How can the intelligence of a super-intelligent person be assessed?

Question

One of the features of my story is a psychological examination of a certain person who lost his memory (found on a bench in a city park with complete amnesia) and after a short examination was taken to a special institution, where it was found that in terms of his intellectual abilities he was much more superior to our level with you. I will not say why he turned out to be smarter than other people, I will only say that if, for example, our average intelligence level corresponds to 100 IQ, then it should have been equal to 400 or more.

But here there is a problem that I would like to talk about. So the IQ tests used today, in fact, are not an invariable unit of measurement of intelligence, assessing individual cognitive abilities, such as the ability to analyze a given situation or remember this or that information. So in fact, you can't even score 300 on most standard IQ tests. The IQ test only works within the specified deviation of your ability, how far you are from the average of the group for which the test was designed. This means that the average IQ will always be one hundred points, since this is how it is defined. Current certified IQ tests are accurate only for plus or minus two standard deviations, ranging from 70 to 130 points. Anything outside this range means that an IQ test is not appropriate for accurately measuring a subject's cognitive capabilities, and that is what needs to be addressed.

The question is: if I can't use standard IQ tests to assess the intelligence of this smarter person than anything we've met before, how should I do it?

Answer 1

You're telling a story. Having a character take an IQ test is bland.

Rather than have some scientist say, "we measured your IQ and it's really high!", have your character actually do something surprising and amazing with their intelligence: Have some complex procedure used to hold a lock shut, and have the character get into it. Have the character go and deduce some deeply held secret of one of their examiners using logic and observation.

Have them build a complex machine with only the tools on hand in their psychiatric cell, even. The important thing here is their ability, not the number of their IQ. Show that off.

Answer 2

The reason why IQ tests and the like have an upper limit is because the people who design the tests don't know how to assess anyone with a greater ability to solve those puzzles... in some ways, being able to assess super-intelligence is one of the ways in which you could identify super-intelligence.

Imagine giving a test designed for children to a clever adult... they'd likely find every question trivially obvious, they'd be able to spot any simplifications or errors, maybe they'd be able to finesse the answers or work out what the test was intended to test for and how they might subvert the expectations of the examiners.

In your case, having the subject simply get a very high or perfect score on the IQ test they were set would be enough to establish them as someone who cannot be usefully ranked by an IQ test as anything other than better at IQ tests than pretty much everyone else.

Note that someone who is substantially more clever than the meatbags around them will probably work out that the meatbags just aren't as smart and are trying to prise information out of the smarter person for unknown and possibly nefarious ends. The smart person may just end up playing dumb, either out of caution, boredom or malice. Intelligent children can certainly do this, if they aren't motivated to succeed (or are motivated not to succeed).

So, yes. Show, don't tell. But please, don't just have them do a Sherlock Scan (CW: TvTropes). That's been overdone, and its easy to get silly and wrong.

Answer 3

Uncharted territory

It is be very difficult to measure intelligence on very smart people. At least the "400 IQ" would be hard to be differentiated from a "200 IQ".

The first hurdle is translating one's intelligence to a number. You can do that with IQ, however, note that it is a test built so that, if one measures a population, the result is(or should be close to) a normal distribution of with average 100 and standard deviation 15.

A Normal distribution is concentrated around its average, it is symmetric: half of the population should have an IQ higher than 100. Furthermore, the proportion of people in a given interval is fixed, 15.8655% of a population should have some measure higher than the average plus 1 standard deviation. In our case, 15.8655% of the population should have an IQ higher than 115. You can consult a table here that, among other things, says, for number of standard deviations(Wikipedia refers to it as z), the proportion of the population with an measurement higher than avg + std * z.

According to Wikipedia(just googled "word population"), as of March 2020, there are around 7,800,000,000 people in the world, with that amount of people, there should be 7 or 8 geniuses in the world with an IQ higher than 190 - 6 standard deviations, so 9.86588E-10 * 7,800,000,000 is the expected value of people with IQ higher - note that the proportion under a region falls very fast as it gets farther from the average. The chance of someone having an IQ higher than 215 is 1.27981E-12, that is 770 times less likely, so it expected that 1 person in all people who have ever lived(estimates around 50-150 Billions).

