations
within a certain volume however the heck
do you find the volume okay so and then
Mass well mass is is mass is associated
with kind of the energy that does not
cause you to that does not somehow
propagate through time yeah I mean one
of the things that was not obvious in
the usual formulation of speciality is
that space and time are connected in a
certain way energy moment and momentum
are also connected in a certain way the
fact that the connection of energy to
momentum is analogous to the connection
to space between space space and time is
not self-evident in ordinary relativity
it is a consequence of this of the way
this model works it's an intrinsic
consequence of the way this model works
and it's all to do with that with with
unraveling that connection that ends up
giving you this this relationship
between energy and and well it's energy
momentum Mass they're all connected and
and so like uh that's hence the general
relativity you have a sense that uh it
appears to be baked in to the
fundamental properties of the way these
hypergraphs are evolved well I didn't
yet get to so I I got as far as special
relativity and equals mc^ s the one last
step is in general relativity the the
final connection is energy Mass cause
curvature in space and that's something
that when you understand this
interpretation of energy and you kind of
understand the correspondence to
coverture and hypergraphs then you can
finally sort of the the big final answer
is you derive the full version of
Einstein's equations for space time and
matter um and that's um so is that have
you that last piece with curvature have
is that have you arrived there yet oh
yeah we're we're there yes and and
here's the here's the way that we here's
how we're really really going to know
we've arrived okay so you know we have
the mathematical derivation it's all
fine but but you know mathematical
derivations okay so one thing that's
sort of a a uh you know we're taking
this limit of what happens when you the
limit you have to look at things which
are large compared to the size of an
elementary length small compared to the
whole size of the universe large
compared to certain kinds of
fluctuations blah blah blah there's a
there's a there's a tower of many many
of these mathematical limits that have
to be taken so if you're a pure
mathematician saying where's the precise
proof it's like well there are all these
limits we can you know we can try each
one of them computationally and we can
say yeah it really works but the formal
mathematics is really hard to do I mean
for example in the case of deriving the
equations of fluid dynamics from
molecular dynamics that derivation has
never been done MH there is no rigorous
version of that derivation so so because
you can't do the limits yeah because you
can't do the limits um but so the limits
allow you to try to describe something
general about the system and very very
particular the kinds of limits that you
need to take with these very right and
and the limits will definitely work the
way we think they work and we can do all
kinds of computer exp hard deration yeah
it's just it's just the mathematical
structure kind of in you know ends up
running right into computational
reducibility and you end up with a bunch
of a bunch of difficulty there but
here's the way that we're getting really
confident that we know completely what
we're talking about which is when people
study things like black hole mergers
using Einstein's equations what do they
actually do well they actually use
Mathematica a whole bunch to analyze the
equations and so on but in the end they
do numerical relativity which means they
take these nice mathematical equations
and they break them down so that they
can run them on a computer and they
break them down into something which is
actually a discrete approximation to
these equations then they run them on a
computer they get results then you look
at the gravitational waves and you see
if they match okay turns out that our
model gives you a direct way to do
numerical relativity so in other words
instead of saying you start from these
Continuum equations from Einstein you
break them down into these discrete
things you run them on a computer you
say we're doing it the other way around
we're starting from these discrete
things that come from our model and
we're just running big versions of them
on the computer and uh you know what
we're saying is and this is this is how
things will work so what I'm the way I'm
calling this is is proof by compilation
so to speak Pro by that is in other
words you're you're taking um something
where you know we've got this
description of a black hole system and
what we're doing is we're we're showing
that the you know what we get by just
running our model agrees with what you
would get by doing the computation from
the Einstein equations as a small
tangent or actually a very big tangent
but
uh proof by compilation is a beautiful
Concept in a sense the way of doing
physics with this model
is by running it or compiling it and
some level yes it have you thought about
and these things can be very large is
there totally new possibilities of
computing hardware and Computing
software which allows you to perform
this kind of compilation well algorithms
software Hardware so so first comment is
these models seem to give one a lot of
inition about distributed computing a
lot of different intuition about how to
think about parallel computation and
that particularly comes from the quantum
mechanic side of things which we didn't
talk about much yet but uh the question
of what you know given our current
computer hardware how can we most
efficiently simulate things yeah that's
actually partly a story of the model
itself because the model itself has deep
parallelism in it yes the ways that
we're simulating it we're just starting
to be able to use that deep parallelism
to be able to be more efficient in the
way that we simulate things but in fact
the structure of the model itself allows
us to think about parallel computation
in different ways and one of my
realizations is that you know so it's
very hard to get in your brain how you
deal with parallel computation and
you're always worrying about you know if
multiple things can happen at different
on different computers at different
times oh what happens if this thing
happens before that thing and we've
really got you know we have these race
conditions where something can race to
get to the answer for another thing and
you get all tangled up because you don't
know which thing is going to come in
first and usually when you do parallel
Computing there's a big Obsession to
lock things down to the point where
you've you've had locks and mutexes and
God knows what else where where you've
you've um you've arranged it so that
there can only be one sequence of things
that can happen so you don't have to
think about all the different kinds of
things that can happen well in these
models physics is throwing us into
forcing us to think about all these
possible things that can happen but
these models together with what we know
from physics is giving us new ways to
think about all possible things
happening about all these different
things happening in parallel and so I'm
I'm guessing they have buil-in
protection for some of the parallelism
well causal invariance is the built-in
protection causal invariance is what
means that even though things happen in
different orders it doesn't matter in
the end as a as a as a person who
struggle with concurrent programming
in in like Java uh with all all the
basic concepts of uh concurrent
programming that that if there could be
built up a strong mathematical framework
for causal invariance that's so
liberating and that that could be not
just liberating but really powerful for
massively distributed computation
absolutely no I mean you know what's
eventual consistency in in distributed
databases is essentially the causal
invariance idea yeah okay so that's but
but but have you thought
about uh you know we're like really
large
simulations yeah I mean I'm also
thinking about look the fact is you know
I've spent much of my life as a language
designer right so I can't possibly not
think about you know what does this mean
for Designing languages for parallel
computation in fact another thing that's
one of these you know I I'm always
embarrassed at how long it's taking me
to figure stuff out but you know back in
the 1980s I worked on trying to make up
languages for parallel computation I
thought about doing graph rewriting I
thought about doing these kinds of
things but I couldn't see how to
actually make the connections to
actually do something useful I think now
physics is kind of showing us how to
make those things useful and so my guess
is that in time we'll be talking about
you know we do parallel programming
we'll be talking about programming in a
certain reference frame just as we think
about thinking about physics in a
certain reference frame it's a certain
coordination of what's going on we say
we're going to program in this reference
frame oh let's change the reference
frame to this reference frame and then
our program will seem different and
we'll have a different way to think
about it but it's still the same program
underneath so let me ask on this topic
because I put out that I'm talking to
you I got way more questions that I can
deal with but what Pops to mind is a
question somebody asked on Reddit I
think is uh please ask uh Dr wlr uh what
are the specs of the computer running
the universe so we we're talking about
specs of hardware and software
simulations of a large scale thing what
about a scale that is comparative to
something that eventually leads to the
two of us talking and about right right
right so so actually I I did try to
estimate that and we have to go a couple
more stages before we can really get to
that answer because because we're we're
talking about um this this thing um you
know this is what happens when you when
you build these abstract systems and
you're trying to explain the universe
there quite a number of levels deep so
to speak um but uh the um you mean
conceptually or like literally cuz
you're talking about small object and
there's 10 to the something number right
it's it's it it is conceptually deep and
one of the things that's happening sort
of structurally in this project is you
know there were ideas there's another
layer of ideas there's another layer of
ideas to get to the different things
that correspond to physics they're just
different layers of ideas and they are
um you know it's actually probably if
anything getting harder to explain this
project because I'm realizing that the
fraction of way through that I am so far
and explaining this to you is less than
than you know it might be because
because we know more now you know in the
every every week basically we know a
little bit more and like those are just
layers on the initial fundamental yes
structure the layers are you know you
you might be asking me you know how do
we get uh you know the difference
between Fons and bosons the difference
between particles that can be all in the
same state and particles that exclude
each other okay last 3 days we've kind
of figured that out okay but um and it's
very interesting it's very cool um and
it's very uh and those are some kind of
properties at a certain level layer of
abstraction on the hypog graph yes and
there's a and there's but the layers of
abstraction are kind of there
compounding stacking up so it's
difficult but but okay but this but the
specs nevertheless remain the same the
the specs underneath so I I have an
estimate so the question is what are the
units so we've got these different
fundamental constants about the world so
one of them is the speed of light which
is the so the thing that's always the
same in all these different ways of
thinking about the universe is the
notion of time because time is
computation and so there's an elementary
time which is sort of the the the amount
of time that we ascribe to elapsing in a
in a single computational step yeah okay
so that's the elementary time so then
there's an El parameter or whatever that
it's a constant it's whatever we Define
it to be because I mean we we don't you
know it's all relative right it doesn't
matter it doesn't matter what it is
because we could be it could be slow
it's just a number which which we use to
convert that to Second so to speak
because we are experiencing things and
we say this amount of time has elapsed
so to speak but we're within this thing
so AB it doesn't it doesn't matter right
but what does matter is the ratio what
we can uh the ratio of the spatial
distance and this hypergraph to this uh
to this moment of time again that's an
arbitrary thing but we measure that in
me/ second for example and that ratio is
the speed of light so the ratio of the
elementary distance to the elementary
time is the speed of light okay perfect
and so there's another there are two
other levels of this okay so there is a
thing which we can talk about uh which
is the maximum entanglement speed which
is a thing that happens at another level
in this whole sort of story of how these
things get constructed um that's a sort
of maximum speed in Quantum in the space
of quantum States just as the speed of
light is a maximum speed in physical
space this is a maximum speed in the
space of quantum States there's another
level which is associated with what we
call Ral space which is a another one of
these maximum speeds we get to this so
these are limitations on the system that
are able to capture the kind of physical
Universe which we live in the quantum
mechanic they are inevitable features of
having a a rule that has only a finite
amount of information in the rule so
long as you have a rule that only
involves a a a bounded amount a limited
amount of only involving a limited
number of elements limited number of
relations it is inevitable there are
these speed constraints we knew about
the one for speed of light we didn't
know about the one for maximum
entanglement speed which is actually
something that is possibly measurable
particularly in black hole systems and
things like this anyway this is long
long story short you're asking what the
processing specs of the universe of the
of the sort of computation of the
universe there's a question of even what
are the units of some of these
measurements okay so the units I'm using
are wol from language instructions per
second okay because you got to have some
you know what the quad computation are
you do it there got to be some kind of
frame of reference right right so and
because it turns out in the end there
will be there's sort of an arbitrariness
in the language that you use to describe
the universe so in those terms I think
it's like 10 the 500 or from language
operations per second I think is the um
I think it's of that order you know B
that's scale of computation what about
memory if there's an interesting thing
to say about storage and memory well
there a question of how many sort of
atoms of space might there be you know
maybe 10 to 400 we don't know exactly
how to estimate these numbers I mean
this is this is based on some some I
would say somewhat rickety way of
estimating things uh you know when there
start to be able to be experiments done
if lucky there will be experiments that
can actually nail down some of these
numbers and uh because of computation
reducibility there's no much hope for
very efficient compression like very uh
efficient representation to this good
question I mean there's probably certain
things you know the fact that we can
deduce any okay the question is how deep
does the reducibility go right okay and
I keep on being surprised that it's a
lot deeper than I thought okay and so um
one of the the things is that that
there's a question of sort of how much
of the whole of physics do we have to be
able to get in order to explain certain
kinds of phenomena like for example if
we want to study Quantum interference do
we have to know what an electron is
turns out I thought we did turns out we
don't I thought to know what energy is
we would have to know what electrons
were we don't you get a lot of really
powerful shortcuts right there's a
there's a bunch of sort of bulk
information about the world the the
thing that I EX Ed about last few days
okay is um uh the idea of fion versus
boson fundamental idea that I mean it's
the the reason we have matter that
doesn't just self-destruct is because of
the exclusion principle that means that
two electrons can never be in the same
Quantum state is it uh useful for us to
maybe first talk about how quantum
mechanics let's talk about quantum
