EMERGENCE.

in this episode of street talk unplugged

and so one thing that i find fascinating

is that there is absolutely no reason

why this should work like at all there

is nothing that we can observe that says

that these kinds of rules should exist

at all this this model in principle is

it's like it's too simple for it to

actually work

welcome back to street talk

this week we are coming live from lisbon

in portugal i haven't had access to my

studio or any of my uh you know normal

recording equipment so it's going to be

a bit of an interesting one but i've

been working out of coffee shops

building an introduction doing all my

stuff so yeah it's going to be a show

about strong and weak emergence

about cellular automata and we're going

to be interviewing dr danielle gratarola

and speaking all about his work on graph

cellular automata so i hope you enjoy it

folks

see you soon

one thing that really fascinates me is

um a lot of the interesting phenomena

happens at a different level a different

rung of the emergence ladder if that

makes sense and i'm starting to see this

everywhere like even at work i'm

building a code review platform and at

the low level the metrics are obvious

i know ken talks about the uh the

tyranny of metrics by the way but you

know it's how many code reviews that has

an engineer done how many customer

engineers do i have it's easy and then i

start going up the levels of abstraction

i'm talking to the senior leaders and

now i'm starting to use much more

abstract language like vertical

information flows and trust and

engineering culture

and all of a sudden it's impossible for

me to quantify and if i do i'm making it

up and it's the same thing

you're talking about these population

scale phenomena that happen now so i've

got all of these intelligent agents

they're doing things and and i can try

and because now i've got a meta

optimization problem right so i want to

encourage interesting phenomena

in the emergent scale so i might say

well this type of thing is interesting i

want more of that but i'm i'm kind of

i'm reaching because i don't know how to

describe it i mean i think one other one

other characteristic you can point to

that that kind of separates um like

population from just individual is

sort of specialization versus

generalization like i think population

driven algorithms sort of

implicitly are more about specialization

a lot of the time because like each

member of the population you want to be

doing some different thing

so they're kind of becoming specialists

but i think there's a huge amount of

generalization snobbery kind of within

machine learning like we're looking for

the ultimate general list all the time

it's like get it to do all the tasks you

can possibly do and then throw more in

and the data set just gets bigger and

we're all very impressed with that the

population implies i feel like

something's in spirit different because

it's more just like

actually i want to see a lot of

different things and like hyper

specializations to all kinds of exotic

things that like probably the generals

won't do because it's basically all

cares about is being general this comes

down to like the focus on like the

particular level of abstraction or the

level of agency that we have professor

melanie mitchell wrote a beautiful book

on complexity about 10 years ago i hope

one day we can get it back on the

podcast and discuss it in detail in the

book she led with a quote from john

locke

i call complex

such as our beauty gratitude a man

an army

the universe

the animal kingdom has several examples

of what i would call externalized or

collective intelligence

melanie quote biologist nigel franks in

her book

the solitary army ant is behaviorally

one of the least sophisticated animals

imaginable

if 100 army ants are placed on a flat

surface

they will walk around and around in

never decreasing circles until they die

of exhaustion

yet if you put half a million of them

together the group as a whole becomes

what some have called a super organism

with collective intelligence

the whole is in some sense more than the

sum of its parts although we need to be

quite careful with the language that we

use here

an emergent behavior or emergent

property can appear when a number of

simple entities or agents operate in an

environment forming more complex

behaviors as a collective

if emergence happens over disparate size

scales then the reason is usually a

causal relation between different scales

western science has a strong tendency

towards reductionism because it assumes

that things have essences so science

keeps chopping up things into smaller

and smaller pieces to find their essence

it's an intellectual and philosophical

position which interprets a complex

system as the sum of its parts

this is in stark contrast with

relationism which you could say is

related to the philosophical ideas we

were discussing with andrew lampanen

from deepmind last week

biologist peter corning asserted that

this whole discussion rather misses the

point

he said that holes produce unique

combined effects but many of these

effects may be co-determined by the

context and the interactions between the

whole and its environments

now weak emergence describes new

properties arising in systems as a

result of low-level interactions these

might be interactions between components

of the system or components and their

environment

emerging properties are scale dependent

though and can only be observed at large

enough system scale one reason emergent

behavior is hard to predict is that the

number of interactions between a

system's components increases

exponentially with the number of

components thus allowing for many new

and subtle types of behavior to emerge

emergence is often a product of

particular patterns of interaction

negative feedback introduces constraints

that serve to fix structures or

behaviors in contrast positive feedback

promotes change allowing local

variations to grow into global patterns

on the other hand merely having a large

number of interactions is not enough by

itself to guarantee emergent behavior

many of the interactions may be

negligible or irrelevant or may cancel

each other out in some cases a large

number of interactions can in fact

hinder the emergence of interesting

behavior by creating a lot of noise to

drown out any emerging signal

the system has to reach a combined

threshold of diversity organization and

connectivity before emergent behavior

appears

mark bedau said in his 1999 paper titled

weak emergence that an innocent form of

emergence what he called weak emergence

is now commonplace in the thriving

interdisciplinary nexus of scientific

activity sometimes called the sciences

of complexity interestingly which he

elected to put in air quotes for some

reason

he said that this included connectionist

modelling and non-linear dynamics which

is now commonly known as chaos theory

and indeed artificial life

he gave two interesting hallmarks of

emergent phenomena in his opinion

one emergent phenomena are somehow

constituted by

and generated from

an underlying process

and two

emergent phenomena are somehow

autonomous from the underlying process

so he said that emergence is a perennial

philosophical puzzle and at best the

idea raises the spectre of

illegitimately getting something from

nothing

he said that any defense of emergence

should aim to explain that is to say

explain away

the apparent illegitimate metaphysics

and indeed demonstrate emergence to be

entirely compatible with materialism

he argued that emergence must be more

than intellectual masturbation putting

words in his mouth here and actually

demonstrate tangible value to the

empirical sciences and be a constructive

player in our understanding of the

natural world

he argued that weak emergence meets

these goals but argued that stronger

forms of emergence are entirely

irrelevant

he said that the failings of strong

emergence can be traced back to this

idea of strong downward causation which

is this notion that things in the lower

resolution emergent domain can cause

things in the high resolution domain

mark said that strong emergence is

uncomfortably like magic

how does a super veniant but irreducibly

downward causal power arise since by

definition it cannot be the result of

the high resolution domain he said this

would discomfort reasonable forms of

materialism and pay homage to the idea

that it's possible to get something from

nothing

mark concluded by saying that strong

emergence is just a mystery which we

don't need

it's interesting to note that his

definition of weak emergence is as

follows

macro state p of s with micro dynamic d

is weakly emergent if and only if p can

be derived from d

and s is external conditions but only by

simulation so interestingly his

definition incorporates the necessity

for computational irreducibility but not

the notion of whether it is effectively

computable

one of the main hallmarks of weak

emergence is the underrivability except

for finite simulation the exponential

divergence of trajectories or indeed the

so-called butterfly effect describing

the sensitivity of a physical simulation

on its starting parameters is a

well-known feature of chaotic systems

but mark says that weak emergence is

present in almost all complex systems

regardless of whether they produce

chaotic dynamics which lead to weak

emergence being part of the definition

of what it means to be a complex system

the popular physics youtuber dr sabine

hossenfelder wrote a paper called the

case for strong emergence she felt that

weak emergence was too deterministic and

a front on free will if you like

she used to think that we're all made of

tiny particles which follow strict laws

and human behavior is really just a

consequence of these particles laws

needless to say she's since changed her

mind and she thinks that you should as

well

she led by saying reductionism works

large things are made of smaller things

and if you know what the smaller things

