After a few million interactions, magic

happens, which is that you go from noise

to programs. You start to see uh complex

programs appear on these tables. This is

the most exciting plot that I've made in

the last few years, and it's the one

that's on the cover of the book. You can

see that in the beginning, it's not very

computational. And then a sudden

transition takes place here. It looks

like a phase transition.

This is the book that I hear is making

the rounds at Sakana, which I'm very

happy to hear. The big one on the right,

what is intelligence is sort of the Lord

of the Rings. And what is life on the

left is kind of the Hobbit. So it's kind

of the single and it's also chapter one

of of what is intelligence. So it goes

kind of inside the other one. Mostly

what I'll be talking about today is is

what's in these two books, but with um

with quite a bit more detail, more

mathematical detail since I think this

is a really good audience for that. And

I'll also be connecting it uh a bit with

some of the the bigger themes of the A

life conference and community and dare I

dare I say even movement. You know in

particular I actually wanted to begin

with this wonderful sort of open

problems in artificial life uh summary

paper which you know has a number of of

very illustrious co-authors uh you know

at least one of whom we heard from

yesterday and and more than one of whom

are are here at the conference. This is

uh you know open problems uh 14 open

problems in artificial life in the year

2000. How does life arise from the

non-living? Uh how do the transition uh

to life uh in an artificial chemistry or

in silicon environment can occur and why

it occurs? I'm sure many of you know

this was the the problem that bedeled

Darwin. You know he made one of the most

uh rich and and uh explanatorily

powerful theories in you know ever in

science in in discovering how evolution

works. But he was unable to explain how

evolution got started. Uh he at some

point in one of his letters said, you

know, you might as well talk about the

origin of matter. Um I think that the

origin of matter and the origin of life

might actually be one and the same thing

and evolution might actually be the

answer to that question, but it's an

evolution that includes uh a term that

Darwin did not account for in his

original formulation. In section B of

these questions, uh determine what is

inevitable in the open-ended evolution

of life. uh I'm I'm hoping to speak a

little bit about that too. Create a

formal framework for synthesizing

dynamical hierarchies at all scales and

develop a theory of information

processing, information flow and

information generation for evolving

systems. Um I won't be going into the

information theory in any detail. Um but

uh but hopefully we'll we'll set up the

problem in in a perhaps somewhat new way

that that I I hope will help to do that.

Um and finally in section C, how is life

related to mind, machines and culture?

Um if I have time, I will get into this

as well and talk a bit about the

emergence of intelligence and mind in an

artificial living system and uh the

influence of machines on the next major

evolutionary transition of life. So uh

you know it was really cool to to read

this paper from 2020 and to see how much

of the perspective uh that that um uh

that you had already been exploring then

uh you know feels you know right and

consistent with uh you know with with a

sort of fresh look at this at these

problems in 2025. Let me just begin with

uh with this question of souls. It used

to be in the 19th century and and

earlier uh that we thought that uh life

had some vital force or spirit that

animated it and made it different from

inanimate matter. In the 19th century

when we began to figure out organic

chemistry and be able to synthesize ura

and so on u the the idea that that no we

should really adopt a strictly

materialist perspective because there's

nothing special or different about the

matter in us versus the matter anywhere

else in the universe uh took hold. And

that's progress for sure. But um but it

also you know when we when we embrace

atoms and materialism fully we're left

with some uh some questions about you

know what differentiates life from

non-life then you know like what can we

even say about life there are at least

some biologists who who say well maybe

it's not even meaningful to talk about

any difference between life and non-life

but I I don't think that that's true uh

and I think that the answer to the to

the conundrum is to invoke function

function is the thing that life has that

non-life doesn't have. In other words,

if we, you know, just to give you a

little parable, if I were to come back

from the future with this object and you

ask me what it is, uh, and I tell you it

is an artificial kidney with a

100red-year lifespan, you can implant it

in a body and it'll it'll, you know,

it'll work the way your kidneys do.

It'll it'll filter ura from the blood

and so on. Um, that's a really important

piece of information, but it's not a

material or a materialist piece of

information. It's not something that you

could read off from the atoms. uh and

you know those atoms could be I don't

know tungsten filaments or carbon nano

tubes are made out of some technology we

don't understand now or it could be

organic it could be made out of uh

cloned tissue um and and the point is

that it working as a kidney doesn't

depend on that matter there is a kind of

separation of concerns between the

matter and the function and so there's

some real sense in which the function is

like a spirit or like something like

something immaterial it's not material

and yet it also relies of course on the

physics of what's going on you can't

have the spirit without the matter as it

were. So function is really important

and uh and function is something that uh

uh you know a rock on a non-living

planet uh somewhere doesn't have. You

know if you if you break a rock on a

non-living planet you now have two

rocks. You don't have a broken rock. Uh

if you break a kidney you now no longer

have a working kidney. That's the

difference between something functional

and something non-functional. This idea

of function was formalized by Alan

Turing who never intended the touring

machine to actually be built uh when he

wrote it in 1936. But there is one that

was built by Mike Davyy in 2010. I don't

need to review Touring machines with all

of you of course um uh you you all know

how they how they work. But I do want to

review briefly uh Vonoman's update to

Turring's thinking about computation uh

which which he did a few years later.

This was published postumously after

Vonoman died. Um but the idea behind

behind vonoman's thinking is he was

trying to answer the same question that

Schroinger had quite had asked in his

what is life book. Uh and in particular

he was trying to ask the question if you

have a robot that is swimming around uh

on a uh you know in in a pond and the

pond has lots of loose Legos around.

There were no I don't know if there were

Legos in 1950 but let's pretend there

were Legos in 1950. And the job of the

robot is to assemble those Legos into a

new robot like itself. you know, there's

something a little bit mysterious about

that. It feels a little bit like pulling

yourself up by your own bootstraps or

like a paradox. And so he asked, what

does it take for something to be able to

make something like itself? Uh, which

seems uh hard, almost paradoxical. And

his conclusion was, well, you need to

have instructions for how to make a MI.

