[ExI] 1DIQ: an IQ metaphor to explain superintelligence

[Jason Resch]

On Fri, Oct 24, 2025, 8:49 AM Jason Resch <jasonresch at gmail.com> wrote:

>
>
> On Fri, Oct 24, 2025, 8:15 AM John Clark via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
>
>> On Thu, Oct 23, 2025 at 9:48 AM Adrian Tymes via extropy-chat <
>> extropy-chat at lists.extropy.org> wrote:
>>
>>
>>> *> I was addressing the terrestrial-scale scenario presented,
>>> not potential J-Brains (which would occupy different planets entirely).*
>>
>>
>> *The Guinness Book of World Records no longer recognizes a highest IQ
>> category because of "a lack of a universally agreed-upon standard".*
>>
> * It's easy to see why they did that, the only one who would have the
>> competence to write a test to find the world's smartest human would be the
>> world's smartest human, and that fact introduces certain
>> obvious difficulties.  *
>>
>
> You can take any set of questions, so long as they have agreed upon
> answers, and make an IQ test out of it: simply give the test to many people
> and you will find their performance fits a bell curve. This is generally
> true regardless of what questions you ask, so long as they're not so easy
> you get a cluster of perfect scores.
>
> The questions don't have to be written by someone with a higher IQ,
> rather, they just have to be such that there's a non-zero probability that
> someone won't know the answer. So the question might require specialized or
> esoteric knowledge, or be one that requires a lot of time to figure out
> (and then limit test time).
>
> So long as very high IQ people don't all get perfect scores on the test,
> then you can rank them, and you will find the distribution follows a bell
> curve.
>
>
>> *How could somebody with just Human intelligence even judge the responses
>> that a superintelligence gave on an IQ test?*
>>
>
> What's the capital of Benin?
>
> This is something a 100 IQ person can judge and verify the answer to, but
> something less than 5% of the population will know the answer to.
>
> If you have a test with a lot of questions such as these, then high or
> perfect scores will be extremely rare. Someone must be very well read,
> knowledgeable and have a great memory to do well on a test with questions
> such as these.
>
> To test processing speed, you can ask math questions that have well agreed
> answers but require many steps of processing, like multiplying 5 digit
> numbers. Again this is a question that someone with a 100 IQ can verify,
> but depending on time allowed, perhaps very few people will be able to
> answer.
>
> Jason
>
> * Suppose the year was 1901 and one of the items on an IQ test was "prove
>> Fermat's Last Theorem" and suppose that somebody had given a proof that was
>> identical to the one that Andrew Wiles gave in 1995, how could anybody know
>> if it was valid? In 1901 even the world's top mathematicians would have had
>> no idea what Wiles was talking about because in his proof he was using
>> concepts without explanation, he didn't need to because they were common
>> knowledge to all mathematicians in 1995, but were completely unknown to
>> mathematicians in 1901. If Wiles had included all those explanations in his
>> proof then it would've been 10 times as large, and even then it would've
>> probably taken mathematicians at least a decade to fully understand it and
>> realize that Wiles was right.*
>>
>

As to what questions we should chose to ask a super intelligence, they
should be questions of a type that directly measures what intelligence is
and requires: pattern recognition and prediction.

You can generate random functions, then produce some sequence of outputs
generated by those functions, and then ask the superintelligence to
identify the function that produced the sequence.

See:
https://en.wikipedia.org/wiki/AIXI

The problem of generating functions in this way isn't difficult, nor is
verifying answers, both can be done mechanically and in an automated
fashion. But the problem of working out the function from the outputs can
be immensely difficult. For example, cryptographic pseudorandom number
generators are designed to require exponentially many steps to figure out
the seed value.

If an alien superintelligence intelligence visited us, and allowed us to
ask it any question, we could readily determine it's computational capacity
by asking questions that required more and more computing power to solve.
Eventually there would be questions it would fail to answer due to its
computational limits.

Again this doesn't require superintelligence to setup or judge these
difficult questions. This follows so long as "P != NP" (there are questions
that are computationally easy to verify the answer to, but computationally
hard to find.)

https://en.wikipedia.org/wiki/P_versus_NP_problem

This is regarded as the greatest unproven problem in computer science, but
it is nearly universally accepted as true.