do you know what the larger things do

physicists call this idea reductionism

now you might not like it but it works

pretty well arguably reductionism

allowed us to understand molecular bonds

and chemical elements atomic fission and

fusion the behavior of an atom's

constituents and the constituents of

those constituents and whoever knows

what the physicist will come up with

next she said

she admits that the best explanation for

the world around us right now is almost

certainly incomplete

sabine decided to discuss the concept of

emergence in respect to physical

theories and how fundamental they are

she said that a physical theory is a set

of mathematically consistent axioms

combined with an identification of some

of the theory's mathematical structures

with observables

if two physical theories give the same

predictions for all possible observables

then they are physically equivalent

she displayed a figure depicting a

directed graph of physical theories an

edge between two theories meant that one

was more fundamental than the other

she said that a physical theory a is

more fundamental than b if b can be

derived from a but not the other way

around

in this case the theory b is weakly

emergent from a

a physical theory is fundamental if it

is to the best current knowledge not

emergent from any other theory so this

is quite interesting weekly emergent is

the opposite of more fundamental the

idea that the theory at low resolution

is always weakly emergent it can be

derived at least in principle from the

theory at high resolution

sabine also discussed the causal

exclusion argument which roughly

speaking says that if a lower resolution

effect can be derived from a theory at

high resolution then the effect cannot

have another cause the causal exclusion

argument combined with effective field

theory is the main reason why physicists

believe that reductionism is correct and

in a sense why strong emergence is not a

thing

she also spoke about top-down causation

which is this idea that the laws of a

system at low resolution can dictate the

laws at high resolution

a good example of this is the mental

states in our brain causing our bodies

to perform physical actions

so it's important not to think of the

emergent layers as being independent or

assuming that they could or should be

modeled in isolation interestingly

though in sabine's article she denied

that top-down causation even exists at

all

in her conclusion sabine did a 180

degrees and she decided that in fact

there are many examples where there

isn't a clear effective computational or

functional path between physical

theories she gave a hypothetical example

of a function which cannot be computed

for negative values of x or a taylor

series expansion around zero and she

said that if there are any points where

the coupling can't be continued between

resolutions you'll need new initial

values which would need to be determined

by measurement and therefore strong

emergence is viable

she said it's only fair on philosophers

who believe that strong emergence exists

that physicists first show the coupling

constraints of a quantum field theory

can always be continued to low energies

for physically realistic systems

so what is emergence emergence is just

the interpretation of a phenomenon from

the perspective of a different scale at

least according to professor david

chalmers

he wrote a paper called strong and weak

emergence where he lamented the abuse of

the term strong emergence by complex

systems scientists and cognitive

scientists echoing mark badal before him

chalmers says that it is strong

emergence which is most common in the

philosophical parlance of emergence and

in particular used by the british

emergentists of the 1920s he thought

that we could say a high-level

phenomenon is strongly emerging with

respect to a low-level domain when the

high-level domain phenomenon arises from

the low level domain but truths

concerning that phenomenon are not

deducible even in principle from truths

in the low level domain

now i think deducible is a bit of a

weasel word but we'll talk more about

that in a minute um he says that weak

emergence does not yield the same sort

of radical metaphysical expansion in our

conception of the world as strong

emergence but it's no less interesting

he says that you can think of weak

emergence in terms of the ease of

understanding of one level in terms of

another level

emergent properties are usually

properties which are more easily

understood in their own right than in

terms of properties at a lower level

indicating that weak emergence appears

to be an observer relative property

now how interesting is this high level

phenomenon to an observer and how

difficult is it to deduce this

phenomenon from the lower level that is

emergence

so chalmers takes emergence in the

general sense to mean surprising or

interesting and indeed an unexpected

phenomena and he uses the strong versus

weak designation to delineate a radical

paradigmatic surprise

he says that the emergence of high-level

patterns and cellular automata a

paradigm of emergence in recent complex

systems theory provides a clear example

if one is given only basic rules

governing a cellular automaton then the

formation of complex high-level patterns

such as gliders may well be unexpected

therefore the patterns are weakly

emerging but the formation of those

patterns is straightforwardly deducible

from the rules and the initial

conditions

he concedes that this might take a fair

amount of computation

which he indicates as a reason why the

emergent behavior wasn't obvious to

start with and i assume by the word

obvious he's kind of

means as an autonym to unexpected

cellular automata are provably

computationally irreducible this means

that there are no analytical shortcuts

to perform the effective calculation

without resorting to running the

sequential simulation in its entirety

since the computational domain is

exponentially large in the case of

discrete cellular automata and

infinitely large in the case of

continuous cellular automata if you were

trying to find the initial conditions

and rules for a given behavior or even

if you had to recompute the simulation

we would argue that this constitutes at

least a semi-strong designation of

emergence because of the effective

computability right the effective

computability must come into it

professor chalmers says that strong

emergence has much more radical

consequences than weak emergence if

there are phenomena that are strongly

emergent with respect to the domain of

physics then our conception of the

natural world would need to be

revolutionized to accommodate them with

new fundamental theories

now i find this a little bit strange i

mean given that a class iv cellular

automata is touring incomplete which is

to say that they can represent any

computer program it seems like a

contentious point that there's no

possible output in a cellular automata

which would be paradigmatically

surprising maybe i'm wrong

to be clear chalmers is a materialist

right he's not subscribing to any kooky

views by saying this he's a

computationalist in the sense that he

agrees that if he replicated him atom by

atom in the natural world according to

our universe then it would have a

consciousness right but he argues that

consciousness isn't a logical necessity

he could imagine a universe which has

all the same physical laws where he

would be a philosophical zombie because

it's not logically necessary yeah so

this term emergence is you know it's so

woolly and uh

ambiguous i mean it gets used for so

many different things

uh in the sciences in philosophy any

kind of phenomenon of a complex system

that we don't fully understand we say oh

yeah well it's emergent and then okay

well great well what's the cash value of

uh of that and i've found it useful to

distinguish as you were weak and strong

emergence where weak emergence is kind

of a matter of mostly of complexity

um where for example you've got some

simple rules at the bottom level that

gives rise to some high level

macroscopic phenomenon

which is complex and surprising

hard to predict and derive as a

practical matter

but it's really more of a practical

limitation you can still see in

principle why those bottom level

principles say laws of physics or

rules in a cellular automaton would in

principle give rise to these high-level

phenomena derivable and principle if not

in practice whereas strong emergence

would require something that's not even

derivable in principle and i guess i

think that most of the things you get in

ai or

complex systems theory and so on involve

weak emergence certainly i was very

influenced by um

doug hofstadter here who's

who's you know good alicia bark is in

some ways all about the powers of weak

emergence how

really

simple processes at one level could give

you complex processes

at a higher level and actually get these

tangled hierarchies he'd talk or strange

loops you'd go up a few levels and then

you'd you'd come down so i guess i'm

probably more sympathetic with

hofstadter's picture of weak emergence

than say george ellis's where causation

is always within a level i think there

are very complex relations between the

levels and some of them may be best

understood as causal you could think of

it you know the butterfly

um

snapping its wings having some causal

relation to some sociological event days

later so you do get these

tangled hierarchies but all that is

still weak emergence

so he's agreeing with mark badal by

saying that any endorsement of strong

emergence is a rejection of physicalism

and reductionism which is to say an

appeal to magic and esoterica

whereas weak emergence can be used to

support the physicalist picture of the

world by showing how all sorts of

phenomena which might seem novel and

irreducible at first sight can

nevertheless be grounded in underlying

simple physical laws

chalmers thinks that there is exactly

one clear example of strong emergence in

our universe which is guess what our

consciousness

[Music]