You need to have a tape with

instructions for how to make a MI, and

you need to have a universal constructor

that will follow the uh the instructions

on that on that tape in order to

assemble the necessary parts. And you

also need to have a tape copier uh so

that you can give your offspring uh a

copy of that tape. And by the way, the

tape has to also include the

instructions for making the universal

constructor and the tape copier. And if

those things all hold, then you have

life. You have something that can build

itself. Uh and uh what's what's so

profound about about Vonoyman's insight?

I mean, first of all, he predicted all

of this before we knew the structure and

function of DNA, before we understood

what ribosomes were or had discovered

DNA polymerase. So he called it exactly

right. Those all of those things really

do exist uh inside cells and he figured

this out from pure theory never having

set foot in a bolab. The the profound

insight is that he said by the way a

universal constructor is a universal

touring machine. Those are literally one

and the same thing. And by by making

that observation what he discovered was

that life is literally embodied

computation. It is computational. You

cannot have life without having

computation. So obviously not everything

that is alive reproduces but everything

that is alive has to be able to make

itself. It has to be able to do some

combination of healing, growing,

maintaining itself, reproducing. All of

that is autopoesis. All of that involves

self- construction and all of that

necessarily involves a universal

constructor. Now what do I mean by

embodied computation? This is a really

important distinction between vonoyman

and touring. in touring the symbols that

the that the head writes are different

from the head itself and the tape and uh

and the table of rules that the that the

head follows whereas in vonoyman it's

it's more like a 3D printer uh the the

memory is atoms not abstract symbols in

other words uh you know you could think

about a touring machine as like this

laptop uh you know which can't extrude

another laptop out the side but a

vonoyman replicator is like a

combination of a laptop and a 3D printer

that can print another laptop. So its

memory is actually atoms. Uh that's what

I mean by embodied. So I don't mean

embodied in the ways that a lot of

roboticists talk about embodied. I mean

that that there is a closure between the

uh the medium in which the computation

happens and the thing that is actually

doing the computation. That's the key.

So uh computation that is embodied in

that sense and that is autopetic is

alive. You can't reproduce non-trivally

evolvably without without uh

computation. No computation, no life. Uh

I do want to say a word briefly about

what I mean by computation. Uh and in

this I'm following the the work of uh

Susan Stephanie, Dominick Horesman, uh

Rob Wagner, Viv Kendon. Uh this is from

a nice paper they wrote in 2023 relating

uh the evolution of a physical system

and the computation that it does. So you

know on top you have logical gates, on

the bottom you have uh you know

transistors in in your computer. Uh this

is important because you know there's

there are no bits in a computer. There

are just voltages that go up and down.

In fact, you know, even the voltages are

an abstraction of something further, you

know, if we go further down. But you

know the the point is that you have to

coarse grain those voltages into bits

and then you have to have a logical

machine that talks about how those bits

uh evolve. What are the what are the

what are the computational processes

that those bits undergo and there is a

mapping from the physical system to the

logical system and vice versa. uh when

we say something computes what we mean

is that it is possible to construct such

a mapping and that therefore as the

physical system evolves that is

equivalent to the logical system

evolving. Uh so you know there are some

caveats you can have stochcastic

computation in which there's a little

bit of randomness injected so it doesn't

have to be fully deterministic. Uh

another really important caveat is that

you don't want that description to be

infinitely complex. Otherwise, you could

have the trivial case of saying like,

you know, the water in the sen is a

computer and the longer my computation,

I just need to make my description

longer and longer in order to match. No,

that doesn't work either. You need a a

kind of alchems razor uh description

that uh for it to be valid. But this is

a good definition of computation, but it

emphasizes that there is something

subjective about computation. You need

to have a model for how the uh how the

physical system translates into the

logical system in order for any of this

stuff to work. There are implications

about entropy, free energy and heat and

so on in this model. Uh and in

particular uh you as you all know we've

talked already you know ectctor Zenil in

his very elegant uh talk of a couple of

days ago talked about uh and actually

Chris Kempus also talked about the

landour limit uh and the fact that in a

computational system you're constantly

reducing the entropy of of your state

space and in doing so you therefore

require free energy. So uh you know you

need need to have free energy available

and you need to eject waste heat. The

exception in a way only proves the rule

which is reversible computation. In

reversible computation you generate

ancill uh and that's equivalent to just

saying there's no exhaust but you know

then you either have to keep on making

your computer bigger and bigger and

bigger as you accumulate these ancill

you have to uh shrink what you consider

to be the computer and then you're back

to reversible to to non-reversible

computation once again. three important

fallacies that I want to point out

before continuing. One of them I will

call the Seapolski error. Robert

Seapolski you know has written famously

about uh people not having free will uh

because we're built on physical systems.

Uh you know the physics is is uh you

know if you like deterministic let's set

aside quantum mechanics uh and stuff

like this. Let's let's imagine we live

in a Newtonian universe. It's fine. It's

good enough. The point is that physics

is reversible. uh all of the basic

physics that we understand uh whether

that's you know Newton's equations

Maxwell's equations Einstein's equations

quantum mechanics all of those are

essentially time reversible uh so you

can move them either forward or back

computation is not reversible when I add

you know 3 + 5 to get 8 once I've got

the 8 uh and I've you know I haven't

kept my ancillates around let's say I no

longer know what was added in order to

make the eight computation is inherently

irreversible and so to say that what

true of the physical system is also true

of the of the computational system or

the logical system is is not is not the

case and reversibility would be one

trivial example of how that is not the

case. Causation by the way only makes

sense in the light of irreversibility.

