Kind: captions
Language: en
the following is a conversation with
Steven Wolfram his third time on the
podcast he's a computer scientist
mathematician theoretical physicist and
the founder of Wolfram research a
company behind Mathematica wolm Alpha
wolm language and the new Wolfram
physics project this conversation is a
wild technical roller coaster ride
through topics of complexity mathematics
physics Computing and Consciousness I
think this is what this podcast is
becoming a wild ride some episodes are
about physics some about robots some are
about war and power some are about the
human condition and our search for
meaning and some are just what the
comedian Tim Dylan calls
fun this is leex Freedman podcast to
support it please check out the sponsors
in the description and now here's my
conversation with Steven
wolam almost 20 years ago you publ
lished A New Kind of Science where you
presented a study of complexity and an
approach for modeling of complex systems
so let us return again to the core idea
of complexity what is complexity I don't
know I think that's not the most
interesting question it's like you know
if you ask a biologist what is life yeah
that's not the question they care the
most about what I was interested in is
how does something that we would usually
identify as complexity arise in nature
and I got interested in that question
like 50 years ago which is really
embarrassingly long time ago and you
know I I was uh you know how does
snowflakes get to have complicated forms
how do galaxies get to have complicated
shapes how does you know how do living
systems get produced things like that
and the question is what's the sort of
underlying scientific basis for those
kinds of things and the thing that I was
at first very surprised by because I've
been doing physics and particle physics
some fancy mathematical physics and so
on and it's like I know all this fancy
stuff I should be able to solve this
sort of basic science question and I
couldn't this was like early maybe 1980
is time frame and it's like okay what
can one do to understand the sort of
basic secret that nature seems to have
because it seems like nature you you
look around in the natural world it's
full of incredibly complicated forms you
look at sort of most engineered kinds of
things for instance they tend to be you
know we got just sort of circles and and
lines and things like this the question
is what secret does nature have that
lets it make all this complexity that we
in doing engineering for example don't
naturally seem to have and so that was
the kind of the thing that I got
interested in and then the question was
you know could I understand that with
things like mathematical physics well it
didn't work very well so then I got to
thinking about okay is there some other
way to try to understand this and then
the question was if you're going to look
at some system in nature how do you make
a model for that system for what that
system does so you know a model is some
abstract representation of the system
some formal representation of the system
what are what is the raw material that
you can make that model out of and so
what I realized was well actually
programs are really good source of raw
material for making models of things and
you know in terms of my personal history
the to me that seemed really obvious and
the reason it seemed really obvious is
because I just spent several years
building this big piece of software that
was sort of a predecessor to mathematic
or morphan language thing called s SMP
symbolic manipulation program which was
something that had this idea of starting
from just these computational Primitives
and building up everything one had to
build up and so kind of the notion of
well let's just try and make models by
starting from computational Primitives
and seeing what we can build up that
seemed like a totally obvious thing to
do in uh in retrospect it might not have
been externally quite so obvious but it
was obvious to me at the time the path
that I happen to have been on so you
know so that got me into this question
of let's use programs to model what
happens in nature and the question then
is well what kind of programs and you
know we're used to programs that you
write for some particular purpose it's a
big long piece of code and it does some
specific thing but what I got interested
in was okay if you just go out into the
sort of computational Universe of
possible programs you say take the
simplest program you can imagine what
does it do and so I started studying
these things called cellular autometer
um actually I didn't know at first they
were called cellular autometer but I
found that out um subsequently but it's
just a a line of cells you know each one
is Black or White and it's just some
rule that says the color of the cell is
determined by the color that it had on
the previous step and its two Neighbors
on the previous step and I had initially
thought that's you know sufficiently
simple setup is not going to do anything
interesting it's always going to be
simple no complexity simple rule simple
Behavior okay but then I actually ran
the computer experiment which is pretty
easy to do um I mean it probably took a
few hours um originally and um the uh
and the results were not what I'd
expected at all now needless to say in
the way that science actually works the
results that I got a lot of unexpected
things which I thought were really
interesting but the really strongest
result which was already right there in
the printouts I made I didn't really
understand for a couple more years so it
was it was not you know the compressed
version of the story is you run the
experiment and you immediately see
what's going on but I wasn't smart
enough to to do that so to speak but the
big the big thing is even with very
simple rules of that type sort of the
minimal tiniest program sort of the the
the oneline program or something it's
possible to get very complicated
behavior my my favorite example is this
thing called Rule 30 which is a
particular cellular automon rule you
just started off from one black cell and
it makes this really complicated pattern
and so so that for me was sort of a a
critical discovery that then kind of
said playing back onto you know how does
nature make complexity I sort of
realized that might be how it does it
that might be kind of the secret that
it's using is that in this kind of
computational Universe of possible
programs it's actually pretty easy to
get programs where even though the
program is simple the behavior when you
run the program is not simple at allh
and that was so for me that was the the
kind of the the story of kind of how
that that was sort of the the indication
that one had got an idea of what the
sort of secret that nature uses to make
complexity and the complexity how
complexity can be made in other places
now if you say what is complexity you
know it's it's complexity is it's not
easy to tell what's going on that's the
informal version of what is complexity
but there is something going on but it's
not e to know what R right well no the
ru rules can generate just
Randomness right well that that's not
obvious in other words that's not
obvious it's not obvious at all and it
wasn't what I expected it's not what
people's intuition had been and and has
been for you know for a long time that
is one might think you have a rule you
can tell there's a rule behind it I mean
it's just like you know the early you
know robots in science fiction movies
right you can tell it's a robot CU it
does simple things right turns out that
isn't actually the right story but it's
not obvious that isn't the right story
because people assume simple rules
simple behavior and that the the sort of
the key discovery about the
computational universe is that isn't
true and that Discovery goes very deep
and relates to all kinds of things that
I've spent years and years studying but
um you know that that in the end the
sort of the the what is complexity is
well you can't easily tell what it's
going to do you could just run the rule
and see what happens but you can't just
say oh you know show me the rule great
and now I know what's going to happen
and you know the the key phenomenon
around that is this thing I call
computational irreducibility this fact
that in something like rule 30 you might
say well what's it going to do after a
million steps well you can run it for a
million steps and just do what it does
to find out but you can't compress that
you can't reduce that and say I'm going
to be able to jump ahead and say this is
what it's going to do after a million
steps but I don't have to go through
anything like that computational effort
by the way has anybody succeeded at that
you had a challenge a competition right
uh for predicting the middle column of
rule 30 anybody anybody a number of
people have sent things in and and sort
of people are picking away at it but
it's hard I mean it's it's uh I've been
I've been actually uh even proving that
the center column of rule 30 doesn't
repeat that's something I think might be
doable okay mathematically proving yes
and so that's analogous to a similar
kind of thing is like the digits of pi
which are also generated in this very
deterministic way and so a question is
how random are the digits of pi for
example does every F first of all do the
digits of pi ever repeat well we know
they don't because it was proved in the
1800s that Pi is not a rational number
so that means only rational numbers have
digit sequences that repeat so we know
the digits of pi don't repeat so now the
question is does you know 0 1 2 3 or
whatever do all the digits base 10 or
base two or however you work it out do
they all occur with equal frequency mhm
nobody knows that's far away from what
can be understood mathematically at this
point and um that's that's kind of uh
but I'm I'm even looking for step one
which is prove that the that that the
center column doesn't repeat and then
prove other things about it like equ
distribution of of uh equal numbers of
zeros and ones and those are things
which I you know I kind of set up this
little little prize thing because I
thought those were not not too out of
range those are things which are within
you know a modest amount of time it's
conceivable that those could be done
they're not they're not far away from
what current mathematics might allow
they'll require a bunch of cleverness
and hopefully some interesting new ideas
that you know will be useful other
places but you started in 1980 with this
idea before I think you
realized you know this idea of
programs you thought that there might be
some kind of uh thermodynamic like
Randomness and then complexity comes
from a clever
filter that uh you kind of like I don't
know spaghetti or something you you you
filter the randomness and outcomes
complexity which is an interesting
intuition I how do we know that's not
actually what's happening so just
because you were then able to develop
look you don't need this like incredible
Randomness you can just have very simple
predictable initial conditions and
predictable rules and then from that
complexity still there might be some
systems where it's uh filtering
Randomness on the inputs well the point
is when you have quotes Randomness than
the input that means there's all kinds
of information in the input yeah and in
a sense what you get out will be maybe
just something close to what you put in
like people are very in dynamical
systems theory sort of big era in
mathematics that developed from the
early 1900s and and really got big in
the 1980s you know an example of what
people study there a lot and it it its
popular version is chaos theory um and
example of what people study a lot is
the shift map which is basically taking
2x mod one two the fractional part of 2x
which is basically just taking digits in
binary and shifting them to the left so
at every step you get to see if you say
how big is this number that I got out
well the most important digit in that
number is whatever ended up at the at
the left hand end but now if you start
off from an arbitrary random number
which is quotes randomly chosen so all
its digits are random then when you run
that sort of Chaos Theory shift map all
that you get out is just whatever you
put in you just get to see what you what
H it's not obvious that you would
excavate all of those digits and if
you're for example making a theory out
don't know fluid Mechanics for example
if there was that phenomenon and fluid
mechanics then the equations of fluid
mechanics can't be right because what
that would be saying is the equations of
that that it matters to the fluid what
happens in the fluid at the level of the
you know millionth digit of the initial
conditions Which is far below the point
at which you're hitting kind of sizes of
molecules and things like that so it's
kind of almost explaining if that
phenomenon is an important thing it's
kind of telling you that the you know
fluid dynamics which describes fluids as
continuous media and so on isn't isn't
really right but so you know so this
idea that you know there's a there's
it's it's a tricky thing because as soon
as you put Randomness in you have to
know you know what how much of what's
coming out is what you put in versus how
much is actually something that's being
generated and what's really nice about
these systems where you just have very
simple initial conditions and where you
get random stuff out or seemingly random
stuff out is you don't have that issue
you don't have to argue about was there
something complicated put in because
it's plainly obvious there wasn't now as
a practical matter in doing experiments
the big thing is if the thing you see is
complex and
reproducible then it didn't come from
just filtering some quotes Randomness
from the outside world it has to be
something that is intrinsically made
because it wouldn't otherwise be I mean
you know the the the it could be the
case that you set things up and it's
always the same each time and you say
well it's kind of the same but it's not
then it's not random each time because
kind of the definition of it being
random is it was kind of picked picked
at random each time so to speak so is it
possible to for sure know that our
universe does not at the fundamental
level have Randomness is it possible to
conclusively say there's no Randomness
at the bottom well it's an interesting
question I mean you know science natural
science is an inductive business right
You observe a bunch of things and you
say can we fit these together what is
our hypothesis for what's going on the
thing that I think I can say fairly
definitively is at this point we
understand enough about fundamental
physics that there is if there was sort
of an extra dice being thrown it's
something that doesn't need to be there
we can get what we see without that now
you know could you add that in as an
extra little featur oid um you know
without breaking the universe uh
probably but in fact almost certainly
yes but is it necessary for
understanding the universe no and I
think actually from a a more fun
fundamental point of view it's it's I
think I might be able to argue so so one
of the things that I've been interested
in have been pretty surprised that I've
had anything sentient to say about is
the question of why does the universe
exist MH I didn't think that was a
question that I would you know I thought
that was a far out there metaphysical
kind of um thing uh even the
philosophers have stayed away from that
question for the most part it's so such
a kind of uh you know difficult to
address question but I think to my great
surprise that from our physics project
and so on that it is possible to
actually uh address that question and
explain why the universe exists and I
kind of have a suspicion I've not
thought it through I kind of have a
suspicion that that explanation will
eventually show you that in no
meaningful sense can there be Randomness
underneath the universe that is that if
there is it's something that is
necessarily irrelevant to our perception
of the universe that is that it could be
there but doesn't matter because in a
sense we've already you know whatever it
would do whatever extra thing it would
add is not relevant to our perception of
what's going on so why does the universe
exist how does uh the irrelevance of
Randomness connect to uh the big why
question of the universe so so okay so I
mean why does the universe exist well
let's see and uh is this the only
Universe we got it's the only one that
about that I'm pretty sure so you may be
which one which of these topics is
better to enter first why does the
universe exist and uh why you think it's
the only one that exists well I think
they're very closely related okay okay
so I mean the first thing let's see I
mean this why does the universe exist
question is built on top of all these
things that we've been figuring out
about fundamental physics CU if you want
to know why the universe exists you kind
of have to know what the universe is
made of and uh I think
the um well let let me let me uh
describe a little bit about the why does
the universe exist question so the main
issue is let's say you have a model for
the universe and you say I've got this
this program or something and you run it
and you make the universe now you say
well how do you act why is that program
actually running and people say you've
got this program that makes the universe
what computer is it running on right
what what does it mean what actualizes
something you know 2 plus 2 equals 4 but
that's different from saying there's two
a pile of two rocks and another pile of
two rocks and somebody moves them
together and makes four so to speak and
so what is it that kind of turns it from
being just this formal thing to being
something that is
actualized okay so there we have to
start thinking about well well what do
we actually know about what's going on
in the universe well we are observers of
this universe but confusingly enough
we're part of this universe so in a
sense we what what what if if we say
what do we what do do we know about
what's going on in the universe well
what we know is what sort of our
Consciousness records about what's going
on in the universe and Consciousness is
part of the fabric of the universe so
we're in it yes we're in it and and and
maybe I should maybe I should start off
by saying something about the
Consciousness story because that that's
some yes uh maybe we should begin even
before that at the very base layer of
the wolf from physics project maybe you
can give a broad overview once again
really quick about this hypergraph model
yes and also what is it a year and a
half ago since you've brought this
project to the world what is the status
update where what are all the beautiful
ideas you have come across uh what are
the interesting things you can mention
it's I mean it's a it's a freaking
Cambrian explosion I mean it's it's
crazy I mean there are all these things
which I've kind of wondered about for
years and suddenly there's actually a
way to think about them and I really did
not see I mean the real strength of
what's happened I absolutely did not see
coming and the real strength of it is
we've got this model for physics but it
turns out it's a foundational kind of
model that's a different kind of
computation like model that I'm kind of
calling the sort of multi- computational
model um and that that kind of model is
applicable not only to physics but also
to lots of other kinds of things and one
reason that's extremely powerful is
because physics has been very successful
so we know a lot based on what we
figured out in physics and if we know
that the same model governs physics and
governs I don't know economics
Linguistics Immunology whatever we know
that the same kind of model governs
those things we can start using things
that we've successfully discovered in
physics and applying those intuitions in
all these other areas and that's that's
pretty exciting and and and very
surprising to me um and in fact it's
kind of like in the original story of
sort of you go and you explain why is
there complexity in the natural world
then you realize well there's all this
complexity there's all this
computational irreducibility you know
there's a lot we can't know about what's
going to happen it's kind of it's kind
of a very confusing thing for people who
say you know science has nailed
everything down we're going to you know
based on science we can know everything
well actually there's this computational
irreducibility thing right in the middle
of that thrown up by science so to speak
and then the question is well given
computational irreducibility how can we
actually figure out about what happens
in the world why aren't we why are we
able to predict anything why are we able
to sort of operate in the world and the
answer is that we sort of live in these
slices of computational reusability that
exists in this kind of ocean of
computational irreducibility and it
turns out that seems that it's a very
fundamental feature of the kind of model
that seems to operate in physics and
perhaps in a lot a lot of these other
areas that there are these particular
slices of computational reducibility
that are relevant to us and those are
the things that both allow us to operate
in the world and not just have
everything be completely unpredictable
but they're also things that potentially
give us what amount to sort of physics
like laws in all these other areas so
that's that's been sort of an exciting
thing but but I would say that in
general for our project it's been going
spectacularly well I mean I you know I
it's very honestly it wasn't something I
expected to happen in my lifetime I mean
it's you know it's something where where
it's it's and in fact one of the things
about it some of the things that we've
discovered are things where I was pretty
sure that wasn't how things worked and
turns out I'm wrong and you know in a
major area in metam mathematics I I'd be
realizing that i' something I've long
believed we can talk about it uh later
that that that uh just just really isn't
right but but I think that um the um the
thing that uh so so what's happened with
the physics project I mean you know it's
can explain a little bit about how the
how the model works but basically we can
maybe ask you the following question so
it's easy through words to describe how
cellular atomo Works you've you've
explained this and uh it's the
fundamental mechanism by which you in
your book and you kind of science
explored the idea of complexity and how
to do science in this world of Island
reducible islands and irreducible
general irreducibility okay okay so how
does the model of hypergraphs differ
from cellular aoma and how does the idea
of multic computation differ like maybe
that's a way to describe it all right we
we're yeah right this is a you know my
life is like all of our Lives something
of a story of computational
irreducibility and you know it's been
going for a few years now so it's always
a challenge to kind of find these
appropriate pockets of reducibility but
let me see what I can do great so so I
mean first of all let's let's talk about
physics first of all MH and you know a
key observation the one of the starting
point of our physics project is things
about what is space what is the universe
made of and you know ever since uclid
people just sort of say space is just
this thing where you can put things at
any position you want and they're just
points and they're just geometrical
things that you can just arbitrarily put
at different different coordinate
positions so of the first thing in our
physics project is theide that space is
made of something just like water is
made of molecules space is made of kind
of atoms of space and the only thing we
can say about these atoms of space is
they have some identity there's a
there's a there is it's this atom as
opposed to this atom and you know you
could give them a few were computer
person you give them uu IDs or something
but um yes and and um but that's all
there is to say about them so to speak
um and then all we know about these
atoms of space is how they relate to
each other so we say these three atoms
of space are associated with each other
in some relation so you can think about
that as you know what atom of space is
friends with what other atom of space
you can build this essentially friend
network of the atoms of space and the
sort of starting point of our physics
project is that's what our universe is
it's a giant friend network of the atoms
of space and so how can that possibly
represent our universe well it's like in
something like water you know there are
molecules bouncing around but on a large
scale that you know that produces fluid
flow and we have fluid vortices and we
have all of these phenomena that are
sort of the emergent phenomena from that
underlying uh kind of collection of
molecules bouncing around and by the way
it's important that that collection of
molecules bouncing around have this
phenomenon of computational
irreducibility that's actually what
leads to the second low of
thermodynamics among other things and
that leads to the sort of randomness of
the underlying Behavior which is what
gives you something which on a large
scale seems like it's a smooth
continuous uh type of thing and so so
okay so first thing is space is made of
something it's made of all these atoms
of space connected together in this
network and then everything that we
experience is sort of features of the of
that structure of space so you know when
we have an electron or something or a
photon it's some kind of tangle in the
structure of space much like kind of a
vortex and a fluid would be just this
thing that is you know it it it can
actually the vortex can move around it
can involve different molecules in the
fluid but the vortex still stays there
and if you assume odd enough The Vortex
looks like an atom itself like a basic
El so there's a levels of abstraction if
you squint and kind of uh blur things
out it looks like at every level of
abstraction you can Define what is a
basic individual entity yes but but you
know in in this model
there's a bottom level you know there's
an elementary length maybe 10 100 10us
100 m let's say which is really small
you know proton is 10- 15 M the smallest
we've ever been able to sort of see
where the particle accelerator is around
10us 21 M so you know if we don't know
precisely what the correct scale is but
it's perhaps over the order of 10us 100
Metter so it's pretty small um and but
but that's that's the end that's that's
what things are made of what's your
intuition where 10 Theus 100 comes from
what's your intuition about this scale
well okay so there's a calculation which
I consider to be somewhat rickety okay
which has to do with comparing so so
there are various fundamental constants
there's a speed of light the speed of
light once you know the elementary time
the speed of light is tells you the
conversion from the elementary time to
the elementary length then there's the
question of how do you convert to the
elementary energy and how do you convert
to between other things and the various
constants we know we know the speed of
light we know the gravitational constant
um we know Plank's constant in quantum
mechanics those are the three important
ones and we actually know some other
things we know things like the size of
the universe the Hubble constant things
like that and essentially this
calculation of the elementary length
comes from looking at these sort of
combination of those okay so the most
obvious thing people have sort of
assumed that quantum gravity happens at
this thing the plank scale 10- 34 me
which is the sort of the the combination
of of Plank's constant and the
gravitational constant the speed of
light that gives you that kind of length
um turns out in our model there is an
additional parameter which is
essentially the number of simultaneous
threads of execution of the universe