we can say that a system is conscious

when there is something it is like to be

that system which is to say it has a

phenomenological experience

chalmers argues that it is a fact of

nature that the universe contains

conscious systems we are existence

proofs of that and there's reason to

believe that the facts about

consciousness are not deducible from any

number of physical facts it makes the

argument that there could be a world

physically identical to this one but

lacking consciousness entirely which is

very similar to that philosophical

zombies argument that i just spoke about

or even containing conscious experiences

which are potentially different to our

own roger penrose said that the human

ability to understand is undecidable and

requires consciousness

if this is true it might be a

mathematical proof that consciousness is

strongly emergent exactly as charm as

claims

and so

the way i the way i view strong

emergence at least for for right now is

that if i have these different

formalizations at different levels

and it's just not possible in any

practical

scheme whatsoever for me to directly

go from

a lower level to a higher level like for

example i just can't computationally do

it or there's

no mathematics that can ever hope to

symbolically you know prove that that uh

the properties i observe at a higher

level derive from a lower level

maybe i you know people say well in

principle you could but in reality you

just may never be able to do that you

know does that qualify as strong

emergence or is that a bad definition of

it and do you think there is such a

thing as strongly emergent behavior or

can we ultimately just reduce everything

down to

uh hypergraph or or loop chrom quantum

gravity or whatever

every level a sense is independent you

cannot expect it to be fully reduced to

a lower one or okay a higher one

or each level has its own value it has

its

concepts it has these conclusions it has

problems that's suitable to be to be

solved at the level not higher or lower

that is

to me that's the first principle but the

second one is you don't want to push it

too far you don't want to say all the

layers have nothing to do with each

other

so as after all we're talking about the

same object okay we're talking about the

same that the google map of the same eye

area even though you zoom in block out a

different level if he is

a two map a different array that's a

different story okay so as far as all

those theories

is in a sense about the same object but

there is the different levels of

description

and they are correlated but they are

kind of like

very overall high level uh

not high level is the wrong way to say

it is confusing

the relation it's kind of like you have

a overall

large scale

correlation

but you don't have one-to-one mapping

among the concepts that's also my

opinion about the relation for example

between neurons and concepts

uh of course they're related but there

is no one to unmapping or if not even

money problem might be

it's more like a money to mine in my

opinion and also it's very messy in my

opinion

uh except if you want to limit your

discussion

to a very special phenomena at a certain

level for example we know that some

basic concepts in chemistry

can be explained very well in physics

right

because villains talk about the details

uh the same story of something in

biology can be explained very well with

physics and chemistry we should talk

about the details

so that's true but on the other hand if

you say that

biology overall can be even truly

reduced it to chemistry and uh feelings

i say not only that's practically wrong

is even theoretically wrong

because when you're seeing that

you're ignoring

the

cognitive capability

of the researcher

and the user of your theory you cannot

really reduce everything

to

uh to the to the lower level without

greatly increase the number of concepts

right computational cost

melanie mitchell pointed out that it's

incredibly mysterious how the intricate

machinery of the immune system fights

disease or how a group of cells

organizes itself to be an eye or a brain

or how independent members of an economy

each working chiefly for their own gain

produce complex but structured global

markets

or most mysteriously how the phenomena

we call intelligence or consciousness

emerge from non-intelligent

non-conscious material substrates

the cognitive scientist douglas

hofstadter in his book go to lescherbach

made an extended analogy between ant

colonies and brains both being complex

systems in which relatively simple

components with only limited

communication among themselves

collectively give rise to complicated

and sophisticated system-wide global

behavior

the ants in our human brain are of

course our neurons they communicate with

each other in a similarly simplistic

manner yet our intelligence and arguably

our consciousness emerge from this

low-level primitive communication

markets are also complex emergent and

self-organizing entities if you like

melanie said in her book that they are

self-organized on the microscopic and

the macroscopic level she said that on

the microscopic level individuals and

companies and markets try to increase

their profitability by learning about

the behavior of other individuals and

companies

the microscopic self-interest has

historically thought to push markets as

a whole on the macroscopic level towards

a so-called nash equilibrium

now the process by which markets obtain

this equilibrium is called the market

efficiency

the 18th century economist adam smith

called this self-organizing behavior of

markets the invisible hand

it arises from the myriad microscopic

actions of individual buyers and sellers

the individual actions on a trading

floor give rise to the hard to predict

large-scale behavior of financial

markets

now melanie gives three core properties

of complex systems in her book

one

complex collective behavior

large networks of individual components

which each one following relatively

simple rules with no central control or

leader it's the collective action of

vast numbers of components that give

rise to the complex hard to predict and

changing patterns of behavior which

fascinate us so much

[Music]