All right. So if you have a purely

physical system then you know to say

that A causes B is equivalent to saying

that B causes A because you know

everything is kind of a block universe

if you like in a uh you know in in that

kind of setup. But in computation uh you

know you you can you can talk about

causality because there are ifs and

thens in there. And this once again

connects with the way uh you know the

way ectctor was talking about how you

know essentially nothing in nothing in

causation makes sense except in the

light of computation. Uh which I fully

agree with. Uh another fallacy uh we

could call the the early victinstein

error. If we say something like birds

exist in the world uh line one of the

tractatus logical philosophy didn't say

birds but whatever. You can't say birds

exist or birds don't exist in a way that

is independent of a model of the

universe. Uh there are no birds in

physics. There are no birds in this

underlying dynamical system. When we

start talking about birds, we already

are talking about having some kind of

some kind of model. And once we start

talking about models, uh you've got

causality, reversibility, all kinds of

other irreversibility, all kinds of

other things in play. And none of these

statements are are are airtight. Uh they

all rely on on an observer. Uh this is

kind of Kant as well I guess. Uh and

this leads to the the early linenets

error uh or the same error that the good

old F good old fashioned AI

practitioners had which is that that

intelligence could be carried out by by

just having a series of uh programs of

of sort of strictly logical uh you know

deductions or inductions. That doesn't

work. This is why good old fashioned AI

never never panned out. And and the

reason is that that you can't start out

with like in math with propositions that

are self-sufficient. Even math is not

self-sufficient, but let's pretend for a

moment and just move from there and kind

of do an algebra in order to work

various things out. When when your

propositions are not airtight and when

you're looking only at regularities and

patterns, this good oldfashioned uh AI

idea simply cannot work. And that's

that's why we never got it to work.

Let's move now to to some of the

artificial life experiments that uh that

uh that I began playing with in at the

end of 2023 and my team and I published

in June of 2024. So just about a year

ago. I think some of you uh many of you

perhaps have heard of these. They're in

the what is life books and I've talked

about them a few times. The the basic

setup here is to try and get

self-replication to get you know

abiogenesis the emergence of life from

non-life to happen in a purely

artificial life system. Uh okay so the

setup is to begin with a minimal touring

complete language uh I used brain [ __ ]

uh because I I really liked the idea of

being able to talk at a conference and

say brain [ __ ] over and over and I'm

fundamentally 12 years old on the

inside. Um but but also because it's

it's uh it it very closely models uh the

touring machine. Uh you know it's it's a

it's a a minimal programming language

only only eight instructions that uh

that looks very touring machineike and

moves the head back and forth. I should

say that in its original version brain

[ __ ] is not embodied computation. It has

basically a separate data tape and code

tape and that means that it cannot make

a copy of itself. So I I made a couple

of modifications to brain [ __ ] that

actually reduce it from eight

instructions to seven in order to make

it embodied. Meaning that as it works on

the tape, it is able to read its own

code and write and write its own code on

that tape as well. There's no separate

console. There's no separation between

the data tape and the uh and the

instruction tape. For those of you who

are unfamiliar with BrainFuck, there is

hello world in it. I'm sure you've

already figured out how it works by just

looking at the program. Um I actually

still haven't, I have to admit. By the

way, this is actually the French brain

[ __ ] page because I thought it was

better uh but translated into English.

It's funnier to read it that way. These

are these are the eight instructions.

You know, the first four are move the

head one step to the left, one step to

the right, increment the bite at the

head, decrement the bite at the head.

We're already halfway through. There's

an input and output instruction, which

in this case really just copy from uh

from one head to another. And there are

jump instructions, open open bracket and

close bracket in order to be able to be

able to make loops. Uh and that's it.

That's all that's all brain [ __ ] is. So

how does how does the uh AIFE experiment

work? The AIFE experiment is called BFF.

Uh the first BF stand for brain [ __ ] and

the second F uh you can draw your own

conclusions. Um but uh you start off

with with a soup of of uh uh I I

actually generally use just 1,000 1,024

tapes. Uh that's enough for this

experiment. Uh so the tapes are of fixed

length. They're of length 64 and they

begin random. So just random bytes. Now,

if a tape is random bytes, that means

that only one in 32 of them or so are

even valid instructions. Most of them

are nos. A no-up will just be skipped

over uh like in most uh programming

languages. So, um so this is what those

tapes look like in the beginning. And

you can see that, you know, the uh I'm

not printing the noops, right? So,

that's all the blank space. Uh the the

operations are quite sparse. On any

given tape, you only have an average of

two instructions or so. And then the

procedure is to pluck two of these tapes

out of the soup at random, concatenate

them end to end, so you have 128 bytes,

and then run uh and then after running,

pull them back apart and put them back

in the soup and repeat. That's it. So

it's just that over and over. That's the

entire experiment. Uh so I'll show you

what happens uh on my laptop

after a few million interactions. um

magic happens which is that you go from

noise to to programs. You start to see

uh complex programs appear on these

tapes. And this is quite wonderful

because these programs take uh you know

they take real effort to reverse

engineer when you when you study them.

You know you it's like studying that

hello world program. You have to you

know they're they're functional in the

sense they really do something. Uh and

it's not trivial to figure out how they

work in order to do that. Uh okay what

are they doing? Well, they're definitely

copying themselves or each other

somehow. We know that because uh if you

know this is a histogram and you could

see, you know, in this case there were

8,000 tapes, there are 5,000 of the top

one, 297 of the next one and so on. So

there's clearly copying going on and

there's this ecology of programs all

copying each other. Uh which is which is

just wonderful to see. I mean that's

that's that's that you know emergence of

of of life in this very functional

minimal sense from randomness. A part of

this is very easy to understand. You

know why why do these things emerge?

Well, because something that copies

itself will be around forever and

something that doesn't copy itself will

be copied over by something that can

copy itself. So, inherently uh something

that can copy itself is more stable than

something that cannot copy itself. So,

it's really just the second law of

thermodynamics but uh but doing

something unexpected which is creating

something more complex because it's more

stable rather than something less

complex which is less stable. This idea

that stability doesn't necessarily mean

uh mean low complexity was worked out in

some detail by Adi Pros the organic

chemist in another book called what is

life. Uh he calls it dynamic kinetic

stability. Meaning usually we think of

stability only in terms of fixed points

in a phase space. But a cycle can be

even more stable than a fixed point. Uh

of course for these cycles to work you

need an input of free energy. Uh but you

know for reasons that we've already gone

into. Uh okay. So mystery mostly solved

but actually mystery not fully solved uh

for for reasons that I will that I will

uh show in a second. But but just to

give you a sense of what of what this

transition looks like from non-life to

life. It's very dramatic. In the

beginning uh you know these interactions

uh only involve you know there only a

few instructions in the soup. It's a

touring gas as Walter Fontano would have

called it. When you do the join and you

run only two operations run in any given

interaction on average uh as as you'd

expect. And that's what it looks like by

the end in this particular run. Uh and

1,374 operations on average are running

per interaction. So the soup has become

intensely computational. Uh there's been

a transition here. And there's a lot

more code uh than than one in 32 uh

bytes. As you can see, this is what that

looks like visually. This is the most

exciting plot that I've made in the last

few years. And it's the one that's on

the cover of the book. So what I've

drawn here are 10 million dots. It's a

scatter plot of interactions. The x-axis

is time and the y-axis for every dot is

how many computations took place. How

many operations took place on that

interaction and you can see that in the

beginning it's not very computational.

