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so if you haven't met me yet my name is

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Cole Mathis and this is a project that

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I've been working on for a couple years

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this is not ABS I con sorry that's

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reducing so yeah emergence of life is a

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first order phase transition so to

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preface this a little bit I give you

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guys a bit of an explanation what's

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going on here this is completely

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different than everything else I've seen

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here so in evolutionary biology and

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mathematical biology you see these

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replicator models every once in a while

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and these are a sort of abstraction to

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help understand biological evolution in

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terms of variation and selection and

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replication and so these models are

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really interesting but I'm more

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interested in how what we call chemical

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evolution eventually became a biological

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evolution and so for this particular

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project I focused in on one function

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that seems to be really important to

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biology and that's replication and if

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you think replication isn't necessary

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for biology or evolution I might agree

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with you depends on the day and I'd love

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to have that conversation so I'm find me

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after but what I became interested in is

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in normal replicator models they sort of

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have you know replicators exist as a

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given and so what I wanted to say is

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okay what if they just don't exist as a

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given they have to be made sort of from

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some underlying chemistry that

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ultimately constraints their ability to

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replicate and evolve so I'm going to

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describe a model and some results that I

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have so cool so the chemistry that I

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described it's really simple it's not

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even really chemistry but there's these

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two elements here they're purple and

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blue one or zero however you want to

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think of them these can come together

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and add one to the end to form sequences

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through polymerization and any sequence

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can degrade at any point and break into

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smaller pieces and if you get above a

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certain length in this case I said

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length 7 you can make a copy of yourself

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and you're constrained by what resources

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are available it's a closed mass system

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so there's always the same number of

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blue and purple squares it's not closed

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energy if you're into rate equations I

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can show you why afterwards but it's

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there's definitely an energy flux going

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on

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novelty is through polymerizing new

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sequences and this might look a little

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bit like a replication first RNA world

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type scenario and it is definitely

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replication first but the actual

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chemistry I'm pretty agnostic this could

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be anything you really like so all right

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so there's replicators so there's two

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different kinds of fitness there's

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static fitness which is associated with

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function and there's environmental

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fitness so the static fitness is

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associated with a fundamental trade-off

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in chemical systems and that is

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molecules that are very functional they

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fold well are hard to copy and molecules

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that are easy to copy tend to not fold

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very well and are not very stable so in

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this system there's two ways to be very

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fit you can either be very stable by

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being all blues or you can be very easy

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to copy by being all purple the fact

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that it's all one and all the other is

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to one show that trade-off and two to be

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very rare in the system you expect that

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functionally fit sequences are rare and

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the scheme of all possible sequences and

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then there's all these other ones that

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are pretty much easy to make and they

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are a little bit stable and they get a

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little bit of a replication enhancement

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but they're not very good at neither all

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right oh and then the dynamic aspect is

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your replication rate is coupled to the

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resources available in the environment

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so for example if you're this blue one

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and there's just a bunch of purples out

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in the environment you your replication

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rate is suppressed and the purple ones

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replication rate is enhanced all right

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and so we do this we run it all together

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and we get sort of two stable

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equilibrium that I've arbitrarily

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decided to call non-life in life and

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they have these properties I don't think

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replication defines life as i said

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earlier but it's not just replication

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it's a selection on functional fitness

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that I really think is the motivating

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factor behind behind calling it life so

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I'm just going to talk about these two

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different phases really fast so if you

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just look at all the different lengths

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sequences and the non life sequence

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production is dominated by

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polymerization so you get this

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exponential decay with a little bit of a

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modification here because it's

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constrained by resources so this is the

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length so like during non life we say

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okay length three what fraction of the

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system ass is like three and it's this

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and then for non-life we do the exact

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same thing you see a very different

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story because everything's tied up in

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replicators right so the like seven was

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the minimum length to replicate and all

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the mass is shifted their your resource

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limited there's very little mass left to

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continue replication because it's all

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tied up here and then you get the

