Things we can't compute | Hacker News Reader

Things we can't compute

alexstjohn.com

6 pointsaycangulez7 comments

TL;DR: "If we can build a big enough computer we can understand anything" is a delusion, but "If we can build a big enough computer we can compute anything" is scientific fact.

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There are many valid points in the article. Sadly, they are shadowed out by misconceptions and/or wrong phrasing.

Since Turing's 1936 paper, we have proof that computation is universal. That means any computation in the universe, including the one occurring in your brain while you read this, can be implemented on a Turing machine.

So, yes, we have proof that a big enough computer can compute the human brain, the global climate, and any other physical phenomenon.

And the argument about indetermination in physics (ping-pong ball in the rapids) is about getting the information, not computing it — computation is universal, but information is sometimes impossible to obtain.

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Universal computation does not mean that a computer can understand itself, and I like that the author suggests such a thing should be impossible.

Universal computation does not mean that building a big enough computer should always be the priority, and I like how the author addresses that.

If the author had put less effort into being cute, and more effort into just saying what he had to say, the article might be worthwhile.

As it is, I have other things to do with my time than train myself to filter out his particular and peculiar attempts at lightening the mood. Repeated references to Jell-O and reminding us that Tesla didn't help us make it to Mars are just plain tedious. Distraction with no point served.

Not quite. We can compute any determinate process, perhaps. (Although as Gödel‎ showed, self-reference introduces computational paradoxes even in closed, limited, artificial, formal systems: how do we compute "this statement is false?") You seem to believe that consciousness is essentially computation, and perhaps you're right. You may be wrong though -- the nature of consciousness is one of the trickiest, most intractable problems. It's an open question. Again as with Gödel‎, self-reference introduces problems. If we believe that consciousness is a mechanical/chemical operation without innate intelligence, then any statement about consciousness is itself a product of a certain balance of chemicals in the brain only. So the whole idea of getting to the truth about such things is a pointless endeavor.

"does not mean that a computer can understand itself" -- not sure I entirely agree here either. My computer seems pretty good at understanding itself: right now it's telling me its internal temperature, what programs it's running, CPU and memory utilization, and so forth. In fact, it probably understands itself much better than I do -- at billions of computations per second, I certainly can't keep up. I'm being cute, yes, but I'm also suggesting you seem to implicitly accept that there's a certain type of self-understanding or consciousness that computers don't have, but living beings (in particular, humans) do. Whereas before you said your brain is just a computer ... ?

Let us make a distinction, shall we?

Determination is not an issue. Any non-deterministic Turing machine has an equivalent deterministic Turing machine.

Consciousness is an issue. Indeed, if consciousness is pure computation, then its self-referencing character make it vulnerable to Gödel's incompletude theorem. However, maybe consciousness is more than mere computation — maybe it cannot be reduced to an axiomatic system. Anyway, as far as neuroscience goes, I think consciousness mostly remains a philosophical debate.

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You misinterpreted my sentence. What I meant is: "universal computation is not, in itself, a proof that a computer can understand itself". This relates to my above remark: maybe consciousness is not pure computation.

Also, a system monitoring its own status is not necessarily understanding itself.

> So, yes, we have proof that a big enough computer can compute the human brain, the global climate, and any other physical phenomenon.

Not true. Quantum effects are (according to most current theories, at least) incalculable.

Case in point: Assume that the system is a single unstable atom. Regardless of how exactly you've measured the system (even if you've somehow measured it exactly, violating the uncertainty principle), you cannot simulate it - you cannot state to arbitrary accuracy if the atom will decay within, say, 10 seconds. You cannot answer the question "Will the atom decay within 10 seconds" to arbitrary accuracy. You can state it probabilistically, but that is not the same thing.

What is to say that the human brain is not the same way? I could easily accept that shot noise affects the human brain, and I we know that a single neuron can produce noticeable effects.

Or, for that matter, take climate. We know that cosmic rays affect the atmosphere, and many collisions produce unstable particles. And the climate is chaotic. As such, I'm willing to accept that the climate is incalculable too, even given the entire state of the universe (somehow).

How is that not just a matter of not all of the information being available? What does uncalculable mean here?

Just for a bit of perspective, Alex St. John is the "Father of DirectX", and created the first video game company that streamed games over a web browser.

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