Blaise Agüera y Arcas: prediction

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…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'll skip the details of how 1 does this, but this is a classic fluctuation analysis. You solve the Lyapunov 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, just as you would expect from Lotka Volterra. But, 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. 2 things that are that are fighting for the same niche are are in a kind of 0 sum relationship with each other. But the cooperation part where where, 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 there are complex cycles in this in this graph on the right of of of co dependency or enablement. So, negative component is symmetric, positive component is is asymmetric and there's this big diagonal. Do the submatrices that are about to undergo symbiogenesis have any special properties? They do. So in other words, if it's these, let's say, 4 rows and columns that are about to about to undergo symbiogenesis, you can ask, what are the what are the eigenvalues of that matrix, of that sub matrix? 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 high dimensional 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, working together. So in other words, there's a relationship between the r and k parts of this equation. Symbiogenesis 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 gelate, or gel. You don't say gelate, say gel. Right? So in particular, if you block the depth of the possible trees to a low number, then the eigenvector the eigenvalues 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 eigenvectors, or the real parts of those leading eigenvectors, pop positive and that means that the system is about to blow. look at larger depth ceilings, you find that more and more of this leading eigenvectors, or the real parts of those leading eigenvectors, pop positive and that means that the system is about to blow. 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 symbiogenesis is about to happen. And that's what leads to this phase transition. Alright. I I just wanna, put a little plug in for what I think could be a really beautiful missing link between the kind of algorithmic information theory that Hector Zenil was talking about and the assembly theory that he has somewhat slammed with a couple of papers that he has written. But, 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 in 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. In this, I fully agree with with where Hector is coming from. And the way that those connect, I think is by starting to look at things like conditional Kolmogorov complexity of the things that are coming together. I think this is a construction point for us to maybe reconcile those 2 different pictures. Alright. So symbiogenesis is what gives you complexification. That in turn is what gives evolution its arrow of time. In classical evolution and Darwinian evolution, there's no reason that things should become more complex over time. You know, they might simplify, they might get more complex, it doesn't matter. But with symbiogenesis, 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 2 fit together. 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 symbogenetic event. So it's actually the thermal randomness of the fact that we pluck 2 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 symbioteneic process. Jor Safmadi and John Maynard Smith have have, have written, you know, extensively about these major evolutionary transitions in which symbiogenesis results in large novel forms of life like eukaryotes, multicellularity and so on. And, I think this work is great, but, but the flaw is that they're only talking about 8 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 symbiogenesis all the way down. t the flaw is that they're only talking about 8 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 symbiogenesis all the way down. Most of these symbogenic 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, really really big, visible stuff happening. So is there evidence for these smaller symbogenetic events in biology? Lots. There's lots of evidence for it. So, 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 half percent of it codes for our proteins and lots of the rest of it is transposons and, other endogenous, 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 shit like, a quarter of the cow genome being a retrotransposon that also lives in lizards and salamanders and stuff. 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, you know, fixed design space and evolution only happening in its usual way. It's not just horizontal gene transfer in bacteria. This single genetic picture, think, is is the engine, that produces novelty, throughout all of life, including including big complex animals like ours, like us. 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, was endogenized, in in the mammal lineage and you can find it in our brains and it turns out that if you knock out the ARC virus in mice, they stop being able to form new memories. So clearly, the ARC virus is doing something important for and that's a source of novelty that that was an endogenized virus. Similar, the mammalian placenta, was, is formed by an endogenized virus that fuses cell membranes together, and so on. Okay. So there's a definition of life that comes out of this. Life, and I I said this, you know, in the panel yesterday, is an embodied autopoietic computation arising and complexifying through symbiogenesis. It's not just neuroscience that's computational. Life was computational from the beginning. And it gets more computationally complex over time through symbiogenesis 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 1 of these of these fusions.…

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