mechanics the wol from physics model yes
let's go there so we talked about
general relativity now
what uh what have you
found uh the story of quantum mechanics
right within and outside of the wol from
physics right so I mean the the the key
idea of quantum mechanics that sort of
the the the typical interpretation is
classical physics says a definite thing
happens quantum physics says there's
this whole set of Paths of things that
might happen and we are just observing
some overall probability of of how those
paths work okay so when you think about
our hypergraphs and all these little
updates that are going on there's a very
remarkable thing to realize which is if
you say well which particular sequence
of updates should you do say well it's
not really defined you can do any of a
whole collection of possible sequences
of updates okay that set of possible
sequences of updates defines yet another
kind of graph that we call a multi-way
graph and a multi-way graph just is a
graph where at every node
there is a choice of several different
possible things that could happen so for
example you go this way go that way
those are two different edges in the
multi-way graph and you're building up
the set of possibilities so actually
like for example I just made the one the
multi-way graph for Tic Tac Toe okay so
Tic Tac Toe you start off with some some
board that you know is everything is
blank and then somebody can put down a
an X somewhere an O somewhere and then
there are different possibilities at
each stage there are different
possibilities and so you build up this
multi-way graph of all those
possibilities now notice that even in Te
tactoe you have the feature that there
can be something where you have two
different things that happen and then
those branches merge because you end up
with the same shape of you know the same
configuration of the board even though
you got there in two different ways so
what the the thing that's sort of an
inevitable feature of our models is that
just like quantum mechanics suggests
definite things don't happen instead you
get this whole multi way graph of all
these
possibilities okay so then the question
is so that okay so that's sort of a a
picture of what's going on now you say
okay well quantum mechanics has all
these features of uh you know all this
mathematical structure and so on how do
you get that mathematical structure okay
couple of couple of things to say so
quantum mechanics is actually in a sense
two different theories glued together
quantum mechanics is a theory of how
Quantum amplitudes work that more or
less give you the probabilities of
things happening
and it's the theory of quantum
measurement which is the theory of how
we actually conclude definite things
because the mathematics just gives you
these Quantum amplitudes which are more
or less probabilities of things
happening but yet we actually observe
definite things in the world um Quantum
measurement has always been a bit
mysterious it's always been something
where people just say well the
mathematics says this but then you do a
measurement and they're philosophical
arguments about what the measurement is
but it's not something where there's a
theory of the measurement some on Reddit
also asked uh please ask Stephen to tell
his story of this the double slit
experiment okay yeah I can does that
does that make sense oh yeah makes sense
absolutely makes sense why is this like
a good way to discuss uh a little bit
let me let me go let me explain a couple
of things first so so the structure of
quantum mechanics is is mathematically
quite complicated um one of the features
let's see well how to how to describe
this
okay so first point is there's this
multi-way graph of all these different
Paths of of things that can happen in
the world and the important point is
that that uh these you can have
branchings and you can have mergings
Okay so this property turns out causal
invariance is the statement that the
number of mergings is equal to the
number of branchings yeah so in other
words every time there's a branch
eventually there will also be a merge
in other words every time there were two
possibilities of what might have
happened eventually those will merge
beautiful concept by the way yeah yeah
yeah so so that so that idea okay so
then uh so that's that's one thing and
that's closely related to the the sort
of objectivity in quantum mechanics the
fact that we believe definite things
happen it's because although there are
all these different paths in some sense
because of causal invariance they all
imply the same thing that's I'm I'm
cheating a little bit in saying that but
that's roughly the essence of what's
going on okay next next thing to think
about is uh you have this multi-way
graph it has all these different
possible things that are happening now
we ask this multi-way graph is sort of
evolving with time o over time it's
branching it's merging it's doing all
these things okay um the question we can
ask is if we slice it a at a particular
time what do we see and that slice
represents in a sense something to do
with the state state of the universe at
a particular time so in other words
we've got this multi-way graph of all
these possibilities and then we're
asking an an okay we take this slice
this slice represents aent okay each of
these different paths corresponds to a
different Quantum possibility for what's
happening right when we take this slice
we're saying what are the set of quantum
possibilities that exist at a particular
time and when you say slice are these
you slice the graph and then there's a
bunch of leaves a bunch of and those
represent the state of things right but
but then okay so the important thing
that you are quickly picking up on is
that um what what matters is kind of how
these leaves are related to each other
so a good way to tell how leaves are
related is just to say on the step
before did they have a common ancestor
so two leaves might be they might have
just branched from one thing or they
might be far away you know way far apart
in this graph where to get to a common
ancestor maybe you have to go all the
way back to the beginning of the graph
all the way back to the beginning so
there's some kind of measure of distance
right and and that but the what you get
is by making the
slice what we call it branchial space
the space of branches um and in this
branchial space um you have a graph that
represents the relationships between
these Quantum States in branchial space
you have this notion of distance in
branchial space okay so it's connected
to Quant
entanglement yes yes it's it's it's
basically the the distance in branchial
space is kind of an entanglement
distance so this that's a very nice
model right it is very nice it's very
beautiful it's it's I mean it's it's so
clean I mean it's it's really you know
and it it it tells one okay so anyway so
then then this this branchial space uh
has this sort of map of the the
entanglements between Quantum States so
in physical space we have so so you know
you can say take let's say the causal
graph and we can slice that um at a
particular time and then we get this map
of how things are laid out in physical
space when we do the same kind of thing
there's a thing called the multi-way
causal graph which is the analog of a
causal graph for the multi-way system we
slice that we get essentially the
relationships between things not in
physical space but in the space of
quantum States it's like which Quantum
state is similar to which other Quantum
State okay so now I think next thing to
say is just to mention how Quantum
measurement works so Quantum measurement
has to do with reference frames in
bronchial space so okay so measurement
in in physical space it matters whether
how we
assign spatial position and how we how
we Define coordinates in space and time
and that's that's how we make
measurements in ordinary space are we
making a measurement based on us sitting
still here are we traveling at half the
speed of light light in making
measurements that way these are
different reference frames in which
we're making our measurements and the
relationship between different events
and different points in space and time
uh will be different depending on what
reference frame we're in okay so then we
have this idea of quantum observation
frames which are the analog of reference
frames but in branchial space and so
what happens is what we realize is that
a Quantum measurement is the The
Observer is sort of arbitrarily
determining this reference frame The
Observer is saying I'm going to
understand the World by saying that
space and time are coordinati this way
I'm going to understand the World by
saying that Quantum States and time are
coordinatization frames so in a sense
the obser
the way the Observer enters is by their
choice of these Quantum observation
frames and what happens is that the
Observer um because okay this is again
another stack of other Concepts but
anyway because the Observer is
computationally bounded there is a limit
to the type of quantum observation
frames that they can construct
interesting okay so there's okay so some
constraints some limit on and that's on
the choice of observation frames right
and by the way I just want to mentioned
that there's a I mean it's it's bizarre
but there's a hierarchy of these things
so in in um uh in
thermodynamics the the fact that we
believe entropy increases we believe
things get more disordered is a
consequence of the fact that we can't
track each individual molecule if we
could track every single molecule we
could run every movie in Reverse so to
speak and we would you know we would not
see that things are getting more
disordered but it's because we are
computationally bounded we can only look
at these big blobs of what all these
molecules collectively do that we think
that things are that we describe it in
terms of of entropy increasing and so on
and it's the same phenomenon basically
also the consequence of computational
irreducibility that causes us to
basically be forced to conclude that
definite things happen in the world even
though there's this Quantum you know
this set of all these different Quantum
processes that are going on so I I mean
I'm I'm I'm I'm skipping a little bit
and the the but that that's a that's a a
rough picture and in the evolution of
the wol from physics project where do
you feel we stand on the some of the
puzzles that are along the way see
you're skipping along a bunch
of it's amazing how much these things
are unraveling I mean you know these
things look it used to be the case that
I would agree with dick fan nobody
understands quantum mechanics including
me okay I'm getting to the point where I
think I actually understand quantum
mechanics my my exercise okay is can I
explain Quantum Mechanics for real at
the level of kind of Middle School type
explanation right and I'm getting closer
it's getting it's getting there I'm not
quite there I've tried it a few times
and I realize that there are things that
um uh where I have to start talking
about elaborate mathematical Concepts
and so on but I think and and you know
you got to realize it's not self-evident
that we can explain you know at an
intuitively graspable level something
which uh you know about the way the
universe works the universe wasn't built
for our understanding so to speak um but
but I think then then um uh okay so
another important important idea is um
uh this idea of branchial space which I
mentioned this sort of space of quantum
states it is okay so I mentioned
Einstein's equations describing you know
the effect of uh the effect of mass and
energy on uh trajectories of particles
on gd6 the curvature of of um of
physical space is associated with uh the
presence of energy according to
Einstein's equations Okay so turns out
that rather amazingly the same thing is
true in branchial space so it turns out
the presence of energy or more
accurately lran density which is a kind
of relativistic invariant version of
energy um the presence of that causes
essentially deflection of
jd6 in this branchial space okay so you
might say so what Well turns out that
the sort of the best formulation we have
of quantum mechanics this the fine path
integral is a thing that describes
Quantum processes in terms of
mathematics that can be interpreted as
well in quantum mechanics the the big
thing is you get these Quantum
amplitudes which are complex numbers
that represent when you combine them
together represent probabilities of
things happening and so the big story
has been how do you derive these Quantum
amplitudes and people think these
Quantum amplitudes they have a complex
number has you know real part and
imaginary part you can also think of it
has a magnitude and a phase um and it um
people have sort of thought these
Quantum amplitudes have magnitude and
phase and you compute those together
turns out that magnitude the magnitude
and the phase come from completely
different places the magnitude comes
okay so what do you how do you compute
things in quantum mechanics roughly I'm
I'm telling you I'm I'm getting there to
be able to do this at a middle school
level but I'm not there yet um the the
roughly what happens is you're asking
does this state in quantum mechanics
evolve to this other state in quantum
mechanics and you can think about that
like a particle traveling or something
traveling through physical space but
instead it's traveling through branchial
space MH and so what's happening is does
this Quantum State evolve to this other
Quantum State it's like saying does this
object move from this place in space to
this other place in space okay now the
way that you these quantum amplitudes
udes characterize kind of um to what
extent the thing will successfully reach
some particular point in branchial space
just like in physical space you could
say oh it had a certain velocity and it
went in this direction in branchial
space there's a similar kind of concept
is there a nice way to visualize for me
now mentally Branch space it's just you
have this hypergraph sorry you have this
multi-way graph it's this big branching
thing branching and merging thing but I
mean like moving through that space I
I'm just trying to understand what that
looks like
is you know that space is probably
exponential dimensional which makes it
again another can of worms in
understanding what's going on that space
as in in ordinary space this hypergraph
the spatial hypergraph limits to
something which is like a manifold like
a like something like threedimensional
space almost certainly the multi-way
graph limits to a hbert space which is
something that I mean it's it's just a
weirder exponential dimensional space
and by the way you can ask I mean there
are much weirder things that go on for
example one of the things I've been
interested in is the expansion of the
universe in branchial space so we know
the universe is expanding in physical
space but the universe is probably also
expanding in BR space so that means the
the number of quantum states of the
universe is increasing with time the
diameter of the thing is growing right
so that means that the and and by the
way uh this is related to whether
Quantum Computing can ever
work um and uh uh why okay so let me
explain why so so let's talk about okay
so first of all just just to finish the
thought about Quantum amplitudes the the
incredibly beautiful thing just this is
just I'm just very excited about this
the the um the F path integral is is
this formula it says that the amplitude
the quantum amplitude is e to the i s
overh bar where s is the thing called
the action and um it uh okay so that can
be thought of as representing a
deflection of the angle of this path in
the multi-way graph so it's a deflection
of a jisc in the multi-way path that is
caused by this thing called the action
which is essentially associated with
energy okay and so this is a deflection
of a path in branchial space that is
described by this path integral which is
the thing that is the mathematical
essence of quantum mechanics m turns out
that deflection is the deflection of gd6
and branchial space follows the exact
same mathematical setup as the
deflection of gd6 in physical space
except the deflection of gd6 in physical
space is described with Einstein's
equations the deflection of gd6 and
branchial space is defined by the F and
path integral and they are the same in
other words they are mathematically the
same so that means that general
relativity is a story of essentially
Motion in physical space uh quantum
mechanics is a story of essentially
Motion in bronchial space and the
underlying equation for those two things
although it's presented differently
because one's interested in different
