How to measure the intelligence of AGI and/or ASI/

As we go on the road to AGI and/or ASI, there is a genuine problem of how to measure intelligence. IQ is based on the assumption of a Gaussian distribution and deviation from the mean as ratio to standard deviation, so it cannot be applied to AI far removed from humans.

Assessing intelligence purely by the vastness of memory and the speed of calculation would be a part of the equation, but not the essential part. Defining AGI and ASI in terms of the tasks they could perform would be helpful, but then we humans might not be able to conceptualize all the relevant tasks.

There is also the problem of Vingean uncertainty and xAI. If ASI ever materializes, it might not be possible for us humans to understand its functionality. It would be difficult to require explainable performance because that would mean mediocrity within the range of human intelligence.

The only hope would be instrumental convergence. Here, defining AGI and ASI in terms of embodied cognition would prove robust and essential.

Formalization of numbers.

I always felt that there was something strange about the way the concept of numbers are formalized by set theory or category theory. Although the concept of numbers do have some problems, unless we deal with infinities there does not seem to be an urgent need for formalization, as far as calculations are concerned, including complex numbers.

Humans seem to have an intuitive understanding of numbers, on par with qualia. By trying to formalize numbers by set or category or other theories, something extra is added, and there are consequently some "evil questions" that shouldn't be asked, as numbers represented by these formalisms have something external to our intuitive understanding of numbers. 

I am not saying that attempts at formalization are meaningless. I just feel that numbers should be treated on the same footing as qualia. Just as attempts at formalizing qualia do not go well, formalization of numbers is bound to be unsatisfactory, because such an approach is not addressing the essential nature of numbers directly.