And then a sudden transition takes place

here at at 6 million interactions and it

becomes intensely computational. It

looks like a phase transition. In fact,

it is a phase transition. You can also

see that in the the entropy of the soup.

So here I'm just ent I'm just estimating

the entropy of the soup by zipping it

and looking at at the size of the zip

relative to the uh to the whole thing.

You can use any compression algorithm

you like. In the beginning it's

uncompressible. So it's a gas you know

in that touring gas sense because all

the bites are random. And you can see

that there's a dramatic change and

suddenly it becomes extremely

compressible right at that transition

moment. And of course this becomes

compressible because there everything is

copying uh right itself and each other.

So if things are copying themselves then

they'll we know that they'll become very

compressible. But it's cool because if

we think about what the phase of matter

is on the left, it is just like a gas.

Nothing is correlated. What would we

call the phase of matter on the right?

It's not a liquid. It's not a solid.

Right? It has structure. It has

structure at every scale. I think you

have to call that phase of matter life.

Uh that's it's a functional phase of

matter. Uh it means that uh that it that

its parts are different from its other

parts. And if you zoom in or out, you

see more structure. So it's what David

Walpert would call self dissimilar. It's

not a fractal. It's a more like a

multiffractal. I'll explain why in a

moment. Uh okay. Uh how long does it

take this transition to happen? Well um

the the answer is it looks more or less

like an airline distribution or uh a

little bit more precisely like this uh

distribution I call a lockpick

distribution which imagines that there

are steps that have to be undertaken and

those steps have a longtail distribution

of difficulty. And how many steps does

it take? Well, the answer is 12. It

takes 12 steps just like uh getting

sober. I suppose this is a you know a

fit of the empirical to the you know to

the heirlong and the lockpick

distribution is a little hard to see but

the lockpick is a bit better than

heirlong. Heirlong assumes pson lockpick

assumes longtailed but it's a process

phase distribution and and what this

tells you is that there are stepping

stones here. You know you can't get that

transition to life immediately. So

something interesting must be going on

here on the left other than just

randomness. It takes multiple things

happening in order to get to that point.

You know in this case you know it

happens somewhere between 1 million and

uh let's say 7 million uh interactions.

Okay. So um this all suggests that

pretty much any universe by the way that

has a source of randomness uh and can

support computation uh will evolve life

uh you know for this simple dynamical

stability reason. But the big mystery is

why does why does it appear to get more

complex over time? Uh you might have

seen in my little video that you know we

saw some programs emerge and then we saw

the we saw them sort of densify more

instructions appeared and and even more

fundamentally why does this work even

without mutation? I didn't mention but

you know in the original version of BFF

I added some random mutation because you

know we're all taught in school that the

way the way evolution works is chance

and necessity. you know, you mutate

things. You're sort of throwing

spaghetti at the wall and whatever

sticks is what is what does better. And

so you need a source of spaghetti. But

if you do this entire experiment with

the mutation rate cranked all the way

down to zero, you still get the same

exact phenomenon. And that is very

mysterious because if you crank mutation

down to zero, you should have no source

of novelty. You should have no

evolution. Why do you still get this

apparent complexification even with zero

mutation? Uh so let's let's go into some

of the some of the theory of this. By

the end uh we have a replicating entity.

It can engage in standard sort of

population evolution dynamics. This is

the kind of of differential equation

that that one generally writes for this

sort of thing. It's a very general

unsat. Uh this is for you know uh

species uh I let's say they're n

species. They could be chemical species.

They could be biological species

whatever. Here's a classic example of of

such an ansat. This is the uh the lotka

volta equations for predator and prey

which I'm sure many of you are very

familiar with. They were co-invented or

or invented independently by Alfred

Lotka and Vto Volatera near the

beginning of the 20th century. This is

what the classic lota equations look

like. There are two species. There is a

prey species and a predator species. And

those four terms are uh reproduction,

getting eaten, uh eating to reproduce

and background death rate. So uh if you

got those four terms, you get these nice

oscillatory solutions uh you know

between your predators and your prey

that arise. Okay. So this is a slightly

more general form of those lotka volta

equations. There is a linear part which

we'll call rx and uh in lotka volta that

linear part is diagonal. Uh so you know

the the uh the wolf can't turn into a

rabbit, the rabbit can't turn into a

wolf. So so the reproduction is

diagonal. And then there's also a

bilinear term which is the the part

where predation, competition and the

fact that niches are finite uh gets

implemented. So the the the right part

is suppressive. The left part makes

things grow. The right part makes things

uh um squish squish down. Keeps them

finite.

But this can't be the whole story of

evolution. Why can't it be the whole

story of evolution? Well, of course,

because it's closed-ended. Uh you know,

we only have two species here. It

doesn't matter how long you run this

damn thing. You're not going to get a

third species. Uh and uh and you're not

going to change the design space either.

uh you can have you know very

complicated terms in here that allow

finch beaks to adapt to different uh

environments but you have to have the

space of finch beaks predefined before

before this uh equation can even be made

to work. So uh this doesn't you know

this doesn't answer the question of how

evolution gets started. It doesn't

answer the question of what happens uh

afterward other than optimization to uh

to niches.

So uh now we bring in another uh Eastern

European uh Dimmitri Sergeovich

Meshovski. So he's the one who first

came up with the idea that maybe uh

mitochondria engaged in some kind of

simogenetic event in order to end up

inside other single-c cellled organisms

to make um to make ukarots. This was

popularized and proven to actually be

the case by Lin Margulus uh in in 1968.