Note that 400 is 20 standard valuations, this is chance of that happening is 2.75362E-89. Even if every atom in the universe(estimates from 1E+78 to 1E+82) had an IQ that followed human distribution, it still would be hard(1E+82 * 2.75362E-89 = 2.75362E-7) to find an atom with an IQ higher than 400.

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The best one can do

If your guy has 400 IQ or more, the best thing one can do is to find a way compare them with the smartest people ever. Then they will know your guy's IQ is at least 190.

Scored 190 while reading a novel and reading the test backwards

Perhaps try handicapping: they could make the person try multiple "tests"(competitions with the best) at the same time, maybe try it in different languages(as suggested by other people), have the test be written backwards and make your character write it with inside-out alternating order(so 1,2,3,4,5 becomes 3, 4, 2, 5, 1), or some other ridiculous thing.

Answer 4

In addition to other answers, be aware that current research shows that exceedingly high ('profound') intelligence routinely manifests in entirely different ways than just being intellectually "smart". You might want to Google "profound IQ" for insight, but some ideas of traits reported in the literature:

• Prodigiously good at empathy. Reading people, reading their emotions, empathising with their feelings, wanting to help. Not something the stereotype sherlock is associated with.
• Often, exceedingly lonely. All the things that interest them were never obvious to others, the things they saw were rubbished by parents and teachers, the things their peers liked were simplistic and childish when young. (Imagine being 6 and finding solving world hunger or learning calculus the most fascinating things when your peers want a Disney doll). Or think of it this way - they have an IQ of 300, but the same need for peer relationships as any other child/adult - and not a single person to share it with in the country, let alone the community or school, who can act as a peer socially, share the same things, see things in common. Much of whats obvious to them will be derided or ignored with what they know is bad reasoning but unarguable, like being in a society of flat earthers; their insights will be worthless. And yet, because of empathy, they understand where others are at, and can't hate others for it, either.
• Exceedingly self directed, the kind of person who knows their own truth and their own path, regardless what anyone tries to force into them. Which can be anything from a mixed blessing to traumatic, for a child, whose social role demands they ultimately accept "adults know best".
• Being intelligent doesn't mean being experienced in life, or having maturity. Being bright but finding farting funny or having a poor control over pranks and childish behaviour isn't incompatible.

Overall, exceedingly high intelligence is more like something that pervades everything and "just is". So it will pervade every part of your characters life, not as some bolt on, but as an integral mundane part of them - their perceptions, their learning, their feeling, their choices, what they see as important, everything.

Answer 5

Harrison Bergeron style

In the near future SF story, persons with inherent abilities (intelligence, beauty, coordination) are handicapped with various devices so that they are the same as every one else.

http://www.tnellen.com/cybereng/harrison.html

"Yup," said George. He tried to think a little about the ballerinas. They weren't really very good-no better than anybody else would have been, anyway. They were burdened with sashweights and bags of birdshot, and their faces were masked, so that no one, seeing a free and graceful gesture or a pretty face, would feel like something the cat drug in. George was toying with the vague notion that maybe dancers shouldn't be handicapped. But he didn't get very far with it before another noise in his ear radio scattered his thoughts.

George winced. So did two out of the eight ballerinas.

Hazel saw him wince. Having no mental handicap herself, she had to ask George what the latest sound had been.

"Sounded like somebody hitting a milk bottle with a ball peen hammer," said George.

In your story, your guy breaks the IQ test. So they bust out the Sherlock Scan and he breaks that too, with prejudice. The scientists scratch their heads. So they give him an IQ test in French. Then in Albanian but he is wearing thick glasses from one of the scientists. Then a test in Punjabi, with the glasses and another pair of glasses on top and he must wear a CPAP attached to a bong.

He does OK until he takes the Punjabi test with the glasses (both) and the bong in a nightclub because it is hard to dance and mark the right answers.

The scientist conclude he has an IQ of 400 and is a better dancer than they thought he would be. It turns out though that when he is not stoned his dancing abilities are less, and that issue might come back to haunt him.

Answer 6

Go "Kobayashi Maru" - Give them "probably impossible" tasks and analyse what they do.

I feel a better measure of intelligence isn't "can you solve this problem?", it's "How do you approach solving it?".

