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As a small part of a SciFi story, a fully developed AI developed by advanced aliens (who think quantum computing is a neat, but outdated technology) happens to visit modern-day Earth. I'm talking about an AI that learns about humanity by reading the Internet. Not some pages, not Wikipedia, the entire Internet, all the change history of all Wikipedia pages, everything in the Way Back Machine, just everything.

Out of boredom, the AI also takes an IQ test (or several). In the story this is used as a humourous smack-down of a (human) character who boasts how smart he is.

An AI that scores a perfect score on an IQ test and delivers the result in a fraction of a second - what score would this result in?

Bonus question: If the AI gets one of the language-comprehension questions wrong, what would be the highest possible score with one error?


My checking indicates that different tests have different maximum values. So I'm looking for a Mensa test or something similar used to measure genius-level IQ.

Sources I found are conflicting. One source said 220 is the limit of the human brain. Another said that the legendary William James Sidis is said to have had an IQ somewhere in the 250-300 range.


Clarifications

I'm not interested in whether or not this would correctly measure the IQ of my AI or whether IQ even makes sense when applied to AI. Also not in discussing the merits of the IQ system. I am aware of how IQ tests work, I took a couple myself in my life.

All I want is a quick number that actually would come out of such a test under the above conditions (zero or one error, less than one second time to complete the test).

That number would probably be off the scale for humans, which is exactly the point. But would it be off the scale as in 300, or 500, or 12,000 ? This is basically one short paragraph in the whole book and I just don't want that someone familiar with how IQ tests are calculated goes "nah, that's nonsense"

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    $\begingroup$ The answer to that question is of course: The IQ score if you answer everything right but one question. But that means you have to ask yourself: In what language? Some languages don't have IQ tests that go that high because there is no need for them. Think of it like this: If you did a 1st grade math test, something small kids do, you would get an A and everything right. But you wouldn't get a super A because you are so good - you would just get the maximum score $\endgroup$ – Raditz_35 Sep 3 '18 at 15:56
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    $\begingroup$ That's not how IQ tests work. See Henning Makholm answer. IQ test by definition compare members of a culturally homogeneous population. It is meaningless to compare results of different tests given at different times to different populations. It is meaningless to give the test to a population which is not culturally homogeneous. $\endgroup$ – AlexP Sep 3 '18 at 16:29
  • $\begingroup$ Yes, I would just get the maximum score. I'm interested in that actual number. $\endgroup$ – Tom Sep 3 '18 at 16:41
  • $\begingroup$ @AlexP - I know that. The AI knows that. It just took a test (or a hundred of them, what is some processing time?) for giggles. This is not the core of the story, it's just a detail, a short exchange, but I want to get it right anyway. $\endgroup$ – Tom Sep 3 '18 at 16:42
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    $\begingroup$ In terms of your story, it would be more fun if the AI smack downed the human by pointing out all the flaws the human has ever made in previous IQ tests. The AI has read the internet, so presumably it also has the test scores of the human. Rather than have two fake geniuses flapping their genitals around let it point out all the flaws that would of allowed the human to achieve a perfect score. I say fake geniuses because I can't imagine an actual genius would actually care about the score of an IQ test and how they compare to other geniuses $\endgroup$ – Shadowzee Sep 4 '18 at 0:56
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155, 160, or maybe 171.1


The answer is different for each different IQ test.2

The most common IQ tests given to adults in the USA for the past 70-odd years are the Wechsler Adult Intelligence Scale series. The WAIS-V is currently under development, expected to be released in 2019; until then, the WAIS-IV is the standard.

On the WAIS-IV, the maximum score is 155+.

However, this is in part because the scaling process effectivly ends with "if the equation spits out a number from 155-160, record it as 155+". The WAIS-IV minus that rule would have a maximum score of 160.


Various high-IQ groups have come up with the idea of designing a test that's more challenging and, more importantly, calibrated specifically against the upper tail (e.g., against Mensa members).

Both Mensa and the Triple Nine Society (who require a higher cutoff of 146) are perfectly happy with the WAIS. But what if you wanted to start a society that required a cutoff of 171? The Prometheus and Four Sigma societies3 both wanted to restrict themselves to one-in-a-million geniuses.

Four Sigma's Kevin Langdon designed a test by basically gathering all of the hardest questions from other IQ tests, getting rid of any time limits, and calibrating it against self-selected geniuses from among the readership of Omni.