Uh one of the really great papers in

biology from the 20 from the 20th

century. uh I'm sure many of you are

familiar with this is that paper sorry

1966 on the origin of mitosing cells. So

she's the one who proved uh that

ukarotes were actually a fusion between

two different kinds of procarots and

popularized this term that Medishovski

had invented symbioenesis.

Okay. So could symbioenesis be happening

as a as a source of novelty in BFF? Yes,

that is the source of novelty in BFF and

indeed that is the source of novelty in

evolution period. This is something that

Lin Margulus believed. Um but uh that

was not uh that had not been widely

accepted by the by the by the bi biology

community even by the time of her death

uh in 2011. Um you know so she she had a

much more expansive idea about about why

symbioenesis was important. Uh only the

particulars of chloroplasts and

mitochondria had been accepted. So the

way we can look for symbioenesis and BFF

is to look for replicators emerging

before that phase transition. And if you

look for them, if you just look for

stretches of bytes that are getting

copied during those interactions, you

find such stretches of bytes. They begin

short and kind of crappy, unreliable,

but they're there from the beginning.

Every time you have a single copy

instruction, after all, one bite is

getting copied from somewhere to

somewhere. So almost by definition, you

have at least one bite long sequences

that are getting copied right from the

beginning. So let's just call them

replicators, right? There are

replicators there from the beginning.

Now if you have these one bite

replicators that are copying themselves

back and forth now and then once in a

while they will come into conjunction

and two of them will will copy better as

a group than the than the two of them

copied on their own and that when that

happens then they'll start to copy as a

group and that is a symbiogenetic event.

uh and and so basically the reason that

even without uh mutation you get these

complex programs arising is because of

these fusion events between smaller

replicators.

So uh can one build singenesis into an

equation like uh like this one that you

know for for lot of volta you can this

is our statistical physicist who came up

with the right kind of term to write

mathematically for describing how

symbioenesis works. He wrote down an

equation for the coagulation of

polymers. Uh so this is uh small hovski

coagulation. Uh this is what happens

when clouds form. It's what happens when

gelatin sets in the fridge. Uh so the

idea is that you have uh let's say

polymers that begin uh as monomers you

know one monomer another monomer they

they stick together and now you have a

dimer and now the dimer and maybe

another monomer stick together and you

have a trimer. Uh two trimers stick

together and now you have a heximer and

so on. These are the equations for that.

This is the mass balance equation. It's

it's very simple. There's a merger gain

term and a merger loss term. The merger

gain term which scales like the

densities of the two things that are

coming together. Uh and the product of

those with some merger kernel K is

increasing the population of cluster K

which is of length I plus J. And then

you have to do the balance of that.

Every time you have two things coming

together to make a new one, you have to

then subtract their populations I and J.

And that's what the right hand side is

about. It's the loss of things that have

merged. So you put those two things

together and you get a stochastic

differential equation for mergers in a

solution.

And by the way there is a phase

transition associated with small husky

coagulation. It's called gilation. And

it's exactly what happens when you put

jello in the fridge and it sets.

Basically, if things are sticking

together and if they stick together with

a scaling exponent that is greater than

one, then you get this finite time

singularity in which the the the things

that stick together diverge to infinite

size and the whole thing sets no matter

how big it is. Uh and that's that's how

jello sets. Could that be galation? Yes.

Uh the short answer is that is gilation.

that phase transition uh that we see of

the emergence of life is ailation phase

transition according to a generalization

of smallhovki coagulation to this case

of BFF strings coming together if you if

you think about quote unquote inanimate

and viral replicators as being

replicators that uh that are not

self-contained in other words where the

code that runs is not fully within the

code that is actually getting copied

then you you you notice something

interesting so what I'm calling here an

inanimate replicator uh and very much in

scare quotes is uh is code that copies

something fully outside itself. In other

words, the code that runs in order to do

the copying is disjoint from the thing

that gets copied. Uh are there such

replicators in the real world? Of

course, that's what water is, right?

Water is a replicator of some kind. It

gets made by stuff, but the stuff that

it gets uh that it gets made from, you

know, like water is not a part of the of

the running process. I mean it is a part

of the running process that makes more

water in some cases but right it's it's

it's um it's it's not uh it's not part

of the code let's say viral is the case

in which the the code and the thing that

is copied overlap. So in other words

some of the code that does the copying

is actually some of the stuff that gets

copied but the uh the code is not fully

contained by what gets copied. So this

is a an an incomplete replicator that

would need to cooperate with another

replicator in order to reproduce. So

that's what I mean by viral. In the

beginning of BFF, all of the replicators

are inanimate and viral. The great

majority are inanimate and a few of them

are viral. A few of them happen to copy

uh you know one of those uh bites that

is actually an instruction that is doing

the copying. But as you move toward uh

the time of gilation which I've

normalized to one here, you can see that

cellular replicators suddenly emerge. So

they can't emerge before you know about

halfway through the run and they and

they shoot upward at the end. And that's

really interesting because that tells

you that that the moment of a cellular

replicator where the machinery for

copying yourself is part of the thing

that is copied emerges through the

symbiosis or the symbioenesis of

inanimate and viral uh replicators.

Okay. So a full equation would have two

terms. It would have this reproduction

and you know like a voltera type type

term and it would have a merger or

smallhovsky type term. One on the left

is normal population dynamics. That's

normal Darwinism. And the one on the

right, uh, you could think about the

left as evolution and the right as

revolution. Right? Those that's the

moments when things come together. Now,

the population dynamics part for BFF

looks like this. It's a little bit more

complicated, but it has the same basic

form as LKA volta. There's a linear part

on the left. I'm just writing that as a

matrix uh, RI operating on the on the

whole thing. And on the right u the

reason that looks a little bit a little

bit different from Lka Voltera is that

when something gets copied it overwrites

other stuff. So uh so now we have to say

well how does how does that suppress the

populations of everything else in the

soup? In order to figure that out you

have to look at niches what are the

bites where something gets copied and

the overlap between the niches of two

replicators tells you you know how much

one thing getting copied you know how

likely it is that that will overwrite uh

something else that shares its niche.

Uh, okay. The symbioenesis part is a bit

of a mess, so I'm not going to go

through it. Uh, I hope that's okay. But

it looks just like Small Hovsky, just

gnarlier. Um, the the reason that it's

gnarlier is because Small Hovsky has

only binary fusion uh between two parts.