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exponential exponential decay from

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dimers again okay so then I said

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functional selection takes hold in the

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life phase so this is a slightly

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different plot if anybody was at my talk

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a tabs icon and this a little bit

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different so what I did here is again

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you have all the different length scales

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one through seven and on top is non life

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and on bottom is life so the solid

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purple is the pure purple sequins and

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the solid blue is the pure blue sequins

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right and so as you see in non life as

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you go up you get these mixed sequences

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dominating stone like seven sequences

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there's replicators there in non life

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but they're these sort of heterogeneous

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mixtures are not very good anything

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there were just what was easy to make

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okay but then in life you see a very

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different story the entire system has

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restructured because you get selection

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on these homogeneous sequences so length

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7 it's about seventy percent of the

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length 7 sequences are the very stable

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ones so they just sit there they're

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stable the replicating and they're using

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up all of the ones or the blues in the

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the system and then the rest are mostly

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these homogeneous zeros that replicate

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very fast but they also break apart

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really easily and then the entire system

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is just being made by breaking these

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lengths seven sequences so you see these

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same patterns being sort of copied

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throughout the entire thing if you're

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interested why it switches from mostly

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blue to mostly purple right here we can

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talk about that after you can ask me

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it's kind of interesting all right so

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then another key distinguishing feature

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between life and non-life I measure with

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an information measure is anybody here

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ever studied any

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in theory even a little bit no presents

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one person cool okay so if you read

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anything on information theory the first

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thing they introduce the stranded

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information which is largely useless and

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then the second thing they introduce is

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mutual information which is a little bit

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more useful so mutual information if you

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like math that's right here if you're

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good with pictures this kind of makes

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sense but the way to think about it is

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if I have two random variables x and y

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the mutual information between x and y

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is what do I learn about x given that I

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fixed why right so it's a way to make

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measure arbitrary correlations between

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two different variables you don't have

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to specify a functional dependence you

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don't have to specify anything you just

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have to have the probability

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distributions and you say given that I

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know X was in this state what do I know

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about the state of why make sense so one

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way to distinguish non life and life in

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this model was that if you look at the

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composition of the Replicators and the

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composition of the free resources in the

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environment you can say what is the

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mutual information between these two so

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what do I know about the Replicators

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given that I fixed the environment and

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in the non-life phase you see a hut high

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positive value around three depends on

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how you set the parameters a model it

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changes a little bit and then in the the

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life phase you see that they're largely

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uncorrelated it tends to 0 so this means

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that the Replicators that exist in the

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non-life phase are completely determined

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by their environment that if you fix the

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environment you know a lot about the

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Replicators that exist and you know

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about their composition whereas in the

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life phase just because you know the

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environment doesn't mean you necessarily

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know much about the composition of the

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Replicators i think is i'm pretty

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interesting sort of effect that's been

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caused by this selection on function

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alright so as I said there's a first

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order phase transition and you might

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have predicted it if you do any

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statistical physics or thermodynamics

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you see these sharp discontinuities and

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state state variables that's the first

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order phase transition so why does this

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happen well the Trent and how does it

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happen so the transition happens when

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the environments available or the

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resources available in the environment

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match the composition of replicators so

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what this

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plot is showing is the relative

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difference between the composition of

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the environment and the free resources

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and it's the frequency of the transition

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actually happening so this is for 256

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different runs and I said okay when the

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transition happens what was the relative

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difference between the number of ones

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over the total mass in replicators and

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the number of ones over the total mass

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in the environment and you see that

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almost sixty percent of them happen when

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they exactly match and then it's a

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pretty nice Gaussian centered around

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there so one thing that's interesting

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about this transition is that you might

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expect that the very fast replicators

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would drive the system into into this

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sort of new state where replications

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dominating everything or that the very

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stable ones would get formed and then

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eventually those would build up enough

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of them to drive the transition but what

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actually happens is because you have to

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match the environment it's the very