Langdom claimed to have just barely reached the goal of an accurate ceiling of 171. Prometheus went with it as well.

Years later, the Langdon test's answers were published on the internet, making it worthless. Prometheus did a comparative study of existing tests and found that a WAIS score of 155+ was actually better correlated with their membership than any of the existing high-tail tests. Which means all of those tests (not necessarily including Langdon's—but probably) are actually useless for distinguishing between 155-170 and 171+ people after all.


Now, when people write that "Einstein had an IQ above 190", what do they mean?

The meaning of IQ numbers is pretty simple: 100 is average, and each standard deviation from the average is 15 points (with the assumption that intelligence follows a normal distribution, of course). So, 190 is 6 standard deviations, about 2 in a billion. And that's basically what it means: Someone made a wild guess that Einstein was a one-in-a-billion genius, and convinced some psychology professor to do the undergrad-level math that converts "one-in-a-billion" to "over 190", and then wrote an article saying that Einstein had an IQ over 190.

The psychologist almost certainly gave the journalist a bunch of caveats about how meaningless that was—not to mention that the first four experts they tried all gave answers more like, "Well, as far as I know he never took a test, but it seems likely he'd have gotten a 155+"—but the journalist ignored all of that, because "Einstein's IQ over 190, says Harvard psychology professor" is a better story than "Journalist doesn't understand IQ but wants to write article on it anyway".

If a super-intelligent AI wanted to aggrandize itself misleadingly, it could pull the same kinds of shenanigans, but I think it would be smart enough to not bother.

If it's anything like smart humans, it's probably more self-impressed with its geek-trivia knowledge than its intelligence, so it would probably put on its best Holly voice and say, "I have an IQ of 6000, the same as 6000 PE teachers".

Or… I'm pretty sure there's a golden-age scifi story that I read as a kid (no idea which one, who it was by, or anything else, except that it was probably in one of my grandmother's old sci-fi story collections) where the world's first supercomputer says something like, "On a test calibrated for humans, I'd get a perfect score of 164. On a test calibrated for my peer group, I'd get a score of 100, because I am my only peer." That struck me as a better way to show its pompous arrogance.


1. Things are slightly different for children; some tests scale up as high as 205. But I assume the AI isn't going to want to claim to be super-smart for a 5-year-old.

2. Academics just rescale stdev=16 results as stdev=15 for comparisons between them, so let's do the same here; otherwise you're just adding confusion for no purpose. But an AI that wanted to be misleading could get away with claiming 175 on a 16-scale instead of 171 on a 15-scale.

3. Each of them being, at that point, one guy, each of whom were deciding whether to let the other guy into his clubhouse…

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    $\begingroup$ Thanks, that was very helpful. Follow-up question: So how do they get the scores when they claim that this or that genius has an IQ of 190 or 205 ? $\endgroup$ – Tom Sep 3 '18 at 20:19
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    $\begingroup$ @Tom I'll edit that into the answer. $\endgroup$ – abarnert Sep 3 '18 at 20:27
  • $\begingroup$ On re-reading it now, an additional thank for footnote 1 because I was always wondering why I never again reached the IQ number they measured for me as a child. I was never interested enough to do the research, but now I get it. $\endgroup$ – Tom Mar 10 at 18:17
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Most IQ tests nowadays are calibrated to give a result that follows a normal distribution with mean 100 and a standard deviation of 15 (other standard deviations have been used in the past; comparing results from tests with different standard deviations requires converting the numbers).

The fundamental assumptions behind this are something like:

  • Some people are more intelligent than others.
  • The tests can, with some degree of accuracy, rank people in order of increasing intelligence.
  • We do not assume intelligence is inherently controlled by any parameter with a numerical value that is meaningful in isolation.

These assumptions are subject to -- sometimes heated -- debate, of course. But if we're speaking of IQ at all, those are what the thing we're speaking of assumes.

If we imagine calibrating our test over the entire human population as of today (about 8 billion, give or take), then the scale cannot in principle distinguish between different varieties of "smarter than every human in the calibration population".

This would (according to Wolfram Alpha) correspond to an IQ of "somewhere between 195 and infinity". The very definition of the scale cannot tell the difference between anything above that point.