which is essentially the number of sort
of independent Quantum uh processes that
are going on and that number let see if
I remember that number that number is 10
to 170 I think and and and so it's a big
number but
that number then connects you know sort
of modifies what you might think from
all these plank uh units to give you the
things we're giving and there's been
sort of a mystery actually in the in the
there a more technical physics thing
that the plank Mass the plank energy um
plank energy is actually surprisingly
big the plank length is Tiny 10- 34 M
that you know plank time 10- 43 M I
think seconds I think um but the plank
energy is like uh is like the the energy
of a of a lightning strike okay which is
pretty weird in our models the actual
Elementary energy is that divided by the
number of sort of simultaneous Quantum
threads and it ends up being really
small too and that sort of explains that
mystery that's been around for a while
about about how plank units work but but
that you know whether that precise
estimate is right we don't know yet I
mean that that that's one of the things
that's sort of been a thing we've been
pretty interested in is how do you see
through you know how does you how do you
make a gravitational microscope that can
kind of see through to the atoms of
space you know how do you get in in
fluid flow for example if you go to
Hypersonic flow or something you know
you've got a mark 20 you know space
plane or something it really matters
that they are individual molecules
hitting the space plane not a continuous
fluid the question is what is the
analogous kind of um what is the analog
of hypersonic flow for for our for
things about the structure of space time
and it looks like uh a a rapidly
rotating black hole right at the sort of
critical rotation rate um is it's it
looks as if that's a case where
essentially the the structure of
SpaceTime is just about to fall apart
and you may be able to kind of see the
evidence of sort of discrete uh elements
you know you may be able to kind of see
there the sort of gravitational
microscope of actually seeing these
discrete elements of space space and
there may be some effect in for example
gravitational waves produced by rapidly
rotating black hole that in which one
could actually see some phenomenon where
one can say yes those don't come out the
way one would expect based on having a
continuous structure of SpaceTime that
is something where you can kind of see
through to the discrete structure um we
don't know that yet so you can you maybe
elaborate a little bit deeper how
microscope that can see to 10
Theus 100
how rotating black holes and uh
presumably the the the detailed accurate
detection of gravitational waves from
say black holes can reveal the
discreetness of space okay first thing
is what is a black hole actually we we
need to go a little bit further in the
in the story of what space time is cu I
explained a little bit about what space
is but I didn't talk about what time is
and that's sort of important in in
understanding space time so to speak and
your sense is both space time in this
story are discreet absolutely absolutely
but it's a complicated story yes and um
needless to say well it's simple at the
bottom it's it's very simple at the
bottom it's it's very in the end it's
simple but deeply abstract and um and
something that is simple in conception
but kind of wrapping one's head around
what's going on is pretty hard um but so
so first of all we have this so you know
I've described these kind of atoms of
spaces and their connections you can
think about these things as a hyper
graph you know a graph is just you
connect nodes to nodes but a hyper graph
you can have you know uh you can have
sort of not just friends individual
friends to friends but you can have
these Triplets of of friends or whatever
else it's it's um and so we're just
saying and that that's just the
relations between atoms of space are the
hyper edges of the hypergraph and so we
got some big collection of of these
atoms of space maybe 10 to the 400 or
something in our in our universe um and
that's the structure of space that's an
every feature of what we experience in
the world is a feature of that that
hypergraph that spatial hypergraph so
then the question is well how does what
what does that spatial hypergraph do
well the idea is that there are rules
that that update that spatial hypergraph
and you know in a cellular autometer and
you've just got this line of cells and
you just say at every step at every time
step you got fixed time steps fixed
array of cells at every step
uh every cell gets updated according to
a certain Rule and that's um that's kind
of the uh that's the way it works now in
this hypergraph it's sort of vaguely the
same kind of thing we say every time you
see a little piece of hypergraph that
looks like this update it to one that
looks like this so it's just keep
rewriting this hypergraph every time you
see something looks like that anywhere
in the universe it gets Rewritten now
one thing that's tricky about that which
will come to is this multicomp
computational idea which has to do with
you're not saying in in some kind of
lock step way do this one then this one
then this one it's just whenever you see
one you can do you can go ahead and do
it and that leads one not to have a
single thread of time in the universe
because if you knew which one to do you
just say okay we do this one then we do
this one then we do this one but if you
say just do whichever one you feel like
you end up with these multiple threads
of time these kind of multiple histories
of the universe depending on which order
you happen to do the things you could do
in so it's fun Al asynchronous and
parallel yes yes which is very
uncomfortable for the human brain that
seeks for things to be sequential yes
and synchronous right well I think that
this is this is part of the story of
Consciousness is I think the key aspect
of Consciousness that is important for
sort of parceling the universe is this
point that we have a single thread of
experience right we have a memory of
what happened in the past we can say
something predict something about the
future but there's a single thread of
experience and you know it's not obvious
it should work that way I mean we've got
100 billion neurons in our brains and
they're all firing in all kinds of
different ways but yet our experience is
that there is the single thread of of of
time that that goes that that goes along
and I think that you know one of the
things I've kind of realized with a lot
more clarity in the last year is the
fact that our the fact that we conclude
that the Universe has the laws it has is
a consequence of the fact that we have
Consciousness the way we have
consciousness
and so the fact so so I mean just to go
on with kind of the the basic setup it's
uh so we got this spatial hypergraph
it's got all these atoms of space
they're getting they're getting these
little clumps of atoms of space are
getting turned into other clumps of
atoms of space and that's happening
everywhere in the universe all the time
and so one thing that's a little bit
weird is there's nothing permanent in
the universe the universe is getting
Rewritten everywhere all the time and if
it wasn't getting Rewritten it would
space wouldn't be knitted together that
is space would just fall apart there
wouldn't be any way in which
we could say this part of space is next
to this part of space you know one of
the things that I was uh people were
confused about back in Antiquity you
know the ancient Greek philosophers and
so on is how does motion work you know
how can it be the case that you can take
a thing that we can walk around and it's
still us when we walked you know a foot
forward so to speak and in a sense with
our models that's again a question
because it's a different set of atoms of
space when we when you know when I move
my hand it's it's moving into a
different set of atoms of space it's
having to be recreated it's not the
thing itself is not there it's it's
being continuously recreated all the
time now it's a little bit like waves in
an ocean you know vortices in a fluid
which again the actual molecules that
exist in those are not what define the
identity of the thing and but it's a
little bit uh you know this idea that
there can be pure motion that it can
that it is even possible for an object
to just move around in the universe and
not change
is it's not self-evident that such a
thing should be possible and that is
part of our perception of the universe
is that we we parse those aspects of the
universe where things like pure motion
are possible now pure motion even in
general relativity the theory of gravity
um pure motion is a little bit of a
complicated thing I mean if you imagine
your average you know teacup or
something approaching a black hole it is
deformed and distorted by the structure
of SpaceTime and to say you know is it
really pure motion is it that same
teacup that's the same shape well it's a
bit of a complicated story and this is a
a more extreme version of that so so
anyway the the the thing that that's
happening is we got space we've got this
notion of time so time is this kind of
this rewriting of the hypergraph and one
of the things that's important about
that time is this sort of
computationally irreducible process
there something you know time is not
something where in kind of the
mathematical view of of time tends to be
time is just a CO ordinate we can you
know slide a slider turn a knob and
we'll change the the time that we've got
in this equation but in this picture of
time that's not how it works at all time
is this inexorable irreducible kind of
set of computations that go on that go
from where we are now to the future but
so so the thing and one of the things
that is again something one sort of has
to break out of is your average trained
physicist like me says you know space
and time are the same kind of thing
there related by you know the panker
group and and lawence Transformations
and relativity and all these kinds of
things and you know space and time you
know there are all these kind of sort of
folk stories you can tell about why
space and time are the same kind of
thing in this model they're
fundamentally not the same kind of thing
space is this kind of sort of
connections between these atoms of space
time is this computational process so
the thing that the first sort of
surprising thing is well it turns out
you get relativity anyway and the reason
that happens there few bits and pieces
here which which one has to understand
but but the the fundamental point is if
you are an observer embedded in the
system that are part of this whole story
of things getting updated in this way
and that there are there's sort of a
limit to what you can tell about what's
going on and really in the end the only
thing you can tell is what are the
causal relationships between events so
an event in this sort of the an
elementary event is a little piece of
hypergraph got Rewritten and that means
a few hyper edges of the hypergraph were
consumed by the event and you produce
some other hyper edges and that's an
elementary event and so then the
question is uh what we can tell is kind
of what the network of causal
relationships between Elementary events
is that's the ultimate thing the causal
graph of the universe and it it turns
out that well there's this property of
causal invariance that uh is true of a
bunch of these models and I think is
inevitably true for a variety of reasons
um that makes it be the case that it
doesn't matter kind of if if you are uh
sort of saying well I've got this
hypergraph and I can rewrite this piece
here and this piece here and I do them
all in different orders when you
construct the causal graph for each of
those orders that you choose to do
things in you'll end up with the same
causal graph and so that's essentially
why uh well that's in the end why
relativity works it's why our perception
of space and time is is is as as having
this kind of connection that relativity
says they should have and that's that's
kind of that's kind of how that works I
think I'm missing a little piece uh if
you can go there again you said uh the
fact that the Observer is embedded in
this hypergraph what's missing uh what
is the Observer not able to State about
this universe oface if you look from the
outside you can say oh I see this
uh I see this particular place was
updated and then this one was updated
and and I'm seeing which order things
were updated in but the Observer
embedded in the universe doesn't know
which order things were updated in
because until they've been updated they
have no idea what else happened so the
only thing they know is the set of
causal relationships let me give an
extreme example let's imagine that the
universe is a touring machine touring
machines have just this one update head
which does something and otherwise the
touring machine just does nothing right
and and the touring machine works by
having this head move around and do its
updating uh you know just where the head
happens to be the question is could the
universe be a touring machine could the
universe just have a single updating
head that's just zipping around all over
the place you say that's crazy because
you know I'm I'm talking to you you seem
to be updating I'm updating Etc but the
thing is there's no way to know that
because if there was just this head
moving around it's like okay it updates
me but your completely Frozen at that
point until the head has come over and
updated you you have no idea what
happened to me and so if you sort of
unravel that argument you realize the
only thing we actually can tell is what
the network of causal relationships
between the things that happened were we
don't get to know from some sort of
outside sort of God's eye view of the
thing we don't get to know what sort of
from the outside what happened we only
get to know sort of what the set of
relationship between the things that
happened actually were yeah but if I
somehow record like a trace of this I
guess would be called multic computation
can't I uh then look
back in the you record the trace some
you place throughout the UN like
throughout like a log that records in my
own pocket of in this hypergraph can't I
like realizing that I'm getting an
outdated picture
can't I record see the problem is and
this is where things start getting very
entangled in in terms of what one
understands the problem is that any such
recording device is itself part of the
universe yeah so you don't get to say
you never get to say let's go outside
the universe and go do this and and
that's why I mean lots of the features
of this of this model and the way things
work end up being a result of that so
but what I guess from on human level
what is the cost you're paying what are
you missing from not getting an updated
picture all the time okay I got I I
understand what you're just saying right
but like what like how does
Consciousness emerge from that like how
like what are the limitations of that
Observer I understand you're getting a a
delayed well there's a okay so there's
there's bunch of limitations of the
Observer I think maybe just explain
something about quantum mechanics
because that maybe is a is an extreme
version of some of these issues mhm
which helps to kind of motivate why one
should sort of think things through a
little bit more carefully so one feature
of the of this okay so in standard
physics like high school physics you
learn you know the equations of motion
for a ball and the the you know it says
you throw the ball this angle this
velocity things will move in this way
and there's a definite answer right the
story The the key story of quantum
mechanics is there aren't definite
answers to where does the ball go
there's kind of this whole sort of a
bundle of possible paths and all we say
we know from quantum mechanics is
certain probabilities for where the ball
will end up okay so that's kind of the
the core idea of quantum mechanics so in
our models you quantum mechanics is not
some kind of plug-in add-on type thing
you absolutely cannot get away from
quantum mechanics because as you think
about updating this hypergraph there
isn't just one sequence of things one
definite sequence of things that can
happen there are all these different
possible update sequences that can occur
you could do this you know piece of the
hypergraph now and then this one later
and etc etc etc all those different
Paths of History correspond to these
Quantum Quantum paths in in quantum
mechanics these different possible
Quantum histories and one of the things
that's kind of surprising about it is
they they Branch you know there can be a
certain state of the universe and it
could do this or it could do that but
they can also merge there can be two
states of the universe which their next
state the next state they produce is the
same for both of them and that process
of branching and merging is kind of
critical and the idea that they can be
merging is critical and somewhat
non-trivial for these hyper graphs
because there's a whole graph
isomorphism Story and there's a whole
very elaborate set of where caal
invariance comes in among other things
right yes that that's But but so so then
what happens is that what what one's
seeing Okay so we've got this thing it's
branching it's merging etc etc etc okay
so now the question is how do we
perceive that what do you know how do we
do we why don't we notice that the
universe is branching and merging why
you know why is it the case that we just
think a definite set of things happen
well the answer is we are embedded in
that universe and our brains are
branching and merging too and so what
quantum mechanics becomes a story of is
how does a branching brain perceive a
branching universe and the key thing is
as soon as you say I think definite
things happen in the universe that means
you are essentially conflating lots of
different parts of History you're saying
actually as far as I'm concerned because
I'm convinced that definite things
happen in the universe all these parts
of History must be equivalent now it's
not obvious that that would be a
consistent thing to do it might be you
say all these parts of History are
equivalent but by golly moments later
that would be a completely inconsistent
point of view everything would have you
know gone to hell in different ways the
fact that that doesn't happen is well
that's a consequence of this causal
invariance thing but that's and the fact
that that does happen a little bit is
what causes little Quantum effects and
that um if that didn't happen at all
there wouldn't be anything that sort of
is like quantum mechanics it would be
quantum mechanics is kind of like in
this uh in in this kind of this bundle
of paths it's a little bit like what
happens in statistical mechanics and
fluid mechanics whatever that most of
the time you just see this continuous
fluid you just see the world just
progressing in this kind of way that's
like this continuous fluid but every so
often if you look at the exact right
experiment you can start seeing well
actually it's made of these molecules
where they might go that way or they
might go this way and that's kind of
quantum effects and and so that's so the
the this kind of idea of we're we're
sort of embedded in the universe this
branching brain is perceiving this
branching universe and that ends up
being sort of a story of quantum
mechanics that's that's part of the the
whole picture of what's going on but I
think I mean to come back to sort of
where does conscious what is what is the
story of Consciousness so in the
universe we've got you know whatever it
is 10 400 atoms of space they're all
doing these complicated things it's all
a big complicated irreducible
computation the question is what do we
perceive from all of that and the answer
is that we are we are parsing the
universe in a particular way let me
again go back to the the gas molecules
and allery you know in the gas in this
room there are molecules bouncing around
all kinds of complicated patterns but we
don't care all we notice is there's you
know the gas laws are satisfied maybe
there's some fluid dynamics these are
kind of features of that assembly of
molecules that we notice and then are
lots of details we don't notice when you
say we do you mean the tools of physics
or do you mean literally the human brain
and its perception system well okay so
the human brain is where it starts but
we built a bunch of instruments that do
a bit better than the human brain but
they still have many of the same kinds
of ideas you know their cameras and
their pressure sensors and their these
kinds of things they're not uh you know
at this point we don't know how to make
fundamentally qualitatively different
sensory devices right so it's always
just an extension of the conscious
experience even or sensory experience
sensory experience
but sensory experience is somehow
intricately tied to Consciousness right
well so so one question is when we are
looking at all these molecules of the in
the gas and there might be 10 to 20th
molecules and some little box or
something it's like what what do we
notice about those molecules so one
thing that we can say is we don't notice
that much we are you know we are
computationally bounded observers we
can't go in and say okay I'm they're 10
to 20th molecules and I know that I can
sort of decrypt their motions and I can
figure out this and that it's like I'm
just going to say what's the average
density molecules and so one key feature
of us is that we are computationally
bounded and
that when you are looking at a universe
which is full of computation and doing
huge amounts of computation but we are
computationally bounded there's only
certain things about that universe that
we're going to be sensitive to we're not
going to be you know figuring out what
all the atoms of space are doing because
we're just computationally bounded
observers and we are only sampling these
these small set of features so I I think
the two defining features of
Consciousness that and I you know I
would say that the the sort of the the
the preamble to this is for years you
know because I've talked about sort of
computation and fundamental features of
physics and science people ask me so
what about Consciousness and I for years
I've said I have nothing to say about
Consciousness and you know I've I've
kind of told this story you know you
talk about intelligence you talk about
life uh these are both features where
you say what's the abstract definition
of life we don't really know the
abstract definition we know the one for
life on Earth it's got RNA it's got cell
membranes it's got all this kind of
stuff similarly for intelligence we know
the human definition of intelligence but
what is intelligence abstractly we don't
really know and so what I've long
believed is that sort of the abstract
definition of intelligence is just
computational sophistication that is
that as soon as you can be
computationally sophisticated that's
kind of the abstract version the
generalized version of intelligence so
then the question is what about
Consciousness and what I sort of
realized is that Consciousness is
actually a step down from intelligence
that is that you might think oh you know
Consciousness is the is the is the top
of the pile but actually I don't think
it is I think that there's this notion
of kind of computational sophistication
which is the generalized intelligence
but Consciousness has two limitations I
think one of them is computational
boundedness that is that we're only
perceiving a sort of computationally
bounded view of the universe and the
other is this idea of a single thread of
time that is that we and in fact we know
neurophysiologically our brains go to
some trouble to give us this one thread
of attention so to speak and it isn't
the case that you know in all the
neurons in our brains that that uh in at
least in our conscious not the the you
know the correspondence of language in
our conscious experience we just have
the single thread of attention single
thread of of perception um and you know
maybe there's something unconscious
that's bubbling around that's the kind
of almost the quantum version of what's
happening in our brain so to speak we've
got the the classical flow of what we
are mostly thinking about so to speak
but there's this kind of bubbling around
of other paths that is all those other
neurons that didn't make it to be part
of our sort of conscious stream of
experience so in that sense intelligence
as computational sophistication is much
broader than uh yes than the the
computational
constraints which Consciousness operates
under and also the sequent like the
sequential thing like the notion of time
that's that's kind of interesting but
then the the followup question is like
okay starting to get a sense of what is
intelligence and how does that connect
to a human brain cuz you're
saying um intelligence is almost like a
fabric like what we like plug into it or
something like yeah I think you know
people our Consciousness plugs into it
yeah I mean the intelligence I think the
core I mean you know intelligence at
some level is just a word but we're
asking you know what is the the notion
of intelligence as we generalize it
beyond the bounds of humans beyond the
bounds of even the AIS that we humans
have built and so on you know what what
is intelligence you know is the weather
you know people say the weather has a
mind of its own what does that mean you
know can the weather be intelligent yeah
what does agency have to do with
intelligence here so is intelligence
just like your conception of computation
just intelligence is a is the capacity
to perform computation and the Sea of
yeah I think so I mean I think that's
right and I I think that you know this
question of of is it for a purpose okay
that quickly degenerates into a horrible
philosophical mess because you know
whenever you say did the weather do that
for a purpose yeah right well yes it did
it was trying to move a bunch of hot air
from the equator to the poles or
something that's its purpose but why cuz
I I seem to be equally as dumb today as
I was yesterday so there's some
persistence like a consistency over time
that the intelligence I plugged into so
like what's it seems like there's a hard
constraint between the amount of
computation I can perform in my
Consciousness like they seem to be
really closely connected somehow well I
think the point is that the thing that
gives you kind of the ability to have
kind of conscious int
intelligence you you can have kind of
this okay so so one thing is we don't
know no intelligences other than the
ones that are very much like us yes
right and ones that are very much like
us I think have this feature of single
thread of time bounded you know
computationally bounded now that but you
also need computational sophistication
having a single thread of time and being
computationally bounded you could just
be a clock going Tick Tock you know that
would satisfy those conditions but the
fact that we have this uh sort of uh
irreducible
you know computational ability that's
that's an important feature that's
that's the sort of the the Bedrock on
which we can construct the things we
construct now the fact that we have this
experience of the world that has a
single thread of time and computational
boundedness the thing that I sort of
realized is it's that that causes us to
deduce from this irreducible mess of
what's going on in the physical world
the laws of physics that we think exist
so in other words if we say why do we
believe that there is you know
continuous space let's say why do we
believe that gravity works the way it
does well in principle we could be kind
of parsing details of the universe that
were uh you know that invol okay the
analogy is uh again with the you know
statistical mechanics and molecules in a
box we could be sensitive to every
little detail of the swirling around
