What do you mean? Is cognition a set of weights on a gradient? Cognition involves conscious reasoning and understanding. How do you know it is computable at all? There are many things which cannot be computed by a program (e.g. whether an arbitrary program will halt or not)...
That's a pretty simplistic view. How do you know we can't determine whether an arbitrary program will halt or not (assuming access to all inputs and enough time to examine it)? What in principle would prevent us from doing so? But computers in principle cannot, since the problem is often non-algorithmic.
For example, consider the following program, which is passed the text of the file it is in as input:
function doesHalt($program, $inputs): bool {...}
$input = $argv[0]; // contents of this file
if (doesHalt($input, [$input])) {
while(true) {
print "Wrong! It doesn't halt!";
}
} else {
print "Wrong! It halts!";
}
Can you tell me if a program which searches for counterexamples to the Collatz conjecture halts?
Turing's entire analysis started from the point of what humans could do.
func main() {
var n = 4;
OUTER: loop {
for (var i = 2; i < n/2; i++) {
if (isPrime(i) && isPrime(n-i)) {
n += 2;
continue OUTER; // Goldbach’s conjecture
}
break;
}
}And while the human brain might not be a bio-computer, I'm not sure, its computational prowess are doubtfully stronger than a quantum turing machine, which can't solve the halting problem either.
If cognition magically exists outside of math and science, then sure, all bets are off.
We don't even know if the flow of water in a river can always be represented by a mathematical function - this is one of the Millennium Problems. And we've known the partial differential equations that govern that system since the 1850's.
We are far, far away from even being able to write down anything resembling a mathematical description of cognition, let alone being able to say whether the solutions to that description are in the class of Lebesgue-integrable functions.
There was, past tense, no reason to believe cognition could be represented as a mathematical function. LLMs with RLHF are forcing us to question that assumption. I would agree that we are a long way from a rigorous mathematical definition of human thought, but in the meantime that doesn't reduce the utility of approximate solutions.
A lot of people who argue that cognition is special to biological systems seem to base the argument on our inability to accurately model the detailed behavior of neurons. And yet kids regularly build universal computers out of stuff in Minecraft. It seems strange to imagine the response characteristics of low-level components of a system determine whether it can be conscious.
Consciousness cannot be accounted for in physical terms. For consciousness is absolutely fundamental. It cannot be accounted for in terms of anything else.
-- Erwin Schrödinger
- Carl Sagan
Many things are non-algorithmic, and thus cannot be done by a computer, yet we can do them (e.g. love someone, enjoy the beauty of a sunset, experience joy or sadness, etc).
Moreover, are you sure that e.g. loving people in non-algorithmic? We can already make chatbots which pretty convincingly act as if they love people. Sure, they don't actually love anyone, they just generate text, but then, what would it mean for a system or even a human to "actually" love someone?
What is your definition of _conscious reasoning and understanding_?