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    $\begingroup$ +1 for explaining that the test is by definition calibrated so that 68% of the members of the population under study score between 85 and 115. Moreover, we cannot calibrate a test over the entire human population. Since the test is inherently culture-specific, it can only be applied to a more-or-less culturally homogeneous population. It is meaningless to give the same test to young United-Statesian adults 18 to 20 years old and to Vietnamese children 8 to 10 years old. $\endgroup$ – AlexP Sep 3 '18 at 16:25
  • $\begingroup$ @AlexP: Very true. My back-of-the envelope calculation here aims to give a strict upper bound for the precision one may meaningfully posit. $\endgroup$ – Henning Makholm Sep 3 '18 at 16:27
  • $\begingroup$ Thanks for the details. I'm aware of how IQ tests work, mathematically. I'm trying to figure out a practical value for someone who would pass the test in basically the form submit time with zero errors. That number is not going to be infinity. But is it 300, or 500, or 12,000 ? $\endgroup$ – Tom Sep 3 '18 at 16:45
  • $\begingroup$ @Tom: The definition of the IQ scale makes each of those numbers equally right -- so which one you get will depend on details of the scoring procedure that are not determined by the scale it tries to implement, and therefore can vary "randomly" from test to test. $\endgroup$ – Henning Makholm Sep 3 '18 at 16:49
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    $\begingroup$ Generally actual IQ tests are scored by rules that says that the highest possible scoring bracket should be reported as "greater than such-and-such" rather than a definite numerical value. $\endgroup$ – Henning Makholm Sep 3 '18 at 16:51
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The thing about IQ tests is that they're far better at measuring minima than they are maxima. Put another way, they're primary use is in detecting the limitations of people, not comparing geniuses against each other.

The WAIS tests of old (a respected paper based IQ test) didn't only measure against the correctness of response, but reaction time. When you understand what intelligence actually is (the ability to identify and recognise patterns) this makes a lot of sense. A 'smarter' person will not only be able to recognise more complex or subtle patterns than someone less smart, they should be able to recognise the simpler patterns faster.

The trouble with this is that intelligence is fundamentally open ended as a scale, and the limitations in measuring the upper end of IQ is usually a limitation of the capacity of the test, not the potential of the mind sitting that test.

There is also the problem that every IQ test on the planet makes some serious assumptions about existing knowledge, which of course in the case of aliens or AI systems, could be very wrong. In point of fact, it doesn't always apply to the human being tested either.

Add to that, human psychology and cognitive limits of the human brain are not going to be shared by an AI or an alien race, and the fact that intelligence on the part of an AI should not be confused with insight, understanding or consciousness (which we humans can't experience separately from our intelligence) and it becomes clear that in this instance, any test is not an accurate comparison between the AI and a human mind, especially when it comes to the ability of that mind to function in society in a useful form.

Ultimately, if your AI is looking for bragging rights, current IQ tests aren't going to be able to give them to it. the AI would probably be better served applying as a contestant on a quiz show. It would get more recognition (and money) that way.

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  • $\begingroup$ I'm not looking to actually measure an AIs IQ. I just want to throw a very high, but possible, number. I found conflicting sources, so I'm asking. I want to avoid that I put an arbitrary number and someone familiar with the subject would immediately go "nah, that is 10 points above the absolute maximum". $\endgroup$ – Tom Sep 3 '18 at 16:43
  • $\begingroup$ @Tom well the fact that the Q in IQ stands for Quotient (answer for a division) means that's not an issue. I'm pretty sure there is no absolute maximum other than one that may be arbitrarily imposed due to perceived limitations of our capacity to measure reaction time. It also means that the scale is logarithmic; that is to say, the difference between 220 and 230 is far more slight than the difference between 80 and 90. $\endgroup$ – Tim B II Sep 11 at 4:51
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IQ is an imperfect test used to measure intelligence of humans.

Matter of fact one incredibly huge fallacy of the IQ test is that it is very age dependent. The more accurate results of the test are obtained from young children while results obtained from adults contain a very large degree of error.

The exam is composed with a lot of theories rooted on human cognitive development as well as assumptions on what we think constitutes intelligence. One fact that has constantly haunted the results is how few achievements MENSA members have made compared to lower scoring individuals. All I am trying to say is its not a great test.

Now in reference to AI, AI is as smart as you make it both in hardware resources and software. Coupled with the data sharing world wonder known as the internet, AI could theoretically be as intelligent as the human race is as a whole.

So to answer your question, the IQ test can not effectively measure AI.


