There is also no guarantee that space aliens won't invade the Earth in the future. Therefore we should start working on giant orbital laser guns now to mitigate the potential risks. Can't be too safe.

Non-negligible vs non-existent.

Are there any proven, even weak, signs of intelligent space-traveling aliens? If so, then yes we should work on that too.

The leaderboards above and pervasive computer vision and equity trading systems are some signs.

The leaderboards above and pervasive computer vision systems are impressive parlor tricks to be sure, but they don't constitute even weak proof of forward progress toward AGI.

Some people claim to have seen intelligent space-travelling aliens. Personally I think they're nuts, but it's impossible to absolutely prove that their claims are false.

How about AlphaStar and OpenAI Five, both of which approach human-champion levels in relatively complex environments that take talented people years to train to achieve similar results?

There are obvious disadvantages to the current machine approaches, but they nonetheless achieve very good results and beat the vast majority of players of those games.

Those environments are not at all complex. They are highly simplified and constrained with simple rules that bear little relationship to the real world.

I wouldn’t say that an environment that takes humans years to master and many hours to comprehend most interactions therein in detail is simple. The rules are not that complex but the interactions between game elements as well as agents are. Those AIs also need to deal with highly trained human opponents.

Real-world relevance is orthogonal to complexity.

You’re not going to believe this but I’ve got an AI that can multiply 26 digit numbers way faster than humans who’ve trained for years at the task.

The Kolmogorov complexities of the best programs to solve those two classes of problems, digit multiplication vs Starcraft, are quite different.

Edit: We don’t know the best programs, but we can approximate the bounds with some confidence that, unless some paradigm-changing discovery is made, the programs to solve digit multiplication would be significantly simpler. (This is not a formal argument, but the intuition is very strong for most people who study the problems seriously.)

Perhaps that's the trick. The machines are better at all these things because it takes a skilled human to do them. The machines are not so good at the things it doesn't take a skilled human to do (walk, dance, fold clothes).

How did you calculate the Kolmogorov complexity of those two classes of program?

I wrote a decent fraction of the code in the original Starcraft, so, yes, I can assure you the Kolmogorov complexity of Starcraft is leaps and bounds above that of multiplication :)

But how did you calculate the Kolmogorov complexity of your code?

Kolmogorov complexity is a distinct quantity. How did you compute this quantity?

You write code. You write the smallest possible amount of code that can solve the problem. The smallest multiprecision multiply is pretty small; I’ve written that. Just for Starcraft pathing alone (the most complex of all the code I wrote in Starcraft) is orders of magnitude more code, even for the smallest possible version that’s not tuned for efficiency.

If you’re a purist, you write the programs in MIX and you count ops. Or whatever your preferred Turing Machine is.

That's not any way to calculate Kolmogorov complexity. That's comparing the length of the two shortest programs that you could write to do digit multiplication and pathfinding in Starcraft.

You can't calculate it. You can make strong comparative statements about it. And it is a much more specifically relevant concept than program length.

Can you, though, "make strong comparative statements"? How do you know what is the shortest program to perform some operation, X, in a language L? I'm prepared to agree that on the balance of probabilities the pathfinding code in Starcraft _should_ be inherently more complex than that for multiplication- but that is just intuition, whereas Kolmogorov complexity is a formal concept that does not admit intuitive judgements. Which is (part of) why it's necessary. If we could just compare the length of programs in some language and determine their relative Kolmogorov complexity from that, then there wouldn't be no need to define Kolmogorov complexity. We'd just make do with program length.

I know that sounds pedantic and this is the internet and not a scientific paper etc, but if this is an informal discussion then formal terminology like "Kolmogorov complexity" has no place in it and the purpose of the OP would, I think, be better served by using an informal term. If you 're gonna use maths, use maths. If you 're gonna wave hands, then wave hands, by all means. But don't mix the two, it just makes a mess.

Because at the end of the day I can just say, "no, I don't believe that multiplication has smaller Kolmogorov complexity than Starcraft's pathfinding"... and then, what? Where do we go from there? The OP says "yes it does", I say "no it doesn't", the OP says "does too", I say "nuh-huh". And we just waste our time.

The OP says:

> yes, I can assure you the Kolmogorov complexity ...

This is a strong comparative statement, and it's clear that it's an assertion but not a proof. So it's perfectly fine for you to say "I don't believe that" and then you would give your reasoning. Of course the conversation didn't go that way because it's pretty obvious to everyone that this is actually true even though we don't have a proof. And it's extremely likely that if you could find a minimal multiplication algorithm and enumerate all the Turing machines up to that length you could prove that none of them solve the harder problem. This is where the intuition comes from.

> using an informal term

But the OPs argument wasn't that one program would happen to be longer, but rather that it must by necessity be longer, because the problem is fundamentally more complex, which is exactly what the formal concept was created to capture.

> Kolmogorov complexity is a formal concept that does not admit intuitive judgements

This is a bad way of thinking about maths. The value of formal concepts is precisely that they give us tools for making intuitive judgements more effectively and give us a wider variety of tools to manipulate and express our intuition. As intuitions become conjectures and theorems, we accumulate new bedrock we can use for new intuitions, but don't short-circuit your thinking by saying that intuition about technical terms is off-limits. That's literally what they are good for.

>> This is a bad way of thinking about maths.

I don't agree. I don't need formal terms to develop intuition. Formal terms are necessary when speaking formally, and they are only detracting from the point of a discussion otherwise.

And I don't agree with this either:

>> But the OPs argument wasn't that one program would happen to be longer, but rather that it must by necessity be longer, because the problem is fundamentally more complex, which is exactly what the formal concept was created to capture.

The way I understand it the formal concept is useful in proofs of the impossibility to calculate various other quantitites. Its utility is not to argue that this or that program should intuitively have lower Kolmogorov complexity.

To be honest, I'm so confused by the use of the term by the OP that I have no idea what they meant to say with it.

Kolmogorov complexity is just the standard name for a concept that's useful across machine learning, AI, compression, etc. It's not just a definition in some obscure result in complexity theory.

OP was simply saying that, in any general-purpose programming language (where all possible programs are expressible and none are unfairly favored) the solution to problem B will inevitably be longer than problem A. This is quite a bit more precise than just saying "a more complicated problem", and if you have the intuition behind it, there's no reason not to use the term.

I'm not convinced but we've taken this far enough I think. Thank you for an insightful conversation.

Thank you too!

No sign of aliens, but many other low probability high threat events. Asteroid strike, solar flare, super volcano eruption, interstellar object collision (including wandering brown dwarf stars).

But there is, also, no thousands of scientists working on create some space ships to attack the earth.