And in BFF, sometimes a bunch of things

come together. So, you have to take into

account these kernels that have more

than two uh parameters in them. Also,

when things come together, they don't

necessarily look like the sum of of the

things that came together. You could

have something that is three bytes long

or something five bytes long come

together and the result that copies

itself is only two bytes, one bite from

each one or or anything uh right along

those lines. So to to account for those

complexities, you end up with a much

more complicated k term, but it's

essentially the same as as a small

huskulation. to prove that this kind of

symbioenesis is needed in order to get

uh these complex programs. Uh you you

can do a very simple intervention which

is uh when you're interacting two tapes

you can sort of do it in a sandbox

before committing and in the sandbox you

see whether uh whether a new replicator

arises and if so what replicators is it

made out of. In other words, uh you

know, when you look at the source, you

can see what you know whether whether

any of those uh source bytes were

actually the output the outputs of

copies of some previous replicator. And

if so, then you have a tree. You have an

ancestry tree for uh for that for that

replicator. That means that you can

think about the depth of such a tree. Uh

you know, how many things have come

together and you can limit the depth of

that tree. You can say if the tree depth

exceeds 10 for a new replicator, then

I'm going to I'm going to actually not

not do this [clears throat] interaction.

and I'm going to take them back apart,

pretend it never happened, put it back

in the soup, and try again. If you if

you limit the depth of the tree to say

24, then the number of operations that

you have to block, the number of

interactions you have to block is

actually very small. You only have to

block one in a thousand operations. But

that one in a thousand operations is

really important. As it turns out, if

you block those, no galation will

happen. You need uh at least tree depths

of 20 or so in order to get these

complex uh programs. So this is a very

nice proof that symbioenesis is what

what is needed in order to get to these

complex tapes. When you do that

blocking, you end up with sort of

logistic curves for the populations of

all the replicators in that soup. They

they they go up and then they saturate

and stabilize. That's fun because it

lets you do a little bit of math. So as

you can see, you know, that not only do

things go up and saturate, but then they

they there's some random uh oscillations

and those oscillations can be

correlated. Sometimes you can see the

two of those populations go up and down

together. So that means that they

they're maybe collaborating with each

other and sometimes they go in opposite

directions. They're anti-correlated and

that means that they're competing with

each other because they're you know one

is overwriting the other for instance.

So that's what one would expect from

from off diagonal production and

competition from those those equations I

wrote earlier. And if you linearize the

dynamics around that steady state, then

you can sample the correlations in those

population fluctuations and you can

reconstruct the matrix R. I will skip

the details of how one does this, but

this is a classic fluctuation analysis.

You solve the leaponov equation and you

get a Jacobian and from that you get the

matrix R. And the matrices R look really

cool. First of all, they have a strong

diagonal that tells you that by and

large things replicate themselves. uh

just as you would expect from Lka

Voltera. But uh there's some other stuff

going on here as well. Aside from that

dominant diagonal of self-replication,

there is some negative stuff off the

diagonal and some positive stuff off the

diagonal. The negative stuff off the

diagonal, you can see looks largely

symmetric about the diagonal. And that's

as you would expect too. Basically, if A

competes with B, then B competes with A.

Two things that are that are fighting

for the same niche are are in a kind of

zero sum relationship with each other.

But the cooperation part where where uh

where something helps something else is

not symmetric and that's as you would

expect too. Just because A helps B or

enables B doesn't mean that B enables A

or at least not directly. Right? So

they're complex cycles in this in this

graph on the right of of of codependency

or enablement.

