Cristopher Moore: belief

Transcript context

…The brain is an FSA and we extend, you know, like we can expand our memory by writing things down on a hard, you know, I can get another whiteboard, I can get another whiteboard and so But his argument is slightly more nuanced. He he's saying that, yes, our brain is a finite state automata. But if you look at all of the algorithms that are inside of that class, there are a subset of algorithms which are those that can control a Turing machine and expand memory and and so on. And those algorithms are not traversable with stochastic gradient descent. So he's roughly saying that we were, you know, maybe the Chomsky argument, maybe you've got the merge operation or something. Know, somehow our brains have learned the special class of FSA algorithms that can expand our memory. I see. That's that's an interesting claim. I mean, I think, you know, we're at this workshop this week where there was a whole discussion yesterday about what do we actually need language for and, you know, and what do we actually need symbolic thinking for because that's where recursion seems to start. Right? And there are plenty of intelligent entities out there, like our close relatives, the great apes, and possibly our ancestors who were already making stone tools and teaching each other to make stone tools using gestures. They didn't need, you know, the full on modular structure of language that we have. And you can do a lot to navigate the world without, if you will, Turing completeness. And, well, assuming that what we mean by Turing completeness is kind of the ability to do symbolic recursion and so on. And the funny thing is, you know, then we're we're starting LLMs as language first things. They're not tactile first things or visual first things or find food first things the way we were. They're language first things. And because language is the medium in which we do symbolic thinking and recursion, then we're like, oh, good. They should be able to leap to all this formal stuff in mathematics. But they're not formal systems. Right? They're they're token producing systems. The way same way most human speech is a token producing system. Right? Formal reasoning is something that we is kind of a thin veneer that we do in specific settings on top of token producing. Right? You know, when we're chatting with each other or even talking about topics that we've had conversations with with, before, we're acting very much like an LLM. You know, we're we're cheerfully in a distribution we're pretty familiar with. We're cheerfully emitting tokens. We're doing it we don't really need to do that much self reflection about it. It's when we hit some edge that we're forced to do, well, kind of the self reflection we were talking about before, about, okay, is what I'm about to say, is it actually does this actually make sense? And that's something most of us don't do that most of the time. Right? You know? Yes. And so yeah. I mean, I feel like the Turing machine itself so for instance, when teach theoretical computer science, I don't do it in a Turing machine centric way. Right? And I think if you look at some more recent textbooks, they don't do what the older textbooks did, where the first thing you do is, here is a Turing machine. And, you know, the Turing machine is partly of historical interest now. I mean, it's a cool minimal thing that's universal, but there are other many very small things that are universal. And, whether those are families of Boolean circuits Mhmm. Of increasing size with, yes, admittedly, some kind of uniformity to them. sal, but there are other many very small things that are universal. And, whether those are families of Boolean circuits Mhmm. Of increasing size with, yes, admittedly, some kind of uniformity to them. Or whether it's counter machines or finite state automata with 2 stacks, you know, people like Minsky and others had a lot of fun in the sixties and seventies finding these smallest possible machines that can do that, or cellular automata or whatever. So for me, the Turing machine isn't central, actually. It was the first thing like it which had this ability to simulate had this universal ability to simulate other machines of its own kind, had this paradoxical ability to simulate itself, and therefore the halting problem and so on. But I don't view that architecture as central. It's very Von Neumann y. Right? You have a CPU. You have a memory. It's very magnetic tape y. You know, you roll the tape over to this part. So, yeah, I I feel I guess for me, mathematically, when I think about computational universality, I think about things like our favorite programming languages and their relationship with the, the theory of partial recursive functions. Right? So as I'm sure a lot of your viewers know, these basic notions of recursion that were invented before Turing came along, Primitive recursion is basically a 4 loop. There's this other operator called minimization, don't worry about it, which is basically a while loop. And then function composition is basically, well, function composition. So these tools can generate all of what are called the partial recursive functions, which are more familiarly now called the computable things. Right? These are the same things a Turing machine can do. And then Church, you know, has his wonderful lambda calculus, and that shows up in Haskell and Lisp and so on. So to me, like, the wonderful thing is that these rather different architectures and the Turing machine, the grand unification which occurred in, like, 1936, what is marvelous is that they can all do the same thing.…

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