The Kobayashi Maru test from Star Trek is an example:

The approaching cadet crew must decide whether to attempt rescue of the Kobayashi Maru crew—endangering their own ship and lives—or leave the Kobayashi Maru to certain destruction. If the cadet chooses to attempt rescue, the simulation is designed to guarantee that the cadet's ship enters a situation that they will have absolutely no chance of winning, escaping, negotiating or even surviving
....
The objective of the test is not for the cadet to outfight or outplan the opponent but rather to force the cadet into a no-win situation and simply observe how they react.

I don't care whether you get the right answer; I care about the thinking process you used to get there!

The best application I've seen of this technique in the real world is actually in job interviews. My company will ask you technical (eg maths, computer science, or algorithm design) questions in the job interview, and we don't care if you get the answer right, we judge you on how you work towards that problem.

We often include unsolved problems from accademia in there, an example which got asked last week:

A irrational number to the power of another irrational number can sometimes make a rational number, for example $e^{i \pi} = -1$. e and $\pi$ are both irrational, -1 is an integer, which by definition is rational.

Is $\pi^{\pi^{\pi^\pi}}$ rational or irrational?

Now this problem is unsolvable on current computer hardware, let alone in someones head. How this is used for measuring superintelligence? the more intelligent you are:

• The more progress you can make towards this problem.
• The more insights you'll have on ways to approach the problem, or how to simplify it.
  • Also - the more unique insights you'll have.
• The more parts of the problem you can solve, stepping stones or proofs of simpler cases than the full problem.
• The faster you can do all of this.

Repeat with a few dozen problems. As intelligence increases, ones notable observations will be either quicker and/or more notable.

Converting this to an "IQ" requires showing experts in the individual problems the interview and getting their (subjective) feedback. If nothing else you're measuring how far their jaw drops at what they're hearing. Averaging these responses out over several tests should help to minimise subjective biases and inaccuracies.

This approach has one additional advantage over many of the others I've read in other answers - an "infinite IQ" or "off-scale high IQ" or "IQ in the trillions" can be detected as they'll able to solve or provide a proof disproving those tests which were previously unsolvable. The beauty of maths being a perfect and immutable truth is us idiots can verify their proofs as correct even if we had no way of generating it.

Answer 7

Intelligence tests are quite dependent on education and familiarity with specific cultural concepts. For example, the IQ tests used for contemporary English-speaking populations would be unable to provide reasonable IQ results for people living in impoverished regions of the world without universal education even if those tests are translated properly. Despite that, it would be wrong to say people in impoverished regions are less intelligent than the population of English-speaking countries.

If your character suffers from complete amnesia (full loss of all memory) than the easiest way to estimate their intelligence is learning speed. A person with full amnesia will have to learn a lot of things from language to social norms. The faster they can assimilate knowledge and put it to practical use the more intelligent they are. This approach will not give you a specific number, but since your character is super-intelligent it would be impossible not to notice that they learn much faster.

Answer 8

There are good answers already, @Matheus Jahnke's as an example

And on its basis, we can ask and have to answer another question, before we get back to the original one.

Note that 400 is 20 standard valuations, this is the chance of that happening is 2.75362E-89. Even if every atom in the universe(estimates from 1E+78 to 1E+82) had an IQ that followed human distribution, it still would be hard(1E+82 * 2.75362E-89 = 2.75362E-7) to find an atom with an IQ higher than 400

Horrific number, but we should understand that rarity does not mean significant superiority.

Let's say we talk about a human who will do all\any of your typical intellectual tasks 10 times faster than an average guy. Can it fit the role of that 2.75362E-89 chosen one? I would say, yeah, good enough. no? let's make him 100 faster - I bet there was no one that fast, in human history, for the last 4 billion years.

Can such a person replace the intellectual work of millions of people over the last 100 years - no. Sure he will have certain advantages, besides the speed, if we think about his judgments, but.

Another one, why 400 points maybe not so much when it is about rarity, how big is a difference between 200 and 400 ones - it may be not that big in absolute results in capacities to solve problems, probably there is some limit about calculation power for a human brain, just because of size of it and how it is build, the closer one is to such a limit rarer is the occurrence in nature/population. it is typical lim(smartness(to improbable)) = 10x as an example.

So intelligence in one meatbag can be qualitative and quantitative. quantitative can easily be measured, there may be some problems in assigning an exact number, but it easily measurable, and more than that can be attributed faster neural activity and be natural or artificial.