two

signaling and information processing

complex systems use information and

signals from both their internal and

external environments

and three

adaptation all of these systems adapt

that is they change their behavior to

improve their chances of survival or

success through learning or some

evolutionary process

so melanie then goes on to give her

definition of a complex system as

follows

a system in which a large network of

components with no central control and

simple rules of operation give rise to

complex collective behavior

sophisticated information processing and

adaptation by learning or evolution

now i spoke with our friend dr duggar on

strong emergence and he said that in his

opinion it describes behaviors which

cannot be analytically derived nor

effectively computed from a lower level

or higher resolution theory this would

place glider wars in a cellular

automaton firmly in the domain of strong

emergence

a cellular automaton is computationally

irreducible there's no effective

computational path from the lower level

rules to the higher level behavior the

only thing you can do is run the

simulation again from scratch

he thought that chalmers and

hossenfelder evade the issue and or beg

the question by phrases like deducible

in principle or a fair amount of

computation or follows from that at

least in principle etcetera etcetera so

you know what he's saying is that they

make claims which

we can in principle do something but

they can't actually demonstrate or

perform with a reasonable amount of

computation

in physical strong emergence you can't

even run the computation at least in a

continuous cellular automaton you're

pretty much in the same boat as the end

body problem

now a lot of this discussion comes down

to whether you believe infinity exists

or not actual infinity this is a teaser

clip from our conversation with dr

joshua bach

can the universe can our actual universe

that we're in right now

be actually infinite in spatial extent

the problem is that you can have

unboundedness in the sense that you have

a computation that doesn't stop giving

you results

but you cannot take the last result of

such a computation and go to the next

step

you cannot have a computation that

relies on knowing the last digit of pi

before it goes to the next step in this

sense you don't have an infinity but the

infinities are about the conclusion of

such a function it means that you

actually run this function to the end

and then do something with the result

unboundedness is different in the sense

that you will always get something new

that you didn't expect that you cannot

predict but it's it's just going on and

on without this end and it i think it's

completely conceivable that our universe

is in this class of systems in the sense

that it doesn't end

but

it doesn't mean that there is anything

that gives you the result of an infinite

computation because if that was the case

then it could not be expressed in any

language

it also means if something cannot be

expressed in any language that you

cannot actually properly think about it

because when you think you need to think

in some kind of language not in english

but in some kind of language of sort or

in a mathematical language that doesn't

have contradictions and what girdle has

shown is that the language that he hoped

to reason in about infinities

breaks that it has contradictions in it

that at some point it blows blows itself

apart so the languages that we can build

are only those in which we have to

assume that infinities cannot be built

so infinity in this sense is meaningless

because we cannot make it in any kind of

language

so the thing is though i'm not limiting

what the universe is capable of based on

human you know mental and linguistic

limitations or even mathematical

limitations like i'm i'm asking you if

it's possible for this universe that

we're in to anticly be right now

actually infinite in spatial extent

the thing is that you try to make a

reference to something that you cannot

observe and cannot conceive of other

than making a model in some kind of

language

and to have that model make sense the

language needs to work right otherwise

you are just

maybe in some kind of delusional thing

you can't get to infinity from

non-infinity and you can't get to

discrete from analog so keith believes

that there are actual infinities in

stark contrast to people like stephen

wolfram but our brains are

computationally bound we are conducting

what is a discrete computation in our

mind but we might have access to oracles

which is to say we're connected to a

turing machine but we can only sample at

a certain rate

keith believes in infinity therefore

there may be many strongly emergent

phenomena because they're not computable

he therefore doesn't think the universe

can even run on a computer or indeed

that we exist inside a simulation

the simplest way to prove the

constructivist hypothesis that natural

systems need to perform computation in

order to succeed and adapt in respect of

its environment is to create an

idealized version of the problem that is

to say let's simplify it as much as

possible while still retaining the

features that make the problem

interesting and that is exactly what a

cellular automaton does

cellular automata are a class of

computational models that exhibit rich

dynamics weakly emerging from the local

interactions of cells arranged on a

regular lattice for example

two-dimensional grid

cellular automata were invented by john

von neumann back in the 1940s they

exhibit extremely complex behavior

that's difficult or impossible to

predict from the cell update rule

now melanie mitchell commented in her

book that this is one of the great

ironies of computer science

since cellular automata often referred

to as non von neumann style

architectures in contrast with the von

neumann style architectures

that he also invented

von neumann was also able to show that

his cellular automaton was equivalent to

a universal turing machine

and therefore capable of universal

computation which is to say computing

anything which a turing machine can

in 1970 john conway invented his own

cellular automata called the game of

life and it had significantly simpler

update rules than von neumann's version

the most simple version is on a 2d grid

with discrete binary values where the

alive or dead state of every single cell

depends on its eight neighboring cells

the rules are as follows

one

any live cell with two or three live

neighbors

survives

two

any dead cell with three live neighbors

becomes a live cell

three all other live cells die in the

next generation similarly all of the

dead cells

stay dead

even though the game of life doesn't

pretend to be the most sophisticated way

to understand complex systems they are a

wonderfully simple way to get acquainted

in the ideas of complexity science and

in particular weak emergence

now many of the patterns are incredibly

lifelike and that's because these are

class four automata they are touring

complete which is to say they're capable

of representing any computation

now being weakly emergent doesn't

preclude useful analysis i mean for

example it's still possible to model how

frequently phenomena like gliders appear

in the emergent domain given many random

initializations

laws governing the weakly emergent

states almost certainly exist but can

only be discovered through empirical

analysis and observation and simulation

we can identify motifs

systems behaviors mechanisms

high level abstractions even in the

emergent layer but nothing from first

principles in what sense do natural

systems compute

at a very general level one might say

that computation is what a complex

system does with information in order to

succeed or adapt in its environment

morphogenesis means the generation of

form

it's colloquially described in a

biological process that causes a cell or

a tissue or an organism to develop its

shape but in an artificial intelligence

context we can think of it as meaning

the blueprint of emergence of any

physical form

professor sebastian riese recently wrote

an article called the future of

artificial intelligence is

self-organizing and self-assembling and

before you ask yes we'll be inviting him

to mlst

he spoke of a current movement which

combines ideas from deep learning with

ideas from self-organization and

collective systems it's a wonderful tree

ties for emergentist open-ended and

biologically inspired ai enthusiasts

searching for parameters of

self-organizing systems which produce

particular patterns is a difficult

optimization problem

trying to make self-organization

programmable is a research field of its

own called morphogenetic engineering he

said that the merger of these ideas

could ultimately allow our ai systems to

escape their current limitations such as

being brittle and rigid and not being

able to deal with novel situations

however the combination of these methods

also poses new challenges and requires

novel ways of training to work as

efficiently as possible

risi said that one of the most

fascinating aspects of nature is that

groups with millions or even trillions

of elements can self-assemble into

complex forms based only on local

interactions and display what is called

a collective type of intelligence

sebastian gave the example of ants which

can join forces to create bridges and

rafts or navigate difficult terrain

termites can build nests several meters

high without an externally imposed plan

and thousands of bees work together as

an integrated whole to make accurate

decisions on when to search for food or

a new nest

he said that achieving these incredible

abilities is a result of following

relatively simple behavioral rules

through a process of self-organization

kamazin

defined self-organization in 2001 as the

following

as a process in which a pattern at the

global level of a system emerges solely

from the numerous interactions among

lower level components of the system

moreover the rules specifying

interactions among the systems

components are executed using only local

information without reference to the

global pattern

in short the pattern is an emergent

property of the system rather than being

imposed on the system by an external

ordering influence

with the emergence of powerful machine

learning algorithms sebastian said that

the key question is instead of hand

designing the algorithms for

self-assembly can we learn these

algorithms instead allowing more complex

forms to be created

sebastian said that self-organizing

systems are made out of many components

which are highly interconnected the

absence of any centralized control

allows them to quickly adjust to new

stimuli and changing environmental

conditions additionally because these

collective intelligence systems are made

of many simpler individuals they have

built-in redundancy with a high degree

of resilience and robustness

individuals in this collective system

can fail without the overall system

breaking down

sebastian points out that evolution was

able to exploit self-organizational

processes to create artifacts of

remarkable complexity however

human-made designs are normally put

together piece by piece this is similar

to the idea of whether an ai

architecture and knowledge should be

human engineered or revolved blank slate

style such as professor rich sutton

pointed out in his bitter lesson essay

the amount of information it takes to

specify the wiring of a sophisticated

brain directly is far greater than the

information stored in the genome instead

of storing a specific configuration of

synapses the genome encodes a much

smaller number of rules that govern how

to wire up a brain through

self-organizing processes and how

synapses should change based on the

activation of neurons this amazing

compression has also been called the

genomic bottleneck

now when humans engineer bridges or

teach curricula there's always a plan a

pedagogy a curriculum

in biological construction there's no

blueprint well not one which defines the

outcome evolution is a kind of meta

optimizer and our dna is incredibly

compressed it can't possibly describe

the complex configuration of our brains

it's a form of optimization which

transgresses rungs of the ladder of

emergence sebastian says that our genes

contain the information to make the

structure by controlling a sequence of

events during morphogenesis

our final physical form is merely a kind

of sampled materialization of this lower

level process this is very similar to

this concept of inverse diffusion which

happens in the open ai daily 2 model by

the way

now as sebastian says in his article

deeper neural networks are totally human