things in branchial space and physical
space but the underlying equation is the
same so in other words it's the this
it's just you know these two theories
which are the two sort of pillars of
20th century physics which have seemed
to be off in different directions are
actually facets of the exact same Theory
there and this I mean that's exciting to
see to see where that evolves and
exciting that that just is there right I
mean to me you know look I having spent
some part of my early life you know
working in these in the context of these
theories of of you know 20th century
physics it's they just they seem so
different and the fact that they're
really the same is just really amazing
actually let me you you mentioned double
slit experiment okay so the double
experiment is a is an interference
phenomenon where you say there are you
know you can have a photon or an
electron and you say there are these two
slits it could have gone through either
one but there is this interference
pattern where it's there's destructive
interference where you might have said
in classical physics oh well if if there
are two slits then there's a better
chance that it gets through one or the
other of them but in quantum mechanics
there's this phenomenon of destructive
interference that means that even though
there are two slits two can lead to
nothing as opposed to two leading to
more than than for example one slit and
in what happens in this model and we've
just been understanding this in the last
few weeks actually is that the um what
essentially happens is that the the
double slit experiment is a story of the
interface between branchial space and
physical space and what's essentially
happening is that the destructive
interference is the result of the two
possible paths associated with photons
going through those two slits winding up
at opposite ends of branchial space and
so they don't and so that's why there's
sort of nothing there when you look at
it is because these two different sort
of branches couldn't get merged together
to produce something that you can
measure in physical space is there a lot
to be understood about brancho space
like
is mathematically speaking yes it's a
very beautiful mathematical thing and
it's very I mean by the way this whole
is just amazingly rich in terms of the
mathematics that it says should exist
okay so for example calculus you know is
a story of infinite decimal change in
integer dimensional space onedimensional
two- dimensional threedimensional space
we need a theory of infinitesimal change
in fractional dimensional and dynamic
dimensional space No Such Theory exists
so there's a tools of mathematics that
are needed here right and this is a
motivation for that actually right and
it's it's you know there are there are
indications and we can do computer
experiments and we can see how it's
going to come out but we need to you
know that the actual mathematics is
doesn't doesn't exist and in branchial
space it's actually even worse there's
there's even more sort of layers of
mathematics that are you know we can see
how it works roughly by doing computer
experiments but to really understand it
we need more more sort of mathematical
sophistication so quantum computers okay
so the basic idea of quantum computers
the the promise of quantum computers is
quantum mechanics does things in
parallel and so you can sort of
intrinsically do computations in
parallel and somehow that can be much
more efficient than just doing them uh
one after another and you know I
actually worked on Quantum Computing a
bit with dick fan back in 1981 2 3 um
that kind of time frame and and we a
fascinating image you you and findan
work on quantum computers well we we
tried to work the the big thing we tried
to do was invent a Randomness chip that
would generate Randomness at a high
speed using quantum mechanics and the
discovery that that wasn't really
possible uh was part of the um the story
of we never really wrote anything about
it I think maybe he wrote some stuff but
I we didn't we didn't write stuff about
what we figured out about sort of the
fact that it really seemed like the
measurement process in quantum mechanics
was a serious damper on what was
possible to do in sort of you know the
possible advantages of quantum mechanics
mecs and for computing but anyway so so
the the the sort of the promise of
quantum Computing is let's say you're
trying to you know Factor an integer
well you can instead of you know when
you factor an integer you might say well
does this Factor work does this Factor
work does this Factor work um in
ordinary Computing it seems like we
pretty much just have to try all these
different factors um you know kind of
one after another but in quantum
mechanics you might have the idea oh you
can just sort of have the physics try
all of them in parallel mhm okay and um
the you know and there's this algorithm
shaes algorithm which which uh allows
you according to the formalism of
quantum mechanics to do everything in
parallel and to do it much faster than
you can on a classical computer okay the
only little footnote is you have to
figure out what the answer is you have
to measure the result so the quantum
mechanics internally has figured out all
these different branches but then you
have to pull all these branches together
to say and the classical answer is this
okay the standard theory of quantum
mechanics does not tell you how to do
that it tells you how the branching
works but it doesn't tell you the
process of corralling all these things
together and that process which
intuitively you can see is going to be
kind of tricky but our model actually
does tell you how that process of
pulling things together works and the
answer seems to be we're not absolutely
sure we've only got to two * three so
far in in uh you know which is kind of
in in in this um in this factorization
in quantum computers but we can um uh
the you know what seems to be the case
is that the advantage you get from the
parallelization from quantum mechanics
is lost from the amount that you have to
spend pulling together all those
parallel threads to get to a classical
answer at the end now that phenomenon is
not unrelated to various decoherence
phenomena that are seen in Practical
quantum computers and so on I mean I
should say as a as a very practical
point I mean it's like should people
stop ing to do Quantum Computing
research no because what they're really
doing is they're trying to use physics
to get to a new level of what's possible
in Computing and that's a completely
valid activity whether whether you can
really put you know whether you can say
oh you can solve an MP complete problem
you can reduce exponential time to
polinomial time you know we're not sure
and and I'm suspecting the answer is no
but that's not relevant to the Practical
speedups you can get by using different
kinds of Technologies different kinds of
physics um to do basic Computing so
you're saying I mean some of the models
you're playing with the indication is
that uh to uh get all the Sheep back
together uh and you know to to Coral
everything together to get the actual
solution to the
algorithm is uh you lose all the you
lose use all by the way I mean so so
again this question do we actually know
what we're talking about about Quantum
Computing and so on so again again uh
we're doing proof by compilation so we
have a Quantum Computing framework yeah
in wolam language and which is you know
a standard Quantum Computing framework
that represents things in terms of the
standard uh you know formalism of
quantum mechanics and we have a compiler
that simply compiles the representation
of quantum Gates into multi-way systems
so and in fact the the message that I
got was from somebody who's working on
the project who has managed to compile
one the sort of uh a core formalism
based on category Theory um in of core
Quantum formalism into multi-way systems
so this when you say multi-way system
these multi-way graphs yes yes so you're
comp yeah okay that's awesome and then
you can do all kinds of experiments on
that multiway graph right well but the
point is that what we're saying is the
thing we've got this representation of
let's say Shaw's algorithm in terms of
standard Quantum Gates and it's just a
pure matter of sort of computation to
just say that is a equivalent we will
get the same result as running this
multi-way system can you do complexity
analysis on that multi-way system well
that's what we've been trying to do yes
we're getting there we haven't done that
yet I mean we we there's a pretty good
indication of how that's going to work
out and we've done it as I say our
computer experiments we've
unimpressively gotten to about 2 * three
in terms of factorization which is kind
of about how far people have got with
physical quantum computers as well but
but that's um but yes we will be able to
we definitely will be able to do
complexity analysis and we will be able
to know so the one remaining hope for
Quantum Computing really really working
at this formal level of you know Quantum
brand exponential stuff being done in
polinomial time and so on the one hope
which is very bizarre is that you can uh
kind of uh piggyback on the expansion of
bronchial space so here's here's how
that might work so you think you know
energy conservation standard thing in
high school physics energy is conserved
right but now you imagine you think
about energy in the context of cosmology
and the context of the whole universe
it's a much more complicated story The
expansion of the universe kind of
violates energy conservation and so for
example if you imagine you've got two
galaxies they're receding from each
other very quickly they've got two big
Central black holes you connect a spring
between these two Central black holes
not easy to do in practice but let's
imagine you could do it now that spring
is being pulled apart it's getting
getting more potential energy in the
spring as a result of the expansion of
the universe so in a sense you are you
are piggybacking on the expansion that
exists in the universe and the sort of
violation of energy conservation that's
associated with that cosmological
expansion to essentially get energy
you're essentially building a perpetual
motion machine by using the expansion of
the universe and that is a physical
version of that it is conceivable that
the same thing can be done in branchial
space
to essentially uh mine the expansion of
the universe in Branch Hill space as a
way to get uh sort of uh Quantum
Computing for free so to speak just from
the expansion of the universe in
branchial space now the physical space
version is kind of absurd and involves
you know Springs between black holes and
so on it's conceivable that the
branchial space version is not as absurd
and that it's actually something you can
reach with physical things you can build
in lab and so on we don't know yet okay
so yeah like you were saying the branch
of space might be uh expanding and there
might be some something that could be
exploited right in the same kind of way
that that um that you can exploit the um
uh you know that expansion of the
universe in principle in physical space
you just have like a glimmer of hope
right I think that the look I think the
real answer is going to be that for
practical purposes you know the official
brand that says you can you can you know
do exponential things in po time is
probably not going to work for people
curious to kind of learn more so this is
more like this is not Middle School
we're going to go to elementary school
for a
second maybe Middle School let's go to
middle
school so if I were to try to maybe
write a write a
pamphlet of like wolf from physics
project for
dummies AKA for me or maybe make a video
on the
basics but not just the basics
of the physics project
but the basics plus the most beautiful
Central
ideas um how would you go about doing
that could you help me out a little bit
yeah yeah I mean we covered a l really
practical matter we have this kind of
visual summary picture that we made um
which I think is a pretty good you know
when I've tried to explain this to
people and you know it's a pretty good
place to start is you got this rule you
know you apply the rule you're building
up this this big hypergraph um you've
got all these possibilities you're kind
of thinking about that in terms of
quantum mechanics I mean that's a that's
a that's a decent place to start so
basically the things we've talked about
which is space represented as a
hypergraph transformation of that space
is kind of time yes and then uh
structure of that space in the curvature
of that space as gravity that's that can
be explain without going anywhere near
quantum mechanics um I would say that's
actually easier to explain than special
robots of day um oh so going into
General so going to curvature yeah I
mean special relativity I I think is
it's a little bit elaborate to explain
yeah and honestly you only care about it
if you know about special relativity if
you know how special relativity is
ordinarily derived and so on general
relativity is easier is easier yes and
what about what's the easiest way to
reveal uh I think the the basic point is
just
this fact that there are all these
different branches that there's this
kind of map of how the branches work and
that um I mean I think I think actually
the recent things that we have about the
double experiment are pretty good
because you can actually see this you
can see how the double slit you know
phenomenon arises from just features of
these graphs now you know having said
that right there is a little bit of of
slight of hand there because the the
true story of the way that double slit
thing works depends on a
coordinatization of branchial space that
for example in our internal team there
is still a vigorous battle going on
about how that works and it's it's
what's becoming clear is I mean what's
becoming clear is that it's
mathematically really quite interesting
I mean that is that there's a you know
it involves essentially putting space
fill in curves you basically have a
thing which is naturally two-dimensional
and you're sort of mapping it into one
dimension and with a space filling curve
and it's like why is it this space
filling curve and not another space
filling curve and that becomes a story
about reman surfaces and things and it's
quite elaborate and um but but the
there's a a more little bit slight of
hand way of doing it where it's you know
it's surprisingly direct it's so a
question that might be difficult to
answer but uh for several levels of
people could you give me advice on how
we can learn more
specifically there is people that are
completely outside and just curious and
are captivated by the beauty of
hypergraphs actually uhhuh so people
there just want to explore play around
with this uh second level is people from
say people like me who somehow got a PhD
and computer science but are not
physicists and but fundamentally the
work you're doing is computational
nature so it feels very accessible yes
so what are what can a person like that
do to learn enough physics or not to be
able to uh one explore the beauty of it
and two the the final level of
contribute something right of a level of
even publishable you know like strong
interesting ideas at all those layers
complete beginner yeah I see person and
the Cs person that wants to publish
right I mean I think that you know I've
written a bunch of stuff uh bu called
Jonathan gorod who's been a key person
working on this project has also written
a bunch of stuff um and some other
people have started writing things too
and he's a physicist physicist well he's
I would say a mathematical physicist he
pretty mathematically sophisticated he's
he regularly out mathematized me yeah
strong yeah strong mathematical
physicist yeah I looked at some of the
papers right but but so so I mean you
know I wrote this kind of original
announcement blog post about this
project which people seem to have found
uh I've been really happy actually that
people um who uh you know people seem to
have gred key points from that much
deeper key points people seem to have
gred than I thought they would grock um
and that that's a kind of a Long blog
post that explains some of the things we
talked about like the hypergraph and the
basic rules and uh I don't does it I
forget doesn't have any quantum
mechanics goes through quantum mechanics
yes it does but we we know a little bit
more since that blog post that probably
clarifies but that blog post is does a
pretty decent job um and you know
talking about things like again
something you didn't mention the fact
that the uncertainty principle as a
consequence of curvature in bronal space