Can this guy outsmart you each and every time - not necessarily, will it be faster at everything than you - yes. Can it from scratch overnight reinvent the theory of general relativity - no.

• there are suggestions of "show, do not tell" - those are not great recommendations for reason that author has to understand the difference of possible and impossible, so as to have some measuring stick for what his character can or can't do. Because without having one, they often fail miserably on that "show" part.

qualitative superiority is harder to assess. But also if it is quantitative changes which in a combination become qualitative ones - like speed, memory, senses - then there is a chance to do some assessments. And I would say it quite a typical trope.

• chimps can count to 9-10, distinguish that number of objects and do that faster than a human does, so as they do have some treats we have - social interactions, linguistic aspects, knowledge transfer, etc - not a surprise, relatives after all. They can fly in space, but we have sea ships and airplanes and the agriculture industry - they do not.

10 times of speed, 100 times of typical memory - those can be measured, especially when we talk about human-type intelligence. Speed and details of visual perception, pattern recognition.

with pattern recognition, we can create some calculation difficulty measuring stick, as we can compare to not only humans, but to artificial algorithms as well, and thus assign some corresponding measurable value - iFLOPS or something.

Sooo, a character with everything is 10 times of usual norm. Can this guy outsmart you each and every time - probably, will it be faster at everything than you - yes. Can it from scratch overnight reinvent the theory of general relativity - no.

• that general relativity stays no, and it will stay no for a very very high level of intelligence, despite it being invented by not so much out of ordinary(compared to the individual we discuss here) guy. layman example - let's go back to chimps - are we superior to them for the most time in therms of intelligence - yes, do we understand them fully - no, not a chance. we do understand them to some degree, but it is far from a full understanding and ease of manipulating them.

  one can build a sound comprehensive theory encompassing the whole universe but the number of such theories is more than one, probably, at least we have more than one spacetime theories and we not sure which one is the correct one, if any. Sitting in a building one can do observations(thing around that person - sunshine, the wind blows, grass grows, etc) and it helps build and sort out theories that are not related to this specific universe. it like finding a proper book that fits the universe in The Library of Babel. And there are things which you can't figure out just because you like to do so, you have to measure or to test, do experiments to figure out their relations with each other. At the same time, you have to be able to produce that or similar Library of Babel and somewhat keep many books which later you sort out as you may find them to be not correct. it requires way more than 10x, 100x human intelligence.

  this is the reason why one can't invent a super-duper wave gun sitting in a cell, to make an escape. Most likely escape strategy will be more mundane. Maybe smart, but not 400 IQ point smart, or you can't understand smart.

  higher the intelligence is, then fewer experiments it may need, and further one experiment propels that process of universe model building. Maybe a stretch, but we can imagine an intelligence that glances casual look at your city and identify the universe in that Library of Babel - one observation act and firm and correct conclusion. But human measuring stick won't fit that intelligence, we as collective as humankind - maybe but barely.

There are examples of superior intelligence we know, as since not so long ago it became a perceivable reality, which you can touch and smell.

one is OpenAI Five - it plays Dota better than anyone on the planet another AlphaGo - plays Go better than anyone on the planet.

Those are not general intelligence, obviously, but are they faster - yes they are, do they have a bigger memory, task-related - yes, they do. Do we understand what they do - yes, somewhat, as an afterthought, for those guys which do play those games. we have a hard time understanding how they come to the conclusion, what specifically did they noticed, we may miss bits and pieces, but our understanding isn't a total blank.

So, to outsmart, your guy does not need to be magical, breaking crypto as one suggested, it just needs to be one step ahead - that is a typical trope with strong roots in a reality, not surprisingly, as there are plenty of humans who are smarter than other humans, so it is not that we do not have a taste of that medicine.

impossible things stay impossible - if it is proven you need the energy of the whole universe to crack the encryption even with quantum computing, then it stays that way for 10x, 100x not matter what. Social engineering is a way much better way to fish things you need - passwords, money, pin codes, call to a president to request a nuke launch, messing with global politics - whatever you choose.

• there are examples of prankers that did call higherups in political circles fooling the whole chain through which the call has to go, and representing themselves as other party higherups.

