> Eg even with seven billion people we’ve never seen someone with a 500 iq.

For two reasons. First of all IQ is defined as a normal distribution with a mean of 100 and a sd15. So by definition only 0.1% of the population can have an IQ of above 145 and this fraction is rapidly diminishing with additional standard deviations.

Secondl: the definition matches reality reasonably well because intelligence is a polygenetic trait and many small factors add up to a normal distribution.[0] It is statistically unlikely that natural processes will yield an IQ500 human. You would have to engineer one. Which leads us back to the AGI concern.

[0] https://en.wikipedia.org/wiki/Central_limit_theorem

A series of connected games [society] is constructed by various groups in mankind. They all have common traits. A human being having no understanding of intelligence creates a measure of potential success in these games [society]. It is called an IQ test. It has nothing to do w/ actual intelligence as there is no fundamental understanding of it. Instead, it correlates to a potential for success in the games certain individuals have constructed. Change the game and the potential for success does as well. Far too much weight is put on the intelligence Quotient especially given a lack of understanding as to what intelligence is and the clearly skewed games mankind creates [society].

Also, I'm still confused as to what you mean by : AGI concern. What's the concern? What's the big fear?

But that sd15 is an empirical fit, is it not, reflecting the variance seen in the actual population?

No, the number is an arbitrary choice and the test results of IQ tests are scaled so that they fit into the distribution, based on random sampling of the population when the test is designed.

IQ is not a linear scale, all it tells you which quantile of the population one falls into. It does not describe the relative strengths between the quantiles in particular tasks.

To figure that out there are additional surveys that map IQ ranges to occupations and the tasks an individual is required to perform.

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.

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

[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.

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.