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unfit the easy to make replicators that

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end up causing it so here these are like

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34 43 even splits between purple and

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blue and then here is 5 to 25 and then

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there's a brief 6116 and then eventually

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at the end you get the very stable once

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selected so this means that if you were

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to observe a transition from non-life to

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life if you like alternative you know

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prebiotic chemistry this is exactly that

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this is saying that the things which

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nucleate the transition into a living

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state are not going to be those that are

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ultimately selected at the end the

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transition is associated with a massive

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explosion of diversity so here I've

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plotted the total number of explored

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sequences on top as a function of time

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and the transition happens right here as

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you can see there's this huge

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discontinuity the exploration rate for

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exploring new sequences this would be

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like speciation rate goes up by two

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orders of magnitude during the

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transition and it's higher after the

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transition than before all right but

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also associated with this transition is

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a mass extinction event because the

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entire system gets restructured so if we

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start here so here I've plotted the

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formation versus degradation rate in the

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total system and the mutual information

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right so if we start stable formation

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degradation here with high mutual

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information this is the non life state

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at steady state

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right up here and then it's going to

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eventually end up over here with the one

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value formation to degradation if you

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have anything other than one the system

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is unstable so it has to end there and

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so as you see the mutual information

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starts going down everything's getting

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ripped apart faster than its being made

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anything below one means for everything

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you're making you're destroying more

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than that thing hits this bottom and

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then eventually stabilizes by finding

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the functionally fit sequences so yeah

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in summary a functional selection leads

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to an observable decoupling from of

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replicators from their environment and

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this by driving a restructuring of that

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environment this restructuring would

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have been associated with an explosion

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of diversity and a mass extinction event

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and the Replicators which came out of

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that would not have been the ones that

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nucleated the transition and for the

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sake of time I'll just skip these future

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directions if you're interested in why

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simple replicators are not the right

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logical architecture for life you can

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ask me about that later it's pretty cool

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and yeah that's it thanks to all these

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people especially my advisor Sarah

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Walker she's super rad and she's been

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very helpful in all this and that's it

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take any questions okay we have time for

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one quick question you already so can

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you say anything about the species that

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nucleate the emergence of life from the

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context of the things that our life so

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they I mean in this model they would

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have been made out of the same basic

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building blocks is all it really says

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but they would have been structured

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completely differently so the sequence

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composition and the actual sequence

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played two different roles in the way

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the fitness landscape is instantiated so

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depending on how you want to interpret

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the chemistry or magic to some kind of

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toy system there are some things you

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might be able to say but it's really

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sort of touchy but they would have been

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reflective of the initial composition of

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the system so they wouldn't have been

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outliers in the scheme of all possible

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sort of compositions as super chair I'm

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granting myself extra time to ask a

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question ah this was super cool so I

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want to know what the future direction

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is just a 30 second yeah where you going

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next yeah so when I made these slides

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actually I had a different idea the this

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project came out of some other ideas

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that I I thought this was going to be

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like the easy step and then like okay

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cool what will actually be able to ask a

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question and then all this phase

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transitions to have happened and I was

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like whoa I didn't understand that I

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respect that so the future direction is

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I'm looking at different evolvable life

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histories or sort of ya life histories

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so you know if you just if you're

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prebiotic chemistry discovers a Palmer

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raised before discovers like something

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that can recycle things or you know a

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synthase or something that makes

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components that you need how does that

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enhance or slow down the evolvability

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and sort of how does that change how

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constrained your rate constants

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basically need to be in that system but

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I'm also interested in so Von Neumanns

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got this great idea about what what

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things need to do to be able to make

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copies themselves and it needs a

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specific logical architecture and I can

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point you to some references but

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basically you need a replicator and a

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vehicle and all of these replicator

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models that have ever been made ignore

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that and they just say oh well we just

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have a replicator but you can press a

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lot of biological function and you

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introduce a lot of logical paradoxes if

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you try to do it that way so I'm