So uh negative component is symmetric,

positive component is is asymmetric and

there's this big diagonal. Do the

submatrices that are about to undergo

symbioenesis have any special

properties? They do. So in other words,

if it's these let's say four rows and

columns that are about to about to

undergo symbioenesis, you can ask what

are the what are the igen values of that

matrix of that submatrix and it turns

out that that they are generally

cooperative. So essentially if you if

you were to pick random rows and columns

from this matrix then you get a

highdimensional picture of the rank of

the matrix. But when you look at the

ones that actually combine, it's much

lower rank. They're already uh working

together. So in other words, there's a

relationship between the R and K parts

of this equation. Symbioenesis happens

among guys who are already working

together. Not all the same, not

independent, cooperative. Here's another

really interesting thing. If you look

not at the R matrix but at the Jacobian

itself then you can find the signs of

imminent instability in it of when it's

about to pop when it's about to go run

away and gellate uh or gel you don't say

gelate you say gel right so in

particular if you block the depth of the

possible trees to a low number then uh

the igen vector the igen values of the

jacobian are always negative meaning

that the system is stable but as you

look at larger depth ceilings you find

that more and more of this leading igon

vectors or the real parts of those

leading igon vectors pop positive and

that means that the system is about to

blow. Uh you can keep it from blowing

for a while by keeping that merger clamp

on but it tells you that essentially the

more you evolve these things the more

they begin to cooperate with each other

and the more incipient symbioenesis is

about to happen. Uh and that's what

leads to this phase transition. Uh, all

right. Um, I I just want to put a little

plug in for what I think could be a

really beautiful missing link between

the kind of algorithmic information

theory that Ector Zanil was talking

about and the assembly theory that he

has somewhat slammed with a couple of

papers that he has written. But uh, you

know, as as those of you who have

followed that might know or might might

realize from what I've just talked

about, there's a very close relationship

between what I've just been describing

and assembly theory. It's things coming

together to make bigger things. But the

assembly theory proponents have have not

really talked about the computational

nature of what they're doing. And in

this I fully agree with with where

ectctor is coming from. Uh and the way

that those connect I think is by

starting to look at things like

conditional cologoral complexity of the

things that are coming together. So I

think this is a construction point for

us to maybe reconcile those two

different pictures. All right. So

symbioenesis is what gives you

complexification that in turn is what

gives evolution its arrow of time. uh in

classical evolution and Darwinian

evolution there's no reason that things

should become more complex over time uh

you know they might simplify they might

get more complex it doesn't matter but

uh with symbioenesis we know that things

get more complex because if A can

replicate itself and and survive into

the future and B can replicate itself

and survive into the future when they

come together you suddenly need A to

replicate itself and B to replicate

itself and there's some additional

information that has been added which is

how the two fit together uh and and

those those extra bits of information

that keep getting added to the program

of what is the large replicator, they

don't come from mutation. They come from

the fact that things encounter each

other randomly in order to possibly

undergo that symbiogenetic event. So

it's actually the thermal randomness of

the fact that we pluck two of these guys

out of the soup at random. That's the

the information source if you like or

the noise source that is selectively

turned into algorithmic information by

the symbioenetic process. yours and John

Mayard Smith have have uh have written

you know extensively about these major

evolutionary transitions in which

symbioenesis results in large novel

forms of life like ukarotes

multisellularity and so on uh and uh I

think this work is great but uh but the

flaw is that they're only talking about

eight events or 12 events and if if what

I'm saying is true then this is just the

tip of a gigantic iceberg basically it's

symbioenesis all the way down most of

these symbioenic events are much more

uneven. There may be just a little bit

of something getting incorporated into

something much bigger, but that is the

source of novelty in all of evolution.

These are just the most dramatic cases

that involve, you know, uh really really

big uh visible stuff happening. So, is

there evidence for these smaller

singogenetic events in biology? Lots

there's lots of evidence for it. So uh

you know I I don't have time to go into

it in any detail but if you look at at

just the human genome you find that you

know only 1 and a.5% of it codes for our

proteins and lots of the rest of it is

transposons and uh other endogenous uh

retroviral elements of various kinds

that involve viruses whose whose ecology

is our own genomes and that reproduce

inside our genomes and sometimes jump

species resulting in weird [ __ ] like uh

a quarter of the cow genome being a a

retroron that also lives and lizards and

salamanders and stuff. Uh, and so, you

know, when you start to look at that,

you you realize that that genomes are

fractal and it's replicators made of

replicators made of replicators just as

I've as I've described, not these kind

of uh, you know, fixed design space and

evolution only happening in its usual

way. It's not just horizontal gene

transfer in bacteria. This synogenetic

picture, I think, is is the engine uh,

that produces novelty throughout all of

life, including including big complex

animals like ours, like us. Um there's

more and more evidence in the in the

last decade of of things like this going

on. You know, for instance, the arc

virus uh was endogenized uh in in the

mammal lineage and you can find it in

our brains and it turns out that if you

knock out the ark virus in mice, they

stop being able to form new memories. So

clearly the arc virus is doing something

important for us and and that's a source

of novelty that that was an endogenized

virus. uh similar the mamalian placenta

uh was uh is formed by an indogenized

virus that fuses cell membranes together

and so on. Okay. So there's a definition

of life that comes out of this life uh

and I I said this uh you know in the

panel yesterday is an embodied

autopoetic computation arising and

complexifying through symbioenesis. It's

not just neuroscience that's

computational. Life was computational

from the beginning and it gets more

computationally complex over time

through symbioenesis at many scales

because remember if life is a computer

from the start then every time things

fuse together you're making a more and

more parallel computer. Those computers

have to be not only running the code

that model themselves and reproduce

themselves but that also do something

about modeling the other and figuring

out how they interact or work with the

other. And this means that an ecology of

functions is building up through

massively parallel computation that

becomes if you like more and more

intelligent with every one of these of

these fusions. And since symbioenesis

makes the computation massively parallel

uh that implies that intelligence and

life are very very closely connected. uh

which is why uh you know I ended up with

the book what is life as part of the

book what is intelligence when you're

not only using that intelligence to

model yourself but also to model your

environment which by the way includes

others most importantly then that's

intelligence and that means that life

was intelligent from the start and the

moment that that modeling of others

begins what we call in in larger more

complex animals theory of mind becomes

fundamental to the way intelligence

develops So uh you know these are really

simple simulations that show how uh you

know just persistence allows you know

the modeling of of of an environment to

turn into learning chemotaxis in these

fake bacteria. Uh but of course you know

in real life uh you're not only learning

about an environment that that exists in

isolation like the like the sugar

crystal but actually all of your friends

right the moment you're reproducing the

greater part of your environment is is

actually all of your all of the other

things that that uh you know even your

own reproduction is creating.

Uh life is never single player. Things

like intelligence explosions in in our

lineage in the hominins and in citations

uh and in bats and a variety of other

species are exactly this kind of runaway

modeling of others resulting in uh

growth of brains and growth of of groups

and and therefore that you know that

when we think about the growth of

advanced intelligence you know in in in

you know human societies or human brains

it's it's really that same sort of of

synogenetic process happening at a much

at a much higher level. Let's end there

and and switch to uh questions.