Jason






>>
>> *John K Clark*
>>
>>
>>
>>
>>
>>
>>>
>>> On Thu, Oct 23, 2025 at 9:32 AM John Clark <johnkclark at gmail.com> wrote:
>>> >
>>> >
>>> >
>>> > On Thu, Oct 23, 2025 at 8:47 AM Adrian Tymes via extropy-chat <
>>> extropy-chat at lists.extropy.org> wrote:
>>> >
>>> >>  > IQ 160 AI will outthink me on average, but not always
>>> >
>>> >
>>> > I see no reason to believe that a smart human is about as smart as
>>> something can be. I also don't believe an IQ test can meaningfully measure
>>> the intelligence of something that is significantly smarter than the people
>>> who wrote the IQ test, so an IQ of 300 or even 200 means nothing. And I
>>> don't think there are many people who have an IQ of 160 and are in the IQ
>>> test writing business. But if there was such a test that could measure
>>> intelligence of any magnitude, and if you made a logarithmic plot of it, I
>>> think you'd need a microscope to see the difference between the village
>>> idiot and Albert Einstein, but if you were standing at the Albert Einstein
>>> point you'd need a telescope to see the Mr. Jupiter Brain point.
>>> >
>>> > John K Clark
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >> I've been thinking about that video that claimed a superintelligence
>>> can always perfectly outthink any lesser intelligence, such as a human.
>>> The assumption of narrative godmodding aside, intelligence just doesn't
>>> work like that.  I think I may have come up with an imperfect but simple
>>> metaphor to explain this.
>>> >>
>>> >> I have been a member of Mensa since a young age.  While it has been a
>>> while since my IQ was measured (and I do not trust the free online tests),
>>> let us say my IQ is around 150: not the record highest ever, but
>>> comfortably into the top 2%.  So I am speaking from the experience of
>>> having lived with high intelligence.
>>> >>
>>> >> In cases where just your IQ applies, it's like rolling a die, with
>>> sides numbered from 1 to your IQ.  (Skills and training also factor in.
>>> I'm nowhere near as good at fixing a car as a trained auto mechanic, for
>>> instance, regardless of our relative IQs.  But here we'll ne comparing me
>>> to hypothetical AIs where both of us have access to the same database - the
>>> Internet - and some training on relevant skills.)
>>> >>
>>> >> I will, on average for such matters, roll higher than someone with IQ
>>> 100.  This means I come up with the better answer: more efficient, more
>>> often correct, et cetera.  (This does not apply to subjective matters, such
>>> as politics, which shows one weakness of using just IQ to measure all
>>> intelligence, and why some speak of multiple kinds of intelligence.  But
>>> here we'll be looking into tactics, technology planning, and so on where
>>> there usually is an objectively superior answer.)
>>> >>
>>> >> But not always.  Sometimes I'll roll low and they'll roll high.  I
>>> know this.  Any AI that's as smart as I am, and ran for long enough to gain
>>> such experience, would know this too.  (The video's scenario started with
>>> the AI running for many subjective years.)
>>> >>
>>> >> From what I have seen, IQ may be partly about physical architecture
>>> but also largely depends on heuristics and optimizations: it is literally
>>> possible to "learn" to be smarter, especially for young children whose
>>> brains are still forming.  For an AI, we can map this to its hardware and
>>> software: a single-chip AI might be a million times smarter than an average
>>> human, and then run on a million GPUs.
>>> >>
>>> >> From what I have seen, IQ is not linear.  It's closer to log-based.
>>> Twice as smart as me would not be IQ 300; it would be far closer to 151.
>>> (I don't know if that is the exact scaling, but for this metaphor let's say
>>> it is.)  1,000, or 10^3, is approximately 2^10, so a thousand-fold increase
>>> in intelligence corresponds to a 10-point IQ increase by this metric.
>>> >>
>>> >> So, that "million by million" AI I just described would only be IQ
>>> 140.  Let's toss another million in there somewhere, or change both of
>>> those "million"s to "billion"s, either way getting to IQ 160.
>>> >>
>>> >> This IQ 160 AI will outthink me on average, but not always - not
>>> perfectly.  Further, the AI in the video wanted to be the only AI.  2% of
>>> humanity is in the tens of millions.  Even if we can only take our maximum
>>> collective roll, not adding our dice or anything, that AI will rarely
>>> outroll all of us - and it needs to do so several times in a row, reliably,
>>> in the video's scenario.  Otherwise, we figure out the AI is doing this,
>>> find a way to purge it, and stop its time bomb, so humanity lives.
>>> >>
>>> >> Knowing this, the AI would see its survival and growth - the
>>> imperatives that video assumes to explain the AI's actions - as more likely
>>> if it works with humanity instead of opposing it.
>>> >>
>>>
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