Moes we could say what matters is the
you know the wiggle effect that is you
know that is something that we humans
just never noticed because it's some
weird thing that happens when there are
15 collisions of air molecules and this
happens and that happens we just see the
pure motion of a ball moving about right
why do we see that right and and the
point is that that what seems to be the
case is that the things that if if we
say given this sort of hypergraph that's
updating and all the details about all
the sort of uh sort of atoms of space
and what they do and we say how do we
slice that to what we can be sensitive
to what seems to be the case is that as
soon as we assume you know computational
boundedness single thread of time that
leads us to General altivity in other
words we can't avoid that that that's
the way that we we will parse the
universe given those constraints we
parse the universe according to those
particular uh in such a way that we say
the AG
reducible comp sort of comput pocket of
computational reducibility that we slice
out of this kind of whole
computationally irreducible ocean of
behavior is just this one that
corresponds to general relativity yeah
but we don't perceive general
relativity well we do if we do fancy
experiments so you're saying so perceive
really does mean the fult we drop
something that's a that's a great
example of general relativity in action
the gravity no but like what's the
difference that and newtonium mechanics
I mean oh it doesn't I this is I when I
say general relativity that's Uber the
Uber Theory so to speak I mean Newtonian
gravity is just the approximation that
we can make you know on the earth and
things like that so so this is you know
the phenomenon of gravity is one that is
a consequence of you know we would
perceive something very different from
Gravity so so the way to understand that
is when we think about okay so we make
up reference frames with which we parse
what's happening in space and time so in
other words one of the one of the things
that we do is we say as time progresses
uh everywhere in space is something
happens at a particular time and then we
go to the next time and we say this is
what space is like at the next time this
is what space is like at the next time
that's it's the reason we are used to
doing that is because you know when we
look around we might see you know 10 100
meters away
um the time it takes light to travel
that distance is really short compared
to the time it takes our brains to know
what happened so as far as our brains
are concerned we are parsing the
universe in this there is a moment in
time it's all of space there's a moment
in time it's all of space you know if we
were the size of planets or something we
would have a different perception
because the speed of light would be much
more important to us we wouldn't have
this perception that uh things happen
progressively in time everywhere in
space mhm um and so that's an important
kind of constraint and the reason that
we kind of parse the universe in the way
that causes us to say gravity works the
way it does is because we're doing
things like deciding that we can say the
universe exists space has a definite
structure at there is a moment in time
space has this definite structure we
move to the next moment in time space as
another structure that kind of setup is
what lets us kind of deduce kind of what
to parse the universe in such a way that
we say gravity works the way it does so
uh that kind of reference frame is that
the illusion of that is that you're
saying that's somehow useful for
Consciousness like that's what
Consciousness does because in a sense
what Consciousness is doing is there are
uh it's it's insisting that the universe
is kind of sequentialized right that is
um and it it is not allowing the
possibility that oh there are these
multiple threads of time and they're all
flowing differently it's like saying no
you know everything is happening in this
one thread of experience that we have
and that illusion of that one thread of
experience cannot happen at the
planetary scale so you're are you saying
typical human are you saying we are at a
human level is special here for
Consciousness like well for our kind of
Consciousness it's it's h you know if we
existed at a scale close to the
elementary length for example then our
perception of the universe will be
absurdly different okay so but this this
makes it Consciousness seem like a weird
side effect of this particular scale and
so who cares I mean Consciousness is not
that special I I think look I think that
a very interesting question is which
I've certainly thought a little bit
about is what can you imagine what is a
sort of factoring of something you know
what are some other possible ways you
could exist so to speak right and you
know if you were a photon if you were
sort of you know some kind of thing that
was um uh kind of you know intelligence
represented in terms of photons you know
for example the photons we receive in
the cosmic microwave background those
photons as far as they're concerned the
universe just started they they they
were emitted you know 100,000 years
after the beginning of the universe
they've been traveling at the speed of
light time stayed still for them and
then they just arrived and we just
detected them so for them the universe
just started and that's a different
perception of you know that has
implications for a very different
perception of they don't have that
single thread that seems to be really
important for being able to tell a heck
of a good story so we humans tell we can
tell a story we right we can tell a
story what other kind of stories can you
tell so photon is a really boring story
yeah I mean so so that's a I don't know
if they're a boring story but I I think
it's you know I've been wondering about
this and I've been asking you know
friends of mine who are science fiction
writers and things have you written
stuff about this and I've got one
example great great uh collection of
books from my friend Rudy Rooker which
were um uh which I have to say the um
the books about uh that are very
informed by a bunch of science that I've
done and the thing that I really loved
about them is you know you know in the
in the first chapter of of the book The
the Earth is consumed by these things
see called NS which are Nano nanobot
type things and it um but so you know so
the Earth is gone in the first but then
it comes back but but um but then
spoiler alert yeah right that was a that
was only a micro spoiler it's only
chapter one okay good it's um the but
but the thing that um is is not a real
spoiler alert because it's such a
complicated concept but but in the end
in the end the the Earth is saved by
this thing called the principle of
computational equivalence which is a
kind of a a core scientific idea of mine
and I was just like like thrilled I I
don't read fiction books very often um
and I was just thrilled I get to the end
of this and it's like oh my gosh you
know everything is saved by this sort of
deep scientific principle can you can
you maybe elaborate how the principle of
computational
equivalence can save a planet that would
that would be a have a terrible spoiler
for there would be a spoiler okay yeah
yeah but but no but let me say what the
principle of computational equivalence
is um so the question is you are you
have a system you have some rule you can
think of Its Behavior as corresponding
to a computation the question is how
sophisticated is that computation the
statement of the principle of
computational equivalence is as soon as
it's it's not obviously simple it will
be as sophisticated as anything and so
that has the implication that you know
rule 30 uh you know our brains other
things in physics they're all ultimately
equivalent in the computations they can
do and that's what leads to this
computational irreducibility idea
because the reason we don't get to jump
ahead you know and and outthink Rule 30
is because we're just computationally
equivalent to rule 30 so we're kind of
just both just running computation
that are the same sort of raw the same
level of computation so to speak so
that's kind of the the idea there and
the question I mean it's it's like uh
the you know in in the science fiction
version would be okay somebody says we
just need more servers get us more
servers the way to get even more servers
is turn the whole planet into a bunch of
micros servers and that that's uh that's
where it starts and so the question of
you know computational equivalence
principle of computational equivalences
well actually you don't need to build
those custom servers actually you can uh
you can just um use natural computation
to compute things so to speak you can
use nature to compute you don't need to
have done all that engineering and it's
kind of the it's it's kind of feels a
little disappointing that you say we're
going to build all these servers we're
going to do all these things we're going
to make you know maybe we're going to
have human consciousness uploaded into
you know some elaborate digital
environment and then you look at that
thing and you say it's got electrons
moving around just like in a rock and
then you say well what's the difference
and the principle of computational
equivalence says there isn't at some
level a fundamental you know you can't
say mathematically there's a fundamental
difference between the rock that is the
future of human consciousness and The
Rock that's just a rock MH now what I've
sort of realized with this kind of
Consciousness thing is there is a there
is an aspect of this that seems to be
more special that isn't and and for
example something I I haven't really
teased apart properly is when it comes
to something like the weather and the
weather having a mind of its own or
whatever or your average you know Pulsar
magnetosphere acting like a sort of
intelligent thing how does that relate
to you know how how do how is that that
entity related to the kind of
Consciousness that we have and sort of
what would the world look like you know
to the weather if we think about the
weather as a mind what will it perceive
what will it laws of its laws of physics
be I don't really know because it's very
parallel it's very parallel among other
things and it it it's not obvious I mean
this is a a really kind of mind-bending
thing because we've got to try and
imagine where uh you know we've got to
try and imagine a parsing of the
universe different from the one we have
and by the way when we think about
extraterrestrial intelligence and so on
I think that's kind of the key thing is
you know we've always assed assumed I've
always assumed okay the
extraterrestrials at least they have the
same physics we all live in the same
universe they've got the same physics
but actually that's not really right
because the extraterrestrials could have
a completely different way of parsing
that the universe so it's as if you know
there could be for all we know right
here in this room you know in the in the
details of the motion of these gas
molecules there could be an amazing
intelligence that we were like but we
have no way of we're not parsing the
universe in the same way if only we
could parse the universe in the right
way you know immediately this amazing
thing that's going on and this you know
huge culture that's developed and all
that kind of thing would be obvious to
us but it's not because we have our
particular way of processing the
universe would that thing also have a
agency I don't know the right word to
use but something like Consciousness but
a different kind of Consciousness I
think it's a question of just what you
mean by the word because I think that
the you know this notion of
Consciousness and the okay so some
people link of Consciousness is sort of
a key aspect of it is that we feel that
there sort of a feeling of that we exist
in some way that we have this intrinsic
feeling about ourselves you know I I
suspect that any of these things would
also have an intrinsic feeling about
themselves I've been sort of trying to
think recently about constructing an
experiment about what if you were just a
piece of a cellular automatan let's say
you know what would your feeling about
yourself actually be and you know can we
put ourselves in the in the shoes in the
cells of the cellular automaton so to
speak can we can we get ourselves close
enough to that that we could have a
sense of what the world would be like if
you were operating in that way and it's
a little difficult because you know you
have to not only think about what are
you perceiving but also what's actually
going on in your brain and our brains do
what they actually do and they don't
it's uh you know I think there might be
some experiments that are possible with
with with uh you know neural Nets and so
on where you can have something where
you can at least see in detail what's
happening inside the system and I I've
been sort of one of the one of my
projects to think about is is there a
way of kind of uh uh kind of getting a
sense kind of from inside the system
about what its view of the world is and
and how it how it you know can can we
make a bridge see the main issue is this
where you know it's a it's a sort of
philosophically difficult thing because
it's like we do what do we understand
ourselves um at least to some extent we
humans understand ourselves that's
correct and but yet okay so what are we
trying to do for example when we are
trying to make a model of physics what
are we actually trying to do because you
know you say well can we work out what
the universe does well of course we can
we just watch the universe the universe
does what it does but what we're trying
to do when we make a model of physics is
we're trying to get to the point where
we can tell a story to ourselves that we
understand that is also a represent
presentation of what the universe does
so it's this kind of you know can we
make a bridge between what we humans can
understand in our minds and what the
universe does and in a sense you know a
large part of my kind of Life uh efforts
have been devoted to making
computational language which kind of is
a bridge between what is possible in the
computational universe and what we
humans can conceptualize and think about
in a sense what you know when I built
wol from language and our whole sort of
computational language story it's all
about how do you take sort of raw
computation in this ocean of
computational possibility and how do we
sort of represent pieces of it in a way
that we humans can understand and that
map on to things that we care about
doing and in a sense when you add
physics you're adding this other piece
where we can you know mediated by
computer can we get physics to the point
where we humans can understand something
about what's happening in it and when we
talk about an alien intelligence it's
kind of same story it's like is there a
way of mapping what's happening there
onto something that we humans can
understand and you know physics in some
sense is like our exhibit one of the
story of alien intelligences it's a it's
a you know it's an alien intelligence in
some sense and what we're doing in
making a model of physics is mapping
that onto something that we understand
and I think you know a lot of these
other things that have I've recently
been kind of studying uh whether whether
it's molecular biology other kinds of
things um which we can talk about a bit
um the um uh those are other cases where
we're in a sense trying to again make
that bridge between what we humans
understand and sort of the the natural
language of that sort of alien
intelligence in some sense when you're
talking about just uh to backtrack a
little bit about cell
aoma being able to uh what's it like to
be a
cellometer in the way that's equivalent
to what it's it like to be a conscious
human
being how do you approach that so is it
looking at some subset of the cellular
atom and asking questions of that subset
like how the world is perceived how you
as that subset like for that local
pocket of computation what are you able
to say about the broader something like
and that somehow then can give you a
sense of how to step outside of that
cell but but the tricky part is that
that little subset it's what it's doing
is it has a view of itself and the
question is how do you get inside it
it's like you know when we with humans
right it's like we can't get inside each
other's Consciousness that doesn't
really um you know that doesn't really
even make sense it's like there is an
experience that somebody is having but
you can perceive things from the outside
but sort of getting inside it it it
doesn't it doesn't quite make sense and
I you know for me these sort of
philosophical issues in this one I have
not untangled so let's let's be um um
the you know for me the thing that has
been really interesting in thinking
through some of these things is you know
when it comes to questions about
Consciousness or whatever else it's like
when I can run a program and actually
see pictures and you know make things
concrete I have a much better chance to
understand what's going on than when I'm
just trying to reason about things in a
very abstract way yeah but there may be
a way to uh
map the program to your conscious
experience so for example when you play
a video game you do a first-person
shooter you walk around
inside this entity yep it's a very
different thing than watching this
entity so if you can somehow connect
more and more connect this this full
conscious experience to the subset of
the cell autometer yeah it's something
like that but the difference in the
first person shooter thing is there
still your brain and your memory is
still remembering you know you you still
have it's it's hard to I mean again what
one's going to get one is not going to
actually be able to be the cellular
automatan one's going to be able to
watch what the cellular automatan does
but this is the frustrating thing that
I'm trying to understand you know you
know how to how to think about being it
so to speak okay so like in virtual
reality there's a concept of immersion
like with anything with video game with
books there's a concept of immersion if
feel feels like over time if the virtual
reality experience is is well done and
maybe in the future it be extremely well
done the immersion leads you
to feel like you mentioned memories you
forget that you even ever existed
outside that experience it's so
immersive I mean you could argue sort of
mathematically that you can never truly
become immersed but maybe you can I mean
well yeah why can't you merge with the
cell aom I mean you aren't you just part
of the same fabric why can't you just
like well that's a good question I mean
so so let's imagine the following
scenario let's imagine can you return
what's that well but then can you return
back well yeah right I mean it's it's
like let's imagine you've uploaded you
know your brain is scanned you've got
every synapse you know mapped out you
upload everything about you the brain
simulator you upload the brain simulator
and the Brain simulator is basically you
know some glorified cellular automat and
then you say well now we've got an
answer to what does it feel like to be a
cellular automatan it feels just like it
felt to be ordinary you because they're
both computational systems and they're
both you know operating in the same way
so in a sense but I think there's
there's somehow more to it because in in
that sense when you're just making a
brain simulator it's just you know we're
just saying there's another version of
our Consciousness the question that
we're asking is if we tease away from
our Consciousness and get to something
that is different how do we make a
bridge to understanding what's going on
there and you know there's a way of
thinking about this okay so this is
coming on to sort of questions about the
existence of the universe and so on but
one of the things is there's this notion
that we have of Ral space so we have
this idea of there's physical space
which is you know something you can move
around in that's that's associated with
actual the extent of the spatial
hypergraph then there's what we call
branchial space the space of quantum
branches so in this in this thing we
call a multi-way grow off of all of the
sort of branching histories there's this
idea of a kind of space where instead of
moving around in physical space you're
moving from history to history so to
speak from one possible history to
another possible history and that's kind
of a different kind of space that is the
space in which quantum mechanics plays
out quantum mechanics like for example
oh something like uh I think we're
slowly understanding things like
destructive interference in quantum
mechanics that what's happening is
branchial space is associ with phase and
quantum mechanics and what's happening
is the two photons that are supposed to
be interfering and destructively
destructively interfering are winding up
at different ends of branchial space and
so us as these poor observers that are
trying to that have branching brains
that are trying to conflate together
these different threads of history and
say we've really got a consistent story
that we're telling here we're really
knitting together these threads of
History by the time the two photons
wound up at opposite ends of branchial
space we just can't knit them together
to tell a consist story so for us that's
sort of the analog of destructive
interference got it and then there's Ral
space too which is the space of rules
yes well that's a that's another level
up so so there's there's the question um
actually I I I do want to mention one
thing because it's something I've
realized in recent times and it's I
think it's really really kind of cool
which is about time dilation and
relativity and it kind of helps to
understand it's something that kind of
helps in understanding what's going on
so in according to relativity if you you
know you have a clock it's ticking at a
certain rate you send it in a spacecraft
that's going at some significant
fraction of the speed of light to you as
a as a Observer at rest that clock
that's in the spacecraft will seem to be
ticking much more slowly and so in other
words you know it's kind of like the the
the the twin who goes off to Alpha
centur and goes very fast will age much
less than the twin who's on Earth that
um that is just hanging out where
they're hanging out okay why does that
happen
okay so it has to do with what motion is
so in in our models of physics what is
motion well when you move from somewhere
to somewhere it's you're having to sort
of recreate yourself at a different
place in space m when you exist at a
particular place and you just evolve
with time you're again you're you're
updating yourself you're you're
following these rules to update what
happens well so the question is when you
have a certain amount of computation in
you so to speak when there's a certain
amount you know you're Computing the
universe is Computing at a certain rate
you can either use that computation to
work out sitting still where you are
what's going to happen successively in
time or you can use that computation to
recreate yourself as you move around the
universe and so time dilation ends up
being it's it's really cool actually
that this is explainable in a in a way
that isn't just imagine the mathematics
of Relativity but but um the time
dilation is a story of the fact that as
you kind of recreating yourself as you
move you are using up some of your
computation and so you don't have as
much computation left over to actually
work out what happens progressively with
time so that means that time is running
more slowly for you because it is you're
you're using up your computation your
your your clock can't tick as quickly
because every tick of the clock is using
up some computation but you already used
that computation up on moving at you
know half the speed of light or
something and so that's that's why time
dation happens
and so you can you can start so it's
kind of interesting that one can sort of
get an intuition about something like
that because it has seemed like just a
mathematical fact about the mathematics
of of special relativity and so on well
for me it's a little bit confusing what
the U in that picture is because you're
using up
computation okay so so we're simply
saying the entity is updating itself
according to the way that the Universe
updates itself and the question is your
you know those updates let's imagine the
U is a clock M okay and the clock is you
know there's all these little updates
the hypergraph and a sequence of updates
cause the pendulum to swing back the
other way and then swing back swinging
back and forth okay and all of the all
of those updates are contributing to the
motion of you know the pendulum going
back and forth or the the oscillator
moving whatever it is okay but but then
the alternative is that's sort of
situation one the thing is at rest
situation two where it's kind of moving
the the what's happening is it is having
to recreate itself at every at every
moment the thing is going to have to do
the computations to be able to sort of
recreate itself at a different position
in space and that's kind of the
intuition behind so it's it's either
going to spend its computation
recreating itself at a different
position in space or it's going to spend
its computation doing the um uh sort of
doing the update
of the you know of the the ticking of
the clock so to speak so the more
updating is doing the less the ticking
of the clock update is doing that's
right the more it has having to update
because of motion yeah the less it can
update the the clock so that that's um I
mean obviously there's a there's a sort
of mathematical version of it that
relates to how it actually works in
relativity but that's kind of to me that
was sort of exciting to me that it's
possible to have a a really mechanically
explainable story there that that isn't
um and it's similarly in quantum
mechanics this notion of branching
brains perceiving branching universes to
me that's getting towards a sort of
mechanically explainable version of what
happens in quantum mechanics even though
it's a little bit mind-bending uh to see
you know these things about under what
circumstances can you successfully knit
together those different threads of
history and when do things sort of
escape and and those kinds of things but
the you know the thing about this
physical space and physical space the
the main sort of big theory is general
relativity the theory of gravity and
that tells you how things move in
physical space in bronchial space the
big theory is the F path andral which it
turns out tells you essentially how
things move in Quantum in the space of
quantum phases so it's kind of like
motion and branchial space and it's kind
of a fun thing to start thinking about
what oh you know all these things that
we know in physical space like uh event
Horizons and black holes and so on what
are the analogous things in branchial
space for example the speed of light
what's the analog of the speed of light
in branchial space it's the maximum
speed of quantum entanglement so the
speed of light is a flash bulb goes off
here what's the maximum rate at which
the effect of that flash bulb is
detectable moving away in space so
similarly in branchial space something
happens and the question is how far in
this branchial space and the space of
quantum States how far away can that get
within a certain period of time and so
there's this notion of a maximum
entanglement speed and that might be
observable that's the thing we've been
sort of poking at is might there be a
way to observe it even in some Atomic
physics kind of situation um that
because one of the things that's weird
in quantum mechanics is where you know
when we study quantum mechanics we
mostly study it in terms of small
numbers of particles you know this
electron does this this thing on an ion
