My issue is that from a scientific point of view, physicalism is all we have. Everything else is belief, or some form of faith.

Your example about relativity is good. It might have sounded insane at some point, but it turns out, it is physics, which nicely falls into the physicalism concept.

If there is a falsifiable scientific theory that there is something other than a physical mechanism behind consciousness and intelligence, I haven't seen it.

Boltzmann brains and A. J. Ayer's "There is a thought now".

Ages ago, it occurred to me that the only thing that seemed to exist without needing a creator, was maths. That 2+2 was always 4, and it still would be even if there were not 4 things to count.

Basically, I independently arrived at similar conclusion as Max Tegmark, only simpler and without his level of rigour: https://benwheatley.github.io/blog/2018/08/26-08.28.24.html

(From the quotation's date stamp, 2007, I had only finished university 6 months earlier, so don't expect anything good).

But as you'll see from my final paragraph, I no longer take this idea seriously, because anything that leads to most minds being free to believe untruths, is cognitively unstable by the same argument that applies to Boltzmann brains.

MUH leads to Aleph-1 infinite number of brains*. I'd need a reason for the probability distribution over minds to be zero almost everywhere in order for it to avoid the cognitively instability argument.

* if there is a bigger infinity, then more; but I have only basic knowledge of transfinites and am unclear if the "bigger" ones I've heard about are considered "real" or more along the lines of "if there was an infinite sequence of infinities, then…"

> this cannot be reached algorithmically

> humans can (somehow) do this

Is this not contradictory?

Alternatively, in order to not be contradictory doesn't it require the assumption that humans are not "algorithmic"? But does that not then presuppose (as the above commenter brought up) that we are not a biochemical machine? Is a machine not inherently algorithmic in nature?

Or at minimum presupposes that humans are more than just a biochemical machine. But then the question comes up again, where is the scientific evidence for this? In my view it's perfectly acceptable if the answer is something to the effect of "we don't currently have evidence for that, but this hints that we ought to look for it".

All that said, does "algorithmically" here perhaps exclude heuristics? Many times something can be shown to be unsolvable in the absolute sense yet readily solvable with extremely high success rate in practice using some heuristic.

> For this paper, It is absolutely sufficient to prove that a) this cannot be reached algorithmically and that b) evidence clearly shows that humans can (somehow) do this , as they have already done this (quite often).

The problem with these kinds of arguments is always that they conflate two possibly related but non-equivalent kinds of computational problem solving.

In computability theory, an uncomputability result essentially only proves that it's impossible to have an algorithm that will in all cases produce the correct result to a given problem. Such an impossibility result is valuable as a purely mathematical result, but also because what computer science generally wants is a provably correct algorithm: one that will, when performed exactly, always produce the correct answer.

However, similarly to any mathematical proof, a single counter-example is enough to invalidate a proof of correctness. Showing that an algorithm fails in a single corner case makes the algorithm not correct in a classical algorithmic sense. Similarly, for a computational problem, showing that any purported algorithm will inevitably fail even in a single case is enough to prove the problem uncomputable -- again, in the classical computability theory sense.

If you cannot have an exact algorithm, for either theoretical or practical reasons, and you still want a computational method for solving the problem in practice, you then turn to heuristics or something else that doesn't guarantee correctness but which might produce workable results often enough to be useful.

Even though something like the halting problem is uncomputable in the classical, always-inevitably-produces-correct-answer-in-finite-time sense, that does not necessarily stop it from being solved in a subset of cases, or to be solved often enough by some kind of a heuristic or non-exact algorithm to be useful.

When you say that something cannot be reached algorithmically, you're saying it's impossible to have an algorithm that would inevitably, systematically, always reach that solution in finite time. And you would in many cases be correct. Symbolic AI research ran into this problem due to the uncomputability of reasoning in predicate logic. (Uncomputability is not the main problem that symbolic AI ran into but it was one of them.)

The problem is that when you say that humans can somehow do this computationally impossible thing, you're not holding human cognition or problem solving to the same standard of computational correctness. We do find solutions to problems, answers to questions, and logical chains of reasoning, but we aren't guaranteed to.

You do seem to be aware of this, of course.

But you then run into the inevitable question of what you mean by AGI. If you hold AGI to the standard of classical computational correctness, to which you don't hold humans, you're correct that it's impossible. But you have also proven nothing new.

A more typical understanding of AGI would be something similar to human cognition -- not having formal guarantees but working well enough for operating in, understanding, or producing useful results the real world. (Human brains do that well in the real world -- thanks to having evolved in it!)

In the latter case, uncomputability results do not prove that kind of AGI to be impossible.

Unless you can show - even a single example would do - that we can compute a function that is outside the Turing computable set, then there is a very strong reason that we should assume a silicon machine has the same capabilities as a carbon machine to compute.

Yeah, but bronze also makes great swords… what’s the point here?

The measure of human intelligence is never what humans are good at, but rather the capabilities of humans to figure out stuff they haven't before. Meaning, we can create and build new pathways inside our brains to perform and optimize tasks we have not done before. Practicing, then, reinforces these pathways. In a sense we do what we wish LLMs could - we use our intelligence to train ourselves.

It's a long (ish) process, but it's this process that actually composes human intelligence. I could take a random human right now and drop them somewhere they've never been before, and they will figure it out.

For example, you may be shocked to know that the human brain has no pathways for reading, as opposed to spoken language. We have to manually make those. We are, literally, modifying our brains when we learn new skills.

It doesn't take 20 years for humans to train new tasks. Perhaps to master very complicated tasks, but there is many tasks you can certainly learn to do in a short amount of time. For example, "Take this hammer, and put nails in top 4 corners of this box, turn it around, do the same". You can master that relatively easy. An AGI ought to be able to practically all such tasks.

In any case, general intelligence merely means the capability to do so, not the amount of time it takes. I would certainly bet a physical theorist for example can learn to code in a matter of days despite never having been introduced to a computer before, because our intelligence is based on a very interconnected world model.