What is the best way to classify Intelligence in a world full of various Intellects?

Question

[This question was posted on Sandbox]

Abstracts

In a world where there are different kinds of intelligence, I am in need to assign classes to each mind encountered. The measurement doesn't have to (and is encouraged to not) be human centric in comparison, so human intelligence may have non-human centric classification in the system.

On my previous attempt to classify it, I do try to use Sentience Quotients to gives how efficient a computing substrate it is, but it couldn't help much when I realized that we could have two beings with different SQ scores, that is vastly different size, having similar computing capability.

Brain size vary vastly, from tiny superdense computronium hosting intelligence equivalent with human level intelligence, to biological computronium like humans, to moon-sized computronium node, up to galactic sized brain with many of its components hosted around stars and is connected through its own wormhole communication backbone. Therefore there must be a sufficiently efficient way to describe how smart they are when referred by normal people.

The Question

What is the best way to classify or scale Intelligence that is as objective as SQ is, yet sufficiently easy for one to know how intelligent a being is just by looking at the number?

Considerations

To narrow the question down,here are some considerations when answering the question:

1. I am asking exactly on the most viable method to derive the idea of how smart it is in term of computing capability.
2. Please bear in mind that the system must be as objective as SQ, but sufficiently clear to describe how powerful the computing capability is.
3. By "objective" I mean the system can't be described as "n times human intelligence". You get the idea.
4. Perhaps it would be nice if the system could address unique traits a computing substrate has, in relative to the other. But this one is optional.
5. Equations are welcomed as it could make things easier.
6. It would be nice to also know where human is on the answer's method of classification for comparison. (just a suggestion, completely optional but will also be considered)

Problem with Sentience Quotient

As I had mentioned it before, I had tried Sentience Quotient (or SQ), and I wish to have a system that is as objective as SQ. I think it is worth explaining about Sentience Quotient, so I'll provide the formula here:

$$SQ=\log_{10} \left(\frac{I}{M}\right)$$

Where $$SQ = \text{Sentience Quotient}$$ $$I = \text{Information processing rate, in bits/s}$$ $$M = \text{Mass of the brain in kilogram}$$

The SQ range from the minimum possible value of SQ-70 while the upper (quantum) limit is SQ+50.

It must be noted that though this might sounds viable, but one may not be able to properly judge a being's intelligence just by knowing this number. For example a brain of 1.5 kg with SQ+13 is roughly as smart as a man, while a brain with just less than 200 grams with SQ+23 is at least some thousand times as powerful as a human brain's computational capability. In the other way around, a computing substrate with SQ scores less than SQ+13 could achieve computational capacity of a man's brain given that it is considerably more massive than a man's brain.

The conclusion is that denoting one's intelligence with just a SQ score could not reliably determine how intelligent a being is, as it also be determined by the size of one's brain. So it must comes with second number or variable, perhaps classes, to denote one's intelligence properly, or different method altogether.

Answer 1

There is a possible solution if you don't use a single number but, a coordinate function such as that of normal distribution functions. (e.g. N(100, 5^2))

This is all from my past learning experience, so no citations. (Yet.)

Human intelligence or human intelligence like intelligence is so hard to measure in a single number because human intelligence isn't just one thing. It's a bundle of intelligence(s), which in fact is compartmentalized across the entire brain. For example, linguistics and speaking are compartmentalized by specialized brain areas called Wernicke's area and Broca's area. Spacial cognition and simple understanding are also specialized by other areas of the brain, long term memory, short term memory, physical control are all part of intelligence.

So to put those things into something simpler, you could use a mean root square of defined intelligence(s), and have another number define its variance. That way if you looked at something like N(1000,1), you'd know for sure that it excels at everything, but if you looked at something like N(1000,500), then you'd know you'd have to go into details to know what its intelligence is really like.