[nopinsight]

Thanks. I came up with that myself although I would like to see if someone can poke holes on it [1]. I am aware that many NP-hard problems, for example, usually have good approximate solutions in non-pathological cases. So that could be a big hole in that argument.

Could a theoretical computer scientist give more insight on this? In particular, what is the hardness of approximate solutions to most problems that could have strong impact in the real world?

[1] I did, in passing, find a similar idea discussed somewhere afterwards. If someone has a reference for that, I would be glad to have it.

[red75prime]

For traveling salesmen problem there is Christofides algorithm which gives result that is no longer than 3/2 of optimal one. Theoretical bound on inapproximability of symmetrical TSP currently is 185/184.

https://arxiv.org/abs/1303.6437

[s1dechnl]

[AGI Developer]

I'll instead give you something to consider : * The totality of mathematics is not fully defined. As such, there are can be completely new mathematics that destroys previous conceptions especially as it relates to the limits of computability. Theoretical Limits often reflect one's limited scope of perception. Your limits or the limits someone theorized ages ago aren't necessarily my limits if I find a path beyond them.

Information theory and computational complexity theory are theories... Solving fundamental aspects of intelligence will invalidate a host of theories, create new mathematics, new algorithms, and new theories. Continuing to frame something as ground breaking as an understanding/implementation of intelligence in yester-years theoretical limits is flawed.

[xamuel]

In a phrase like "information theory", "theory" means "body of literature", not "unproven hypothesis". Information theory isn't really something that can be invalidated, no more than the Pythagorean Theorem can be invalidated.