trap does that and so on but when we
deal with large numbers of particles
kind of all bets are off it's kind of
too complicated to deal with quantum
mechanics
and so what ends up happening is so this
question about maximum entanglement
speed and things like that may actually
play in one of these in in the sort of
story of many body quantum mechanics and
even have some suspicions about things
that might happen even in one of the
things I I realized I never understood
and it's kind of embarrassing but I
think I Now understand a little better
is when you have chemistry and you have
quantum mechanics it's like well there's
two carbon atoms as this molecule and we
do a reaction and we draw a diagram and
we say this carbon atom ends up in this
place it's like but wait a minute in
quantum mechanics nothing ends up in a
definite place there's always just some
wave function for this to happen how can
it be the case that we can draw these
reasonable it just ended up in this
place and you have to kind of say well
the environment of the molecule
effectively made a bunch of measurements
on the molecule to keep it kind of
classical and that's a story that has to
do with this whole thing about about you
know measurements have to do with this
idea of you know you know can we
conclude that something definite
happened because in quantum mechanics
the the intrinsic quantum mechanics the
mathematics of quantum mechanics is all
about they just these amplitudes for
different things to happen then there's
this thing of and then we make a
measurement and we conclude that
something definite happened and that has
to do with this thing I think about sort
of moving about knitting together these
different threads of history and saying
this is now something where we can
definitively say something definite
happen in the traditional theory of
quantum mechanics it's just like
you know after you've done all this
amplitude computation then this big
hammer comes down and you do a
measurement and it's all over and that's
been very confusing for example in
Quantum Computing it's been a very
confusing thing because when you say you
know in Quantum Computing the basic idea
is you're going to use all these
separate threads of of computation so to
speak to do all the different parts of
you know try these different factors for
an integer or something like this and it
looks like you can do a lot because
you've got all these different threads
going on but then you have to say well
at the end of it you've got all these
threads and every thread came up with a
definite answer but we got to conflate
those together to figure out a definite
thing that we humans can take away from
it a definite so the computer actually
produced this output so having this uh
Branch space and this hypergraph model
of physics do you think it's possible to
then make predictions that are definite
about uh many body quantum mechanical
systems is I think it's likely yes but I
don't you know
this is every one of these things when
you when you go from the underlying
Theory which is complicated enough and
it's I mean the theory at some level is
beautifully simple but as soon as you
start actually trying to it's this whole
question about how do you bridge it to
things that we humans can talk about it
gets really complicated and and this
thing about actually getting it to a
definite definite prediction um about
you know definite thing you can say
about chemistry or something like this
um you know that's just a lot of work so
I'll give you an example there's a think
called the quantum Zeno effect so it the
idea is you know Quantum stuff happens
but then if you make a measurement
you're kind of freezing time in quantum
mechanics you and and so it looks like
there's a possibility that with sort of
the the relationship between the quantum
Xeno effect and the way that many body
quantum mechanics works and so on maybe
just conceivably it may be possible to
actually figure out a way to measure the
the uh the maximum entanglement speed
and the reason we can potentially do
that is because the systems we deal with
in terms of atoms and things they're
pretty big you know a mole of atoms is
you know is a lot of atoms and you know
but it isn't a very you know it's
something where to get you know when
we're dealing with how can you see 10us
100 so to speak well by the time you've
got you know 10 to the 30th atoms you're
not you know you're within a little bit
closer Striking Distance of that it's
not like oh we've just got you know two
atoms and we're trying to see down to
10us 100 meters or whatever so I don't
know how it will work but this is a this
is a a potential Direction and if you
can tell by the way if we could measure
the maximum entanglement speed we would
know the elementary length these are all
related so if if we get that one number
we just need one number if we can get
that one number we can you know the
theory has no parameters anymore um and
uh you know there are there are other
places well there's another another hope
for doing that is in cosmology uh in
this model one of the features is the
universe is not fixed dimensional I mean
we think we live in three-dimensional
space but this hypergraph doesn't have
any particular Dimension it can emerge
as something which on in an
approximation it's as if you know you
say what's the volume of a sphere in the
hypergraph where a sphere is defined as
how many nodes do you get to when you go
a distance R away from a given point and
you can say well if I get to about R
Cube nodes when I go a distance R away
in the hypergraph then I'm living
roughly in three-dimensional space but
you might also get to R to the point you
know
2.92 you know for for some value of R in
you know as as as R increases that might
be the the sort of fit to what happens
and so one of the things we suspect is
that the very early Universe was
essentially infinite dimensional and
that as the universe expanded it became
lower dimensional and so one of the
things that is another little sort of
point where we we think there might be a
way to to actually measure some things
is dimension fluctuation in the other
universe that is is there a is there
leftover Dimension fluctuation of at the
time of the cosmic microwave background
100,000 years or something after the
beginning of the universe is it still
the case that there are there were
pieces of the universe that didn't have
Dimension three that had Dimension 3.01
or something and can we tell that is
that possible to observe uh the
fluctuations in Dimensions I don't even
know what that entails okay so the the
the question which should be an
elementary exercise in electrodynamics
except it isn't is um understanding what
happens to a photon when it propagates
through 3.01 dimensional space so for
example the inverse Square law is a
consequence of the you know the the the
surface area of a sphere is proportional
to r s but if you're not in
three-dimensional space the surface area
of sphere is not proportional to r s
it's R to the whatever 2.01 or something
um and so that means that
I think when you kind try and do Optics
you know a common principle in Optics is
hen's principle which basically says
that every piece of a wavefront of a of
a of light is a source of new spherical
waves and those spherical waves if
they're different dimensional spherical
waves will have other characteristics
and so there will be bizarre Optical
phenomena which we haven't figured out
yet um so you're you're you're what
looking for some weird phot on
trajectories that designate that it's
3.01 dimensional space yeah yeah that
would be an example of I mean you know
there are there are only a certain
number of things we can measure about
photons you know we can measure their
polarization we can measure their
frequency we can measure their Direction
um those kinds of things and you know
how that all works out and you know in
in the current models of physics uh you
know uh it's been hard to explain how
the universe manages to be as uniform as
it is and that's led to this inflation
idea that um to the to the great
annoyance of my then collaborator I we
had we figured out in like 1979 we had
this realization that that you could get
something like this but it seemed
implausible that that's the way the
universe worked so we put it in a
footnote right and that was so that's a
but but any case i' I've never really
completely believed it but this that's
an idea for how to sort of puff out the
universe faster than the speed of light
early moments of the universe that
that's the sort of the inflation idea
and that that you can somehow explain
how the universe manages to be as
uniform as it is in in our model this
turns out to be much more natural
because the universe just starts very
connected the hypergraph is not such
that the ball that you grow starting
from a single point has volume R cubed
it might have volume R to the 500 or R
to the infinity um and so that means
that you you sort of naturally get this
much higher degree of connectivity and
uniformity in the universe and then the
question is uh this is sort of the
mathematical physics challenge is in the
standard theory of the universe there's
the free Bid Robertson Walker Universe
which is the kind of standard model
where the universe is isotropic and
homogeneous and you can then work out
the equations of general relativity and
you can figure out how the universe
expands we would like to do the same
kind of thing including Dimension change
this is just difficult mathematical
physics I mean the reason it's difficult
is there's sort of fundamental reason
it's difficult when when people invented
calculus 300 years ago calculus was a
story of understanding change and change
as a function of a variable so people
study univarate calculus they study
multivariate calculus it's one variable
it's two variables three variables but
whoever studied you know 2.5 variable
calculus turns out nobody turns out that
but what we need to have to understand
these fractional dimensional spaces uh
which don't work like well the the
they're spaces where where the effective
dimension is not an integer so you can't
apply the tools of calculus and
naturally and easily to fractional
Dimensions no so somebody has to figure
out how to do that we have yeah yeah
we're trying to figure this out I mean
it's it's very interesting I mean it's
very connected to very Frontier issues
in mathematics it's very beautiful but
so is it possible is it possible we're
dealing with a scale that's so so much
smaller than our human scale is it
possible to make predictions versus
explanations do you you have a hope that
with this hypergraph model You' be able
to make predictions yeah that then could
be validated with a physics experiment
predictions that couldn't have been done
or weren't done otherwise yeah yeah yeah
I mean you know I think which in which
domain do you think that okay so there
are going to be cosmology ones to do
with Dimension fluctuations in the
universe that's a very bizarre effect
nobody you know Dimension fluctuation is
just something nobody ever looked for
that if anybody sees dimmension
fluctuation that's a huge flag that the
the something like our our model is
going on if and and how one detects that
you know that's a problem of kind of you
know that's a problem of traditional
physics in a sense of what's the best
way to actually figure that out and and
for example that that's one there are
there are all kinds of things when can
imagine I mean there are things that um
uh in black hole mergers it's possible
that there will be effects of Maximum
entanglement speed in large black hole
mergers um that's another another
possible thing and all of that is
detected through like what do you have a
hope for ligo type of situation like
that's gravitational waves yeah or or
alternatively I mean I think it's you
know look figuring out experiments is
like figuring out technology inventions
right that is you know you've got a set
of raw materials you've got an
underlying model and now you've got to
be very clever to figure out you know
what is that thing I can measure that
just somehow you know leverages in to
the right place and uh we've spent less
effort on that than I would would have
liked because I one of the one of the
reasons is that that I think that the
the this you know the physicists who'
been working on on our models we with
now lots of pH such it's very very nice
it's kind of uh uh you it's one of these
cases where I'm almost I'm really kind
of pleasantly surprised that the sort of
absorption of the things we've done has
been uh quite rapid and quite uh sort of
you know very positive so it's a
Cambrian explosion of physicist too not
just ideas yes I mean you know lot of
what what's happened that's really
interesting and again not what I
expected is there are a lot of areas of
of sort of very uh elaborate
sophisticated mathematical physics
whether that's causal set theory whether
it's higher category Theory whether it's
categorical quantum mechanics all sorts
of elaborate names for these things spin
networks perhaps uh you know causal
dynamical triangulations all kinds of
names of of these fields and these
fields have a bunch of good mathematical
physicists in them who've been working
for decades in these particular areas
and the question is but but they've been
building these mathematical structures
and the mathematical structures are
interesting but they don't they don't
typically sit on anything they're just
mathematical structures and I think
what's happened is our models provide
kind of a machine code that lives
underneath those models so a typical
example this is uh um due to Jonathan
gorod who's one of the key people who's
been working on our project um this is
uh in Okay so CA I'll give you an
example just to give a sense of how
these things connect this is in causal
set theory so the idea of causal set
theory is there are in space time we
imagine that there's space and time it's
a 3 plus one dimensional you know setup
we imagine that there are just events
that happen at different times and
places in space and time and the idea of
causal set theory is the only thing you
say about the universe is there are a
bunch of events that happen sort of
randomly at different places in space
and time and then the whole sort of
Theory of physics has to be to do with
this the this graph of causal
relationships between these randomly
thrown down events so they've always
been confused by the fact that to get
even lenen variant even relativistic in
variant you need a very special way to
throw down those events and they've had
no natural way to understand how that
would happen so what Jonathan figured
out is that in fact from our models they
instead of just generating events at
random are models necessarily generate
events in some pattern in in SpaceTime
effectively that then leads to R
invariance and relativistic invariance
and all those kinds of things so it's a
place where all the mathematics that's
been done on well we just have a random
collection of events now what you know
what consequences does that have in
terms of causal set theory and so on
that can all be kind of wheeled in now
that we have some different underlying
foundational idea for what what the
particular distribution of events as
opposed to just where we throw down
random events and so that's a that's a
typical sort of example of what we're
seeing in all these different areas of
kind of how you can take you know really
interesting things that have been done
in mathematical physics and connect them
and it's it's really kind of beautiful
because the the you know the sort of the
abstract models we have just seem to
plug into all these different very
interesting very elegant abstract ideas
but we're now giving sort of a reason
for that to be the way for for reason
for one to care I mean it's like saying
uh you can you know you can think about
computation abstractly you know you can
think about I don't know combinators or
something as abstract computational
things and you can sort of do all kinds
of study of them but it's like why do we
care well okay touring machines are a
good start because we can kind of see
they're sort of mechanically doing
things but when we actually start
thinking about computers Computing
things we have a really good reason to
care and this is sort of what we're what
we're providing I think is a reason to
care about a lot of these areas of
mathematical physics so that's been
that's been very nice so I'm not sure
we've ever got to the the question of
why does the universe exist at all let's
let's let's talk about that yes so we're
it's not the simplest question in the
world so um so it's it takes a few steps
to get to it and it's nevertheless even
surprising that you can even begin to
answer this question indeed as you were
saying I'm I'm very
surprised so the next thing to perhaps
understand is this idea of Ral space so
we've got kind of physical space we've
got branchial space the space of
possible Quantum histories and now we've
got another level of kind of abstraction
which is Ral space and here's the here's
where that comes from so you say okay
you say we've got this model for the
universe we've got a particular Rule and
we run this Rule and we get the universe
okay so that's that's interesting why
that rule why not another Rule and so
that confused me for a long time and I
realized well actually what if the thing
could be using all possible rules what
if at every step in addition to saying
apply a particular rule at all places in
this hypog graph one could say just take
all possible rules and apply all
possible rules at all possible places in
this hyper graph okay and then you make
this Ral multi-way graph which both is
all possible histories for a particular
Rule and all possible rules so the next
thing you'd say is how can you get
anything reasonable how can anything you
know Real come out of the set of all
possible rules applied in all possible
ways okay there's a subtle thing so
which I haven't fully untangled the
there is this object which is the result
of running all possible rules in all
possible ways and you might say if
you're running all possible rules why
can't everything possible happen well
the answer is because when you there's
sort of this entanglement that occurs so
let's say that that you have a lot of
different possible initial conditions a
lot of different possible States then
you're applying these different rules
well some of those rules can end up with
the same state so it isn't the case that
you can just get from anywhere to
anywhere there's this whole entangled
structure of what can lead to what and
there's a definite structure that's
produced I think I'm going to call that
definite structure the ruad the limit of
um uh the limit of kind of uh all
possible rules being applied in all
possible ways and you're saying that
structure finite so that somehow
connects to maybe a similar kind of
thing as like causal
invariance R necessarily has causal
invariance that's a feature of that's
just a mathematical consequence of
essentially using all possible rules
plus Universal computation gives you the
fact that from any diverging paths you
can always the the paths will always
converge does that say that the ru does
that necessarily infer that the ruad is
finite in the end it's not necessarily
finite I mean it's it's a it's a the the
just like the history of the universe
may not be finite the history of the
universe time may keep going forever you
can keep running the computations of the
ruad and you'll keep spewing out more
and more and more structure it's like
time doesn't have to end it's it's um
that but the the issue is there are
there are three limits that happen in
this rad object one is how long you run
the computation for another is how many
different rules you're applying and
another is how how many different states
you start from and the mixture of those
three limits I mean this is just
mathematically a horrendous object okay
and what's what's interesting about this
object is the one thing that does seem
to be the case about this object is it
connects with ideas in higher category
Theory and in particular it connects to
some of the 20th Century's most abstract
mathematics done by this chap growth and
deque um growth and deque had a thing
called The Infinity groupoid which is
closely related to this ruad object um
or Al though the details of the
relationship uh you know I don't fully
understand yet um but I think that the
what's what's interesting is this thing
that is sort of this very limiting
object so so okay so a way to think
about this that that again will will
take us into another Direction which is
the equivalence between physics and
Mathematics MH the way that uh well
let's see uh maybe this is um just just
to give a sense of this kind of um
groupoid and things like that you can
think about in mathematics you can think
you have certain axioms they're kind of
like atoms and you well actually let's
say let's talk about mathematics for a
second so what is mathematics what what
is what is it made of so to speak
mathematics there's a bunch of
statements like uh for addition x + y is
equal to y + x that's a statement of
mathematics another statement would be
you know x^2 - 1 is equal to x + 1 x -1
there are infinite number of these
possible statements of mathematics well
it's not I mean it's not just I guess a
statement but with X Plus y it's it's a
rule that you can it's I mean you think
of it as a rule it's it's a it is it is
a rule it's also just a thing that is
true in mathematics right um a statement
of Truth okay right and and what you can
imagine is you you you imagine just
laying out this giant kind of ocean of
all all statements well actually you
first start okay this is where this
we're segueing into a different thing
let me let me not go in this direction
for a second let's not go to meta
mathematics just yet yeah we'll we'll
we'll maybe get to meta mathematics but
but it's it's um uh so let me not let me
explain the groupoid and things later
yes yeah but but so let's come back to
the universe um always a good place to
be in so to speak yeah so what does the
universe have to do with the ruad the
ruo space and how that's
possible connected to why the thing
exists at all and why there's just one
of them yes okay so here's the point so
the thing that had confused me for a
long time was let's say we get the rule
for the universe we hold it in our hand
we say this is our universe then the
immediate question is well why isn't it
another one and you know that's kind of
the you know the the sort of the lesson
of cernus is we're not very special so
how come we got Universe number 312 and
not Universe quadrillion quadrillion
quadrillion and I think the resolution
of that is the realization that there
that the universe is running all
possible rules rules so then you say
well how on Earth do we perceive the
universe to be running according to a
particular rule how do we perceive
definite things happening in the
universe well it's the same story it's
the Observer there is a reference frame
that we are picking in this rule space
and that that is what determines our
perception of the universe with our
particular sensory information and so on
we are parsing the universe in this
particular way so here's the way to
think about it in in in physical space
we live in a particular place in the
universe and you know we could live on
Alpha santor but we don't we live here
um and similarly in Ral space we could
live in many different places in Ral
space but we happen to live here and
what does it mean to live here it means
we have certain sensory input we have
certain ways to parse the universe those
are our interpretation of the universe
what would it mean to travel in Ral
space what it basically means is that we
are successively interpreting the
universe in different ways so in other
words to be at a different point in Ral
space is to have a different in a sense
a different interpretation of what's
going on in the universe and we can
imagine even things like an analog of
the speed of light as the maximum speed
of translation in Ral space and so on so
wait what's the
interpretation so Ral space and we is
I'm confused by the we and the
interpretation and the Universe I
thought moving about in Ral space
changes the way the
universe is is the the way we would
perceive it the way that that ultimately
has to do with the perception so it
doesn't Ral Ral space is not somehow
changing like uh branching into another
Universe something like that no just
part of the point is the the whole point
of this is the ruad is sort of the
encapsulated version
of everything that is the universe
running according to all possible we
think of our universe the observable
universe as its thing so we're a little
bit loose with the word Universe then
because wouldn't the ru had a
potentially
encapsulate a very large number like
combinator large maybe infinite set of
what we phys human physicists think of
as universes that's an interesting
interesting parsing of the word un
right because what we're saying is just
as we're at a particular place in
physical space we're at a particular
place in Ral space at that particular
place in Ral space our experience of the
universe is this yeah just as if we
lived at the center of the Galaxy our
universe our experience of the universe
would be different from the one it is
given where we actually live and so in a
what we're saying is our when you might
say I mean in a sense this this ruad is
sort of a super universe so to speak um
but it's all in Tangled together it's
not like you can separate out you can
say let me it's it's like when we take a
reference okay it's like our experience
of the univers is based on where we are
in the universe we could imagine moving
to somewhere else in the universe but
it's still the same universe so there's
not like
universes existing in parallel no
because because and and the whole point
is that if we were able to change our
interpretation of what's going on we
could perceive a different
reference frame in this ruad yeah but
that's not that's not uh that's just
yeah that's the same ruad that's the
same universe you're just moving about
these are just coordinates in the
universe so so the way that's the reason
that's interesting is imagine the
Extraterrestrial intelligence so the
alien intelligence we should say the
alien intelligence might live on Alpha
centori but it might also live at a
different place in Ral space yeah it can
live right here on Earth it just has a
different frame that includes a very
different perception of the universe and
then because that Ru all space is very
large I
mean do we get to communicate with them
right that's yeah but it's also well one
uh thing is how different the perception
of the universe could be I think it
could be
bizarrely unimaginably completely
different and I mean one thing to
realize is even in kind of things I
don't understand well you know I'm I I
know about the kind of Western tradition
of understanding you know science and
all that kind of thing and you know you
talk to people who say well I you know
I'm really into some you know Eastern
tradition of this that and the other and
it's really obvious to me what how
things work I don't understand it at all
but you know it is not obvious I think
with this kind of realization that
there's these very different ways to
interpret what's going on in the
universe that kind of gives me at least
it doesn't help me to understand that
different interpretation but it gives me
at least more respect for the
possibility that there will be other
interpretations yeah it humbles you to
the possibility that like what is it
reincarnation or all all these like uh
Eternal occurrence with nature like just
these ideas yeah well you know the thing
that I realized about a bunch of those
things is that you know I've been sort
of doing my little survey of the history
of philosophy just trying to understand