how much physics should a person know to
be able to understand the beauty of this
framework and to contribute something
novel okay so I I think that
those are different questions so I mean
I think that the why does this work why
does this make any sense um uh to really
know that you have to know a fair amount
of physics okay um and for example have
a why does this work you're you're
referring to the connection between this
model and general relativity for example
you have to understand something about
General of there there's also a side of
this where just as the pure mathematical
framework is fascinating yeah yes if you
throw the physics out then it's quite
accessible to I mean you know I I wrote
this sort of long technical introduction
to the project which seems to have been
very accessible to people who are you
know who understand computation and and
formal abstract ideas but are not
specialists in physics or or other kinds
of things I mean the thing with the
physics part of it is you
know it's there's both a way of thinking
and a literally a mathematical formalism
I mean it's like you know to know that
we get the Einstein equations to know we
get the ener of momentum tensor you kind
of have to know what the energ of
momentum tensor is and that's physics I
mean that's kind of graduate level
physics basically um and uh so so that
you know making that final connection is
requires some depth of physics knowledge
I mean that's the unfortunate thing the
difference between machine learning in
physics in the 21st century is it uh
really Out Of Reach of a year or two
worth of study no you could get it in a
year or two but you can't get it in a in
a month right I mean so but it doesn't
require necessarily like 15 years no it
does not and and in fact a lot of what
has happened with this project makes a
lot of this stuff much more accessible
there are things where it has been quite
difficult to explain what's going on and
it it requires much more you know having
the concreteness of being able to do
simulations knowing knowing that this
thing that you might have thought was
just an analogy is really actually
what's going going on makes one feel
much more secure about just sort of
saying this is how this works um and I
think it will be you know the I'm hoping
the textbooks of the future the physics
textbooks of the future there will be a
certain compression there will be things
that used to be very much more elaborate
because for example even doing
continuous mathematics versus this
discret mathematics you know to know how
things work in continuous mathematics
you have to be talking about stuff and
waving your hands about things whereas
with discreet the discreet version it's
just like here is a picture this is how
it works and there's no oh did we get
the limit right did this you know did
this thing that is of you know uh zero
you know measure zero object you know
interact with this thing in the right
way you don't have to have that whole
discussion it's just like here's a
picture you know this is what it does
and you know you can then it takes more
effort to say what does it do in the
limit when the picture gets very big but
you can do experiments to build up an
intuition actually yes right and you can
get sort of core intuition for what's
going on now in terms of contributing to
this the you know I would say that the
study of the computational universe and
how all these programs work in the
computational universe there's just an
unbelievable amount to do there and it
is very close to the surface that is you
know high school kids you can do
experiments it's not um you know and you
can discover things I mean you know we
you can discover stuff about I don't
know like this thing about expansion of
bronal space that's an absolutely
accessible thing to look at now now you
know the main issue with doing these
things is not there isn't a lot of
technical depth difficulty there the
actual doing of the experiments you know
all the code is all on our website to do
all these things the real thing is sort
of the Judgment of what's the right
experiment to do how do you interpret
what you see that's the part that you
know people will do amazing things with
and that's the part that but but it
isn't like you have to have done 10
years of of study to get to the point
where you can do the experiments you D
the cool thing you can do experiments
day one basically it's that that that's
the amazing thing about and you've
actually put the tools out there it's
beautiful it's mysterious uh there's
still I would say maybe you can correct
me it feels like there's a huge number
of L hanging fruit oh on the
mathematical side at least not the not
the physics side perhaps no no there's
look on the on the okay on the physics
side we are we're definitely in
harvesting mode you know
of which which fruit the low hanging
ones or the low hanging ones yeah right
I mean basically here's the thing
there's a certain list of you know here
are the effects in quantum mechanics
here are the effects in general activity
it's just like industrial harvesting
it's like can we get this one this one
this one this one this one and and the
thing that's really you know interesting
and satisfying and it's like you know is
one climbing the right Mountain does one
have the right model the thing that's
just amazing is you know we keep on like
are we going to get this one one how
hard is this one it's like oh you know
it looks really hard it looks really
hard oh actually we can get it um and uh
and you're you're continually surprised
I mean it seems like I've been following
your progress It's kind of exciting all
the in harvesting mode all the things
you're picking up along the way right
right no I mean it's it's the thing that
is I keep on thinking it's going to be
more difficult than it is now that's a
you know that's a who knows what um I
mean the one thing so the the the um the
thing that's been was
big thing that I think we're we're
pretty close to I mean I can give you a
little bit of the road map it's sort of
interesting to see is like what are
particles what are things like electrons
how do they really work um are you close
to get like what what's uh are you close
to trying to understand like the atom
the electrons neutrons
protons this is this is the stack so the
first thing we want to understand is uh
the quantization of spin so particles
they they kind of spin they have a
certain Ang angular momentum that
angular momentum even though the masses
of particles are all over the place you
know the electron has a mass of 511 M
the but you know the proton is 938 M etc
etc etc they're all kind of random
numbers the the spins of all these
particles are either integers or half
integers and that's a fact that was
discovered in the 1920s I guess um the U
uh I think that we are close to
understanding why spin is quantized um
and that's a and it it appears to be a
quite elaborate mathematical story about
homotopic groups in twist space and all
kinds of things but bottom line is that
seems Within Reach and that's that's a
big deal because that's a very core
feature of understanding how particles
work in quantum mechanics another core
feature is this difference between
particles that obey the Exclusion
Principle and sort of stay apart that
leads to the stability of matter and
things like that and particles that love
to get together and be in the same state
things like photons
that um and that's what leads to
phenomena like lasers um where you can
get sort of coherently everything in the
same state that difference is the
particles of integer spin or bons like
to get together in the same state the
particles of half integer spin of ferons
like electrons that they tend to stay
apart and um so the question is can we
can we get that in our models and uh oh
just the last few days I think we made
um I mean I think the story of um I mean
it's it's it's one of these things where
we're really close it's is this connect
to fans and bans you you talking so this
was what happens is what seems to happen
okay it's you know subject to revision
next even next few days but what seems
to be the case is that uh bons are
associated with essentially merging in
multi-way graphs and firion are
associated with branching in multi-way
graphs and that essentially the
Exclusion Principle is the fact that in
branchial space things have a certain
extent in branchial space that in which
things are being sort of forced apart in
branchial space whereas the case of bans
they get they they Clump together in
branchial space and the real question is
can we explain the relationship between
that and these things called Spinners
which are the representation of half
integer spin particles that have this
weird feature that usually when you go
around 360° rotation you get back to
where you started from but for a spinner
you don't get back to where you started
from it takes 720 of rotation to get
back to where you started from and we
are just it feels like we are we're just
incredibly close to actually having that
understanding how that works and it
turns out it looks like my current
speculation is that it's as simple as
the uh directed hypergraphs versus
undirected hypergraphs interesting uh
the relationship between Spinners and
vectors so which is just nice
interesting yeah that would be
interesting if these are all these kind
of uh nice properties of this multiway
graphs of of branching andjoin Spinners
have been very mysterious and if that's
what they turn out to be there's going
to be an easy explanation directed vers
undirected it's just and that's why
there's only two different cases it's
why are Spinners important in quantum
mechanics can you just give a yeah so
Spinners are important because they are
um they're the representation of of for
electrons which have half anra spin they
are the the wave functions of electrons
are spin Spinners just like the wave
functions of photons are vectors the
wave functions of electrons are Spinners
and and they have this property that
when you rotate by by 360° they come
back to minus1 of themselves and take
720° to get back to the original value
and and they are a consequence of of um
uh in we usually think of of of rotation
in space as being you know when you have
this notion of rotation invariance and
rotational invariance as we ordinarily
experience it doesn't have the feature
you know if you go through 360° you go
back to where you started from but
that's not true for electrons and so
that's that's why understanding how that
works is important yeah I've been
playing with Mobius uh strip quite a bit
lately just for fun and yes yes it adds
some funk it has the same kind of funky
properties yes right exactly you can
have this the So-Cal belt trick which is
this way of taking an extended object
and you can see properties like SP with
that kind of extended object that um
yeah it would be very cool if there's it
somehow connects to direcor versus
undirected I think that's what it's
going to be I think it's going to be as
simple as that but we'll see I mean this
is this is the thing that that you know
this is the big sort of bizarre surprise
is that you know because you know I I I
learned physics as probably let's say
let's say a fifth generation in the
sense that you know if you go back to
the 1920s and so on there were the
people who were originating quantum
mechanics and so on maybe it's a little
less than that maybe I was like a a a
third generation or something I don't
know but but you know the people from
whom I learned physics were the people
who were you know have been students of
the students of the the people who
originated the the current understanding
of physics and we're now at you know
probably the seventh generation of
physicists or something from the from
the early days of 20th century physics
and you know whenever a field gets that
many generations deep it seems the
foundations seem quite inaccessible and
they seem you know it seems like you
can't possibly understand that we've
gone through you know seven academic
generations and that's been you know
that's been this thing that's been
difficult to understand for for that
long it just can't be that simple um and
well in a sense maybe that Journey takes
you to a to a simple explanation that
was there all along as the whole right
right right I mean you know and the
thing for me personally the thing that's
been quite interesting is you know I
didn't expect this project to work in
this way and I you know but I had this
sort of weird piece of personal history
that I used to be a physicist and I used
to do all this stuff and I know you know
the the standard Canon of physics I knew
it very well and um you know but then
I've been working on this kind of
computational Paradigm for basically 40
years and uh the fact that you know I'm
sort of now coming back to to you know
trying to apply that in physics it kind
of felt like that Journey was necessary
was this uh when did you first try to
play play with a
hypergraph so I what happen yeah so so
what I had was okay so this is again you
know one one always feels dumb after the
fact it's it's um it's obvious after the
fact but but so back in the early 1990s
I realized that using graphs as a sort
of underlying thing underneath space and
time was going to be a useful thing to
do I figured out about multi-way systems
um I figured out the things about
general relativity I figured out by the
end of the 1990s but I always felt there
was a certain inelegance because I was
using these graphs and there were
certain constraints on these graphs that
seemed like they were they were kind of
awkward it was kind of like you can pick
it's like you couldn't pick any rule it
was like pick any number but the number
has to be prime was kind of like you
couldn't it was a kind of an awkward
special constraint I had these trivalent
graphs graphs with just three
connections from every node okay so but
but I discovered a bunch of stuff with
that but I thought it was kind of
inelegant and you know the other piece
of sort of personal history is obviously
I spent my life as a language
computational language designer and so
the story of computational language
design is a story of how do you take all
these random ideas in the world and kind
of grind them down into something that
is computationally as simple as possible
and so you know I've been very
interested in kind of simple
computational Frameworks for
representing things and have you know
ridiculous amounts of experience in in
trying to do that and actually all of
those trajectories of your life kind of
came together so you make it sound like
you could have come up with uh
everything you're working on now decades
ago but in reality look two things
slowed me down I mean one thing that
slowed me down was I couldn't figure out
how to make it elegant and and that
turns out hypergraphs were the key to
that and that I figured out but about
less than two years ago now um and um
the other I mean I I think so that was
that was sort of a a key thing well okay
so the real embarrassment of this
project okay is that the final structure
that we have that is the foundation for
this project is basically a a kind of an
idealized version a formalized version
of the exact same structure that I've
used to build computational languages
for more than 40 years yeah but it took
me but I didn't realize that and and you
know and there yet may be other so we're
focused on physics now but I mean that's
what the new kind of science is about
same kind of stuff and this in terms of
mathematically um the beauty of it so so
there could be entire other kind of
objects they're useful for like we we're
not talking about you know machine
learning for example maybe there's other
variants of the hypog graph that are
very useful for reasoning well we'll see
whether the multi-way graph for machine
Learning System is
interesting okay let's leave it at that
that's conversation number three that's
that's that's we're not going to go
there right now but so one of the things
you've mentioned is um the space of all
possible rules that we kind of discussed
a little bit uh that you know there
could be I guess the set of possible
rules is
infinite right well so here's here's the
big sort of one of the conundrums that
that I'm kind of trying to deal with is
let's say we think we found the rule for
the universe and we say here it is you
know write it down it's a little tiny
thing and then we say gosh that's really
weird why did we get that
one right and then we're in this whole
situation because let's say it's fairly
simple how did we come up the winners
getting one of the simple possible
Universe rules why didn't we get what
