Blaise Agüera y Arcas: evaluation

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…that, you know, we saw some programs emerge and then we saw the pro 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. 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 0, you still get the same exact phenomenon, and that is very mysterious. Because if you crank mutation down to 0, you should have no source of novelty, you should have no evolution. Why do you still get this apparent complexification even with 0 mutation? So let's let's go into some of the some of the theory of this. By the end, 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 1 generally writes for this sort of thing. It's a very general ansatz. This is for, you know, species 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 ansatz. This is the the Lotka Volterra 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 Vito Volterra near the beginning of the twentieth century. This is what the classic Lotka Volterra equations look like. There are 2 species. There is a prey species and a predator species. And those 4 terms are, reproduction, getting eaten, eating to reproduce and background death rate. So, if you've got those 4 terms, you get these nice oscillatory solutions, you know, between between your predators and your prey that arise. Okay. So this is a slightly more general form of those Lotka Volterra equations. There is a linear part which we'll call r x and, in Lotka Volterra that linear part is diagonal. So, you know, the the, 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, gets implemented. So the the the right part is suppressive. The left part makes things grow. The right part makes things, 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. You know, we only have 2 species here. It doesn't matter how long you run this damn thing, you're not gonna get a third species. And and you're not going to change the design space either. You can have, you know, very complicated terms in here that allow finch beaks to adapt to different environments, but you have to have the space of finch beaks predefined before before this equation can even be made to work. very complicated terms in here that allow finch beaks to adapt to different environments, but you have to have the space of finch beaks predefined before before this equation can even be made to work. So 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 afterward other than optimization to niches. So now we bring in another Eastern European, Dmitry Sergeyevich Mereshkovsky. So he's the 1 who first came up with the idea that maybe mitochondria engaged in some kind of semogenetic event in order to end up inside other single celled organisms to make, to make eukaryotes. This was popularised and proven to actually be the case by Lin Margulis, in in 1968. 1 of the really great papers in biology from the twentieth from the twentieth century. 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 1 who proved, that eukaryotes were actually a fusion between 2 different kinds of prokaryotes and popularized this term that Medichevsky had invented, symbiogenesis. Okay. So could symbiogenesis 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 Lyn Margulis believed, but, that was not, that had not been widely accepted by the by the by the biology community even by the time of her death, in 2011. You know, so she she had a much more expansive idea about about why symbiogenesis was important. Only the particulars of chloroplasts and mitochondria had been accepted. So the way we can look for symbiogenesis in 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, 1 byte is getting copied from somewhere to somewhere, so almost by definition, you have at least 1 byte 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 1 byte replicators that are copying themselves back and forth now and then, once in a while, they will come into conjunction, and 2 of them will copy better as a group than the 2 of them copied on their own. When that happens, then they'll start to copy as a group and that is a symbiogenetic event. So basically, the reason that even without mutation you get these complex programs arising is because of these fusion events between smaller replicators. So can 1 build syngogenesis into an equation like like this 1 that, you know, for for Lotka Volterra? You can. This is our statistical physicist who came up with the right kind of term to write mathematically for describing how symbiogenesis works. He wrote down an equation for the coagulation of polymers. So this is Smolowski coagulation. This is what happens when clouds form. term to write mathematically for describing how symbiogenesis works. He wrote down an equation for the coagulation of polymers. So this is Smolowski coagulation. This is what happens when clouds form. It's what happens when gelatin sets in the fridge. So the idea is that you have, let's say, polymers that begin, as monomers, you know, 1 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. 2 trimers stick together and now you have a hexamer 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 2 things that are coming together, 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 2 things coming together to make a new 1, 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 2 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 hosky coagulation. It's called gelation and it's exactly what happens when you put jello in the fridge and it sets. Basically, things are sticking together and if they stick together with a scaling exponent that is greater than 1, 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. And that's that's how jello sets. Could that be gelation? Yes. The short answer is that is gelation. That phase transition, that we see of the emergence of life is a gelation phase transition according to a generalization of Smolhofky, 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, 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, and very much in scare quotes, is, is code that copies something fully outside itself. In other words, the code that runs in order to do the copy is disjoint from the thing that gets copied. 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, 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 to mix more water in some cases, but, right, it's it's it's it's not, 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.…

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