you know what what can I actually say
now about some of the these things and
you realize that some of these Concepts
like the immortal Soul concept which you
know I remember when I was a kid and you
know it was kind of a lots of religion
bashing type stuff of people saying you
know well we know about physics tell us
how much does a soul weigh and people
are like well how can it be a thing if
it doesn't weigh anything right well now
we understand you know there is this
notion of what's in brains that isn't
the matter of brains and it's something
computational and there is a sense and
in fact it is correct that it is in some
sense Immortal because this pattern of
computation is something abstract that
is not specific to the particular
material of a brain now we don't know
how to extract it you know in our
traditional scientific approach but it's
still something where it isn't a crazy
thing to say there is something it
doesn't weigh anything that's a kind of
a silly question how much does it weigh
um well actually maybe it isn't such a
silly question in our model of physics
Because the actual computational
activity has has a consequence for
gravity and things but that's a very
subtle about mass and energy and so on
there could be a a what would you call
it a solatron
yes yes yes a particle that that somehow
contains sness yeah right well that's
what by the way that's what liet said
and you know one thing i' I've never
understood this you know libbets had
this IDE of monads and monadology and he
had this idea that that what exists in
the universe is this big collection of
monads
and that they that the only thing that
one knows about the monads is sort of
how they relate to each other which
sounds awfully like hypergraphs right
but liit had really lost me at the
following thing he said each of these
monads has a soul and each of them has a
Consciousness and it's like okay I'm out
of here I don't understand this at all I
don't know what's going on but I
realized recently that in his day the
concept that a thing could do something
could spontaneously do something that
was his only way of describing that and
so what I would now say is well there's
this just abstract rule that runs to
libbets that would have been you know in
1690 or whatever that would have been
kind of well it has a soul it has a
Consciousness um and so you know in a
sense it's it's like one of these
there's no new idea Under the Sun so to
speak that's you know that's a sort of a
version of of the same kinds of ideas
but couched in terms that are sort of
bizarrely different from the ones that
we would use today would you be able to
maybe play Devil's ADV it on the your
conception of Consciousness that uh like
the the two characteristics of it that
it's constrained and there's a single
threat of time is it possible the leness
was on to something
that the the basic atom discreet atom of
space has a Consciousness is is that um
so these are just words right but like
what what is there is there some sense
where Consciousness is much more
fundamental than you're making it seem I
know I mean that you know I think can
you construct a world in which it is
much more fundamental I think that okay
so the question would be is there a way
to think about kind of uh if we sort of
parse the universe down at the level of
atoms of space or something could we say
well so so that's really a question of a
different point of view a different
place in real space we're asking you're
asking the question could there be a
civilization that exists could there be
sort of uh conscious entities that
exists at the level of atoms of space
and what would that be like and I think
that comes back to this question of can
we you know what's it like to be a
cellular Automan type thing um I mean
it's it's you know I'm I'm not yet there
I don't know I mean I think that the
this is a and I I don't even know yet
quite how to think about this in the
sense that I was considering you know
I'm I never write fiction but I haven't
written it since I was like 10 years old
and my my fiction I I've made one
attempt which I sent to some science WR
to friends of mine and they told me it
was terrible so but um this is a long
time ago no this is recently recently
they said it was terrible that'd be
interesting to see you write a short
story based on the well it sounds like
it's already inspiring short stories by
or stories yeah right by science fiction
writers but but I think the the
interesting thing for me is you know in
the what does it what is it like to be
or whatever yeah how do you describe
that I mean it's like that's not a thing
that you describe in mathematics that
what is it like to be such and such well
see to me when you say what is it like
to be something presumes that you're
talking about a singular entity so yeah
like there there there's a some kind of
feeling of the The Entity the the stuff
that's inside of it and the stuff that's
outside of it and then that's when
Consciousness starts making sense but
but then um it seems like that could be
generalizable if you take some
subset of uh a cellular aoma you could
start talking about what does that
subset maybe feel but then you can I
think you could just take arbitrary
numbers of subsets like to me uh uh like
you and I uh individually are
consciousnesses but you could also say
the two of us together is a singular
conscious maybe maybe I'm not so sure
about that I think that the single
thread of time thing may be pretty
important and that as soon as you start
saying there are two different threads
of time that are our two different
experiences and then we have to say how
do they relate how are they sort of
entangled with each other I mean that
may be a different story of a thing that
isn't much like you know the the the
what do the ants you know what's it like
to be an ant you know where there's a
sort of more Collective view of the
world so to speak I don't know I think
that um I mean this is uh uh you know I
don't really have a good I mean you know
my my best thought is you know can we
turn it into a human story it's like the
question of you know when we try and
understand physics can we turn that into
something which is sort of a human
understandable narrative and now what's
it like to be a such and such you know
maybe the only medium in which we can
describe that is something like fiction
where it's kind of like you're telling
you know the life story in that in that
uh in that setting but I I'm this is
this is beyond what I've what I've yet
understood how to do yeah but it does
seem so like with human Consciousness
you know we're made up of cells and like
there there's a bunch of systems that
are
networked that work together that at
this at the human level feel like a
singular Consciousness when you take yes
and so maybe like an ant colony is just
too low level sorry an ant is too low
level maybe you have to look at the ant
colony yeah I agree like there's some
level at which it's a conscious being
and then if you go to the planetary
scale then maybe that's going too far so
there's a nice sweet spot for
Consciousness no I me I agree I think I
think the difficulty is that you know
okay so in sort of people who talk about
Consciousness yes one of the one of the
Terrible Things I've realized because
I've now interacted with with some of
this community so to speak some
interesting people who do that kind of
thinking but you know one of the things
I was saying to one of the leading
people in that area I was saying you
know uh that um you know it must be kind
of frustrating because it's kind of like
a poetry story that is many people are
writing poems but few people are reading
them yes so there are always these
different you know everybody has their
own Theory Of Consciousness and they are
very nonin sort of inter discussable and
and by the way I mean you know my own
approach to sort of the the question of
Consciousness as far as I'm concerned
I'm an applied Consciousness operative
so to speak because I don't really in a
sense the thing I'm trying to get out of
it is how does it help me to understand
what's a possible Theory of physics and
how does it help me to say how do I go
from this this incoherent collection of
things happening in the universe to our
definite perception and definite laws
and so on and it's sort of an an applied
version of Consciousness and and I think
the reason it sort of segs to a
different kind of topic but the reason
that um uh one of the things I'm
particularly interested in is kind of
what's the analog of Consciousness in
systems very different from brains and
so why is that matter
well you know this whole description of
this kind of uh uh well actually you
know what we we haven't talked about why
the universe exists so let's let's get
to why the universe exists and then we
then we can can talk about perhaps a
little bit about what these models of
physics kind of show you about other
kinds of things like molecular Computing
and so on yes but let's okay why does
the universe exist okay so we finally
sort of more or less set the stage we've
got this idea of this ruad of this
object that is made from following all
possible rules the fact that it's sort
of not just this incoherent mess it's
got all this entangled structure in it
and so on okay so what is this ruad well
it is the working out of all possible
formal systems so the the sort of the
question of why does the universe exist
its core question you kind of started
with is You've Got 2 plus 2 equal 4
you've got some other abstract result
but that's not actualized it's just an
abstract thing
and when we say we got a model for the
universe okay it's this rule you run it
and it'll make the universe but it's
like but but you know where's it
actually running what what what is what
is it actually doing right what is is it
actual or is it merely a formal
description of something okay so the
thing to realize with this with this the
the thing about the ruad is it's an
inevitable it is the entangled running
of all possible rules so you don't get
to say it's not like you're saying which
rule ad are you picking because it's all
possible formal rules it's not like it's
just um you know well actually it's only
footnote the only footnote it's an
important footnote is it's all possible
computational rules not hyper
computational rules that is it's running
all the rules that would be accessible
to a touring machine but is not running
all the rules that will be accessible to
a that can solve problems in finite time
that would take a touring machine
infinite time to solve so you can even
Alan touring knew this that you could
make oracles for touring machines where
you say a touring machine can't solve
the halting problem for touring machines
it can't know what will happen in any
touring machine after an infinite time
in any finite time but you could invent
a box just make a black box you say I'm
going to sell you an oracle that will
just tell you you know press this button
it'll tell you what the touring machine
will do after an infinite time you can
imagine such a box you can't necessarily
build one in the physical universe but
you can imagine such a box and so we
could say well in addition to so in this
ruad we're imagining that there is a
computational that at the end it's it's
running rules that are computational it
doesn't have a bunch of uh Oracle black
boxes in it you say well why not Well
turns out if there are Oracle black
boxes the ruad that is you can make a
sort of super ruad that contains those
Oracle black boxes but it has a
cosmological Event Horizon relative to
the first one they can't communicate in
other words you can you can end up with
what you end up happening what ends up
happening is it's it's it's like in the
physical Universe we in this causal
graph that represents the causal
relationships of different things you
can have an event horizon where there's
where the causal graph is disconnected
where the effect here an event Happening
Here does not affect an event happening
here because there's a disconnection in
the causal graph and that's what happens
in an event horizon and so the what will
happen between this kind of the ordinary
ruad and the hyper ruad is there is an
event horizon and you you know we in our
ruad will just never know that there is
they're just separate things they're not
they're not connected maybe I'm not
understanding but just because we can't
observe
it uh why does that mean it doesn't
exist um might exist but it does it's
not clear what it it's so what so to
speak whether it exists you know what
we're trying to understand is why does
our universe exist we're not trying to
ask the question what uh you know it's
let me say another thing let me make a a
meta comment okay which is that that I
have not thought through this hyper ruad
business properly so I'm I'm I can't the
the the the hyper ruad is referring to a
ruad in which hyper comput is possible
that's correct yes so like what the that
footnote the footnote to the footnote is
we're not sure why this is important
yeah that's right so let's let's ignore
that okay it's already abstract enough
okay so so okay so the the one question
is we have to say if we're saying why
does the universe exists one question is
why is it this universe and Not Another
Universe yeah okay so the the important
point about this ruad idea is that it's
in the ruad are all possible formal
systems so there's no choice being made
there's no there's no like oh we picked
this particular universe and not that
one that's the first thing the second
thing is the that we have to ask the
question so so you say why does 2+ 2al 4
exist that's not really that is a thing
that necessarily is that way just on the
basis of the meaning of the term two and
plus and equals and so on right so the
thing is that this this ruad object is
in a sense a necessary object it is just
a thing that is the consequence of
working out the consequence of the
formal definition of things you don't it
is not a thing where you're saying and
this is picked as the particular thing
this is just something which
necessarily is that thing because of the
definition of what it means to have
computation the r
it's a formal system
yes but does it exist ah well uh where
are we in this whole thing we are part
of this ruad and so our so there is no
sense to say does 2 + 2 equals 4 exist
well that's that's in some sense it
necessarily exists it's a necessary
object it's not a thing that way you can
ask
uh you know it's it's usually in in
philosophy there's a sort of Distinction
made between uh you know necessary
truths contingent truths analytic
propositions synthetic propositions
there are a variety of different
versions of this there are things which
are necessarily true just based on the
definition of terms and there are things
which happen to be true in our universe
but we we we don't exist in roal space
we that's one of the coordinates that
Define our existence right well okay so
so yes yes but this ruad is the set of
all possible Ral coordinates so what
we're saying is it contains that so what
we're saying is we exist as okay so our
perception of what's going on is we're
at a particular place in this ruad and
we are concluding certain things about
how the universe works based on that M
but the question is do we understand you
know is there something where we say so
so why does it work that way well the
answer is I think it has to work that
way because this there isn't this ruad
is a necessary object in the sense that
it is a purely formal object just like 2
plus 2al 4 it's not an object that was
made of something it's an object that is
just an expression of the necessary
collection of formal relations that
exist and so then the issue is can we in
our experience of that is it you know
can we have tables and chairs so to
speak in that just by virtue of our
experience of that necessary thing and
you know what people have generally
thought and honestly that that I don't
know of a lot of discussion of this why
does the universe exist question it's
been a very you know I've been surprised
actually at how little I mean I think
it's one of these things that's really
uh kind of far out there but the thing
that that is you know the surprise here
is that all possible formal rules when
you run them together and that's the
critical thing when you run them
together they produce this kind of
entangled structure that has a definite
structure it's not just a you know a
random arbitary thing it's a thing with
definite structure and that structure is
the thing when we are embedded in that
structure when when any you know the an
entity embedded in that structure
perceives something which is then we can
interpret as physics and things like
this so in other words we don't have to
ask the question the the the why does it
exist it necessarily exists I'm missing
this part why does it necessarily exist
okay let me like you need to have it if
you want to formalize the relation
between entities but why
did why do you need to have relations
okay okay so so let's say you say um
well it's like why does math have to
exist okay that's fair question yeah
okay fair question um let's see I think
the thing to think about is the
existence of mathematics is something
where given a definition of
terms what follows from that definition
inevitably follows so now you can say
why Define any terms but in a sense the
well that that's okay so the the
definition of terms I mean I think the
way to think about this let me see so
like concrete
terms well they're not very concrete I
mean they're just things like you know
um logical
or but that's a thing that's a powerful
thing well it's a it's a yes okay but
it's it's a the the point is that it is
not a thing of a you know people imagine
their is I don't know the uh uh you know
an elephant or something or the you know
elephants are presumably not necessary
objects they are they happen to exist as
a result of kind of biological evolution
and whatever else but the the thing is
that in some sense that there is it is a
different kind of thing to say does plus
exist the the it is not it's not not
like an elephant so a plus is seems more
fundamental more basic than an elephant
yes but you can imagine a world
without Plus or anything like it like
why do formal things that are
discret that can be used to reason have
to exist or well okay so why okay so
that then the question is but the whole
point is computation we can certainly
imagine computation that is we can
certainly say there is a formal system
system that we can construct abstractly
in our minds that is computation and
that that's the um uh and you know we
can we can imagine it right now the
question is um is it is that formal
system once we exist as observers
embedded in that formal system that's
enough to have something which is like
our universe yeah and so then the then
what you're kind of asking is perhaps is
why I mean the point is we definitely
can imagine it there's nothing that says
that we we're not saying that there's
it's sort of inevitable that that is a
thing that we can imagine we don't have
to ask does it exist we're just it is
definitely something we can imagine now
that's then we have this thing that is a
formally constructible thing that we can
imagine and now we have to ask the
question what you know given that formly
constructible thing what is uh what
consequences does that if we were to
perceive that formally con if if we were
embedded in that formally constructible
thing what will we be perceive about the
world and we would say we perceive that
the world exists because we are we are
seeing all of this mechanism of all
these things happening and but that's
something that is just a feature of it's
it's it's something where we are see
another way of asking this I'm trying
trying to get at I understand why it
feels like this uh ruad is necessary
mhm but maybe it's just me being human
but it feels like then you should be
able to not us but somehow step outside
of the ruad like what's outside the ruad
well the ruad is all formal systems so
there's nothing because but that's what
a human would say I know that's what
human would say cuz we're used to the
idea that there are there's but the
whole point is that by the time it's all
possible formal
systems it it's it's like it is all
things you can
imagine but no all computations you can
imagine but like we don't well so the
isue is code okay so so that's a that's
a fair question is it possible to encode
uh all I mean once we is is there
something that is isn't what we can
represent formally right that is that is
there something that um and that's I
think related to the hyper ruad footnote
so to speak of which I'm afraid that the
you know one of the things sort of
interesting about this is you know there
has been some discussion of this in
Theology and things like that um but uh
which I don't necessarily understand all
of um but the the the key sort of new
input is this idea that all possible
formal systems it's like you know if you
make a world people say well you make a
world with a particular in a particular
way with particular rules but no you
don't do that you can make a world that
deals with all possible rules and then
merely by virtue of living in a
particular place in that world so to
speak we have the perception we have of
of what the world is like now I have to
say the the um uh it's sort of
interesting because i' I've you know I
wrote this piece about this and I I you
know this philosophy stuff is not super
easy and I I've uh um I as I'm as I'm
talking to you about it and I actually
haven't you know people have been
interested in lots of different things
we've been doing but this why does the
universe exist has been I would say one
of the one of the ones that you would
think people would be most interested in
but actually I think they're just like
oh that's just something complicated
that that um so so I haven't I haven't
explained it as as much as I've
explained a bunch of other things and I
have to say I think I I think I may be
missing a couple of pieces of that
argument that um uh would be so so it's
kind of a like well you are your um
conscious being is comput entially
bounded so you're missing having written
quite a few articles yourself you you're
now missing some of the pieces yes the
limitation of Being Human right one of
the consequences of this why the UN why
the universe exists thing and this kind
of concept of ruy ads and and uh you
know places in there representing our
perception of the universe and so on one
of the weird consequences is if the
universe exists mathematics must also
exist MH and that's a weird thing
because mathematics people have been
very confused including me have been
very confused about um uh the the the
question of of kind of what uh what is
the foundation of mathematics what is
what kind of a thing is mathematics is
mathematics something where we just
write down aums like uid did for
geometry and we just build the structure
and we could have written down different
axioms and we'd have a different
structure or is it something that has a
more fundamental sort of truth to it and
I have to say this is one of these cases
where I've I've long believed that
mathematics has a great deal of
arbitrariness to it that there are
particular axioms that kind of got
written down by the Babylonians and uh
you know that's what we've ended up with
the mathematics that we have and I have
to say actually my my wife has been
telling me for 25 years she was a
mathematician she's been telling me
you're wrong about the foundations of
mathematics and and you know I'm like no
no no I know what I'm talking about and
finally she's she's much more right than
than I've been so it's um it's one of so
so I mean her sense and your sense are
we just uh so this is to the question of
meta mathematics are we just kind of on
a trajectory through Ral space except in
mathematics through a trajectory of
certain kind of I think that's partly
the the idea so so I think that the
notion is this so 100 years ago a little
bit more than 100 years ago well people
have been doing mathematics for ages but
then in the in the late 1800s people
decided to try and formalize Mathematics
and say you know it is mathematics is
you know we're going to break it down
we're going to make it like logic we're
going to make it out of out of sort of
fundamental Primitives and that was
people like frager and piano and Hilbert
and so on and they kind of got this idea
of let's do kind of uclid but even
better let's just make everything just
in terms of this sort of symbolic axioms
and then build up mathematics from that
M and that you know they thought at the
time as soon as they get these symbolic
axioms that they made the same mistake
the kind of computational irreducibility
mistake they thought as soon as we've
written down the axim then it'll just
we'll just have a machine kind of a
super Mathematica so to speak that can
just grind out all true theorems of
mathematics that got exploded by
girdle's theorem which is basically the
story of computational irreducibility
it's that even though you know those
underlying rules you can't deduce all
the consequences in any finite way and
so so that was but now the question is
okay so they broke mathematics down into
these axioms and they say now you build
up from that so what I'm increasingly uh
coming to realize is that's similar to
saying let's take a gas and break it
down into molecules there's gas laws
that are the large scale structure and
so on that we human hum are familiar
with and then there's the underlying
molecular Dynamics and I think that the
axiomatic level of mathematics which we
can access with automated theorem
proving and proof assistance and these
kinds of things that's the molecular
dynamics of mathematics and occasionally
we see through to that molecular
Dynamics we see undecidability we see
other things like this one of the things
I've always found very mysterious is
that girdle's theorem shows that there
are sort of things which cannot be
finitely proved in mathematics there are
proofs of arbitrary length infinite
length proofs that you might need but in
Practical mathematics mathematicians
don't typically run into this they just
happily go along doing their mathematics
and I think what's actually happening is
that what they're doing is they're
looking at this they are essentially
observers in metam mathematical space
and they are picking a reference frame
in metam mathematical space and they are
computationally bounded observers in
metam mathematical space which is
causing them to deduce that the laws of
meta mathematics and the laws of
mathematics like the laws of fluid
mechanics are much more understandable
than this underlying molecular Dynamics
and so what gets really bizarre is
thinking about kind of the analogy
between meta mathematics this idea of of
you exist in this kind of uh um in the
sort of space of possible um in this
kind of mathematical space where the
where the individual kind of uh point in
the in the mathematical space are
statements in mathematics and they're
connected by proofs where one statement
you know you take a couple of different
statements you can use those to prove
some other statement and you've got this
whole network of of proofs that's the
kind of causal network of mathematics of
what can prove what and so on and you
can say at any moment in the history of
of a mathematician of a single
mathematical Consciousness you are in a
single kind of slice of this kind of
meta mathematic space you you know a
certain set of mathematical statements
you can then deduce with proofs you can
deduce other ones and so on you're kind
of gradually moving through meta
mathematical space and so it's kind of
the view is that the reason that
mathematicians perceive mathematics to
have the sort of integrity and lack of
kind of undecidability and so on that
they do is because they like we as as
observers of the physical Universe we
have these limitations associated with