some incredibly complicated rule why do
we get one of the simpler ones and and
that's a thing which you know in the
history of science you know the whole
sort of story of kernus and so on was
you know we used to think the Earth was
the center of the universe but now we
find out it's not and we're actually
just and some you know random corner of
some random Galaxy out in this big
universe there's nothing special about
us so if we get you know Universe number
3177 out of all the infinite number of
possibilities how do we get something
that small and simple right so I was
very confused by this and it's like what
are we going to say about this how are
we going to explain this and I thought
it was might be one of these things
where you just you know you can get it
to the threshold and then you find out
its rule number such and such and you
just have no idea why it's like that
yeah okay so then I realized it's
actually more bizarre than that okay so
we talked about multi-way graphs we
talked about this idea that you take
these underlying transformation rules on
these hypergraphs and you apply them
wherever the rule can apply you apply it
and that makes this whole multi-way
graph of possibilities okay so let's go
a little bit weirder let's say that at
every place not only do you apply a
particular rule in all possible ways it
can apply but you apply all possible
rules in all possible ways they can
apply okay so you say that's just crazy
that's way too complicated you're never
going to be able to conclude anything
okay however turns out oh that don't
tell me there's some kind of invariance
yeah yeah so so what happens is man that
would be amazing right so so this thing
that you get this this kind of Ral
multi-way graph this multi-way graph
that is a branching of rules as well as
a branching
of possible applications of rules this
thing has causal invariance it's a it's
an inevitable feature that it shows
causal invariance and that means that
you can take different reference frames
different ways of slicing this thing and
they will all in some sense be
equivalent if you if you make the right
translation they will be equivalent so
okay so the the basic Point here is that
that's true that would be beautiful it
is true and it is beautiful so you you
it's not just an intuition there is some
no no no there's real mathematics behind
this and it and it's it is it is okay so
here's here's how it comes yeah that
that would be that's amazing right so so
by the way I mean the mathematics that's
connected to is the mathematics of
higher category Theory and groupoids and
things like this which I've always been
afraid of but now I'm I'm I'm finally
wrapping my arms around it but um um
it's also related to uh it also relates
to computational complexity Theory um
it's also deeply related to the P versus
NP problem and other things like this
again seems completely bizarre that
these things are connected but here's
why it's connected the this space of all
possible okay so a touring machine very
simple model of computation you know you
just got a this tape where you write
down you know ones and zeros or
something on the tape and you have this
this rule that says you know you you
change the number you move the head of
the on the tape Etc you have a definite
rule for doing that a deterministic
touring machine just does that
deterministically given the
configuration of the tape it will always
do the same thing a non-deterministic
touring machine can have different
choices that it makes at every step yeah
and so you know um you know this stuff
you probably teach this stuff the um it
um uh you know so a non-deterministic
touring machine has the set of branching
possibilities which is in fact one of
these multi-way graphs and in fact if
you say imagine the extremely
non-deterministic touring machine the
touring machine that can just do uh that
takes any possible rule at each step
that is this Ral multi-way graph the set
of the set of trans the set of possible
histories of that extreme
non-deterministic tur machine is a ruo
multi-way graph and you're uh what term
you using ruo ruo it's a weird word yeah
it's a weird word right multi-way graph
okay so this so that I'm trying think
of I'm trying to think of the space of
rules uh so these are basic
Transformations so in a turning machine
it's like it says move left move you
know if it's a one if it's a black
Square under the head move left and
right a green square that's a rule
that's a very basic rule but I'm trying
to see the rules on the hypergraphs how
rich of the programs can they be or do
they all ultimately just map into
something simple yeah they will I mean
hypergraphs that's another layer of
complexity on this whole thing you can
you can think about these in
transformations of hypergraphs but
touring machines are a little bit put
touring machines okay right they're a
little bit simpler so if you look at
these extreme non-deterministic touring
machines you're mapping out all the
possible non-deterministic paths that
the turing machine can follow yeah and
and if you ask the question uh can you
reach okay so so a deterministic turing
machine follows a single path the
non-deterministic turing machine fills
out this whole uh sort of ball of
possibilities and so then the P versus
MP problem ends up being questions about
and we haven't completely figured out
all the details of this but it's
basically has to do with questions about
the the growth of that ball relative to
what happens with individual paths and
so on so essentially there's a
geometrization of the P versus MP
problem that comes out of this that's a
sideshow okay the main the main event
here is the statement that you can look
at this multi-way graph where the
branches correspond not just to
different applications of a single rule
but to different application to
Applications of different rules okay and
that then that when you say I'm going to
be an observer embedded in that system
and I'm going to try and make sense of
what's going on in the system and to do
that I essentially I'm picking a
reference frame and that turns out to be
uh well okay so the way this comes out
essentially is the reference frame you
pick is the rule that you infer is
what's going on in the universe even
though all possible rules are being run
although all those possible rules are in
a sense giving the same answer because
of causal invariance MH but what you see
will be could be completely different if
you pick different reference frames you
essentially have a different description
language for describing the universe
okay so how does what does this really
mean in practice so imagine there's us
we think about the universe in terms of
space and time and we have various kinds
of description models and so on now
let's imagine the friendly aliens for
example right how do they describe their
Universe well you know our description
of the universe probably is affected by
the fact that you know we are about the
size we are you know meter is tall so to
speak we have brain processing speeds we
about the speeds we have we're not the
size of planets for example we the speed
of light really would matter you know in
our everyday life the speed of light
doesn't really matter everything can be
you know the fact that speed of light is
finite is irrelevant it could as well be
infinite we wouldn't wouldn't make any
difference you know it affects the the
Ping times on the internet that's about
that's about the level of of um of how
we notice the speed of light in our sort
of everyday existence we don't really
notice it um and so we have a way of
describing the universe that's based on
our sensory you know our senses our uh
in these days also on the mathematics
we've constructed and so on but the
realization is it's not the only way to
do it there will be completely
completely utterly incoherent
descriptions of the universe which
correspond to different reference frames
in this sort of Ral space in the Ral
space that's fascinating so we're we
have some kind of reference frame in
this Ral space right and from
that that's why we are attributing this
rule to the universe so in other words
when we say why is it this Rule and not
another the answer is just you know
Shine the Light back on us so to speak
it's because of the reference frame that
we've picked in our way of understanding
what's happening in the sort of uh space
of all possible rules and so on but also
in the space from this reference
frame because of the royal the
the the
invariance that
simple that the rule on which the
universe
with which you can run the universe
might as well be simple yes yes but okay
so so here's another point so this is
again these are a little bit mind
twisting in some ways but but the the
the um um okay another thing that's sort
of we know from computation is this idea
of computation universality the fact
that given that we have a program that
runs on one kind of computer we can as
well you know we can convert it to run
on any other kind of computer we can
emulate one kind of computer with
another so that might lead you to say
well you think you have the rule for the
universe but you might as well be
running it on a touring machine because
we know we can emulate any computational
rule on any kind of machine and that's
essentially the same thing that's being
said here that is that what we're doing
is we're saying um these different
interpretations of physics correspond to
essentially running physics on different
underlying you know thinking about the
physics as running in different with
different underlying rules as if
different underlying computers were
running them and but because of
computation universality or more
accurately because of this principle of
computational equivalence thing of mine
there's that they are um these things
are ultimately equivalent so the only
thing that is the ultimate fact about
the universe the ultimate fact that
doesn't depend on any of these you know
we don't have to talk about specific
rules etc etc etc the ultimate fact is
the universe is computational and it is
the the things that happen in the
universe are the kinds of computations
that the principle of computational
equivalence says should happen now that
might sound like you're not really
saying anything there but you are
because you can you could in principle
have a hypercomp computer that things
that take an ordinary computer in
infinite time to do the hypercom
computer can just say oh I know the
answer it's this immediately what this
is saying is the universe is not a hyper
Compu it's not simpler than a an
ordinary touring machine type computer
it's exactly like an ordinary touring
machine type computer and so that's the
that's in the end the sort of net net
conclusion is that's the thing that is
the sort of the hard immovable fact
about the universe that's sort of the
the fundamental principle of the
universe is that it is computational and
not hyper computational and not sort of
for computational it is this level of
computational ability and it's um it
kind of has and that's sort of the the
The Core Fact but now you know this this
idea that you can have these different
kind of uh Ral reference frames these
different description languages for the
universe it it makes me you know I I
used to think okay you know imagine the
aliens imagine the Extraterrestrial
intelligence thing you know at least
they experience the same physics right
and now I've realized isn't true they
could have a different roal frame that's
that's fascinating they can end up with
a a a a description of the universe that
is utterly utterly incoherent with ours
and and that's also interesting in terms
of how we think about well intelligence
the nature of intelligence and so on you
know I'm I'm fond of the quote you know
the weather has a mind of its own
because these are you know these are
sort of computationally that that system
is computationally equivalent to the
system that is our brains and so on and
what's different is we don't have a way
to understand you know what the weather
is trying to do so to speak we have a
story about what's happening in our
brains we don't have a sort of
connection to what's happening there so
we actually it's funny last time we
talked maybe over a year ago uh we
talked about how it was more based on
your work with a rival uh we talked
about how would we communicate with
alien
intelligences can you maybe comment on
how we might how the wol from physics
project changed your view how we might
be able to communicate with alien
intelligence like if they showed up is
it possible that because of our com
comprehension of the physics of the
world might be completely different we
would just not be able to communicate at
all here's here's the here's the thing
you know intelligence is everywhere the
fact this idea that there's this notion
of oh there's going to be this amazing
extraterrestrial intelligence and it's
going to be this unique thing it's just
not true it's the same thing you know I
I think people will realize this about
the time when people decide that
artificial intelligences are kind of
just natural things that are like human
intelligences they'll realize that that
extraterrestrial intelligences or
intelligences associated with physical
systems and so on it's all the same kind
of thing ultimately computation it's all
the same it's all just computation and
the issue is can you are you sort of
inside it are you are you thinking about
it do you have sort of a story you're
telling yourself about it and you know
the weather could have a story it's
telling itself about what it's doing we
just it's utterly incoherent with the
stories that we tell ourselves based on
how our brains work I mean ultimately it
must be a a question whether we can
align exactly Aline with the kind of
intelligence systematic way of doing it
right so the question is in the space of
all possible intelligences what's the
how do you think about the distance
between description languages for one
intelligence versus another and needless
to say I have thought about this and uh
um you know I I don't I don't have a
great answer yet but but I think that's
a that's a thing where there will be
things that can be said and there'll be
things that where you can sort of start
to characterize you know what is the
translation distance between this you
know version of the universe or this you
know kind of set of computational rules
in this other one in fact okay so this
is a you know there's this idea of
algorithmic information Theory there's
this question of sort of what is the uh
when you have some something what is the
sort of shortest description you can
make of it where that description could
be saying run this program to get the
thing right so I'm pretty sure that that
the um uh
that there will be a physicalization of
the idea of GIC information and that
okay this is again a little bit bizarre
but so I mentioned that there's the
speed of light maximum speed of
information Transmission in physical
space there's a maximum speed of
information Transmission in branchial
space which is a maximum entanglement
speed there's a maximum speed of
information Transmission in roual space
which is has to do with a maximum speed
of translation between different uh
description languages and again I'm I'm
not fully wrapped my brain around this
one yeah that one just blows my mind to
think about that but that starts getting
closer to the yeah the kind of
physicalization right it's a and it's
also a physicalization of of algorithmic
information and I think there's probably
a connection between I mean there's
probably a connection between the notion
of energy and some of these things which
again I I you know hadn't seen all this
coming I i' I've always been a little
bit resistant to the idea of connecting
physical energy to things in in in
computation Theory but I I think that's
probably coming and that's what
essentially at the core with the the
physics project is that you're
connecting information Theory with well
physics yeah it's computation in
computation with our physical Universe
yeah right I mean the fact that our
physical universe is is right that we
can think of it as a computation and
that we can have discussions like you
know the theory of the physical universe
is the same kind of a theory as the P
versus MP problem and so on is is really
uh you know I think that's really
interesting and and the fact that well
uh okay so this this kind of brings me
to one one more thing that I have to in
terms of this sort of unification of
different ideas which is meta
mathematics yeah let's talk about that
you mentioned that earlier what the heck
is M mathematics and uh okay so here's