engineered whether it's the architecture

itself or indeed the optimization

algorithm which is stochastic gradient

descent given enough data deep learning

algorithms can learn to decompose any

space into a highly sophisticated

geometrically tessellated nested

compressed representation

the problem is that this representation

is extremely brittle and breaks with

even minor changes in the environment

deep learning models efficiently

compress what they have seen before with

laser-like effectiveness but the problem

is that many domains are open-ended and

combinatorially large and are not

amenable to memorization in this way

sebastian argues that using emergence

and self-organization might help

robustify neural networks in a similar

way to how biological systems are robust

although he conceded that

self-organization is not the only

principle that allows biological

organisms to display high-level

robustness anyway i highly recommend you

check out sebastian's article it's

brilliant

to follow up a bit on this idea of

centralized versus decentralized if we

look at decentralized systems not always

but very often they sort of

self-organize into a centralized system

for example the brain has the sort of

the prefrontal cortex directing

everything if we look at humans the

first thing humans do is they band

together and they elect a leader right

um if if we build decentralized

computing systems there's always like

one leader and

so how how much how much do you think

this the emergence

of properties such as intelligence or

whatnot is a property of really

decentralized computing or how how

important is this sort of leader

election among decentralized systems and

can we do without it

oh uh yeah i think that's a great

question again you always ask a great

question so

you're right like in many decentralized

systems like our brain or in

civilization

eventually something like a centralized

system is formed

and and usually maybe via our genotype

our genes the same

centralized system is usually formed

across

all humans and in even societal

structures like this

typically you have a leader

or a few leaders and they govern the

society in a few types of

ways right

but but

i i think the emergence of that

structure is very important compared to

uh designing it uh top down at the

beginning uh let me tell you why uh

because like take the example of of say

our bodies or the brain right there

there are cases like the the the way the

uh the structure is is emerged may be

the same for most people but for people

with certain disabilities of unfortunate

disabilities from from birth or

accidents uh

we're able to see

brains or structures evolve differently

but they they still function as a whole

like like certain certain infants are

known to

to have half their brain and like uh

not functioning at birth and you know

like the the it has to be removed like

uh from birth but they still grow into a

functional brain that has a different

structure than what what we

traditionally know for most humans

and and even for for people with

disabilities like like blindness or

death they eventually

their brain structures would would like

change functionalities a blind person

would use their visual cortex to process

audio for instance so so

where the emergence property is very

useful for

for tackling like changes in the

environments as i mentioned in the

beginning so so ultimately the goal is

to have something that will work even

when the environment changes but

it'll work maybe optimally when the

environment is expected but it's not

going to completely not work when the

environment changes

alexander maude vinsef another guy that

we definitely need to get on the show

wrote a fascinating article called

growing neural cellular automata i've

been looking into this and essentially

it's a convolutional or neural network

type architecture which produces what

appears to be an rgb

value for every single pixel but

actually the output is a 16 channel

space including a bunch of other

information they've turned a

self-healing image generation process

into an emergent phenomena and so

they're kind of continuously applying

this convolutional neural network over

the um input space much like you would

do with the traditional cellular

automata except this one of course is a

continuous cellular automata which is

learned with a neural network

but then it has this incredible thing

where if you interactively delete

components of the image or perturb

components of the image it'll

dynamically repair itself which is

fascinating just imagine some of the

applications for this where you could

have self-healing systems and you could

have these agents that

learn to heal a system as an emergent

behavior

so there's this really interesting

intellectual journey here which starts

with discrete cellular automata which

are binary and run on a regular lattice

which is say a two-dimensional grid and

then all sorts of interesting things

happen when we increase the resolution

or run on different manifolds or have

continuous values and then even use

something like a learnable neural

network for performing the update rules

dr danielle gratarola is a scientist and

postdoctoral researcher at epfl he

recently published a fascinating paper

called learning graph cellular automata

which was published in in eurips and in

that work he focused on a generalized

version of a typical cellular automata

called a graph cellular automata in

which the lattice structure is replaced

by an arbitrary graph uh in particular

they extended the previous work which i

just showed you from alex malvinsef you

know which was when they they

learned a 2d convolutional neural

network for applying um the cellular

automaton update rule to now using a

graph neural network and learning the

update rule on that with message passing

it's absolutely fascinating so now i

give you danielle gratarola cool

right let me get my notes out by the way

i've i've just been on a crash course in

cellular automata oh nice

uh it it is absolutely fascinating yeah

um i'm completely hooked on it actually

yeah it is it is fascinating tim i'm

gonna i i have to share with you i have

to share with you my little uh

cellular tama that that tries to do um

you know uh

light casting or shadow casting

roguelike roguelike games oh nice

yeah many of those like tiny games like

even uh i think it's called gnome

fortress something like that yeah it was

an old-school linux game uh it's used

like celero tamato to generate the

terrain and stuff like that it's super

fast fascinating

yeah i played around with with simple

simple cellular automata quite a bit and

little hobby

yeah you know hobby games or simulations

i mean even the um you know tim that

that uh galton board simulation in our

our video that was a solar automata yeah

i hadn't thought about that of course

yeah it's fascinating i mean and by the

way i mean because you linked

alexander's article um you know he did

the kind of the the 2d gridded cnn

version of uh morphogenesis and i mean

maybe you should just introduce i'll

tell you what

we're we're doing this all wrong uh

daniel why don't you introduce all right

right so uh yeah

so my name is daniel i am currently i

just graduated actually from idcia in

lugano so i'm currently working

at epfl in lausanne so i moved to the

french-speaking part of switzerland

and

so right now i'm working in the domain

of proteins

and my formal training during my phd was

in graph neural networks and

at some point i reached out to

my current

let's say supervisors or pi that were

starting out this project on applying

graph neural networks to the protein

domain in particular protein design

which is like

essentially the inverse problem to alpha

fold if you've heard about alpha fold

recently so alpha false goes from the

sequence of amino acids to the folded

structure and one still open and very

interesting problem is so how to do the

opposite so if i want a particular

structure what is the sequence that

would fall into that structure right and

you would think that having solved one

direction would essentially means you've

solved the other but it's still com

computationally expensive to go over all

possible sequence and try and see if

they fall in the correct state and so

like um there's still like this open

question of uh whether the structure of

a folded protein somehow informs uh the

sequence and as you can if you can

predict one from the other uh and so i'm

working in that whole domain

uh right now but as i said like my

background is in graph neural networks

uh during my phd i've worked on a

thousand different things related to

graph neural networks and by the way i

started like 2017 i started my bhd so it

was still at the time where graph neural

networks were starting to emerge a

little bit so there was like this

feeding frenzy of you know finding

applications and trying to see if stuff

worked which was a really exciting time

to be in graph neural networks i should

say um and then like uh at some point

during my phd towards the end i

i decided to link back to one of my

oldest passions which was this idea of

the cellular automata

and and trying to see if some of the

tools that i have been working on had

been working on would actually be useful

to to say something about that whole

world and it turned out it did so yeah

yeah well i i mean i'm so inspired by

geometric deep learning after i spoke

with michael bronstein and and his

friends um but yeah i mean so much of

the work that we've been brought up on

is is uh

euclidean or gridded data and then when

you start to think about some of the

applications that you can do with graphs

and and you know curved surfaces and so

on it blows my mind but before we get

there why don't we go on a kind of

intellectual journey here and start

talking about cellular automata now

anyone who's had the misfortune of doing

leeco challenges in the tech industry

probably would have had to implement

conway's game of life at some point and

um usually the way you know these

challenges are formulated is and they

are binary which means the cells are one

or zero

and it's on a regular lattice usually a

2d grid and you have a whole bunch of

update rules which are a function of the

neighboring cells and then you just kind

of execute all of these rules and you

just get this emergent phenomena happen

when you zoom out it's fascinating so

can you just tell us a little bit about

about cellular yeah sure so basically

the

the short story is what you just said so

you have this uh essentially it's a

computer program or a computational

model that has a state

and typically the status what you said

it's just a bunch of cells arranged in

these regular structures which can be

you know 1d or 2d or even 3d or whatever

and and then every cell has a particular

state of its own and then you have this

transition rule or update functions

however you want to call it that

is applied synchronously to every cell

and essentially decide what the next

state of the cell will be as a function

of the cell itself and the neighbors um

and really the cool thing that you find

is that even though like the complexity

at the level of the rule is fairly low

so you have pretty simple rules that you

can define um you know the behavior that

emerges can be like very life like like

the the tiny creatures that you see

emerging on this on these grids uh

really

you know they kind of click with with

our pattern matching system as humans

because they they look like uh tiny

creatures moving around the grid they're

able to spawn new creatures they're

they're they're able to you know move

coherently and they add periodicity over

time and and so it's either living

things or or engineered things there

they have the same that kind of

regularity that we that we recognize as

interesting um

and that's like the just the basic

version but then

with time people have started to

complicate the definition of cellular

automata right so for example instead of

you know binary you can ask the question

of okay what happens if i allow the

states to be

n and possible states over the grid so

and i can color the states differently

or i can ask you i can ask what happens

if the state is continuous right

and as you start doing that what you see

is that uh the the behavior becomes more

and more complex in a sense even though

uh let's say the common god of

complexity at the level of the rule

remains fairly low as you start

introducing just that tiny bit more of

complication you see this insanely

complicated patterns that emerge as a

result and so for example at some point

people started uh let's say playing with

the definition of the neighborhood right

so you make it a bit a bit larger so