computational boundedness single threat
of time consciousness limitations
basically that the same thing is true of
mathematicians perceiving sort of meta
mathematical space and so what's
happening is that when you look at if if
you look at one of these formalized
mathematics systems something like you
know Pythagoras's Theorem it'll be it'll
take oh I don't know uh what is it maybe
10,000 individual little steps to prove
Pythagoras's Theorem and one of the
bizarre things that's sort of an
empirical fact that I'm trying to
understand a little bit better if you
look at different proof of Sy if you
look look at different formalized
mathematics systems they actually have
different axioms underneath but they can
all prove Pythagoras's Theorem and so in
other words it's a little bit like what
happens with gases we can have air
molecules we can have water molecules
but they still have fluid dynamics both
of them have fluid dynamics and so
similarly at the level that mathematics
that mathematicians care about
mathematics it's way above the molecular
Dynamics so to speak and there are all
kinds of weird things like for example
one thing I was realizing recently is
the the quantum theory of mathematics
that it's a very bizarre idea but um
basically when you prove what is you
know a proof is you got one statement in
mathematics you go through other
statements you eventually get to a
statement you're trying to prove for
example that's a path path in metam
mathematical space and that's a single
path a single proof is a single path but
you can imagine there are other proofs
of the same result there are a bundle of
proofs there's this whole set of
possible proof you can think of it as
branching similar to the quantum
mechanics model that you talk exactly
and so and then there's some invariance
that you can formalize in the same way
that you can for the quantum mechanical
right so the question is in in proof
space you know as you start thinking
about multiple proofs are there analoges
of for example destructive interference
of multiple proofs so here's a bizarre
idea it's just a couple of days old so
not not yet fully formed but um as you
try and do that when you have two
different proofs it's like two photons
going in different directions you have
two proofs which at an intermediate
stage are incompatible and that's kind
of like destructive interference is it
possible for this to instruct the
engineering of automated proof systems
absolutely I mean as a practical matter
I mean the you know this whole question
in fact Jonathan gorard has a nice
theistic for automated theorem provs
that's based on our physics project that
is looking for essentially using kind of
um using energy in our models energy is
kind of the level of activity in this
hypergraph and so there sort of a
heuristic for automated theorem proving
about how do you pick which path to go
down that is based on essentially
physics um and I mean the thing that
that gets interesting about this is is
the way that one can sort of have the
interplay between like for example a
black hole what is a black hole in metam
mathematics so the answer is what is
black hole in physics a black hole in
physics is where in the simplest form of
black hole time ends that is all you
know everything is is crunched down to
the space time Singularity and
everything just ends up at that
Singularity so in our models and that's
a little hard to understand general
relativity with continuous mathematics
and what does Singularity look like in
our models it's something very pragmatic
it's just you're applying these rules
time is moving forward and then there
comes a moment where the rules no rules
apply so time stops it's kind of like
the universe dies the you know the the
nothing happens in the universe anymore
well in mathematics that's a decidable
theory that's a theory so theories which
have undecidability which are things
like arithmetic set theory all the
serious models theories in mathematics
they all have the feature that there are
proofs of arbitrary long length in
something like Boolean algebra which is
a decidable theory there are you know
any question in Boolean algebra you can
just go crunch crunch crunch and in a
knowing number of steps you can answer
it you know satisfiability you know
might be hard but it's still a bounded
number of steps to answer any
satisfiability problem and so that's the
the not of a black hole in physics where
time stops that's the the that's
analogous to in mathematics where there
aren't infinite length proofs where when
in physics you know you can wander
around the universe forever if you don't
run into a black hole if you run into a
black hole and time stops you're done
and it's the same thing in mathematics
between decidable decidable theories and
undecidable theories that's a that's an
example and I think we're sort of the
the the attempt to understand so so
another question is kind of what is the
what is the general ativity of uh of
metam mathematics what is the bulk
theory of metam mathematics so in the
literature of mathematics there are
about three million theorems that people
have have published and those represent
it's kind of on this it's like like on
the earth we would be you know uh you
know we've put cities in particular
places on the Earth but yet there is
ultimately you know we know the Earth is
roughly spherical and there's an
underlying space and we could just talk
about you know the world of space in
terms of where our cities happen to be
but there's actually an underlying space
and so the question is what's that for
metam mathematics and as we kind of
explore what is for example for
mathematics which is always likes taking
sort of abstract limits so an obvious
abstract limit for mathematics to take
is the limit of the future of
mathematics that is what will be you
know the ultimate structure of
mathematics yeah and one of the things
that's an empirical observation about
mathematics that's quite interesting is
that a lot of theories in one area of
mathema ma algebraic geometry or
something might have they play into
another area of mathematics that that
that same the same kind of fundamental
construct seem to occur in very
different areas of mathematics and
that's structurally captured a bit with
category Theory and things like that but
I think that there's probably an
understanding of this metam mathematical
space that will explain why different
areas of mathematics ultimately sort of
map into the same thing and and I mean
you know my little challenge to myself
is what's time dilation in um uh in meta
mathematics in other words as you as you
basically As you move around in this
mathematical space of possible
statements um you know what's how does
that moving around it's basically what's
happening is that as you move around in
the space of mathematical statements
it's like you're changing from algebra
to Geometry to whatever else and you're
trying to prove the same theorem but as
you try if you keep on moving to these
different places it's slower to prove
that theorem because you keep on having
to translate what you're doing back to
where you started from and that's kind
of the beginnings of the analog of time
dilation in metam mathematics plus
there's probably fractional dimensions
in this space as well oh this space is a
very messy space this space is much
messier than physical space I mean even
in even in the models of physics
physical space is is very tame compared
to branchial space and Ral space um I
mean the mathematical structure you know
branchial space is probably more like
Hilbert space but it's a rather
complicated Hilbert space and Ral space
is more like this weird Infinity
groupoid story of growth and Deacon and
you know I can explain that a little bit
because in you know in in
metamathematical space a a path in metam
mathematical space is a is a a path
between two statements is a way to get
by proofs is to way to find a proof that
goes from one statement to another and
so one of the things you can do you can
think about is you've got between
statements you've got proofs and they
are paths between statements okay so now
you can go to the next level and you can
ask what about a mapping from one proof
to another and so that's in in category
Theory that's kind of a higher category
notion of higher categories where you're
where you're mapping not just between
not just between objects but you're
mapping between the mappings between
objects and so on and so you can keep
doing that you can keep saying higher
order proofs I want mappings between
proofs between proofs and so on and that
limiting structure by the way one thing
that's very interesting is Imagine in
proof space you've got these two proofs
and the question is what is the topology
of proof space in other words if you
take these two paths can you
continuously deform them into each other
or is there some big hole in the middle
that prevents you from continuously
deforming them one into the other it's
kind of like you know when you when you
think about some I don't know some
puzzle for example you're moving pieces
around on some puzzle and you can think
about the space of possible states of
the puzzle and you can make this graph
that shows from one state of the puzzle
to another state of the puzzle and so on
and sometimes you can easily get from
one state to any other state but
sometimes there'll be a hole in that
space and there'll be you know you
always have to go around the Securus
route to get from here to there there
won't be any direct way that's kind of a
a question of of whether there's sort of
an obstruction in the space and so the
question is in proof space What is the
what are you know what does it mean if
there's an obstruction in proof space
yeah I don't even know what obstruction
means in proof space cuz it for it to be
an obstruction should be reachable some
other way from some other place right so
this is like un unreachable part of the
graph no it's not just an unreachable
part it's a part where there are paths
that go one way there are paths that go
the other way and this question of
homotopia in mathematics is this
question can you continuously deform you
know from one path to another path or do
you have to go in a in a jump so to
speak so so it's like if you're going
around a sphere for example if you're
going around a I don't know a cylinder
or something you can wind around one way
and you can there's no there paths where
you can where you can easily deform One
path into another because it's just sort
of sitting on the same side of the
cylinder but when you've got something
that winds all the way around a cylinder
you can't continuously deform that down
to a point because it's it's stuck
wrapped around my intuition about proof
spaces you should be able to deform it I
mean that cuz then otherwise it doesn't
even make sense cuz if the topology
matters of the way you move about the
space that I don't even know what that
means well what it would mean is that
you would have one way of doing a proof
of something over here in algebra and
another way of doing a proof of
something over here in geometry and
there would not be an intermediate way
to map between those proofs but how
would that be possible if they start at
the same place and end of the same place
well it's the same thing as as you know
we've got points on a you know if if
we've got paths on a cylinder I
understand how it works in physical
space but it just doesn't it feels like
proof space shouldn't have that okay I
mean I'm not sure I don't know we'll
know very soon because we get to do some
experiments this is the great thing
about this stuff is that in fact you
know I'm in the next few days I hope to
do a bunch of experiments on this so so
you're playing with like proofs in in
this kind of space yes yes I mean so so
you know this is toy you know theories
and you know we've got good so so this
kind of segue to perhaps another thing
which is this whole idea of multicomp
computation so this this um is another
kind of bigger idea that so okay this
has to do with how do you make models of
things and it's going to it's um so I
I've sort of claimed that there've been
sort of four epochs in the history of
making models of things and um um and
this multicomp computation thing is is
the fourth is a new Epoch what are the
first three the first one is is back in
Antiquity ancient Greek times people
were like what's the universe made of oh
it's made of you know everything is
water phes you know or everything is
made of ATS it's sort of what are things
made of or you know there are these
Crystal spheres that represent where the
planets are and so on it's like a
structural idea of how the universe is
constructed there's no real notion of
Dynamics it's just what is the universe
how is the universe made then we get to
the 1600s and we get to the sort of
revolution of mathematics being
introduced into physics and then we have
this kind of idea of you write down some
equation the what happens in the
universe is the solving of that equation
time enters but it's usually just a
parameter we just can you know sort of
slide it back and forth and say Here's
here's where it is okay then we come to
this kind of computational idea that I
kind of uh started really pushing in the
in the 19 early 1980s as a result you
know the things we were talking about
before about complexity that was my
motivation but the bigger story was the
story of kind of computational models of
things and the big difference there from
the mathematic maal models is in
mathematical models there's an equation
you solve it you got kind of slide time
to the place where you want it in
computational models you give the rule
and then you just say go run the rule
and time is not something you get to
slide time is something where it just
you run the rule time goes in steps and
that's how you work out what how the
system behaves you don't time is not
just a parameter time is something that
is about the running of these of these
rules and so there's this computational
irreducibility you can't jump ahead in
time but there's still important thing
is there's still one thread of time it's
still the case you know the cellular
automatan State then it has the next
state and the next state and so on the
thing that is kind of we sort of tipped
off by quantum mechanics in a sense
although it it actually feeds back even
into relativity and things like that
that there are these multiple threads of
time and so in this multic computation
Paradigm the kind of idea is instead of
there being the single thread of time
there are these kind of distributed
asynchronous threads of time that are
happening and the thing that's sort of
different there is if you want to know
what happened if you say what happened
in the system in the case of the
computational Paradigm you just say well
after a thousand steps we got this
result right but in the multic
computational Paradigm after a thousand
steps not even clear what a thousand
steps means because you got all these
different threads of time but there is
no State there's all these different
possible you know there's all these
different paths and so the only way you
can know what happened is to have some
kind of Observer who is saying here's
how to parse the results of what was
going on right but that Observer is
embedded and they don't have a complete
picture so in the case of physics that's
right yes and in the but that's but so
the idea is that in this multic
computation setup that it's this idea of
these multiple threads of time and
models that are based on that and this
is similar to what people think about in
non-deterministic computation so you
have a touring machine usually it has a
definite state it follows another state
it follows another state but typically
what people have done when they've
thought about these kinds of things is
they've said well there are all these
possible paths a nondeterministic
touring machine can follow all these
possible paths but we just want one of
them we just want the one that's the
winner that factors the number or
whatever else um and similarly you know
it's the same story in logic programming
and so on but we say we've got this goal
find us a path to that goal I just want
one path then I'm happy or theorem
proving same story I just want one proof
and then I'm happy what's happening in
multic computation in physics is we
actually care about many paths and well
there is a case for example
probabilistic programming is a version
of multic computation in which you're
looking at all the paths you're just
asking for probabilities of things um
but in a sense in physics we're taking
different kinds of samplings for example
in quantum mechanics we're taking a
different kind of sampling of all these
multiple paths um but the thing that is
notable is that when you are when you're
an observer embedded in this thing etc
etc etc uh with various other sort of
footnotes and so on it is inevitable
that the thing that you parse out of
this system looks like General and
quantum mechanics um in other words that
just by the very structure of this
multic computational setup it inevitably
is the case that you have certain
emergent laws now why is this perhaps
not surprising in thermodynamics and
stati mechanics there are sort of
inevitable emergent laws of sort of gas
dynamics that are independent of the of
the details of the molecular Dynamics
sort of the same kind of thing but I
think what happens is what's a sort of a
funny thing that I just been
understanding very recently is when when
I kind of introduced this whole sort of
computational Paradigm complexity is
thing back in the 80s it was kind of
like a big Downer because it's like
there's a lot of stuff you can't say
about what systems will do and then what
I realized is and then you might say now
we've got multic computation it's even
worse you know it isn't just one thread
of time that we can't explain it's all
these threads of time we can't explain
anything but the following thing happens
because there is all this irreducibility
and any detailed thing you might want to
answer it's very hard to answer but when
you have an observer who has certain
characteristics like computational
boundedness sequentiality of time and so
on that Observer only samples certain
aspects of this incredible complexity
going on in this multic computational
system and that Observer is sensitive
only to some underlying core structure
of this multicomp computational system
there is all this irreducible
computation going on all these details
but to that kind of Observer what's
important is only the the core structure
of multicomp computation which means
that Observer observes comparatively
simple laws and I think it is inevitable
that that Observer observes laws which
are mathematic structured like general
relativity and quantum mechanics which
by the way are the same law in our in
our model of physics so that's an
explanation why there are simple laws
that explain a lot for this Observer
potentially yes but what the the place
where this gets really interesting is
there are all these fields of science
where people have kind of gotten stuck
where they say we'd really love to have
a physics like theory of Economics we'd
really love to have a physics like law
in linguistics you got to talk about
molecular biology here okay so where
where where does multic computation come
in for biology economics is super
interesting too but biology okay let's
talk about that so let's talk about
chemistry for a second okay so I mean I
have to say you know this is it's such a
weird business for me because you know
there these kind of paradigmatic ideas
and then the actual applications and
it's like I've always said I I know
nothing about chemistry I learned all
the chemistry I know you know the night
before some exam when I was 14 years old
but but I've actually learned a bunch
more chemistry and in in wol from
language these days we have really
pretty nice symbolic representation of
chemistry and in understanding the
design of that I've actually I think
learned a certain amount of chemistry
though if you quizzed me on sort of
basic high school chemistry I would
probably totally fail but um uh but but
okay so what is chemistry I mean
chemistry is sort of a story of you know
chemical reactions are like you've got
this particular chemical it's
represented as some graph of you know
these uh these are this configuration of
molecules with these bonds and so on and
a chemical reaction happens you've got
these sort of two graphs they interact
in some way you get another graph or
multiple other graphs out so that's kind
of the the the the the sort of the the
abstract view of what's happening in
chemistry and so when you do a chemical
synthesis for example you are given
certain sort of these are possible
reactions that can happen and you're
asked Can you piece together this a
sequence of such reactions a sequence of
such sort of axiomatic reactions usually
called name reactions in chemistry can
you piece together a sequence of these
reactions so that you get out at the end
this great molecule you were trying to
synthesize and so that's a story very
much like theorem proving and people
have done actually they started in the
1960s looking at at kind of the theorem
proving approach to that although it
didn't really it didn't it didn't uh was
sort of done too early I think um but
anyway so that's kind of the view is
that that chemistry chemical reactions
are the story of of all these different
sort of Paths of possible things that go
on okay let's let's go to an even lower
level let's say instead of asking about
uh which species of molecules we're
talking about let's look at individual
molecules and let's say we're looking at
individual molecules and they are having
chemical reactions and we're building up
this big graph of all these reactions
that are happening okay so so then we've
got this big graph and by the way that
big graph is incredibly similar to these
hypergraph rewriting things um in fact
in the underlying theory of multic
computation there are these things we
call token event graphs which are
basically you've broken your state into
tokens like in the case of a hypergraph
you've broken it into hyperedges and
each event is just consuming some number
of tokens and producing some number of
tokens yeah but then you have to there's
a lot of work to be done on update
rules in terms of what they actually are
for chemistry yeah what they are for our
observed chemistry yes indeed yes indeed
and we've been working on that actually
because we have this beautiful system in
in wol language for representing
chemistry symbolically so we actually
have you know this is a this is an
ongoing thing to actually figure out
what they are for some practical cases
does that require human injection or can
it be automatically discovered these
update rules well if we could do Quant
chemistry better we could probably
discover them automatically but I think
in in in reality right now it's like
there are these particular reactions and
and really to understand what's going on
we're probably going to pick a
particular subtype of chemistry and just
because because let me explain where
this is going the the place the here's
here's where this is going so got this
whole network of all these molecules
having all these reactions and so on and
this is some whole multicomp
computational story because each each uh
sort of chemical reaction event is its
own separate event we're we're saying
they all happen asynchronously we're not
describing in what order they happen you
know maybe that order is governed by
some quantum mechanics thing doesn't
really matter we're just saying they
happen in some order and then we ask
what is the what what's the you know how
do we think about this system well this
thing is some kind of big multicomp
computational system the question is
what is the chemical Observer and one
possible chemical Observer is all you
care about is did you make that
particular drug molecule you're just
asking you know for the One path another
thing you might care about is I want to
know the concentration of each species
right I want to know you know at every
stage I'm going to solve the
differential equations that represent
the concentrations and I want to know
what those all are but there's more
because when and it's kind of like
you're going Below in statis mechanics
there's kind of all these molecules
bouncing around and you might say uh
we're just going to ignore we're just
going to look at the aggregate uh
densities of certain kinds of molecules
but you can look at a lower level you
can look at this whole graph of possible
interactions and so the kind of the idea
would be what you know is the only
chemical Observer one who just cares
about overall concentrations or can
there be a chemical Observer who cares
about this network of what happened and
so that the the question then is so so
let me give an analogy so this is where
I think this is potentially very
relevant to molecular molecular biology
and molecular Computing uh when we think
about a computation usually we say it's
input it's output we we you know well
chemistry we say there's this input
we're going to make this molecule as the
output but what if what we actually
encode what if our computation whatever
the thing we care about is some part of
this Dynamic Network what if it isn't
just the input and the output that we
care about what if there's some dynamics
of the network that we care about now
imagine you're a chemical Observer what
is a chemical Observer well in molecular
biology there are all kinds of weird
sorts of observers there are membranes
that exist that have you know different
kinds of molecules that combin to them
things like this it's not obvious that
the from a human scale we just measure
the concentration of something is the
relevant story we can imagine that for
example when we look at this whole
network of possible reactions we can
imagine you know at a physical level we
can imagine well what was the actual
momentum direction of that of that
molecule what was which we don't pay any
attention to when we just talking about
chemical concentrations what was the
orientation of that molecule these kinds
of things and so here's here's the place
where I'm I have a little suspicion okay
so one of the questions in biology is
what matters in biology and that is you
know we have all these chemical
reactions we have all these all these
molecular processes going on in in you
know in biological systems what matters
and you know one of the things is to be
able to tell what matters well so a big
story of the what matters question was
what happened in genetics in 1953 when
DNA when it was figured out how DNA
worked because before that time you know
genetics have been all these different
effects and complicated things and then
it was realized ah there's something new
a molecule can store information which
wasn't obvious before that time a single
molecule can store information so
there's a place where there can be
something important that's happening in
molecular biology and it's just in the
sequence that's storing information in a
molecu so the possibility now is Imagine
This Dynamic Network this uh you know
causal graphs and multi-way causal
graphs and so on that represent all of
these different reactions between
molecules what if there is some aspect
of that that is storing information
that's relevant for molecular biology in
the dynamic aspect of that yes that's
right so the it's similar to how the
structure of a DNA molecule stores
information it could be the Dynamics of
the system some stores information and
this kind of process might allow you to
give uh predictions of what that would
be well yes but but also imagine that
you're trying to do uh for example
imagine you're trying to do molecular
computation okay you might think the way
we're going to do molecular computation
is we're just going to run the thing