here's what here's okay so what is
mathematics
mathematics uh sort of at a a lowest
level one thinks of mathematics as you
have certain axioms you say you know you
say things like x + y is the same as y +
x that's an axom um about addition and
then you say we got these axioms and we
and and from these axioms we derive all
these theorems that fill up the
literature of mathematics the the the
activity of mathematicians is to derive
all these theorems actually the axm of
mathematics are very small you can fit
you know when I did my new kind of
science book I fit all of the standard
axm of mathematics on basically a page
and a half um it's not much stuff it's
like a very simple rule from which all
of mathematics arises um the way it
works though is a little different from
the way things work in in sort of uh a
computation because in mathematics what
you're interested in is a proof and the
proof says from here you can use from
this expression for example you can use
these axioms to get to this other
expression so that proves these two
things are equal okay so we can we can
begin to see how this is going to work
what what's going to what happen is
there are paths in metam mathematical
space so what happens is each um two
different ways to look at it you can
just look at it as mathematical
expressions or you can look at it as
mathematical statements postulates or
something but either way you think of
these things and they are connected uh
by these axioms so in other words you
have some fact you or you have some
expression you apply this axum you get
some other expression and in general
given some expression there may be many
possible different Expressions you can
get you basically build up a multi-way
graph and a proof is a path through the
multi-way graph that goes from one thing
to another thing it the path tells you
how did you get from one thing to the
other thing it's the it's the story of
how you got from this to that the
theorem is the thing at one end is equal
to the thing at the other end the proof
is the path you go down to get from one
thing to the other you mentioned that
G's incompetance theem is not natural it
fits naturally there how hard is yeah so
so what happens there is that the
girdles theorem is basically saying that
there are pods of infinite length that
is that there's no upper bound if you
know these two things you say I'm trying
to get from here to here how long do I
have to go you say well I've looked at
all the paths of length 10 somebody says
that's not good enough that path might
be of length a billion and and you
there's no up bound on how long that
path is and that's that's what leads to
the incompleteness theorem so I mean the
the thing that is kind of an emerging
idea is you can start asking what's the
analog of Einstein's equations in metam
mathematical space what's the analog of
a black hole in metam mathematical space
what's the whole so yeah it's
fascinating to model all the mathematics
in this well so so here's here's what it
is this is mathematics in bulk so human
mathematicians have made a few million
theorems they published a few million
theorems but imagine the infinite future
of mathematics apply something to
mathematics that mathematics likes to
apply to other things take a limit what
is the limit of the infinite future of
mathematics what does it look like what
is the Continuum limit of mathematics
what is the as you just fill in more and
more and more theorems what does it look
like what does it do how does what kinds
of conclusions can you make so for
example one thing I've just been doing
is taking uid so uclid very impressive
he had 10 axioms he derived 465 theorems
okay his book you know that was was the
sort of defining book of mathematics for
2,000 years um so you can actually map
out and I I I I actually did this 20
years ago but I've done it more
seriously now you can map out the
theorem dependency of those 465 theorems
so from the axioms you grow this graph
it's actually a multi-way graph of how
all these theorems get proved from other
theorems and so you can ask questions
about you know well you can ask things
like what's the hardest theorem in ukle
the answer is the hardest theorem is
that there are five plutonic solids that
turns out to be the hardest theorem in
ucle that's actually his his Last
Theorem in all his books that's the
final what's the hardness the the
distance you have to travel yeah that's
it's 33 Steps From the the longest path
in the graph is 33 steps so that's the
there there's a 33 step path you have to
follow to go from the axioms according
to ukids proofs to the statement there
are five platonic solids so so okay so
then then then the the question is in uh
what does it
mean if you have this map okay so in a
sense this meta mathematical space is
the infrastructural space of all
possible theorems that you could prove
in mathematics MH that's the geometry of
meta mathematics there's also the
geography of mathematics that is where
did people choose to live right in space
and that's what for example exploring
the sort of empirical metam mathematics
of ID is doing each individual like
human mathematician you can embed them
into that space I mean they they kind
they they represent a path in the things
they do maybe a set of paths right so
like and a set of axioms that are chosen
right so so for example here's an
example of of a thing that I realized so
one of the surprising things about well
there two surprising facts about math
one is that it's hard and the other is
that it's doable okay so first question
is why is math hard you know you've got
these axioms they're very small why
can't just solve every problem in math
easily yeah it's just logic right yeah
well logic happens to be a particular
special case that does have certain
Simplicity to it um but General
mathematics even arithmetic already
doesn't have the Simplicity that logic
has so why is it hard because of
computational
irreducibility right right because what
happens is to know what's true and this
is this whole story about the path you
have to follow and how long is the path
and goal theorem is the statement there
could be an in that the path is not a
bounded length but the fact that the
path is not always compressible to
something tiny is a story of
computational irreducibility so that's
that's why math is hard now the next
question is why is math doable because
it might be the case that most things
you care about don't have finite length
paths most things you care about might
be things where you get lost in the sea
of computational irreducibility and
worse undecidability that is there's
just no finite length path that gets you
there
um you know why is mathematics doable
you know girdle proved his
incompleteness theorem in 1931 most
working mathematicians don't really care
about it they just go ahead and do
mathematics even though it could be that
the questions they're asking are
undecidable it could have been that
format's L theorem is undecidable it
turned out it had a proof it's a long
complicated proof the twin Prime
conjecture might be undecidable the
reman hypothesis might be undecidable
these things might be the axioms of
mathematics might not be strong enough
to reach those statements it might be
the case that depending on what axioms
you choose you can either say that's
true or that's not true so and and by
the way from as Last Theorem there could
be a shorter path absolutely yeah so
that the notion of j6 in metam
mathematical space is a notion of
shortest proofs in metam mathematical
space and that's a you know human
mathematicians do not find shortest
paths nor do automated theorem provs um
but the fact and and by the way the I
mean this stuff is so bizarrely
connected I mean if you if you're into
automated theorem proving there are
these so-called critical pair Lamas and
automated theorem proving those are
precisely the branch pairs in our um
that in multi-ray graphs let me just
finish on the why mathematics is doable
oh yes the second part so we know why
it's hard why is it doable right why do
we not just get lost in undecidability
all the time yeah um so and and here's
another fact is in doing computer
experiments and doing experimental
mathematics you do get lost in that way
when you just say I'm picking a random
integer equation how do I does it have a
solution or not and you just pick it at
random without any human sort of path
getting there often it's really really
hard it's really hard to answer those
questions when you just pick them up
random from the space of possibilities
but what's what I think is happening is
and that's a case where you just fell
off into this ocean of sort of
irreducibility and so on what's
happening is human mathematics is a
story of building a path you you started
off you're you're always building out on
this path where you are proving things
you you you've got this proof trajectory
and you're basically the human
mathematics is the sort of the
exploration of the world along this
proof trajectory so to speak you're not
you're not just you know uh parachuting
In from from you know from from anywhere
you're following you know Lewis and
Clark or whatever you're actually you're
actually going doing the PA and the fact
that you are constrained to go along
that path is the reason you don't end up
with lot every so often you'll see a
little piece of undecidability and
you'll avoid that that part of the path
but that's basically the story of why
human mathematics is has seemed to be
doable it's a story of exploring these
paths that that are by their nature they
have been constructed to be paths that
can be followed and so you can follow
them further now you know what why is
this relevant to anything so okay so
here's the the my my my belief the fact
that human mathematics works that way is
I think there's some sort of connections
between the way that observers work in
physics and the way that the axium
systems of mathematics are set up to
make mathematics be doable in that kind
of way and so in other words in
particular I think there is an analog of
causal invariance which I think is um
and this is again in sort of the upper
reaches of mathematics and and stuff
that um uh it's a thing there's this
thing called homotopy type Theory which
is an abstract it's came out of category
Theory and it's sort of an abstraction
of mathematics mathematics itself is an
abstraction but it's an abstraction of
the abstraction of mathematics and there
is a thing called the univalence axium
which is a sort of a a key axom in that
set of ideas and I'm pretty sure the
univance axium is equivalent to causal
variance what was the term you use again
uni univance is that something for
somebody like me accessible um or is
this there's a statement of it that's
fairly accessible I mean the statement
of it is um uh basically it says things
which are equivalent can be considered
to be
identical in which but in which space
yeah it's it's in in higher category
okay in Category 3 okay so it's it's a
it's a but I mean the thing just to give
sketch of how that works so category
theory is an attempt to idealize it's an
attempt to sort of have a formal theory
of mathematics that is at a sort of
higher level than mathematics it's where
where you just think think about these
mathematical objects and these
categories of objects and these these
morphisms these connections between
categories okay so it turns out the
morphisms and categories the least weak
categories are very much like the paths
in our hypergraphs and things and it
turns out again this is this is where it
all gets gets crazy I mean it's it's the
fact that these things are connected is
just bizarre so category Theory uh the
our causal graphs are like second order
category Theory and it turns out you can
take the limit of infinite order
category Theory so just just give rough
roughly the idea this is a this is a
roughly explainable idea so a
mathematical proof will be a path that
says you can get from this thing to this
other thing and here's the path you get
from this thing to this other thing but
in general there may be many paths many
proofs that get you many different paths
that all successfully go from this thing
to this other thing okay now you can
define a higher order proof which is a
proof of the equivalence of those proofs
mhm okay so you're saying there's a go
path between those proofs essentially
yes a path between the paths yeah okay
and so you do that that's the sort of
second order thing that path between the
paths is essentially related to our
causal graphs then take limit wow path
between path between path between path
the infinite limit that infinite limit
turns out to be our Ral multi-way system
yeah the Ral the the Ral multi-way
system that's a fascinating thing both
in the physics world and and as you're
saying now that's that's I'm not sure
I've loaded it in completely but well
I'm not sure I have either and it may be
one of these things where where you know
in another another five years or
something it's like this was obvious but
I didn't see it no but the thing which
is sort of interesting to me is that
there's sort of an upper reach of of
mathematics of the abstraction of
mathematics um this thing there's this
mathematician called grth and deque
who's generally viewed as being sort of
one of the most abstract sort of creator
of the most abstract mathematics of
1970s is time frame um and one of the
things that he constructed was this
thing he called the infinity groupoid um
and he has the sort of hypothesis about
the inevitable appearance of geometry
from essentially logic in the structure
of this thing well it turns out this Ral
multiway system is the infinity group
void so it's a it's this limiting object
and this is an this is an instance of
that limiting object so what to me is I
mean again I I've been always afraid of
this kind of mathematics because it
seemed incomprehensibly abstract to me
um but what's what's what I'm sort of
excited about with this is that that
we've sort of concre ified the way that
you can reach this kind of mathematics
which makes it uh well both seem more
relevant and also the fact that that you
know I don't yet know exactly what
mileage we're going to get from using
the sort of the apparatus that's been
built in those areas of mathematics to
analyze what we're doing but the thing
that's so both ways so use mathematics
understand what you're doing and using
what you're doing computationally to
understand that right so so for example
the the understand of uh meta
mathematical space one of the reasons I
really want to do that is because I want
to understand quantum mechanics better
and and that what you see you know we
live that uh kind of the multi-way graph
of mathematics because we actually know
this is a theorem we've heard of this is
another one we've heard of we can
actually say these are actual things in
the world that we relate to which we
can't really do as as readily for the
the physics case and so it's kind of a
way to help my intuition it's also you
know there are bizarre things like the
what's the analog of Einstein's
equations in metam mathematical space
what's the analog of a black hole you
know it turns out it looks like not
completely sure yet but there's this
notion of non-constructive proofs in
mathematics and I think those relate to
well actually the the they they relate
to things and related to event Horizons
um so the fact that you can take ideas
from physics like event Horizons into
the same kind of it's it's really so do
you think there'll be do you think you
might stumble upon some breakthrough
ideas in theorem proving like for from
the the other direction yeah yeah yeah
no I mean what's really nice is that we
are using so this this absolutely
directly maps to theorem proving so
paths and multi-way graphs that's what a
theorem improver is trying to do but I
also mean like like automated de yeah
yeah yeah that that's what right so the
finding of PODS the finding of shortest
parts s or finding a paths at all is
what automated theorem provs do and
actually what what we've been doing so
we've you know we've actually been using
automated theorem proving both in the
physics project to prove things and
using that as a way to understand
multi-way graphs and because what an
automated theorem prover is doing is
it's trying to find a path through a
multi-way graph and its critical pair
lemas are precisely little stubs of
Branch pairs going off into branchial
space and that's I mean it's really
weird you know we have these
visualizations in W language of our of
of um proof graphs from our automative
theorem proving system and they look
reminiscent of well it's just bizarre
because we made these up a few years ago