So to wrap it up - distinguish impossible things and those which come from a better knowledge and ability to operate such to be a step ahead of situations, events, people, etc.

And you measure things as usual - by decomposing elements which combined create that intelligence. So in your case, you do it not with a general test, but each aspect you can separate in a separate way, as we do tests for animals or humans. So just more tests that are focused on their own aspects and as a whole are broader more encompassing measure, as we do with animals in our attempts to understand their intelligence, shape and strength of their intelligence, not a synthetic test you typically do to get your's 120 free internet points.

Answer 9

You can compare him to hyper intelligent entities that exist in the real world today. The only things that exhibit that so far are groups of people working together (but maybe AI will compete soon). If you give an intelligence test to a corporation and allow the people in it to work together to answer it then most corporations would absolutely ace it, that's why trivia night is a lot easier with friends. Countries have also managed to single handedly invent nuclear bombs and go to the moon, feats that can not be accomplished by a single human today even if you pick the most intelligent of us.

Unfortunately this technique has a few problems. First, is it the limitation of his body and his time the limiting factor? Second is that we're all standing on the shoulder of giants, so did any one country developed the tech to go to the moon or was it the cumulative conscience of all humans. The answer to your problem is really not easy, in fact measuring intelligence is an unsolved but active area of research. And given that loss and reward functions are a major component of AI systems today, developing an objective measure for intelligence would be half the battle towards general AI.

Nevertheless in a story you could set up the conditions that allows for direct comparison between a single person and a huge group of people. Something that comes to mind is that the rovers currently exploring Mars are commanded by a large and intelligent group of people at NASA in order to effectively explore the planet. To control it though, the entire group distils its strategy into a small packet of information that is sent and used by a robot with limited capabilities and time. If this intelligent person somehow gets control of such a robot (let's say he revives one that NASA gave up on) and he can produce equally good results or better than the NASA controlled one, then you know he's got some spark in there.

To go back to the paper I linked to. A key feature that Chollet requires of intelligence tests is novelty; because intelligence itself is a measure of how you approach new situations. This is also the reason why IQ tests use these unusual abstract patterns in them. I suspect it's also the reason why standard IQ tests are of very little real life use since these abstract patterns have now become common knowledge, and practicing on them makes it easy to game the test. It's possible there can never be a "standard" test, so embrace the unusual!

Answer 10

To be convincing, I would suggest that for the story that you take the time to describe how a number of other people engage in the very type of discussions and testing that are going on here in this thread with the result that not a single one of them succeeds in determining just how intelligent this person (?) is.

Their reaction time is so fast that it's impossible to measure it accurately (reaction times are correlated with intelligence); they can calculate results immediately, including complex mathematical problems, statistical analyses, etc. of vast quantities of data as fast as it can be displayed, etc. Rather than giving an estimate, the conclusion should be that the psychologists and so on just cannot determine how to measure it regardless of what they do. Leave it at that.

Answer 11

What you illustrate doesn't show our inability to test for a score like 400, it shows the lack of meaning of such a score. 130 is a 1-in-20 score (95th percentile). 150 is a 1-in-1000 score. 175 is a 1-in-a-million score.

400 is a 1-in-10^88 score. That's a number bigger than we have SI prefixes for. It's a number bigger than the number of atoms in the observable universe. If an oracle came by and gave you a perfectly fair and accurate IQ test, and you were able to administer that test to the smartest human who lived, or will live, in ten millennia, they wouldn't get a 400, they'd get something like a 210.

Answer 12

Crypto.

The psychologist's receptionist apologizes that he can't process the appointment, because his computer is showing a ransomware notice with the usual message to send Bitcoin before a deadline. He bought the Bitcoin for the doctor but can't figure out how to use it and the timer is running out. Your hero offers to help, so he quickly deduces the private key of the ransom account and transfers all their stolen money to the psychologist, then enters the key to the hard drive files.

Cracking public key crypto could make him popular in all the wrong places. I anticipate drone attacks ... but he can work with that.

Answer 13

First time posting in this StackExchange, but we kind of have a basis for this in Computer Science.. We have pretty well-defined measures of the "difficulty" of problems. We know at least enough to be able to group problems that are "hard" in a way that if you solve one you can solve them all (this is a layman's explanation of NPC problems). This should allow you to (relatively) compare his time solving any of the NPC problems against anyone else (also, if he solves it proportional to any P problem he's proven P = NP).