which is equivalent to increasing the

resolution right so your your grid

approximation which if you think about

it like a grid is just a discretization

of 3d space or 2d space right but at the

same time we are like as humans we are

very far from that kind of level of

discretization of space if it even

exists right so we're we're used to

thinking about high resolution in a

sense and so what you what you observe

if you start to increase the resolution

of these models is that their behavior

starts to become you know eeriely like

living things and so you see like tiny

cells forming and moving around and then

they start to organize into membranes

and stuff like that and this all happens

by that same convolution like process

that's happening on this grid

and and that's why i think they're so

fascinating you know leading back also

to your comment before like they have

this

they let you observe

behaviors that typically you only see in

nature but at the same time you are

aware of this

inherent simplicity that the behavior

stems from

and uh and so i'm already like kind of

diverging because this topic like

automatically makes me go on rants of

how these things are super simple and

yet super complicated and super

fascinating

maybe maybe um

just playing devil's advocate here

because i i too love solar automatize we

were talking about before we started the

show

but just to perhaps pull things back to

some grounding here which is that uh

in a way folks working on cellular

automata have converged in some ways to

a very old

set of numerical techniques called

finite difference

you know modeling right so and

the way what engineers do with finite

difference is they say okay look i have

this set of partial differential

equations right and as we know

tons of things in the world physical

phenomena can be described by pdes

partial differential equations and they

say

okay can't solve these symbolically so

but i can do it numerically if i have a

grid then i can start to write down

how the pdes you know result in changing

continuous values based on kind of

neighboring grid cells and they do this

exact thing they create a mesh

they uh write down what uh what

transition rules the pdes would would

imply for each individual cell

and then you run simulations and so you

wind up with things like

you know uh

the equivalent of cellular automata with

continuous values for the wave equation

or for diffusion equations or for all

this kind of thing and so in one sense

it shouldn't surprise us that

cellular automata can reproduce all the

behaviors that we see

in life because indeed the majority of

that or all of it you know stems from

partial differential equations at some

level and we know that we can

approximate those solutions

with cellular automata via the you know

finite difference route

um but at the same time

it feels it definitely feels mysterious

and i think there is something

something deep there and this even goes

back to say mandelbrot right with his

discovery of

of fractals i mean what the heck i just

had this simple little

quadratic equation in complex space and

if i just iterate that map over and over

again i wind up with this absurdly

complex you know in a sense like

infinitely complex

you know boundary and and interesting

connections

so

there's these kind of two opposing

viewpoints i wonder how you how you

reconcile those like on the one hand it

seems very

interesting and mysterious and yet on

the other hand it seems like of course

if we go to a high enough resolution we

can simulate arbitrary differential

equations i think it's like the i don't

know if it's an answer but one possible

explanation of this apparent dichotomy

is uh it's a matter of scale right so if

you go low enough with the scale and by

low i mean you know modeling uh the low

level physics in a sense uh

you probably get to the point where the

skill is so low that everything makes

sense to be modeled as a continuous

differential equation right

and so at some point you know cellular

automata or a set of pdes what's the

difference it's not even that well

defined like it's like a sort of

spectrum that you can decide where you

want to place yourself in um

what is interesting though is that i

think that

this idea of locality

and and having you know update rules or

transition rules or whatever you know

execution kind of engine you want to

have

for your inherent program

at that point it

it becomes

as you go up in the abstraction

hierarchy it just makes sense to

consider your elements yourselves as

discrete objects and then this is maybe

not true if you are if you're modeling

for example the flow of some some water

or whatever for example i had this

professor uh when i was at the

during the bachelor that he was using

cellular automata to model how water

moves in like inside coffee for example

right and and then you can you can then

you can ask the question of okay is it a

cellular automata should i be using some

something else that is actually

continuous but what i think is really

fascinating about the idea at least of

cas is that as you go up in the

hierarchy then it makes more and more

sense to think about you know discrete

agents interacting according to some

rules and at that point the continuum

like kind of gets lost anyway or at

least it gets lost in the way you want

to model it right so if you're modeling

you know again low-level physics it

makes sense to be working with a grid

but if you're you know working out

modeling human interaction for example

which you can probably still

model fairly well as a sort of local

kind of dynamical system

then it doesn't make sense to model

humans as living on a continuous trade

well no you kind of want to model them

as individual

objects in a sense right

yeah what's what's interesting to me is

as as you're bringing up so you were

going in in this direction of

um

if we're at a very low level it might

make sense to think of of a continuum

but then at some level of abstraction

uh things really behave as these

discrete

you know objects or say in the case of

of carl fristen you know a markov

boundary a thing that has this kind of

stochastic dynamic

you know markup boundary yet it behaves

as a unified you know whole um

and and what's odd is that

neither at the highest scale nor the

lower scale

does either continuity or discrete

nature ever disappear it just seems to

be continuously

i shouldn't have said continuously it

just seems to be forever intertwined you

know that okay if i keep going down in

this direction i get to a continuum but

maybe if i go even deeper i get back to

some discrete you know hypergraph or if

i'm going in the opposite direction i

get up to say the discrete level of

molecules but if i keep going it starts

to behave as a continuous fluid if i go

further it starts to behave as a

discrete cell if i go further than that

it's a you know you keep interleaving

back and forth between discrete being

the correct level of analysis versus

continuous being the correct level

analysis that's kind of the mystery is

that they're they don't exist at either

extreme they just are constantly

interleaved that's the real cool thing

that

it's like it appears very arbitrary that

we as humans at some point decide no

this is like i i recognize this as a

layer of of this abstraction it's like

you know i i can

pretty clearly distinguish between being

at the layer of atoms and being at

layers of cells although if you look

close enough then cells are composed of

proteins and proteins and composites of

atoms so you can kind of always go back

uh but at some point there's there's

also this kind of uh

limit uh that defines um or that decides

how far can a layer kind of communicate

with the other layers right so we as

humans we have no agency to interact

with atoms although we are made of atoms

but we have kind of essentially zero

ability to interact with that layer and

so it's like there is a sort of

intrinsic boundary that lets you operate

on some levels of these obstructions and

these levels appear to be fairly close

to one another so i might be able to

influence the level above me and below

me which might be in i don't know if we

want to look at some discretization

maybe i can act on my organs and i can

act on society right one level that one

level up but already i cannot act on my

proteins right or or my individual cells

it's gonna be much much harder uh and as

you go down in the hierarchy and of

course up in the hierarchy the

contribution of that particular layer

becomes less and less relevant right so

it's like it you you're definitely able

uh

to recognize those boundaries or like i

don't know if you can give a precise

definition but there definitely appears

to be some level of

discreteness uh or at least some ranges

where it makes sense to talk about a

level of abstraction that stands on its

own i would say

yeah i'm really interested actually that

there's a kind of observer relative

problem that you know depending on the

ladder of the um

let's call it an emergence ladder we're

on a rung of the emergence ladder and

maybe that determines how we can

formalize and understand phenomena on

different rungs of the emergent ladder

but just to pull the discussion back a

tiny bit so um this is all quite new to

me and i'm fascinated by it i've

actually just started reading a new kind

of science by wolfram uh inspired by all

the links that that you sent us and um

you know one of the one of the first

things to learn about with cellular

automata is is the basic discrete

one-dimensional version and um wolfram's

actually given all of them names right

because if you think about it in the

one-dimensional discrete cellular

automata you have a neighborhood of

three and then if it's binary you've got

two to the power of three which means

you've got eight patterns and then for

every single pattern it could be one or

zero so you've got two to the power of

eight which is 256 things and and all of

those things you know so for example

there's um rule 110 which he says

exhibits class 4 behavior now this is

interesting as well because i'm

interested in you know did he just pluck

this out of thin air that you can kind

of classify the behavior subjectively of

of phenomena in in the emerging uh

domain

and uh but anyway he said class iv

behavior which is neither completely

random nor completely repetitive

localized structures appear and interact

in various complicated looking ways and

and then there's this guy called matthew

cook who used to work for wolfram and

and he said these structures are rich

enough to support universality all right

this result is interesting because rule

110 apparently is is an extremely simple

one-dimensional system and difficult to

engineer the form specific behavior

anyway so i'm reading wolfram's book and

i'm interested like what's he talking

about you know universal communication

and um he he has he has this wonderful

image where he says oh you know look um

here are the occurrences of

progressively longer blocks than the

pattern generated by rule 30 starting

from a single black cell and as far as

he could tell all of the possible

eventual blocks will appear potentially

letting the pattern serve as a kind of

directory of all possible computations

and that was kind of like his argument

about the the uh touring universality so

what's your take on that uh yeah so

they're definitely fascinating objects

in that regard meaning that so i think

that for rule 110 in particular the

argument there is that you can build

logic gates essentially with them

because you kind of have this and i

might be messing up with the specific uh

you know one of the 256 ones but like at

some point you're you're able to uh

shoot this kind of race in one direction

and another in another direction and at

some point if they interact uh the rays

disappear and if they don't interact uh

the array goes on and so it's like a

zero and a one depending on if the rays

survive or dies um and so like

all the arguments for universality of

these models by the way are not

arguments for their efficiency in doing

computation they're just like you know

showing equivalence

is that you can essentially build the

basic machinery that you would need to

perform computation which is like basic

manipulation like the nand gate and

stuff like that and i think that the

formal proof of computation actually uh

goes in a completely different direction

with a different computational model but

like the general idea is that one right

you can simulate a turing machine just

by encoding the various rules in

essentially the state and that's a very

fascinating thing that i've been

thinking about a lot recently because