>> I think there are multiple different

ways to represent the symbiosis. I think

in the real biology we maintain those

high record structures and that there

are fundamental mathematical differences

how how you treat those symbiosis that

do you have any insight how we can

implement that? Yes, in biology we often

uh sort of raify one particular level of

detail and we say you know these are the

life forms and you know maybe there's a

symbiosis between uh you know let's say

you know algae and a sea slug but we

still think of the algae and the sea

slug as as as separate and we think

about population dynamics within that

rather than modeling them separately. Is

there a reason to prefer one scale or

another? You know, for me, one of the

lessons I the reason that I spent so

much time on the relationship between R

and K is that you can always move

something from one from from R to K and

back. Uh, you know, Lin Margulus

famously said we're just colonies of

bacteria, you know, some of which live

inside each other. And that's true. You

know, you could describe us as just

colonies of bacteria. But the reason

that it's useful to to move up a level

of detail is because you know humans

also you know reproduce as a unit you

know hence the mess and uh and there are

a lot of things that you can uh you can

learn about when you study at that

higher level uh a lot of abstractions

you can make from a computational

perspective that are hard if you're only

modeling at the lower level. So I don't

think that there's any there's any one

layer layer level that is true and we

have lots of boundary cases like lyken

or like uh colony insects right where

you can model the entire colony or you

can model the individuals I don't think

there's a right answer to those two uh

so you know do you do you keep a block

of rows and columns in R that are that

are uh that are in you know that always

end up or mostly end up getting copied

together uh or do you add a new row you

know it's it's it's actually a coarse

graining choice and you can make either

one

>> symbiosis is not symbiogenesis like you

What is the thing that you would claim

is kind of like you know a good insight

for how like you know A and B stop being

A and B in symbiosis and they become

something else. the fact that that uh

phase transitions don't come from R

alone, you know, but but you have to

look at K. Now, you you do you do get

this these runaway modes, right, which

which tell you that something is about

to is about to happen. But in order to

understand that phase transition, right,

in other words, in order to see that a

major evolutionary transition has

occurred, right, to put it in biological

terms, you you actually have to

understand the physics of K. It's only

by understanding the physics of K that

you can do the theory that lets you you

know predict and understand what is

going on right here. So you know if you

model a body as just a bunch of bacteria

then it's not wrong but but then uh you

know it's invisible to you that uh you

know that something amazing happened

when we became multisellular or when

ukarotes formed out of out of out of

bacteria. So this allows higher order

modeling and and in particular by the

way that higher order modeling you know

if we just take the subjective

perspective for a moment if you are one

of those bodies if you are one of those

people then you know you're not going to

survive very well if you're only

modeling other people as collections of

bacteria right you have to build higher

order models of them because that

becomes an essential part of your envelt

and you have to simplify or coar grain

the world in order to build a model that

is that is ecologically relevant to you

so uh you know I'm kind mixing here of

of subjective and and an objective

perspective. But the subjective

perspective ultimately is super

important. Uh you know it's a little bit

similar to like why do we need

temperature and pressure in physics? You

know those don't exist if we just look

at the microscopics. But it's only by by

coarse graining and looking at the

larger scale that you can understand

thermodynamics. And in the same way,

it's only by zooming out and looking at

the symbioenesis that you can understand

the dynamics of transitions of phase

transitions, messes and smaller and

coarser grained models that you know

where higher orders of things emerge.

>> Well, actually that's exactly what I was

doing like 30 years ago, right?

>> Exactly. That's that's why I began with

your nearly 30 years ago paper. There

was a big problem like it's always you

know the symbol is possible like you

know we burn the wood then it becomes

complicated coupling with each other

however the function itself is not

becoming complex or become high water

the function itself is just

>> I have three answers I suppose uh

depending on depending on which way we

we talk about it so uh first answer

actually comes from from software

engineering uh so composition or or from

mathematics for for that matter

composition of functions is uh

symbioenesis as as I've described it and

when you compose you know two functions

to make a a higher order function you

are making something more complex uh

than than the than the primitives uh you

know and and and you know the what I

hinted at with uh you know the Eric Eric

Mosnino's you know beginnings of

conditional complexity can quantify that

sort of compositional complexity you

could find signatures of it in you know

if you don't want to look in DNA you

could look in GitHub at the way you

every time somebody writes some code,

right? It it begins by importing a bunch

of other things and combining them and

and and and you you you do see a

tendency toward toward complexity. Now

that is constrained by energy. Uh you

know, the more complex a thing you make,

the the the more uh free energy it has

to use. But uh now you get uh some of

Chris Kempus's beautiful work in which

you see that there are energetic

benefits to teamwork. Uh right. So, so

the the the way the scaling laws work

for this uh which are also

environmentally dependent. I mean, you

know, I don't know Chris if you got to

like the snow the snowball earth type

stuff, but there were certain very

specific conditions at certain points in

the earth's history that became

favorable for ukarioenesis if I'm

remembering correctly and and and so

there there are some external conditions

as well. But the other cool thing is

that when you start to have more uh

complexity in the in the computers when

you start to have massively parallel

computation that greater intelligence

also unlocks new energy sources and and

that gives you a bigger budget to play

with uh which which in turn allows the

next me to take place. So I think

there's an energetic perspective,

there's a compositional perspective, a

comorical perspective, there's a scaling

law perspective that that can all come

to rescue uh that that uh that question,

but we should talk more about it. I'd

love to I'd love to get into this in

more detail.

>> It's essential for life to have some

functionality pointing for the brain

programs their strings in which their

functionality by external goals aka the

CPU.

>> I agree. So I made claims that maybe

sound contradictory. You know, one of

which was that, you know, Vonoyman is

embodied computation and different from

touring in that sense, but on the other

hand that BFF uh, you know, looks like,

you know, very much like a touring

machine. And um, and yet I I also said

it was embodied because I I made one

tape. So you know, even the question of

whether something is embodied or not is

a little bit perspective dependent as

well because in a in a Vonoyman system,

for instance, there's of course the same

rule operating at every pixel. You know,

you can ask yourself the question, is a

computer the thing that I make, you

know, with lots of parts, right? You

know, of the kinds that designed, or is

it just the operation of a single pixel?

The usual answer is to say what happens

at a single pixel is just the physics of

that world. But what constitutes the

physics and what constitutes the

computation is actually a movable

boundary. So uh you know embodiment is

is is essential in a very minimal sense

that you need to be able to uh to

operate on the the thing that is going

to you need to be able to make coins

essentially right in and um uh and in

ordinary um uh brain [ __ ] you you can't

make a quin because the data tape is

separate from the from the program tape

but you bring them together you're now

in the same realm as as a as a cellular

automaton albeit with a different coarse

graining of what you consider to be the

physics and what you consider to be the

the the code. Now I mean in our world we

know that it's possible to build

computers or else we wouldn't be able to

build computers and we wouldn't be here

either. Um but you know what constitutes

the physics if you like the the physics

that makes up computers itself had to

evolve. You know we began as I guess

nothing but a quant you know quantum

field theory and then things came

together you know into particles uh you

know and the particles come together

into atoms the atoms come together into

molecules and so on. Those are

essentially what I would call the

inanimate replicators right in in the

system. And and there there's a there's

an important phase transition when those

suddenly are rich uh form a rich enough

set that not only do you have an autoc

catalytic system as mold fontana would

have said but also that that you can

form a touring complete instruction set

and and therefore you know open the door

to generality of of computing. I hope

that I hope that makes uh some sense.

>> All right. I think we're

>> And yeah, I'm afraid we have to wrap up.

So, let's thank once again. [applause]

[applause]

>> Thank you so much for this amazing this

amazing talk. Great questions, too.