Answer 14

I'd think more about the one with where he has to dance in the night club, attached to a bong wearing thick glasses. Now that's fucking hard. - Super interesting concept.

Anyways, there are still a lot of aspects of intelligence I didn't see taken into account reading the other answers:

Let the person be cautious and use game theory to determine their behaviour. Let them adapt their basic strategy to a more complex form every time they learn more about strategies of other humans. (For a introduction to game theory I recommend this video: https://www.youtube.com/watch?v=Y0Oa4Lp5fLE) You could make it so that most scientists he interacts with would be fooled by his likeable, average behavior, but the smartest of them would prove that the person is much smarter than they act.

Most IQ tests have a time limit in which they have to be solved, even though it's generally more important to think correctly and deeply than to think fast. Instead of letting them solve stupid puzzles for an hour, rather make them play a strategy game for hundreds of hours and reward them for getting better at it. You could make them beat alpha zero or something like that.

There are studies that say chess masters would burn three times as much energy as regular people a day when they are playing in tournaments. Make it so that the person constantly has low blood sugar and make them eat everything they give them immediately. Maybe they'd even eat things like insects, dust or candles out of hunger.

Make them abnormal to make their abnormal intelligence feel more natural. Let them switch topics a hundred times in a minute, changing their minds while they are analyzing, thinking and talking at the same time. Make them uninterested in any cooperation, even when it's highly benefitial.'This lamp here is a 10.2, nice.' Let them masturbate and then try to commit suicide, after they see the world clearly again.

Also, please don't note in your story how unlikely it is that somebody would have such a high IQ, because most aspects of human intelligence have little to nothing to do with IQ. We don't understand our brains in the slightest, so why would we try to rate their performance? I knew an autistic kid that had an IQ of 77 at age 16 and an IQ of 130 at age 19 at a different test, both done by an institution. He was probably distracted, depressed or couldn't understand the questions the first time. It's likely that he'd score even higher than 130 under different circumstances.

Answer 15

Off the charts

You can't.

IQ is a standardized test, which is the only way to get reproducible results. In order to standardize it, they tested it against many, many, many people, and then compared any new test takers to them to figure out where in the distribution they were.

There is no one even remotely in the sample to compare him to.

Therefore, what they will be saying is not that his IQ is 400, but that he is beyond index, broke the standard, or off the charts. They may be able to add such tidbits as he got a perfect score in fifteen minutes in a test where the subject gets four hours.

After that, they can offer other anecdotal evidence of his brilliance.

Answer 16

Step One: Define Intelligence:

Most of the answers had a different take on this, for this answer I will be defining intelligence as “the ability to acquire and apply knowledge and skills.” (The first defnition from oxford languages)

Step Two: Measure Inteliigence:

Make up some random thing that has never been seen before, and so utterly ridiculous that it is impossible that the ultra-intelligent person already knows it (something like this). Other options are there, such as making an instrument using a completely random number generator (which also has the added bonus of being cool). Then measure how quickly an average person can learn this new thing (shouldn’t be too hard, just a normal scientific study), and compare it to your ultra-intelligent person. That covers aqquiring knowledge and skills.

The other part is to test applying knowledge and skills, which is a bit harder. One idea I have here (though it is most likely far from perfect), is to make this person have a swordfight with an AI that learns from them. Make this AI x% stronger than the main charecter (what x is is up to you), and have the ultra-intelligent person duel the AI (which knows nothing other its supposed to hit its enemy with a sword, and that its supposed to learn from its enemy), and measure the amount of times the ultra-intelligent person can beat the AI before it beats them, then compare this to the average population (again, not too difficult, a simple scientific study should suffice).

Other possibilities (aka things that might go wrong):

The main charecter can find a way to “game the system” and somehow prove that they can beat the AI perpetually (second paragraph of step 2). The main charecter already knows the language, or has already played the instrument in the past, or maybe has played every possible instrument or learned every possible language in the past (first paragraph of step 2).

Why this answers the question:

This should be a way to measure intelligence relative to the general population, and it should also (hopefully) be fairly interesting for any reader. (After all, who doesn’t love swordfights and wierd new instruments/languages?).