uh what's what we see and and much of

the things we can do with cellular

automata

are not necessarily uh given by the rule

itself so the rule is always simple and

in fact uh it's not necessarily new in a

new kind of science but i think in the

next work by wolfram which is the

wolfram physics project uh like he kind

of makes this argument that uh the rules

that govern the universal cellular

automata should be fairly simple right

um and so like there is this bias

towards simple rules but the complexity

that we typically observe comes from the

configuration of the states right and so

all of the computation that you might

want to to do with the cellular automata

comes from configuring the state in the

correct way in fact if you google it up

it should should be fairly easy to find

at some point people uh had this

challenge on stack overflow of

implementing a functional clock in the

game of life as it turns out you can't

implement the functional clock in the

game of life you just need to configure

the states in a particularly smart way

and the state in the states will evolve

on their own and they will create digits

and then change the digits according to

the time once uh every second and so on

uh and so this is like this is what i

find fascinating about the kind of

computation that cas do right because

you can prove that they are universal

because you can do basic operations with

them uh but then much of the complexity

that you can actually observe comes from

the actual states that you have to

configure and that of course is by no

means trivial which is also why people

haven't been using you know cas to

implement computers you use different

architectures and computational models

yeah and and to that point and by the

way so the cook proved rule 110 you know

turning complete by mapping it to

another turing complete system like the

cyclic tag systems

or something i think it was and then and

i think there's only one other rule that

might be

turing complete but it hasn't been

proven you know one way or the other

like rule 30

may or may not be touring complete i

don't think this is quite fascinating

right just this little

simple set of rules and maybe the

simplest turing complete system out

there but as you were just saying the

difficulty lies in going from

a simple set of rules and some complex

initial conditions to then being able to

really predict

what the large-scale behavior is going

to be and i think wolfram you know

points us out himself

which is that um

you know he he has this concept of

computational irreducibility which which

essentially says

look uh predicting what this computation

is going to do

is just as hard as actually running the

computation so there's no shortcuts in a

sense you can't you know and it's

related to to you know

turning completeness you know as well or

rather rather the uh you know the

halting problem which is essentially a

similar kind of problem it says that

trying to compute whether or not a

turing machine an arbitrary turing

machine will halt is just as difficult

as running it itself and therefore you

can't yeah you can't do it without

halting or without failing to halt that

sort of thing um so my question to you

is and this is kind of this emergence

question is

is this just an impossible barrier so in

other words is it the case that you know

something in physical reality runs

runs things you know whether you believe

it's a computation or not whatever

there's some substrate that's executing

this uh you know this this automata of

the universe okay and it just it

displays all this multi-scale behavior

and so you get these emergent you know

things happening human beings planets

you know uh super clusters in the galaxy

whatever

is it

even possible in any

in any sense to predict from

lower levels higher level

emergent behavior or is there just this

barrier

that in a sense this irreducible

complexity that we there's no shortcuts

we can't actually predict

a higher layer of emergence or

abstraction from a lower layer one

without just running the universe itself

a very interesting question and i don't

think i'm really equipped to answer that

without making anybody angry i would say

so that there's a lot of speculation

that you can do

uh

don't worry i've made people angry by

just asking a question so yeah so

what i can say is that so first of all

like we were saying before there seems

to be some some degree of

communication or or ability to predict

what the layer above or below you will

do right so if you are let's say

configuring a cellular automata if we

accept that that is uh how the universe

runs so if you're you're trying to

configure or or to study uh cellular

attack at a particular level you might

have some intuition a priori but what

they will do right so it is possible to

engineer an emergent system if you are

you know even without you know running

it necessarily but you probably can come

up with some smart rules that have a

desired behavior that you might want to

have now it's a much more it's a much

harder question to say

can we build a particular cellular

automata that acts like we see in the

universe and and that's like

because that requires uh us to answer

the question of what are we actually

trying to model and at what scale are we

trying to model the physical reality are

we trying to model you know a brain or a

network of humans right um and and that

i guess uh you can also make that

irreducibility argument for intelligence

in general right so do i necessarily

need to model the brain in order to have

intelligence or can i just approximate

intelligent behaviors and and maybe just

train a neural network to do that right

so i think it's a much more profound

question than just what is the cellular

summary doing and how do i reproduce

that in a computer um it's it's a

question of about like the nature of

reality itself and and whether it's the

only possible way to obtain a particular

computation is to simulate it starting

from the lowest possible level now we

have some evidence that this is not

necessarily the case like we're having

some uh some you know models of

computation that are able to emulate

some of the phenomenas we see right um

and so i guess this is you know it gives

us some kind of hope that

we

might be able to design one such system

and people for example have been started

to using

machine learning to try and design

cellular or someone that do a particular

thing right

so there might be

some degree of approximation that we can

achieve without necessarily computing

everything starting from the lower level

and this is in a sense of course

wolfram's uh physics program i think he

calls it is all about

can we start

at the lowest

possible and i mean like finest scale

you know i don't even know 10 to the

minus 100 meters or something uh

you know substrate in the form of this

this hyper graph and then and then

with these simple rules does the

universe as we know it

you know emerge from that at least on

that that seems to be the uh

you know the case and i mean it or

rather that's that's the that's his

program and

could be could be possible um i think

there's so many open questions there and

of course it's a very active area of

research and almost a new branch of

of mathematics too and i or physics at

least and i think um wolfram himself

said if it can do if it can do these

predictions like for example if we can

derive general relativity or you know

quantum mechanics it's it's at least a

century yeah a century out so

you know we have a while to wait but i'm

curious what you think about

the possibility of that so if it if we

have this interleaved so here's a

question we talked earlier about the

interleaved discrete and continuous you

know that as you move along kind of

scales of emergence or reduction you

keep coming across

the need to either view things as a

continuum or is a is a discrete you know

spectrum of something and so it's like

this alternating series you know in math

that we learned that never converges

right it's plus one minus one it never

converges well if you go to zero so if

you go to that end of infinity all the

way down to the smallest possible scale

do you think we arrive at a discrete

system like a hypergraph like like

wolfram's envisioning or is zero

actually a continuum i'm curious what

you think

that answer is and and what you think

about uh wolfram's paradigm of right so

i think that i was reading about this

some time ago and

the question of whether at the lowest

possible level you actually can see

something like a cell and that kind of

discreteness to it i think it's still an

open question in physics

yeah exactly the atom of space like

that's probably from what i understand

it's still an entirely open question in

physics like they haven't been able to

answer that uh and and the question

there would be like can we actually

discretize the notion of space and the

notion of time because that would be an

answer answering yes to that question

would be a fairly strong argument for

wolf from theory of you know the

universe being this huge l system that's

constantly

rewriting itself right um

but of course it's it's difficult to say

like and at some point one should even

ask a question of whether

for us it's even important to be going

at that particular level which is what

you were asking before like do we

necessarily need to answer the question

of whether the universe is continuous to

be doing interesting things and then

then it becomes like a matter of goals

so

personally i find it fascinating to be

talking about all this localized

emerging computation because i see it as

a potential path forward towards agi for

example right um and and and the

question there at that point becomes can

we achieve something like that without

necessarily needing to go and simulate

the whole universe just to get you know

you simulate this huge

environment just that maybe it will

develop intelligence that seems insanely

costly to do for achieving something

that we can describe fairly well

um and so i i don't know really if at

some point it will become obvious or

people will be able to answer the

question of whether the universe is

continuous

which would probably discredit the

cellular automata theory

uh but i think it's interesting that

this idea of cellular automata

especially how you know wolfram has

instantiated it in one particular way

but the general paradigm is much more

flexible in a sense um

it's interesting that we can describe

things with this model and you know

whatever the level we decide to start at

it we also know that if we set the rules

right then we will be able to observe

the same kinds of emergence and so it

becomes kind of arbitrary to for us to

decide where do we start simulating the

the universe or the system we're trying

to simulate right

yeah

i mean

there are so many things to unpack here

i find that's absolutely fascinating you

know so you know how does our universe

work and you know wolfram was kind of

making the point that underneath all of

this richness and complexity that we see

in physics they could just be really

simple rules

so is the universe an emergent

phenomenon and it kind of see i mean

that's it's very subjective right it's

very vague it seems like it is because

when you recreate so many of these

emergent systems they produce phenomena

that look a lot like the universe right

but then there's this notion of well

could we find the exact simple rules and

the exact representation to create

something like the universe and then

there's this notion of irreducibility

and then it becomes very very vague but

what's fascinating though is just by

applying the the same rules over and

over again you can produce something

that looks really really complicated and

that's just not what our intuition tells

us at all

yeah that's true and i think like i just

had this uh you know kind of follow up

to to the discussion which is this uh

idea that at some point

you're interested in understanding the

universe at some particular scale right

so you you might be interested in

understanding intelligent systems or you

know just living system if you want to

be at one level lower and so at some

point the questions you need to be

asking it goes it goes back to what we

were saying before right you if you if

you're interested in a particular level

you don't necessarily need to go all the

way down and start there you might just

go one level lower and start modeling

things there and know that you maybe

maybe you will introduce some

approximation errors but if you do

things well enough then you will kind of

see that emergence and you can build on

top of that layer of player after layer