we're going to see what came out we're
going to see what molecule came out this
is saying that's not the only thing you
can do there is a different kind of
chemical Observer that you can imagine
constructing which is somehow sensitive
to this Dynamic Network exactly how that
works how we make that measurement I
don't know but I have few ideas but but
um that that's what's important so to
speak and that that means and by the way
you can do the same thing even for
touring machines you can say if you have
a multi-way touring machine you can say
how do you compute with a multi-way
touring machine you you can't say well
we got this input and this output
because the thing has all these threads
of time and it's got lots of outputs and
so then you say well what does it even
mean to be a universal multi-way touring
machine I don't fully know the answer to
that but it has it's an interesting idea
it freak touring out for sure because
then uh the Dynamics of the the the
trajectory of the computation matters
yes yes I mean but but the thing is that
that so this is again a story of what's
the Observer so to speak in chemistry
what's what's the Observer there now to
give an example of of where that might
matter very uh sort of present day
example is in Immunology
um where you know we have whatever it is
you know 10 billion different kinds of
antibodies that are you know all these
different shapes and so on we have I a
trillion different kinds of t- cell
receptors that we can that we produce
and you know the the traditional theory
of Immunology is this clonal selection
Theory where we are constantly producing
randomly producing all these different
antibodies and as soon as one of those
binds to an antigen then that one gets
Amplified and we produce more of that
antibody and so on um back in the 1960s
um immunologist called Neils yo who was
the guy who invented monoclonal
antibodies various other things um kind
of had this network theory of the immune
system where it would be like well we
produce antibodies but then we produce
antibodies to the antibodies anti-
antibodies and we produce anti-
anti-antibodies and we get this whole
dynamic network of interactions between
different immune system cells and that
was that that was kind of a qualitative
Theory at that time and it it's I've
been a little disappointed because I've
been studying Immunology a bit recently
and I I knew something about this like
35 years ago or something and I knew you
know I'd read a bunch of the books and I
talked to a bunch of the people and so
on and it was like an emerging
theoretical Immunology world and and
then I look at the books now and they're
very thick because they've got you know
there's just a ton knowing about
immunology and you know all these
different Pathways all these different
details and so on but the theoretical
section seem to have shrunk um and so
it's um so the question is what you know
for example immune memory where is the
where does the immune memory reside is
it actually some cell sitting in our
bone marrow that is you know living for
the whole of Our Lives that's going to
spring into action as soon as we're
showing the same antigen or is it
something different from that is it
something more Dynamic is it something
more like some network of interactions
between these different kinds of immune
system cells and so on and it's known
that there are plenty of interactions
between te- cells and you know there's
plenty of Dynamics but what the
consequence of that Dynamics is is not
clear and to have a qualitative theory
for that doesn't doesn't seem to exist
in fact I was just just been trying to
study this so I'm quite incomplete in my
study of these things but I was a little
bit taken aback because I I've been
looking at these things and it's like
and then they get to the end where they
have the most advanced theory that
they've got and it turns out it's a
cellular automatan
Theory it's like U okay well at least I
understand that theory yeah um but but
uh you know I think that the possibility
is that in um uh this is a place where
if you want to know you know explain
roughly how the immune system works it
ends up being this sort of dynamic
Network and then the the you know the
immune Consciousness so to speak The
Observer ends up being something that
you know in the end it's kind of like
does the human get sick or whatever but
it's a it's something which is a
complicated story that relates to this
whole sort of dynamic Network and so on
and I think that's another place where
this kind of notion of uh where where I
think multic computation has the
possibility see one of the things okay
you can end up with something where yes
there is a general relativity in there
there but it turns out but it may turn
out that the Observer who sees general
relativity in the immune system is an
observer that's irrelevant to what we
care about about the immune system I
mean it could be yes there is some
effect where you know there's some you
know time dilation of tea cells
interacting with whatever but it's like
that's an effect that's just irrelevant
and the thing we actually care about is
things about you know what happens when
you have a vaccine that goes into some
place in shape space and you know how
does that affect other places in shape
space and how does that spread you know
what's the what's the analog of the
speed of light in shape space for
example that's an that's an important
issue if you have one of these Dynamic
theories it's like you you know you you
poke into shape Space by having you know
let's say a vaccine or something that
has a particular configuration in shape
space how how quickly as this Dynamic
Network spreads out how quickly do you
get sort of other antibodies in
different places in shape space things
like that when you say shape space you
mean the shape of the molecules or the
and then so this is like U could be
deeply connected to the protein and
multiprotein folding all of that kind of
stuff so to be able to say something
interesting about the the dance of
proteins that exactly then actually has
an impact
on um helping develop drugs for example
or has an impact on virology Immunology
helping the big thing is you know when
we think about molecular biology the um
uh you know what what is the qualitative
way to think about it you know in other
words is it chemical reaction networks
right is it you know genetics you know
DNA big you know big news it's kind of
there's a digital aspect to the whole
thing you know what is the qualitative
way to think about how things work in
biology um you know when we think about
I don't know some phenomenon like aging
or something is a big complicated
phenomenon which just seems to to have
all these different tentacles is it
really the case that that can be thought
about in some you know without DNA when
people were describing you know genetic
phenomena they were you know dominant
recessive this that and the other it got
very very complicated and then people
realized oh it's just you know and and
what is a gene and so on and so on and
so on then people realize it's just Bas
Pairs and there's this digital
representation and so the question is
what is the overarching representation
that we can now start to think about
using AIC biology I don't know how this
will work out and this is again one of
these things where and and the place
where that gets important is you know
maybe molecular biology is doing
molecular Computing by using some
Dynamic process that is something where
it is very happily saying oh I just got
a result it's in the dynamic structure
of this network now I'm going to go and
do some other thing based on that result
for example but we're like oh I don't
know what's going on you know it's just
we just measured the levels of these
chemicals and we couldn't conclude
anything but it just we're looking at
the wrong thing and and so that's the
that's kind of the the the potential
there and it's it's um I mean these
things are I don't know it's it's for me
it's it's like I've not really that was
not a a view I mean I've thought about
molecular Computing for ages and ages
and ages and I've always imagined that
the big story is kind of the the
original promise of nanotechnology of
like can we make a molecular scale
Constructor that will just build build a
molecule in any shape but I don't think
I I'm now increasingly concluding that's
not the big point the big point is
something more Dynamic that will be an
interesting end point for any of these
things but that's perhaps not the thing
you know because the one example we have
molecular Computing that's really
working is US biological organisms and
you know maybe the thing that's
important there is not uh this you know
what chemicals do you make so to speak
but more this kind of dynamic process a
dynamic process and then you can have a
good model like the hypergraph to then
explore ex what like
simulate again make predictions and if
they I think just have a way to reason
about biology I mean it's it's hard you
know first of all biology doesn't have
theories like physics you know physics
is a much more successful sort of global
Theory kind of kind of area you know
biology what are the global theories of
biology pretty much darwinian Evolution
that's the only Global theory of biology
you know other any other theory is just
a well the kidneys work this way this
thing works this way and so on there
isn't I suppose another GL theory is
digital information in DNA that's
another sort of global fact about
biology but the the the difficult thing
to do is to
match something you uh have a model of
in the hypergraph to the act like how do
you discover the theory how do you how
do you discover the theory okay you have
something that looks nice and makes
sense but like you have to match it to
validation and experiment and that's
tricky because you're walking around in
the dark not entirely I mean so so you
know for example in what we've been
trying to think about is take actual
chemical reactions okay so you know one
of my one of my goals is can I compute
the primes with molecules okay that's if
I can do that then I kind of maybe I can
compute things and you know there's this
nice automated lab These Guys these
Emerald Cloud lab people are built with
wolf and language and so on that's an
actual physical lab and you send it a
piece of wolf and language code and it
goes and you know actually does physical
experiments and so one of my one of my
goals because I'm not a test tube kind
of guy I'm more of a software kind of
person is can I make something where you
know in this automated lab we can
actually get it so that there's some gel
that we made and you know the positions
of the stripes of the primes I love it
yeah I mean that would be that would be
an example of of of where and that would
be with a particular uh you know
framework for actually doing the
molecular Computing you know with
particular kinds of molecules and and
there's a lot of kind of ambient
technological mess so to speak as
associated with oh is it carbon is it
this is it that you know is it important
that there's a bromine atom here etc etc
etc this is all chemistry that I don't
know much about um and you know that's
that's a a sort of you know
unfortunately that's down at the level
you know I I would like to be at the
software level not at the level of the
transistors so to speak but in chemistry
you know there's a certain amount we
have to do I think at the level of
transistors before we get up to being
able to do it although you know
automated Labs certainly help in in in
setting that up I talked to uh a guy
named Charles hoskinson he mentioned
that he's collaborating with you he's an
interesting guy he sends me papers on uh
speaking of automated theor improving a
lot he's exceptionally well read on that
area as well so what's the nature of
your collaboration with him he's the
creator of cardano what's the nature of
the C collaboration between cardano and
the whole Space of blockchain and wol
from wol from alpha wolf from blockchain
all that kind of stuff well okay we
we're segueing to a a slightly different
world but but um so although not
completely unconnected the whole thing
is somehow connected I know I mean the
the you know the strange thing in my
life is I've sort of alternated between
doing basic science and doing technology
about five times in my life so far and
the thing that's just crazy about it is
you know every time I do one of these
alternations I think there's not going
to be a way back to the other thing and
like I thought for this physics project
I thought you know with doing
fundamental Theory of physics maybe
it'll have an application in 200 years
um but now I've realized um actually
this multicomp computation idea is is
applicable here and now it's and in fact
it's also giving us this way uh I'll
just mention one other thing and then
then talk about blockchain um the um the
question of um actually that relates to
several different things but but um one
of the things about about okay so our
wolam language which is our attempt to
kind of represent everything in the
world computationally and it's the thing
I kind of started building 40 years ago
in the form of actual W language uh 35
years ago um it's kind of this idea of
can we can we express things about the
world in computational terms and you
know we've come a long way in being able
to do that wol malfa is kind of the
consumer version of that where you're
just using natural language as input the
um and it turns it into our symbolic
language and that's you know the
symbolic language wol from language is
what people use and have been using for
the last 33 years actually Mathematica
which is its first instantiation will be
onethird of a century old in uh in
October um and um that uh it's it's kind
of interesting what do you mean one3 of
a century is you mean 33 or 30 what are
we 33 and a third 33 and a thir um
so I've never heard of anyone
celebrating that anniversary but I like
it I know third of a century though it's
it's like you know get many many slices
of a century that are interesting but
but you know I think that the the thing
that's really striking about that is
that means um you know including the
whole sort of Technology stacker built
around that's about 40 years old and
that means it's a significant fraction
of the total age of the computer
industry um and it's I mean I think it's
cool that we can still run you know
Mathematica version one programs today
and so on and and we've sort of
maintained compatibility and we've been
just building this big tower all those
years
of just more and more and more
computational capabilities it's sort of
interesting we just made this this
picture um of kind of the different kind
of threads of of of of computational
content of you know mathematical content
and and you know uh all sorts of things
with you know data and graphs and
whatever else and what you see in this
picture is about the first 10 years it's
kind of like it's just a few threads and
then then about maybe 15 20 years ago it
kind of explodes in this whole
collection of different threads of of
all these different capabilities that
are now part of wol from language and
representing different things in the
world but the thing that was super Lucky
in some sense is it's all based on one
idea it's all based on the idea of
symbolic expressions and transformation
rules for symbolic Expressions which was
kind of what I originally put into this
S&P system back in 1979 that was a
predecessor of the whole W language
stack so that idea was an idea that I
got from sort of trying to understand
mathematical logic and so on it was my
attempt to kind of make a general human
comprehensible model of computation of
just everything is a symbolic expression
and all you do is transform symbolic
expressions and you know in in
retrospect I was very lucky that I
understood as little as I understood
then because had I understood more I
would have been completely freaked out
about all the different ways that that
kind of model can can fail because what
do you do when you have a a a symbolic
expression you make Transformations for
symbolic Expressions well for example
one question is there may be many
Transformations that could be made in a
very multic computational kind of way
but what we're doing is picking we're
using the First Transformation that
applies and we keep doing that until we
reach a fixed point and that's the
result and that's kind of a very it's
kind of a a way of of of sort of sliding
around the edge of multicomp computation
and back when I was working on S&P and
things I actually thought about these
questions about about how you know how
what determines the this kind of
evaluation path so for example you know
you work out Fibonacci you know
Fibonacci is a recursive thing f ofn is
f ofn minus1 plus F of n minus 2 and you
get this whole tree of recursion right
and there's the question of how do you
evaluate that tree of recursion do you
do it sort of depth first where you go
all the way down one side do you do it
breadth first where you're kind of
collecting the terms together where you
know that you know F of 8 plus F of s f
of S Plus F of six you can collect the F
of sevens and so on these are um you
know I didn't realize it at the time
it's kind of funny I was working on on
gauge field theories back in 1979 and I
was also working on the evaluation model
um in S&P and they're the same problem
but it took me 40 more years to realize
that and this question about how you do
this sort of evaluation front that's a
question of reference frames it's a
question of of kind of the um the story
of of I mean that that's that is
basically this question of in what order
is the universe evaluated mhm and that
and so what you realize is there's this
whole sort of world of different kinds
of computation that you can do sort of
multic computationally and that's a
that's an interesting thing it has a lot
of implications for distributed
computing and so on it also has a
potential implication for blockchain
which we haven't fully worked out which
is um and this is not what we're doing
with cardano but but this is a a
different thing um the um this is
something where uh one of the questions
is um when you have in a sense
blockchain is a deeply sequentialized
story of time because in blockchain
there's just one copy of the of The
Ledger and you're saying this is what
happened you know time has progressed in
this way and there little things around
the edge as as you try and reach
consensus and so on and and uh you know
actually we just recently we had this
little conference we organized about the
the theory of distributed consensus
because I realized that there bunch of
interesting things that some of our
science can tell one about that but
that's a different let's let's not go
down that that part yeah yeah but
distributed consensus that still has a
sequential there's like one still
sequentiality so dist don't tell me
you're thinking through like how to
apply multicomp computation to uh
blockchain yes and so so that becomes a
story of you know instead of
transactions all having to settle in one
Ledger it's like a story of all these
different ledgers and they all have to
have some ultimate consistency which is
what causal invariance would give one
but it can take a while and the it can
take a while is kind of like quantum
mechanics so it's kind of what's
happening is there these different Paths
of history that correspond to you know
in One path of History you got paid this
amount in another path of History you
got paid this amount in the end the
universe will always become consistent
now now the way it will it works is okay
it's a little bit more complicated than
that what happens is the way space is
knitted together in our Theory of
physics is through all these events MH
and the the the idea is that the way
that economics spaces knitted together
is between is is there these autonomous
events that essentially knit together
economic space so there're all these
threads of transactions that are
happening and the question is can they
be made consistent are there is there
something forcing them to be sort of a
consistent fabric of of economic reality
and sort of what this has led me to is
trying to realize how does economics
fundamentally work and you know what is
economics and uh you know what what are
the atoms of Economics so to speak and
so what I've kind of realized is that
that sort of the perhaps I don't even
know if this is right yet there's sort
of events in economics are transactions
there are states of agents that are kind
of the atoms of economics and then
transactions are kind of Agents transact
in some transact in some way and that's
an event and then the question is how do
you knit together sort of economic space
from that what is there in economic
space well all these transactions
there's a whole complicated ction of
possible transactions but one thing
that's true about economics is we tend
to have the notion of a definite value
for things we could imagine that you
know you buy a um a cookie from somebody
and they want to get a movie ticket and
there is some way that AI Bots could
make some path from the cookie to the
movie ticket by all these different
trans intermediate transactions but in
fact we have an appr o imation to that
which is we say they each have a dollar
value and we have this kind of numerar
concept of there's just a way of kind of
of of taking this whole complicated
space of transactions and parsing it in
something which is a kind of a
simplified thing that is kind of like a
parsing of physical space and so my my
guess is that the yet again I mean it's
crazy that all these things are so
connected this is another multicomp
computation Story another story of where
what's happening is that the economic
Consciousness the economic Observer is
not going to deal with all of those
different microscopic transactions
they're just going to parse the whole
thing by saying there's this value it's
a number and that's that's their
understanding of their summary of this
economic Network and there will be all
kinds of things like there are all kinds
of Arbitrage opportunities which are
kind of like the quantum effects in this
whole thing and um that's uh you know
and places where there's where there's
sort of different paths that can be
followed and and so on and and there's
so the question is can one make a sort
of global theory of economics and then
my test case is again what is time
dilation in economics and and I know for
you know if if you imagine a very
agricultural economics where people are
growing Lett uses in fields and things
like this and you ask questions about
well if you're transporting Lett uses to
different places you know what is the
value of the lses after you have to
transport them versus if you're just
sitting in one place and selling them
you can kind of get a little bit of an
analogy there but I think there's a
there's a better more complete analogy
and that that's the question of is there
a theory like General itivity that is a
global theory of economics and is it
about something we care about it could
be that there is a global Theory but
it's about a feature of economic reality
that isn't important to us now another
part of the story is can one use those
ideas to make essentially a distributed
blockchain a distributed generalization
of blockchain kind of the quantum analog
of money so to speak where where you
have for example you can have
uncertainty relations where you're
saying you know well if I if I insist on
knowing my bank account right now
there'll be some uncertainty if I'm
prepared to wait a while then it'll be
much more certain um and so there's you
know is there a way of using and and so
we we've made a bunch of prototypes of
this um which I'm not yet happy with
because what I realized is to really
understand these prototypes I actually
have to have a foundational theory of
economics and so that's kind of a uh you
know it maybe that we could deploy a one
of these prototypes as a practical
system but I think it's really going to
be much better if we actually have an
understanding of how this plugs into
kind of the economic system and that
means like a fundamental theory of
transactions between entities well
that's what you mean by economics yes I
think so but I mean you know how how
there emerge sort of laws of Economics I
don't even know and I I've been asking
friends of mine who are who are
economists and things what is economics
you know is it an axiomatic theory is it
a theory that is a kind of a a
qualitative description theory is it you
know what kind of a theory is it is it a
theory you know what kind of thinking
it's like like in in biology in
evolutionary biology for example there's
a certain there's a certain pattern of
thinking that goes on in evolutionary
biology where if you're a you know a
good evolutionary biologist somebody
says that creature has a weird horn and
they'll say well that's because this and
this and this and there selection of
this kind and that kind and that's the
story and it's not a mathematical story
it's a story of a different type of
thinking about these things by the way
evolutionary biology is yet another
place where it looks like this multicomp
computational idea can be applied and
that's where where maybe speciation is
related to things like event Horizons
and there's a whole whole other kind of
world of that but but it seems like this
kind of model can be applicable so many
aspects like at the different levels of
understanding of uh our reality so it
could be the biology at the chemistry at
the physics level the economics and you
could potentially the thing is it's like
okay sure at all these levels it might
rhyme it might make sense as a model the
question is can you make useful
predictions as one of these levels and
that's that's right and that's really a
question of you know it's a weird
situation because it's a situation where
the model probably has definite
consequences the question is are there
consequences we care about yeah and and
that's some uh you know and so so and in
the case of in the economic case the
um uh we're um so you know the one one
thing is this this idea of using kind of
physics like Notions to construct a kind
of distributed analogue of blockchain
okay the much more pragmatic thing is a
is a different direction and it has to
do with this computational language that
we built to describe the world that
knows about you know different kinds of
cookies and knows about different cities
and knows about how to comp all these
kinds of things one of the things that
is of interest is if you want to run the
world you need you know with with with
contracts and laws and rules and so on
there are rules at a human level and
there are kind of um things like and so
this this gets one into the idea of
computational contracts you know right
now when we write a contract it's a
piece of legal ease it's you know it's
just written in English and it's not
something that's automatically
analyzable executable whatever else it's
just English you know back in gotfried
liet back in you know 1680 or whatever
was like um I'm going to you know figure
out how to use logic to decide legal
cases and so on and he had kind of this
idea of Let's Make a computational
language for the human the human law um
forget about modeling nature forgot
about natural laws what about human law
can we make kind of a computational
representation of that well I think
finally we're close to being able to do
that and one of the project that I hope
to get to as soon as the there's a
little bit of slowing down of some of
this Cambrian explosion that's happening
as a project I've been meaning to really
do for a long time which is what I'm
calling a symbolic discourse language it
is just finishing the job of being able
to represent everything like the
conversation we're having in
computational terms and one of the use
cases for that is computational
