[jove_]

Really good. I'm a computer scientist who takes a passing interest in the subject and usually I'm just disappointed by the computer science errors and the wild claims that it leads to. This, however, cuts to the heart of the issue, how do you measure consciousness? It's the same question Turing tried to answer with the Turing test but now that language models are starting to pass it, despite being way below a dog according to our intuition, I think it's a question needs asking again and not an easy one.

There is one mistake in there, more of an oversight really and one that's tangential to the main point but I think it's important to understanding the issue in general. To say the brain computes a function is meaningless. When I say my computer is computing a function, let's say 1+1=2, implicit in that is the idea that high electric on a wire means 1 and low electric means 0 and we can arrange these into binary to make a 2. Computer science is pure mathematics. It's only capable of symbolic manipulation. It can do 1 and 0 but not electric or neuron. Any relation from the second to the first must be defined and this is true of any bringing mathematics into practice. For most of science and engineering this means units of measurement. We use bits of information but it's not at all clear how that should be applied to a brain. The first question is what properties of a brain matter for the calculation we care about? As one of the other commenters said, "There's no "pure information", it's always information over the space of events we care to distinguish as different."

Worse, any relation is arbitrary. Computers are all very neatly arranged but they don't need to be. I could watch any physical process and map each of its states to the states in any Turing machine and call it a computer performing a computation of my choice and from a theoretical perspective there's nothing to distinguish that from me declaring my computing is computing 1+1=2. Moreover, humans have a pressing need to keep things practical, ordered and understandable for other humans. Evolution needs only practical.

This actual comes up in practical computing more than you might expect. Imagine my 1+1=2 is part of a program keeping track of flea populations. It's very hard to track fleas individually so we round to the nearest thousand. Did I calculate 1+1=2 or was it ~1000+~1000=~2000? It's both really, there's a symbolic level where it's just 1+1 and a practical level where it's a thousand fleas. To further confuse things, if I got my C compiler out and wrote some natural code that included a function that given a person would return their age (as references in both cases for the pedants) and then wrote a different function that given an integer will add 4 to it. There's a very real chance those two functions will produce identical machine code.

The computational stack leading from metal to firefox is presented as big question marks but it's not. It's very well known, we literally made it up ourselves. Humanity knows it as well as Tolkien knew middle earth. Not only could we describe its makeup and workings in all level of detail, we prescribed them in meticulous detail. The same can't be said of brains.

I've heard a lot of this referred to as the triviality argument. That is, it's trivial to say something is a computer doing a computation, but then I find a lot of the conclusions drawn from this to be off. It's presented as if it undermines the idea of the brain as a computer, when on the contrary it confirms it. The computer science behind explaining this gets a bit heavier, but I think even without it you can smell something is off here. It's the same as with Xeno's paradox, even if you know nothing about math, you know the tortoise moves. Brains are not merely a trivial computer. They look like some maybe very alien but still genuinely structured and practical information processing systems and these workings are clearly strongly related to our behaviors and consciousness.

Going into the heavier comp sci. Brains are definitely not Turing machines. Neither is my computer. Turing machines can't exist. The part where it says "infinite tape" is a hard requirement. Any finite limit implies that a system has no more computing power than a finite state automaton. Fun fact: Such systems are incapable of doing basic arithmetic. If you're having trouble believing that your computer can't do arithmetic try adding something to 2^n where n is the number of bits of memory you have. This may sound bad but it's great. They're still powerful enough to do whatever they like within their finite bounds and things like the halting problem, Godel's incompleteness theorem? Not applicable. Given some assumptions like the universe is finite and consciousness can be represented symbolically, it becomes very difficult to argue that a relation between the two couldn't be represented computationally.

But it's not enough to know that such a mapping must exist or that it must be representable with simple computation. The idea that there are a vast number of possible mappings is still somewhat relevant, but no more than saying to a physicist "I could invent a world where gravity works differently" or even "There are many different models for reality" and like the physicists it's going to take experiments to sort out which one is the correct one. The key to any experiment is good measurement and so we come inexorably back to the heart of the issue. How do we measure this?