Edit since you are hell bent on a number:

In addition to the above factors, the score is normalized across the population that takes the test. What that means is that what could be 100pt score today could be a 5 pts 1000 years from now. The score is based on deviations from averages. The scale is relevant to the version of the test which could have changed by that time.

In current iterations of the test scores greater than 170 points are said to indicate "immeasurable genius" as in the test cannot effectively quantify their intelligence.

So to get the "number" you want you could define your scale between 1 and 200 with AI getting a score of 200 with your character getting a score of 1.

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  • $\begingroup$ Yes, I know. The AI took the test for giggles, and the number is used just to smack down a human character who thinks he is very smart. It's not a main point of the story and the question of whether it actually measures an AI intelligence is not here or there. I just want a number that theoretically would come out of a test if I submitted it with zero errors in under one second. $\endgroup$ – Tom Sep 3 '18 at 16:46
  • $\begingroup$ @anon "AI could theoretically be as intelligent as the human race is as a whole". Actually a human genius could make that claim, saying that he can think of (and sometimes take) better courses of action, but not convince the human race as a whole to take that course of action because other humans are not intelligent enough to understand or be convinced of the superiority of those courses of action. So that human genius might claim that his individual intelligence is higher than the collective intelligence of the human race as a whole. $\endgroup$ – M. A. Golding Sep 3 '18 at 16:58
  • $\begingroup$ @M.A.Golding A genius could make that claim like any arrogant human but an AI actually physically can achieve that claim. A single brain cannot match the cognitive parallelization offered by its whole species. However, an AI being comprised of computers can parallelize its cognitive tasks by as many computers it is given to compete with said species. In a world where compute resources can exceed individual humans it is even possible for the AI to exceed the cognitive ability of the whole human race. $\endgroup$ – anon Sep 3 '18 at 17:10
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Modern IQ tests are designed first, and then calibrated. So the answer depends on the specific IQ test you take. Some might only be good up to 130. Others might provide useful data up until 160. But as Henning Makholm put in his answer the common pattern in IQ tests is to have a mean of 100 and a standard deviation of 15. That's all.

If you wanted to have some arbitrarily awesome score, don't give the AI a number at all. Instead give the AI a fictitious test where the calculation of the score involves iterating some sequence until it converges. We do that all the time in engineering, so it wouldn't be too big of a surprise. Argue that the iteration is required to handle IQs over 205 (205 is 7 standard deviations. That's starting to approach "one in a billion" scores). Then, explain that when the AI took the test, the score didn't converge. The mathematics which worked to turn every human mind into one number (an IQ score) didn't even function properly when th AI took it.

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  • $\begingroup$ 7 standard deviations is about one in a long billion, i.e. 10^12. $\endgroup$ – Henning Makholm Sep 3 '18 at 19:07
  • $\begingroup$ @henningmakholm I couldn't decide the best way to express it without assuming a normal distribution. My instincts say the tails will not be well modeled as normal, because we'll start to see the quirks of the test shaping the distribution. $\endgroup$ – Cort Ammon Sep 3 '18 at 20:57
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All I want is a quick number that actually would come out of such a test under the above conditions

There's no RIGHT answer to this question, but 250 is a number that shouldn't set off anybody's bullshit detector. As I mentioned in one of the comments, no human is likely to create an IQ test that's capable of scoring over 300.

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  • $\begingroup$ When you cajole a child into good behaviour.. using white lies or petty bribary.. it seems easy. That's how easy it's going to be for a super human intelligence to impose it's will on humans. They won't be measured on the same scale as us. $\endgroup$ – Richard Sep 3 '18 at 18:14
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    $\begingroup$ @Richard ok... what does that have to do with OP's question or my answer? $\endgroup$ – Morris The Cat Sep 3 '18 at 18:22
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    $\begingroup$ Sorry. Posted comment under wrong conversation. $\endgroup$ – Richard Sep 3 '18 at 18:23
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    $\begingroup$ Unless we're also positing human civilization spanning thousands of galaxies, 250 would certainly set off my bullshit detector -- that would mean, "smarter than about 1 in 10^23 humans". $\endgroup$ – Henning Makholm Sep 3 '18 at 19:04
  • $\begingroup$ @HenningMakholm really? are you sure? Because we already have at least one person with an IQ supposedly above that, and you're telling me that you think it's bullshit to even have a test that's CAPABLE of scoring 250? Are you sure that's your final answer? $\endgroup$ – Morris The Cat Sep 3 '18 at 19:27

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