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 mechani