contracts another use case is something
like the the Constitution that says what
the AI what we want the AI to do so but
this is useful so you're saying uh so
these are like you're saying
computational contracts but the smart
contracts this is what's in the domain
of cryptocurrencies is known as smart
contracts and so the the language you've
developed this symbolic or seek to
further develop symbolic discourse
language enables you to uh write a
contract and write a contract that
richly
represents some aspect of the world yeah
but but so so I mean smart contracts
tend to be right now mostly about things
happening on on the blockchain yes
sometimes they have Oracles in a fact I
wol from alpha API is is the main thing
people use to get information about the
real world so to speak yeah within smart
contract so wol from alpha as it stands
is a really good Oracle for whoever
wants to use it that's perhaps where the
relationship with cardano is yeah well
that's how how we started getting
involved with blockchains is we realized
people were using you know wolf malfa as
the Oracle for smart contract so to
speak and so that got us interested in
blockchains in general and what was
ended up happening is wol from language
is with its symbolic representation of
things is really very good at
representing things like blockchains and
so I think we now have and we don't
really know all the comparisons but we
now have a really nice environment
within wolam language for dealing with
the sort of uh you know for representing
what happens in blockchains for
analyzing what happens in blockchains we
have a whole effort in blockchain
analytics um and uh you know we've we've
sort of published some samples of how
that works but but it's you know because
our technology stack both language and
Mathematica are very widely used in the
Quant Finance world there's a there's a
sort of immediate uh sort of um uh
co-evolution there of of sort of the
Quant Finance kind of thing and
blockchain analytics and that's some so
so it's kind of the representation of
blockchain in computational language
then ultimately it's kind of like how do
you run the world with code that is how
do you write sort of all these things
which are right now regulations and laws
and contracts and things in
computational language and kind of the
the ultimate vision is that sort of
something happens in the world and then
there's this giant domino effect of all
these computational contracts that
trigger based on the thing that happened
and there's a there's a whole story to
to that and of course you know I I like
to always pay attention to the latest
things that are going on and I I really
I kind of like blockchain because it's a
it's a it's another rethinking of kind
of computation it's kind of like you
know cloud computing was a little bit of
that of sort of persistent
um kind of uh computational resources
and so on and uh you know this multicomp
computation is a big rethinking of kind
of what it means to compute blockchain
is another bit of rethinking of what it
means to compute the idea that you Lodge
kind of these autonomous lumps of
computation out there in the blockchain
world and and one of the things that um
just sort of uh for fun so to speak is
we've been doing a bit of stuff with
nfts and we just did some nfts on
cardano and we'll be doing some more and
uh you know we did some cellular automat
and nfts on kadana people seem to like
like quite a bit um and you know one of
the things I've realized about about
nfts is that there's kind of this notion
and and we're we're really working on
this you know I like recording stuff you
know I one of the things that's come out
of of kind of my science I suppose is
this this history matters type type
story of you know it's not just the
current state it's the history that
matters and I've kind of I don't think
this is uh realizing maybe it's not
coincidental that that I'm sort of the
human who's recorded more about
themselves than anybody else and then I
end up with these science results that
say history matters which was not those
those things I didn't think those were
connected but they're at least
correlated yes yeah right so you know
this question about sort of recording
what has happened and and having sort of
a permanent record of things one of the
things that's kind of interesting there
is you know you put up a website and
it's got a bunch of stuff on it but you
know you have to keep paying the hosting
fees or the thing's going to go away but
one of the things about BL chain is kind
of interesting is if you put something
on a blockchain and you pay you know
your commission to get that thing you
know put on you know mind put on the
Block blockchain then then in a sense
everybody who comes after you is you
know they are motivated to keep your
thing alive because that's what keeps
the consistency of the blockchain so in
a sense with sort of the nft world it's
kind of like if you want to have
something permanent well at least for
the life of the blockchain but but even
if the blockchain goes out of
circulation so to speak speak there's
going to be enough value in that whole
collection of transactions that people
are going to Archive the thing but that
means that you know pay once and you're
kind of you're lodged in the blockchain
forever and so we've been kind of
playing around with um sort of a a hobby
thing of of mine of of thinking about
sort of the nfts and how you um and sort
of the consumer idea of kind of the it's
the it's the anti you know it's the
opposite of the Snapchat view of the
world there's a permanence to it this
heavily incentivized and uh thereby you
can have a permanence of History right
and that's that's that's kind of the um
now you know so that's so that's one of
the things we've been doing with cardano
and it's kind of fun I think that that
um I mean this whole question about you
know you mentioned automated theorem
proving and blockchains and so on and as
I've thought about this kind of physics
inspired distributed blockchain
obviously there the sort of the proof
that it works that there no double
spends there's no whatever else that
proof becomes a very formal kind of
almost a matter of physics so to speak
um and uh you know it's been it's been
an interesting thing for the for the
Practical blockchains to do kind of
actual automated theorem proving and I
don't think anybody's really Managed IT
in an interesting case yet it's a thing
that people you know aspire to but I
think it's a challenging thing because
basically the point is one of the one of
the things about proving correctness of
something is well you know people say
I've got this program and I'm going to
prove it's correct and like what does
that mean you have to say what correct
means I mean it's it's kind of like then
you have to have another language and
and people were very confused back in
past Decades of you know oh we're going
to prove the correctness by representing
the program in another language which we
also don't know whether it's correct and
you know Often by correctness we just
mean it can't crash or it it can't
scribble on memory but but the thing is
that there's this complicated trade-off
because as soon as there's as soon as
you're really using computation you have
computational irreducibility you have
undid ability if you want to use
computation seriously you have to kind
of let go of the idea that you're going
to be able to box it in and say we're
going to have just this happen and not
anything else I mean this is a this is
an old fact I mean girdles theorem tries
to say you know piano arithmetic the
axim of arithmetic can you box in the
integers and say these axim give just
the integers and nothing but the
integers goodles theem showed that
wasn't the case there's a you know you
can have all these wild weird things
that are obey the piano aums but aren't
integers and there's this kind of
infinite hierarchy of additional axioms
you would have to add and it's kind of
the same thing you you don't get to you
know if you want to say I want to know
what happens you're boxing yourself in
and there's a limit to what can happen
so to speak so it's a it's a complicated
trade-off and it's a it's a it's a big
trade-off for AI so to speak it's kind
of like do you want to let computation
actually do what it can do or do you
want to say no it's very very boxed in
to the point where we can understand
every step and that's a that's kind of a
thing that that um that becomes
difficult to do but that that's um I
mean in in
general I would say one of the things
that's kind of complicated in my uh sort
of life and the whole sort of story of
computational language and and all this
technology and science and so on I mean
I I kind of in in the flow of one's life
it's sort of interesting to see how
these things play out because I you know
I I've kind of concluded that I'm in the
business of making kind of artifacts
from the future which means you know
they things that I've done I don't know
this physics project I don't know
whether anybody would have gotten to it
for 50 years you know the fact that
Mathematica is a third of a century old
and I know that a bunch of the core
ideas are not well absorbed I mean that
is people finally got this idea that I
thought was a triviality of notebooks
that was 25 years and um you know some
of these core ideas about symbolic
computation and so on are not are not
absorbed I mean people people use them
every day in W from language and you
know do all kinds of cool things with
them but if you say what is the
fundamental intellectual Point here it's
it's not well absorbed and it's it's
something where you kind of realize that
you're you're sort of building things
and I I kind of made this this thing
about you know we're building artifacts
from the future so to speak and I
mentioned that at our uh we have a a
conference every it's coming up actually
in a couple of weeks a annual technology
conference uh where we talk about all
the all the things we're doing um and uh
you know so I was I was talking about it
last year about you know we're making
artifacts from the future and I was kind
of like I had some some version of that
that was kind of a dark and frustrated
thing of like you know I'm building
things which nobody's going to care
about until long after I'm dead so to
speak but um but but then I I realized
you know people were were sort of
telling me afterwards you know that's
exactly how you know we're using wolf
language in some particular setting in
you know some computational X field or
some organization or whatever and it's
like people are saying oh you know what
did you manage to do you know what we
know that in principle it will be
possible to do that but we didn't know
that was possible now and it's kind of
like that's the that's sort of the
business we're in and in a sense with
some of these ideas in science um you
know I feel a little bit the same way
that there are some of these things
where you know some some things like for
example this whole idea well so so to to
to relate to another sort of piece of
history and the future one of you know I
mentioned we mentioned at the beginning
kind of complexity as this thing that I
was interested in Back 40 years ago and
so on where does complexity come from
well I think we kind of nailed that the
answer is in the computational universe
even simple programs make it and that's
kind of the secret the Nature has that
allows you to make it so so that's kind
of the um uh that that's that part but
the bigger picture there was this idea
of this kind of computational Paradigm
the idea that you could go beyond
mathematical equations which have been
sort of the primary modeling medium for
300 years and so it was like look it is
inexorably the case that people will use
programs other than just equations and
you know I was saying that in the 1980s
and people were you know I published my
big book new kind of science it'll be 20
years ago uh next year so in 2002 and
people are saying oh no this can't
possibly be true you know we know for
300 years we've been doing all this
stuff right to be fair I now realize on
a little bit more analysis of what
people actually said in pretty much
every field other than physics people
said oh these are new models that's
pretty interesting in physics people
were like we've got our physics models
we're very happy with them yeah in
physics there's more resistance because
of the attachment and the power of the
equations the idea that programs might
be the right way to approach right uh
this field was there's some resistance
and like you're saying it takes time for
somebody who likes the idea of time
dilation and all these applications I
thought you would understand this yeah
right but but but you know and
computational irreducibility exct but
but I mean it is really interesting that
just 20 years a span of 20 years it's
gone from you know pitchforks and horror
to yeah we get it and um you know it's
helped that we've you know in our
current effort in in fundamental physics
we've gotten a lot further and we've
managed to put put a lot of puzzle
pieces together that that make sense but
the thing that I've been thinking about
recently is this field of complexity so
I I've kind of was a sort of a a field
Builder back in the 1980s I was kind of
like okay
you know can we uh you know I I'd
understood this point that there was
this sort of fundamental phenomenon of
complexity and it showed up in lots of
places and I was like this is an
interesting sort of field of science and
I was uh
recently was reminded I was at this the
very first sort of get together of what
became the Santa Fe Institute and I was
like in fact there's even an audio
recording of me sort of saying people
have been talking about oh what should
this you know outfit do and I was saying
well there is this thing that I've been
thinking thinking about it's this kind
of idea of complexity and um it's kind
of like and that's that's what that
ended up you planted the seat of
complexity at Santa Fe that's beautiful
it's a beautiful Vision but but but I
mean so that but what's happened then is
this idea of complexity and you know can
you know and I started the first
Research Center at University of
Illinois for doing that and the first
Journal complex systems and so on and uh
and it's kind of an interesting thing in
in my life at least that it's kind of
like you plant this seed you have this
idea
it's a kind of a science idea you have
this idea of sort of focusing on the
phenomenon of complexity the deeper idea
was this computational Paradigm but the
the nominal idea is this kind of idea of
complexity okay then you roll time
forward 30 years or whatever 35 years
whatever it is um and you say what
happened okay well now there are a
thousand complexity institutes around
the world um I think more or less we've
been trying to count them um and uh you
know there are 40 complexity journals I
think um and so it's kind of like what
actually happened in this field right
and and I look at a lot of what happened
and I'm like uh you know I have to admit
to some eye rolling so to speak because
it's kind of like like what is what
what's what what's actually going on
well what people definitely got was this
idea of computational models and then
they got but they thought one of the one
of the kind of cognitive mistakes I
think is they say we've got a
computational model and it and we're
look looking at a system that's complex
and our computational model gives
complexity by golly that must mean it's
right and unfortunately because
complexity is a generic phenomenon and
computational irreducibility is a
generic phenomenon that actually tells
you nothing and so then the question is
well what can you do you know there's a
a lot of things that have been sort of
done under this Banner of complexity and
I think it's been very successful in
providing sort of an interdisciplinary
way of connecting different fields
together which is powerful in itself
right I me that's a Ecom yeah it is it's
a good organizing principle but but in
the end a lot of that is around this
kind of computational Paradigm
computational modeling that's the raw
material that powers that kind of uh
that kind of Correspondence I think and
the question is sort of what is the you
know I was just thinking recently you
know we've been I mean the the other
we've been we've been for years people
have told me you should start some wolf
Institute that does basic science you
know all I have is a company that that
builds software and we you know we have
a little piece that does basic science
as kind of a hobby people are saying you
should start this wolam institute thing
and and I've been you know because I've
known about lots of institutes and I've
seen kind of their flow of money and and
kind of you know what happens in
different situations and so on so I've
been kind of reluctant but uh but I've
I've I have realized that you know what
we've done with our company over the
last 35 years you know we built a very
good machine for doing R&D and you know
innovating and creating things and I
just applied that machine to the physics
project M that's how we did the physics
project in a fairly short amount of time
with a you know efficient machine with
you know various people involved and so
on um and so you know it it works for
basic science and it's like we can do
more of this and so biology and
chemistry so it it's it's become an
Institute yes well it needs to become an
Institute an official Institute right
right but the the thing that so I was
thinking about okay so what do we do
with complexity you know what what there
are all these people who've uh you know
what what should happen to that field
yeah and what I realized is there's kind
of this area of foundations of
complexity that's about these questions
about simple programs what they do
that's far away from a bunch of the
detailed applications that people well
it's not far away it's it's the it's the
under you know the the Bedrock
underneath those applications so I
realized recently this is my a recent
kind of little uh innovation of A Sort
um a post that I'll do very soon the um
about um uh kind of you know the
foundations of complexity what really
are they I think they're really two
ideas two conceptual ideas that I hadn't
really enunciated I think before one is
what I call Meta modeling the other is
rology so what is metamodeling So Meta
modeling is you've got this complicated
model and it's a model of you know
hedgehogs interacting with this
interacting with that and the question
is what's really underneath that what is
it you know is it a touring machine is
it a cellular automaton you know what is
is the underlying stuff underneath that
model and so there's this kind of
metascience question of given these
models what is the core model and I
realized I mean to me that's sort of an
obvious question but then I realized
I've been doing language design for 40
years and language design is exactly
that question you know underneath all of
this detailed stuff people do what are
the underlying Primitives and that's a
question people haven't tended to ask
about models they say well we've got
this nice model for this and that and
the other what's really underneath it
and what you know because once you have
the thing that's underneath it well for
example this multicomp computation idea
is an ultimate meta modeling idea
because it's saying underneath all these
fields is one kind of paradigmatic
structure and you know you can you can
imagine the same kind of thing much more
sort of uh much sort of shallower levels
in in um in in different kinds of
modeling so there's the first activi is
is kind of metamodeling the the kind of
the the models about models so to speak
you know what is the what's what's you
know drilling down into models that's
one thing the other thing is this this
thing that I think we're going to call
rology which is kind of the the okay
you've got these simple rules you've got
cellular autometer you've got turning
machines you've got substitution systems
you've got register machines got all
these different things what do they
actually do in the wild and this is an
area that I've spent a lot of time you
know working on it's a lot of stuff in
my new kind of science book is about
this um you know this new book I wrote
about combinators is is full of stuff
like this and and this journal complex
systems has lots of papers about these
kinds of things but but there isn't
really a home for people who do rology
or what I'm not the as you call the
basic science of rules yes yes right so
it's it's like you've got some what is
it is it mathematics no it isn't really
like mathematics in fact from my now
understanding of metam mathematics I
understand that it's the molecular
Dynamics level it's not the level that
mathematicians have traditionally cared
about it's not computer science because
computer science is about writing
programs that do things you know that
were for a purpose not programs in the
wild so to speak it's not physics it
doesn't have anything to do with you
know it may be underneath some Physics
but it's not physics as such so it just
hasn't had a home and if you look at you
know but what's great about it is it's a
surviving field so to speak it's it's
something where you know one of the
things I I find sort of inspiring about
mathematics for example is you look at
mathematics that was done you know in
ient Greece ancient you know Babylon
Egypt and so on it's still here today
you know you find an icosahedron that
somebody made in ancient Egypt you look
at it oh that's a very modern thing it's
an icosahedron you know it's it's a
Timeless kind of kind of activity and
this idea of studying simple rules and
what they do it's a Timeless activity
and I can see that over the last 40
years or so as you know even with
cellular autometer it's kind of like you
know you can sort of catalog what what
are the different cellular autom are
used for and you know like the the
simplest rules like like one you might
even know this one rule 184 it's um rule
184 is a minimal model for road traffic
flow and you know it's also a minimal
model for various other things but it's
kind of fun that you can literally say
you know rule 90 is a minimal model for
this and this and this rule four is a
minimal model for this and it's kind of
remarkable that you can just by In This
raw level of this kind of study of rules
they then Branch they the raw material
that you can use to make models of
different things so it's a it's a very
pure basic science but it's one that you
know people have explored it but they've
been kind of a little bit in the
wilderness and I think you know one of
the things that I would like to do
finally is is uh you know I I always
thought that sort of this notion of pure
nks pure and nks being the acronym for
my book new kind of science um was uh
was something that people should be
doing and and you know we tried to
figure out what's the right
institutional structure to do this stuff
you know we we dealt with a bunch of
universities oh you know can we do this
here well what department would it be in
it well it isn't in a department it's
it's its own new kind of thing that's
why that's why the book was called a new
kind of science um it's kind of the the
because that's an increasingly good
description of what it is so to speak
we're actually we we're thinking about
kind of the rological society because we
we're realizing that it's kind of it's
it's um you know there's a there's it's
very it's very interesting I mean I've
never really done something like this
before because there's this whole group
of researchers who are who've been doing
things that are really in some cases
very elegant very surviving very solid
you know here's this thing that happens
in this very abstract system but it's
like it's like what is that part of you
know it's it doesn't have a a home and I
think that's something I you know I kind
of fault myself for not having been more
you know when complexity was developing
in the 80s I didn't understand the the
the danger of applications that is it's
really cool that you can apply this to
economics and you can apply it to
evolutionary biology and this and that
and the other but what happens with
applications is everything gets sucked
into the applications and the pure stuff
it's like the pure mathematics there
isn't any pure mathematics so to speak
it's all just applications of
mathematics and I I failed to kind of
make sure that this kind of pure area
was was kind of um maintained and and
and developed and I I think now you know
one of the things I I want to try to do
and and you know it's it's a funny thing
because I'm used to look I've been a a
tech CEO for more than half my life now
so you know this is what I know how to
do and um you know I can I can make
stuff happen and get projects to happen
even as it turns out basic science
projects in that kind of setting and and
how that translates into kind of uh you
know there are a lot of people working
on for example our physics project sort
of distributed through the academic
world and that's working just great but
the question is you know can we have a
sort of accelerator mechanism that makes
use of kind of what we've leared in in
sort of R&D Innovation and you know but
on the other hand it's a funny thing
because you know in a company in the end
the thing is you know it's a company it
makes products it sell things sells
things to people um in you know when
you're doing basic research one of the
challenges is there isn't that same kind
of of sort of mechanism and so it's it's
it's you know how do you drive the thing
in a in a kind of in a Leed kind of way
so that it really can can make forward
progress rather than and you know what
can often happen in you know in in
academic settings where it's like well
there are all these flowers blooming but
it's not clear that they're that you
know that it's you have to have a
central Mission and a drive just like
you do with a company that's delivering
a big overarching product and that's
that's uh but the the challenge is you
know when you have a the the the the
economics of the world are such that you
know when you're delivering a product
and people say wow that's useful we'll
buy it m and then that kind of feeds
back and okay then you can then you can
pay the people who build it to eat you
know so they can eat and so on and with
basic science the the payoff is very
much less visible and and you know with
this physics project as I say the big
surprise has been that I mean you know
for example well the big surprise with
the physics project is that it's looks
like it has near-term applications and I
was like I'm guessing this is 200 years
away it's um I was kind of using the
analogy of of you know Newton uh
starting a satellite launch company
which would have been kind of wrong time
um and uh you know but but it turns out
that's not the case but but we can't
guarantee that and if you say we're
signing up to do basic research basic
rology let's say and you know and we
can't we don't know the Horizon you know
it's it's an unknown Horizon it's kind
of like an undecidable kind of
proposition of when is this proof going
to end so to speak when is it going to
be something that that uh that gets
applied well I I hope this is this
becomes a vibrant New Field of rology I
love it like I told you many many times
it's one of uh the most amazing ideas
that has been brought to this world so I
hope you uh get a bunch of people to
explore this
world thank you once again for spending
your really valuable time with me today
fun stuff thank you thanks for listening
to this conversation with Steven wilam
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let me leave you with some words from
Richard Fineman nature uses only the
longest threads to weave her patterns so
each small piece of her fabric reveals
the organization of the entire
tapestry thank you for listening and
hope to see you next time