and they have these little triangle
things and they are they are we we
didn't quite get it right we didn't
quite get the analogy perfectly right
but it's very close you know just to say
in terms of the how these things are
connected so there's another bizarre
connection that I I have to mention
because because um um
which is uh which again we don't fully
know but it's a connection to uh uh
something else you might not have
thought was in the slightest bit
connected which is distributed
blockchain like things now you might
figure out that that's you you would
figure out that that's connected because
because it's a story of distributed
computing yeah and the issue you know
with a blockchain you're saying there's
going to be this one Ledger that that
globally says this is what happened in
the world but that's a bad deal if
you've got all the different
transactions that are happening and you
know this transaction in country a
doesn't have to be reconciled with a
transaction in country B at least not
for a while and that
story is just like what happens when our
causal graphs that whole reconciliation
thing is just like what happens with
light cones and all that's where the
cause in variance comes into play I mean
that that's you know most of your
conversations are about physics but it's
kind of funny that the this probably and
possibly might have even bigger impact
and uh revolutionary ideas in totally
other disciplines right well see see
yeah right so the question is why is
that happening right and and the reason
it's happening I I've thought about this
obviously because I like to think about
these meta questions of you know what's
happening is this model that we have is
an incredibly minimal model yeah and
once you have an incredibly minimal
model and this happened with cellular
autometer as well cellular autometer
inedibly minimal model and so it's
inevitable that it gets you sort of an
upstream thing that gets used in lots of
different places and it's like you know
the fact that it gets used you know
cellular autometer as sort of a minimal
model of let's say road traffic flow or
something and they're also a minimal
model of something in you know chemistry
and they're also a minimal model of
something in in epidemiology right it's
because they're such a simple model that
they can that they use apply to all
these different things similarly this
model that we have with the physics
project is a is another
it's a cellular autometer are a minimal
model of parallel of of basically of
parallel computation where you've
defined space and time these models are
minimal models where you have not
defined space and time and they have
been very hard to understand in the past
but the I think the perhaps the most
important breakthrough there is the
realization that these are models of
physics and therefore that you can use
everything that's been developed in
physics to get intuition about how
things like that work and that's why you
can potentially use ideas from physics
to get intuition about how to do
parallel Computing and because the
underlying model is the same and but but
we have all of this achievement in
physics I mean you know you might say oh
you've come up with the fundamental
Theory of physics that throws out what
people have done in physics before well
it doesn't but also the real power is to
use what's been done before in physics
to apply it in these other places yes
and absolutely this kind of brings up I
know you probably don't
particularly love commenting on the work
of others but let me let me bring up a
couple personalities just because it's
fun people are curious about it so
there's
uh uh Sabine Hassen Felder I don't know
if you're familiar with her she uh she
wrote this book uh that I need to read
but it Bas I forget what the title is
but it's uh Beauty leads us astray in
physics is a subtitle something like
that which so much about what we're
talking about now like the
simplification is uh to us humans seems
to be beautiful like there's a certain
intuition with physicists with people
that A Simple Theory like this
reducibility pockets of reducibility is
the ultimate goal and I think what she
tries to argue is uh no we just need to
come up with theories that are just
really good at predicting physical
phenomena it's okay to have a bunch of
uh disperate theories as as opposed to
trying to chase this
beautiful Theory of Everything Is the
ultimate beautiful Theory uh a simple
one you know it's always what's your
response to that well so what you're
quoting so I don't know the Sabine
hassenfeld is you know exactly what she
said but I meting the I'm quoting the
title of a book okay let me let me let
me respond to what you were describing
which may or may not have nothing to do
with what you know what Sabin Hassen
Felder says or thinks sorry
San right sorry for misquoting um but I
mean the the question is you know does
is beauty a guide to whether something
is correct that's right which is kind of
also the story of aam's Razer you know
if you've got a bunch of different
explanations of things you know is the
thing that is the simplest explanation
likely to be the correct explanation and
there are situations where that's true
and there are situations where it isn't
true sometimes in human systems it is
true because people have kind of you
know in evolutionary systems sometimes
it's true because it's sort of been
kicked to the point where it's minimized
um but uh you know in physics does
Arkham's Razer work you know is there a
simple quotes beautiful explanation for
things or is it a big mess um you know
we don't intrinsically no you know I
think that the I wouldn't before I
worked on the project in recent times I
would have said we do not know how
complicated the rule for the universe
will be and and I would have said you
know the one thing we know which is a
fundamental fact about science that's
the thing that makes science possible is
that there is order in the universe I
mean you know early theologians would
have used that as an argument for the
existence of God because it's like why
is there order in the universe why
doesn't every single particle in the
universe just do its own thing yeah um
you know something must be making there
be order in the universe we you know in
in the sort of early theology point of
view that's you know the role of God is
to do that so to speak in our uh you
know we might say it's the role of a
formal Theory to do that and then the
question is but how simple should that
theory be and should that theory be one
that that you know where I think the
point is if it's simple it's almost
inevitably somewhat beautiful in the
sense that because all the stuff that we
see has to fit into this little tiny
Theory and the way it does that has to
be you know it it depends on your notion
of beauty but I mean in for me the the
sort of the surprising con connectivity
of it is at least in my aesthetic that's
something that uh respond to my
aesthetic but the question is uh I mean
you're you you're a fascinating person
in the sense that you're at once talking
about computational the fundamental
computational reducibility of the
universe and and the other hand trying
to come up with a Theory of Everything
which simply describes the
the the simple origins of that
computational reducibility right I mean
both of those things are kind of it's
paralyzing to think that we can't make
any sense of the universe in the general
case but in it's hopeful to think like
one we can think of a rule and uh that
generates this whole complexity and two
we can find uh pockets of uh
reducibility that are powerful for our
everyday life to do different kinds of
predictions I suppose sine would wants
to find focus on the finding of small
pockets of reducibility versus the uh
Theory of Everything You know it's a
funny thing because because you know a
bunch of people have started working on
this this you know physics project
people who are you know physicists
basically um and it is really a
fascinating sociological phenomenon
because what you know when I was working
on this before and the 1990s you know
wrote it up put it it's 100 pages of
this 1200 page book that I wrote new
kind of science it's you know 100 pages
of that is about physics right I I saw
it at in that at that time not as a
pinnacle achievement but rather as a use
case so to speak I mean my main point
was this new kind of Science and it's
like you can apply it to biology you can
apply it to you know other kinds of
physics you can apply it to fundamental
physics it's just it's just an
application so to speak it's not the
core thing but um but then you know one
of the things was interesting with that
with that book was you know book comes
out lots of people think it's pretty
interesting and lots of people start
using what it has in different kinds of
fields the one field where there was
sort of a a heavy pitchforking was from
my friends the fundamental physics
people yeah which was it's like no this
can't possibly be right and you know
it's like you know if what you're doing
is right it'll overturn 50 years of what
we've been doing and it's like no it
won't was what I was saying and it's
like um but uh you know for a while when
I started you know I I was going to go
on back in 2002 well 2004 actually I was
going to go on working on this project
and I actually stopped partly because
it's like why am I you know this is like
I've been in business a long time right
I'm I'm building a product for a target
market that doesn't want the product and
it's like why work yeah yeah why why
work against the swim against the
current or whatever but but you see
what's happened which is sort of
interesting is is that so A couple of
things happened and it was it was like
uh you know it was like I I I don't want
to do this project because I can do so
many other things which I'm really
interested in where you know people say
great thanks for those tools thanks for
those ideas Etc whereas you know if
you're dealing with kind of a a uh you
know sort of a structure where people
are saying no no we don't want this new
stuff we don't need any new stuff we're
really fine with what what we there's
like literally like I don't know
millions of people who are thankful for
wolf from alpha a bunch of people wrote
to me how thankful they are they are a
different crowd than uh the theoretical
physics Community perhaps yeah well
right but you know the theoretical
physics Community pretty much
uniformally uses uh W from language and
Mathematica right and so it's it's kind
of like like um you know and that that's
but the thing is what happens you know
this is what happens mature fields do
not you know it's like we're doing what
we're doing we have the methods that we
have and we're we're just fine here now
what's happened in the last 18 years or
so I think there's a couple of things
have happened first of all the the hope
that you know String Theory or whatever
would would deliver the fundamental
Theory of physics that hope has
disappeared that the another thing
that's happened is the the sort of the
interest in computation around physics
has been greatly enhanced by the whole
Quantum information Quantum Computing
story people you know the idea there
might be something sort of
computational uh related to physics is
somehow somehow growing and I think you
know it's it's sort of interesting I
mean right now if we say you know it's
like if you're like who else is trying
to come up with the fundamental Theory
of physics it's like there aren't
professional no professional physic no
professional physicists what are
your uh I mean you've talked with him
but just as a matter of personalities CU
it's a beautiful story what are your
thoughts about Eric Weinstein's
work I you know I I think his his um I
mean he did a PhD thesis in mathematical
physics at Harvard mathematical
physicist and and you know
it's it seems like it's kind of you know
it's in that framework and it's kind of
like I'm not sure how much further it's
got than his PhD thesis which was 20
years ago or something and I think that
you know the the you know it's a fairly
specific piece of mathematical physics
that's quite nice and um what trajectory
do you hope it takes I mean well I think
in his particular case I mean from what
I understand which is not everything at
all but you know I think I know the
rough Tradition at least he's operating
in is sort of theory gauge theories
gauge theories yeah local gauge and
variance and so on okay we are very
close to understanding how local gauge
and variance Works in our models and
it's very beautiful and it's very um and
you know does some of the mathematical
structure that he's enthusiastic about
fit quite possibly yes so there might be
a possibility of trying to understand
how those things fit how gauge Theory
fits well the question is you know so
there are a couple of things one might
try to get in the world so for example
it's like can we get three dimensions of
space we haven't managed to get that yet
gauge Theory the standard model of
particle physics says that it's su3
cross su2 cross U1 those are the
designations of these um Le groups um it
doesn't but but anyway so those are
those are sort of representations of
symmetries of the theory and um so you
know it is conceivable that it is
generically true okay so all those are
subgroups of a group called E8 which is
a weird exceptional Le group okay it is
conceivable I don't know whether it's
the case that that will be generic in
these models that it will be generic
that the gaug and variance of the model
has this property just as things like
general relativity which corresponds to
thing called U general covariance which
is another GA like invariance it could
conceivably be the case that the kind of
local gauge invariance that we see in
particle physics is somehow generic and
and that would be a you know the thing
that's that's really cool I think you
know sociologically although this hasn't
really hit yet is that all of these
different things all these different
things people have been working on in
these in some cases is quite abstruse
areas of mathematical physics an awful
lot of them seem to tie into what we're
doing and you know it might not be that
way yeah absolutely that's a beautiful
thing in the theory I mean but the
reason I so the reason Eric Weinstein is
important is to the point that you
mentioned before which is it's strange
that The Theory of Everything Is Not at
the core of uh the passion the dream the
focus the funding of the physics
community
it's too
hard it's too hard and people gave up I
mean basically what happened is ancient
Greece people thought we're nearly there
you know the world is made of platonic
solids it's you know water is a
tetrahedron or something yes we're
almost there okay long period of time
where people were like no we don't know
how it works you know time of Newton uh
you know we're almost there everything
is gravitation you know time of Faraday
and Maxwell we almost there everything
is Fields everything is The Ether you
know then the whole time we're making
big progress though oh yes absolutely
but the fundamental Theory of physics is
almost a footnote because it's like it's
the machine code it's like we're
operating in the high level languages
yeah um you know that's what we really
care about that's what's relevant for
our everyday physics you talked about
different centuries and the 21st century
will be uh everything is computation yes
if that takes us all the way we don't
know but it might take us pretty far yes
right that's right and but I think the
point is that it's like you know if
you're doing biology you might say how
can you not be really interested in the
origin of life and the definition of
life well it's irrelevant you know
you're studying the properties of some
virus it doesn't matter you know where
you know you're you're operating at some
much higher level and it's the same what
what's happened with physics is I was
sort of surprised actually I was sort of
mapping out this history of of people's
efforts to understand the fundamental
Theory of physics and it's remarkable
how little has been done on this
question and it's you know because you
know there have been times when there's
been bursts of enthusiasm and we're
almost there and and then it decays and
and people just say oh it's too hard but
it's not relevant anyway and I think
that the um the thing that um you know
so so the question of of you know one
question is why does anybody why should
anybody care right why should anybody
care what the fundamental Theory of
physics is I think it's intellectually
interesting but what will be the sort of
what will be the impact of this what I