right and and and i agree that it is

fascinating that this kind of emergence

appears to be like a sort of constant

throughout the different layers right so

you it doesn't it doesn't really matter

the specific rules that are acting at a

particular layer right it what matters

is that the same kind of computational

engine appears to be working at every

layer and so you might have the similar

phenomena happening at the physics level

or at the cell level or at the society

level and the rules will change and in

fact michael actually makes this very

interesting argument about

different layers being recognizable by

the kind of goals they're trying to

solve right and so for example you might

recognize the a layer the layer of

society because it's

trying to solve the goal i don't know of

of surviving as a species for example um

and the rules that you will find at that

layer will be in a sense

emerging to solve that particular goal

exactly like i don't know in a very

similar simple level atoms will have

very simple rules that just try to

satisfy some electrical or physical

constraints right and so as you move up

and down you will find different rules

but the same computational principle so

i will have a rule that tries to solve

an objective through localized

computation and and that is what i

really find fascinating about cas and

and just the general idea of of this

kind of models because they appear to be

reasonable to explain different layers

in this architecture

and so this is really interesting to me

so so i mean this is getting to um

something we were just previously

talking about with a with our other

guests about um formalizing what happens

in that emergent space and actually when

we speak with ai alignment people they

bring up asimov's laws and you can get

into you know utilitarianism versus

deontological

but um

you know the thing is even because we're

gonna get on to your work when we're

talking about morphogenesis and what's

fascinating there is that actually you

almost want to um evaluate the rules

that you're creating based on the

emergent phenomena and then there's this

thing about how do i how do i formalize

the nature of that phenomenon i mean if

i was steve stephen wolfram for example

how would i formalize universe like

behavior right oh this thing's emerging

and it looks like the uni looks like the

universe how do i formalize that

so yeah i think what you're describing

is

a property that we might find in

different aspects of life right once you

have the same rules applied in an

interconnected system of sort and so

there's like this interconnected graph

of of information flow and how you act

on that on that graph so as you have

that system and and it goes on over time

probably at some point you will see some

emerging phenomena and i guess at that

point the question is how do i control

that emergence like how can i introduce

some sort of metric of my own to try and

understand what's going on and how to

control it which

to which i would answer that it's

impossible to tell a priori like it's so

task dependent and it's so dependent on

what you're doing that

like if you are trying to optimize for

something then you should have

you should go at the level that we were

saying before like you should go at that

level of abstraction and trying to

understand what are your goals at that

point right so it could be that you're

optimizing for the overall success of

the company

or or whatever it is that you're

developing code for right and so you

might introduce that as a higher level

goal

and hope that what's happening at the

lower level

gets optimized to it to essentially

achieve that objective right which

nature has done to selective evolution

but if you're trying to introduce

that signal into your own control

process uh you you might need to to do

some particular actions at the lower

level so that maybe you can achieve that

higher level objective

i know but this is the tyranny of

objectives though right there's the

shortcut rule there's all of these

because as soon as soon as you formalize

something you you block stepping stones

and and you exclude the actual behavior

that might lead you to where you

actually want to go yeah it's

fascinating but um i do want to move on

a little bit i want to kind of slowly

move the conversation towards your work

but i want to go via this fascinating

article that you that you shared with me

about morphogenesis and actually it was

by this guy i think he's at google he's

called alexander maude vincent vince

and the article was called growing

neural cellular automata and it was

performing uh morphogenesis and more for

jet i mean that sounds like a

ridiculously complicated word but it's

about um you know it's essentially how

if i perturb something or if i have some

initial starting state how could i how

could i create something that i want to

uh create right so um this was using a

cellular automata on images on the 2d

plane and he was able to design a

cellular automata and an update rule

which would quickly converge to a

desired image so there was a a picture

of a lizard

and you could you could damage it and

perturb it and then it would it would

just come back to the lizard and

it's just it's it's incredible to me

right because um it's like from these

local low-level rules you could actually

create something that had global

coherence yeah and i've just never seen

anything like that before so um tell me

a bit about that article yeah that's

amazing uh so that article in particular

uh was inspired by uh this idea of the

flat warm which is like a tiny creature

that if you take it you cut it in half

like both halves are able to regrow into

the whole thing like independently and

so the the question there was how can

this animal be doing this like because

you know the decision to grow is a local

decision and the decision to stop must

be a global decision so there must be

something inside the growing process

that's somehow coordinating the global

shape right and and in fact this this

idea of morphogenesis in cellular

automata was already uh present in

literature of course um and people like

had been doing it uh even ten years

priors uh you know trying to generate uh

or to generate like uh flags so you have

like three states uh cellular automata

with uh different colors and you try to

arrange the cells of a particular color

in a particular region of the images

that you can generate like the flag of

italy or the uk or whatever right so you

can kind of uh see that it grows into

that shape um and what they did in that

paper was bringing it to the absolute

next level right so it was looking at

this platform and say okay it's able to

regrow into the full thing okay can we

do the same thing with a neural network

and so can can we learn to do the same

thing because this goes back to probably

what we were saying before which is

designing these kind of rules can be

insanely hard like you don't know what

the rule is that just by letting it

evolve locally on inputs of pixels

it eventually gives you the lizard or

you know they have this smiley emojis

they have different kinds of emotions

and images

and so how do we design that well the

answer in that case was well we'll take

a convolutional neural network which if

you look at it has essentially the exact

same kind of

shape as the cellular automata so it has

like a local three by three kernel uh

that updates the the state of every

pixel uh synchronously so it's like

there's there's a lot of overlap there

and they said okay let's just uh train

this neural network

in a recurrent way so we're just gonna

propagate forward and then use by

propagation through time to adjust the

weights so that after some steps of

computation we land in a particular

object or objective state um

and and so this is this is what they did

and they were able to

to to make this very very robust

actually so they were able to have the

image grow from a single pixel into the

full thing and then you can start trying

to make that robust perturbation so you

put what happens if i cut the image in

half i would like to grow it i would

like it to grow back into the full thing

and you can actually can introduce that

type of input output examples in the

training process and so that's what they

did and then they have this whole

analysis of what the cellular automata

does

or the neural cellular automata does

for example they let it evolve

way past the training horizon that it

they trained it for uh and so they let

it compute over and over and over again

and at some point what happens is that

it breaks the stability and it kind of

starts producing the same pattern

everywhere on the image so it kind of

the single lizard becomes a pattern of

textured lasers everywhere and in fact

they actually have done some really cool

follow-up work where they actually do

the same to actually generate textures

so you can use that instability to

generate textures on an image um which

is very cool and uh and nature like if

you look at the images

well it is possible to because i know

they did a whole bunch of stuff to

robustify it if you like but it is

possible to make it lose its global

coherence so like on the lizard i would

press in the middle of the lizard and if

i kind of oscillate the mouse cursor a

little bit i could make the lizard grow

another pair of legs and feet yeah but

what fascinates me is is that this is i

don't think it was synchronous either i

think they um to make it resemble real

life a little bit more they they formed

the the update rules randomly and and

stochastically but um it's incredible

though isn't it that just by having

essentially what is a filter back i

think it's a bit more complicated than

that they have a notion of if it's

growing and dead and alpha they've got

about 16 different values of are they

not just rgb for every single pixel but

but but basically it's it's a gridded

cnn and you're just updating this thing

and you get an insane amount of global

coherence from these bottom-up rules and

there are loads of people we're speaking

to that that think that ai must be top

down you know it's not possible for it

to be bottom-up but but this is this is

fascinating right it is it is and so one

thing that i find fascinating is that

there is absolutely no reason why this

should work like at all there is nothing

that we can observe that says that these

kinds of rules should exist at all this

this model in principle is it's like

it's too simple for it to actually work

but in fact it turns out that these

models that these cnns in particular uh

and then in like in my own work we

proved it for for genetic graphs but

like these are universal models so if

there is some kind of computation that

can be expressed in the cellular somata

and like you know by extension as a gnn

as a cnn

then the cnn can implement that

computation and i think that it is

really fascinating that this computation

exists so what what this paper answers

to me is it's not the question of

whether can we do it with a cnn but the

really fascinating thing is that yes

this can be expressed as a process that

you know iteratively and locally kind of

grows the image into what we want and

that's a real fascinating thing like

that

they were able like to actually do this

at all and it is not at all obvious that

they could and but yeah they could do it

yeah

i think the important thing for the

listeners to know is that

yes it has this the small grid which is

its input however the cellular automata

is absolutely not the simple rules you

know that we're used to right like it's

actually a

a a relatively deep

you know neural network behind that

taking a look at that input deciding you

know what to do is that correct oh yeah

i mean it depends on what stream by

complexity like i i would say that you

know being able to compress the

information of the image into you know a

relatively small kernel of a cnn it's

still a

fairly simple way of doing it right so

maybe it's not as simple as you would

have the game of life so you still have

several thousands or probably even

millions of parameters in that neural

network but it's still like it's

encoding a lot of information and

especially what's fascinating to me it's

not that it's just like outputting the

image one shot which of course you know

there would be better better ways to do

it but the fact that it's doing it like

iteratively

like this is a process that by you know

by applying the same rule at every pixel

and doing it doing so iteratively it's

able to output the image and so this is

what i think is really fascinating

yeah so i agree with that i'm just i'm

just trying to set a baseline here so

one thing for the listeners to