mean this is the key question what do
you think will happen if we figure out
the fundamental Theory of physics right
outside of the intellectual curiosity of
us this my best guess okay so if you
look at the history of science I think a
very interesting analogy is
cernus okay so what did cernus do there
had been this toic system for working
out the motion of planets it did pretty
well it used epicycles etc etc etc it
had all this computational ways of
working out where planets will be when
we work out where planets are today
we're basically using epicycles but
cernus had this different way of
formulating things in which he said you
know and the Earth is going around the
Sun and that had a consequence the
consequence was you can use this
mathematical Theory to conclude
something which is absolutely not what
we can tell from common sense
right so it's like trust the mathematics
trust the science okay now fast forward
400 years and um you know and now we're
in this pandemic and it's kind of like
everybody thinks the science will figure
out everything it's like from the
science we can just figure out what to
do we can figure out everything that was
before cernus nobody would have thought
if the science says something that
doesn't agree with our everyday
experience where we just have to you
know compute the science and then figure
out what to do people say that's
completely crazy and so your sense is
once we figure out the framework of
computation that can basically do any
understand the the fabric of reality
will be able
to derive totally counterintuitive
things no the the the point I think is
the following that that right now you
know I talk about computational
irreducibility people you know I was was
very proud that I managed to get the
term computational irreducibility into
the Congressional record last year um
that's right that's a whole another
topic we could talk about different
different topic different different
topic but but um um in any case you know
but so computational reducibility is one
of these sort of Concepts that I think
is important in understanding lots of
things in the world but the question is
it's only important if you believe the
world is fundamentally computational
right and but if you if you know the
fundamental Theory of physics and it's
fundamentally computational then you've
rooted the whole thing that is you know
the world is computational and while you
can discuss whether you know uh it's not
the case that people say well you have
this whole computational reducibility
all these features of computation we
don't care about those because after all
the world isn't computational you might
say but if you know you know Bas space
based thing physics is computational
then you know that that stuff is you
know that's kind of the grounding for
that stuff just as in a sense cernus was
the grounding for the idea that you
could figure out something with math
science that was not what you would
intuitively think from your senses so
now we've got to this point where for
example we say you know once we have the
idea that computation is the
foundational thing that explains our
whole universe then we have to say well
what does it mean for other things like
it means there's computational
irreducibility that means science is
limited in certain ways that means this
that means that but the fact that we
have that grounding means that you know
and I think for example for kernus for
instance the implications of his work on
the sort of mathematics of astronomy
were cool but they involved a very small
number of people the implications of his
work for sort of the philosophy of how
you think about things were vast and
involved you know everybody more or less
but do you think so that's actually the
way scientists and people see the world
around us so it has a huge impact in
that sense do you think it might have an
impact more directly to engineering
derivations from physics like propulsion
systems our ability to colonize the
world like for example okay this is like
sci-fi but if you if you
understand the computational nature say
of uh of the different forces of physics
you know there's there's a notion of
being able to you know warp gravity
things like this like can we make warp
drive warp drive yeah so like would we
be able to will it will uh you know will
like Elon Musk start paying attention
like it's awfully costly to launch these
Rockets do you think we'll be able to
yeah create warp drive and uh you know I
I I set myself some homework I agreed to
give a talk at some NASA Workshop in a
few weeks about faster than light travel
so I I haven't figured it out yet but
but no but you got two weeks yeah right
but do you think that kind of
understanding of fundamental Theory of
physics can lead to those engineering
breakthroughs okay I think it's far away
but I'm not certain I mean and you know
this is the thing that that um I set
myself an exercise When Gravity waves
gravitational waves were discovered
right I set myself the exercise of what
would black hole technology look like in
other words right now you know black
holes are far away they're you know how
on Earth can we do things with them but
just imagine that we could get you know
pet black holes right in our backyard
you know what kind of Technology could
we build with them I I got a certain
distance not that far but I think in in
um you know so there are ideas you know
I have this one of the weirder ideas is
the things I'm calling SpaceTime tunnels
which are higher dimensional pieces of
the of of SpaceTime where basically you
can you know in in our three-dimensional
space there might be a five-dimensional
you know uh region which actually will
appear as a white hole at one end and a
black hole at the other end you know who
knows whether they exist and then the
questions another one okay this is
another crazy one is the thing that I'm
calling a vacuum cleaner okay so so so I
I I mentioned that you know there's all
this activity in the universe which is
meant Ming the structure of space yes
and that leads to a certain uh energy
density effectively in space and so the
question in fact dark energy is a story
of essentially negative mass produced by
uh the absence of energy you thought
would be there so to speak and we don't
know exactly how it works in in our
either our model or the physical
universe but this notion of a vacuum
cleaner is a thing where you know you
have all these things that maintaining
the structure of space but what if you
could clean out some of that stuff
that's maintaining the structure of
space and make a simpler vacuum
somewhere yeah you know what would that
do a totally different kind of vacuum
right and that that would lead to
negative energy density which would need
to so gravity is is usually a purely
attractive Force but negative Mass would
lead to rep repulsive gravity um and uh
lead to all kinds of weird things now
can it be done in our universe um you
know my immediate thought is no but but
you know the fact is that okay so so
here once you understand the fact
because you're saying like at this level
abstraction can we reach to the lower
levels and mess with it uh once you
understand the levels I think you can
start and I'm I'm you know I have to say
that that this reminds me of people
telling one years ago that you know
you'll never transmit data over a copper
wire at more than a th you know a th000
board or something right and and this is
why did that not happen you know why why
did why do we have this much much faster
data transmission because we've
understood many more of the details of
what's actually going on and and it's
the same exact story here and it it's
the same you know I think that this as I
say I think one of the features of sort
of one of the things about our time that
will seem incredibly naive in the future
is the belief that you know things like
heat is just random motional molecules
that that that it's just just throw up
your hands it's just random we can't say
about it that will seem naive yeah the
at the heat depth of the universe those
particles would be laughing at us humans
thinking yes right that life is not
civilization um you know humans used to
think they're special with their little
brains well right but but also but but
and they used to think that this would
just be random and uninteresting but
that's but so so this question about
whether you can you know mess with the
underlying structure and how you find a
way to mess with the underlying
structure that's a you know I have to
say you know my immediate thing is boy
that seems really hard but then and and
you know possibly computational
irreducibility will bite you but then
there's always some path of
computational reducibility and that path
of computational reducibility is the
engineering invention exact that has to
be made those little pockets can have
huge engineering impact right and and I
think that that's right and I mean we
live in you know we make use of so many
of those pockets and the fact is you
know I I um uh you know this this is yes
it's it's a you know it's one of these
things where where you know I am a
person who likes to figure out ideas and
so on and the sort of tests of my level
of imagination so to speak and so a
couple of places where there's sort of
serious humility in terms of my level of
imagination one is this thing about
different reference frames for
understanding the universe where like
imagine the physics of the aliens what
will it be like like and I'm like that's
really hard I don't know you know and
and I mean once you have the framework
in place you can at least reason about
the things you don't know or maybe can't
know or like it's too hard for for you
to know but then the the mathematics can
that's exactly it allow you to reach
beyond what you can uh reason about
right well so so I'm you know I'm I'm
I'm trying to not have you know if you
think back to Alan Turing for example
and you know when he invented Turing
machines you know and and imagining what
computers would end up doing so to speak
yeah um you know and very difficult it's
difficult right and it's it's I mean
made a few reasonable predictions but
most of it he couldn't predict possibly
by the time by 1950 he was making
reasonable predictions about something
but not the 30s yeah right not not not
in the not when he first you know
conceptualized you know and he
conceptualized Universal Computing for a
very specific mathematical reason that
wasn't um uh wasn't as general but but
yes it's a it's a good sort of exercise
and humility to realize that that it's
kind of like it's it's really hard to
figure these things out the engineering
of of um the universe if we know how the
universe works how can we engineer it
that's such a beautiful Vision that's
such a beautiful by the way I have to
mention one more which is the the
ultimate question of of from physics is
okay so we have this abstract model of
the universe why does the universe exist
at
all right so you know we might say there
there is a a formal model that if you
run this model you get the universe or
the model gives you you know a model of
the universe right you you you you run
this mathematical thing and the
mathematics unfolds in the way that
corresponds to the universe but the
question is why was that actualized why
does the actual Universe actually exist
and um so this is this is another one of
these humility and and um is like can
you figure this out I have a guess okay
about the answer to that and um my guess
is somewhat unsatisfying but my guess is
that it's a little bit similar to girdle
second incompleteness theorem which is
the statement that from within as an
axiomatic Theory like P arithmetic you
cannot from within that theory prove the
consistency of the theory so my guess is
that for entities within the
universe there is no finite
determination that can be made of the
the statement the universe exists is
essentially undecidable to any entity
that is embedded in the universe within
that Universe how does that make you
feel is that is that does that put you
at peace that it's
impossible or is it really ultimately
frustrating well I think it just says
that it's not a kind of question that
you know it's there are things that it
is reasonable I mean there's kinds of
you know you can talk about
hypercomputation as well you can say
imagine there was a hypercom computer
here's what it would do so okay great it
would be lovely to have a hypercom
computer but unfortunately we can't make
it in the universe like it would be
lovely to answer this but unfortunately
we can't do it in the universe um and
you know this is all we have so to speak
um and I think it it's it's really just
a a statement it's sort of in the end
it'll be a a kind of a
logical logically inevitable statement I
think I think it will be something where
it is as you understand what it means to
have what it means to have a sort of
predicate of existence and what it means
to have these kinds of things it will
sort of be inevitable that this has to
be the case that from within that
Universe you can't establish the reason
for its existence so to speak you can't
prove that it exists and so on and
nevertheless because of computation or
reducibility the future is uh ultimately
not predictable full of mystery and
that's what makes life worth living
right I mean right and you know it's
funny for me because as a just a pure
sort of human being doing what I do
it's you know I'm I'm uh you know I like
I'm interested in people I like sort of
the you know the whole Human Experience
so to speak and yet it's a little bit
weird when I'm thinking you know it's
all hypergraphs down there and it's all
just uh hypergraphs all the way down
right like turtles all the way down
right and and and it's kind of you know
it's to me it is a funny thing because
every so often I get this you know as
I'm thinking about I think we've really
gotten you know we've really figured out
kind of the essence of how physics works
and I'm like thinking to myself you know
here's this physical thing and I'm like
you know this feels like a very definite
thing how can it be the case that this
is just some Ral reference frame of you
know this infinite creature that that is
uh so abstract and so on and I kind of
it is a it's a it's a funny sort of
feeling that that you know we are we're
sort of uh um it's like it's in the end
it's just sort of um be happy we're just
humans type thing and and it's it's kind
of like but but we're making we make
things as it's not like we're just a
tiny Speck we are in a sense the we are
more important by virtue of the fact
that in a sense it's not like there's
there is no ultimate you know it's like
we're important
because because you know we're here so
to speak and we're not it's not like
there's a thing where we're saying um
you know we are just but one sort of
intelligence out of all these other
intelligences and so you know ultimately
there'll be the Super intelligence which
is all of these put together and they'll
be very different from us no it's
actually going to be equivalent to us
and the thing that makes us sort of
special is just the details of us so to
speak it's not something where we can
say oh there's this other thing you know
just you think humans are cool just wait
until you've seen this
you know it's going to be much more
impressive well no it's all going to be
kind of computationally equivalent and
the thing that you know it's not going
to be oh this thing is is amazingly much
more impressive and amazingly much more
meaningful let's say no we're it I mean
that's that's that that's the um and and
the symbolism of this particular moment
so this has been one of the one of the
favorite conversations I've ever had
Stephen it's a huge honor to talk to you
to talk about a topic like this for four
plus hours on the fundamental Theory of
physics and yet we're just two finite
descendants of Apes that have to end
this conversation because Darkness have
come upon us right and and we're going
to get bitten by mosquitoes and all
kinds of terrible the symbolism of that
we're talking about the most basic
fabric of reality and having to end
because of the fact that things end um
it's tragic and beautiful Stephen thank
you so much huge honor I can't wait to
see what you do in the next couple of
days and next week month we're all
watching with excitement thank you so
much thanks thanks for listening to this
conversation with Stephen wlr and thank
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at Lex Friedman and now let me leave you
with some words from Richard
fan physics isn't the most important
thing love
is thank you for listening and hope to
see you next time