The Hierarchy Of Intelligences & IQ: We’re Not As Smart As We Think

The Hierarchy Of Intelligences & IQ: We’re Not As Smart As We Think
Full title: The Assumption of the Virgin.Artist: Francesco Botticini.Date made: probably about 1475-6.Source: © The National Gallery, London

Let’s think about degrees of intelligence; specifically, our knowledge of them.

Now many believe that intelligence, vaguely defined, can be quantified to good, or even ideal, degree with IQ. I do not. All the reasons why I think not are in the article “The Limitations And Usefulness Of IQ“, so I won’t repeat them here.

Nobody has an IQ like they do height; they have a score on a test, at a given time under certain circumstances. Relying on IQ as a complete quantification is to guarantee over-certainty. However, IQ has some use. It is a rough guide to a certain kind of intellectual operation. But, as the linked article and this one will show, it can be no more than that.

With that out of the way, let’s look at a summary of a thread on Twitter, which provides a reasonable summary of certain intellectual operations. There is nothing special about the thread; the information is available in many sources. But this one is succinct. Because threads disappear (this originated at Reddit, ackshually), I’ll repeat all the pertinent information here.

To quote (my emphasis): “Most people (95%+) with less than 90 IQ can’t understand conditional hypotheticals.” Examples:

>How would you have felt if you didn’t eat lunch?
>What do you mean? I did
>Yes, but if you didn’t, how would you feel?
>Why are you saying I didn’t? I told you I did
>Imagine you hadn’t, though. How would you have felt?
>I don’t understand
50% of convicts respond like this

Then comes recursion:

>Write a story with 2 named characters, each with one line of dialogue
>Most literate people can manage this, especially once you give them an example
>Write a story with 2 named characters, each with one line of dialogue
>In this story, one of the characters must be describing a story with at least 2 named characters, each of whom have at least one line of dialogue
>If you have less than 90 IQ, this second exercise is basically impossible
>Add a third level (‘frame’) to the story, and even 100 IQs start to get mixed up with the names of who’s talking

This limitation is well documented.

I trust all my regular readers have no problem whatsoever with these forms of reasoning. Nor with time, which some cannot fathom beyond the immediate.

The tweeter also lists the ability to put yourself in another’s shoes, as it were, which might indeed be lacking in some, but the evidence here is not as clear. Much of this evidence comes often from people are not necessarily remorseful for crimes. But not from the loving multitude who never become noticed. So we needn’t believe this.

Next is mapping, “which in abstract reasoning is expressing one thing in terms of another”.

For example, imagine a picture of an arrow, colored in a gradient from yellow to green. following the direction of the arrow
>Imagine a one-way street, with ascending house numbers, lowest at the entrance and highest at the exit
>If you mapped the arrow onto the street, what color would house #1 be?
>This isn’t tricky for most 100+s. It has some minor ambiguities, but anyone of normal intelligence can do the ‘mapping’, that is, the expression of one thing in term(s) of another
>However, for sub 90s, its very difficult. They struggle, and sub 80s just can’t do it at all.

We may also think of the power to create analogies.

But this is enough. There are also niceties to all these constructions, as is obvious. We’ll let these pass, too.

What should be clear, ignoring the IQ quantifications, is that a person who cannot fathom recursion doesn’t understand recursion. Not understanding it, he cannot form an idea of it, how it feels, what it’s like to have this power, as it were. Those of you who can grasp recursion, feel this power, and know its nature.

It is certain your dog, which is an intelligent creature, as long as we’re being loose with “intelligent”, cannot do recursion. It doesn’t have the intellect man does. It cannot know what it is like to be a man and have this power. Nor can it know the power of speech, a form of intellection, and all that flows from it.

And then even a bee knows how to find its way back to the hive. And it has almost no kind of mind at all.

On the other hand, there are certain people, Newton, for instance, who we call geniuses. People whose power of thought soars beyond anything we can do. Whose way of thinking we cannot grasp, but whose effects we can appreciate.

Be careful. Here we are not interested in why these things are so; the causes of them. These causes must be present. We don’t have to know what they are, to know that they are. So feel free to pick any of your favorite explanation.

As long as you come to the conclusion there is a hierarchy of “intelligences”. Which is an undeniable observation.

Many “high IQ” people, especially in our decadent culture, feel mighty proud to be in the class that, for instance, understand recursions. (Of course, many who say they can, cannot, though they are well credentialed.) They allow themselves to feel superior. Which, in the matters of recursion anyway, they are.

But it does not follow, at all, that they are therefore superior in all things, or in toto. After all, a dog cannot do recursion, and while any man is superior to a dog in this, none would claim superiority, in all things, over a dog.

Which, I know, you will agree with.

Here’s the kicker. The grand conclusion. As smart as you are, Mr Expert, PhD, you do not know what you cannot know. Nobody can. That there is a hierarchy of intelligences, well observed, implies—via induction, our strongest form of reasoning—that there are ways of thinking, modes of intellection, beyond which we can understand. This is true in the small, when we cannot fathom how geniuses think, but also true in the large.

Not knowing what these kinds of intelligences are like, we cannot test for them. We therefore cannot measure them. For that reason alone, IQ is incomplete.

We can’t know what these higher forms of thinking are, or are like, in the same way a man who cannot understand recursion cannot know what recursion is like. He may form the idea that that ability has certain manifestations, which he can see. But he knows he cannot reproduce them, or understand the whys behind that power’s use.

It’s the same with us, we “high IQ” people. We’re so busy congratulating ourselves, we forget that we could very well fit in the overall scheme of things like dogs do with us. Or bees.

Now many of you won’t believe, though at this late date it’s hard to see how, in angels. This isn’t the place for it, but the idea is that each angel is a different species. Each has intellectual powers the others don’t. The hierarchy we posited extends upward in these created beings, all the way to the highest created being.

This created being is not nice. Which shows the power of intelligence does not imply goodness. The smartest being is the evilest. We, too, have seen, all throughout history, the greatest evils arise from the very intelligent.

Infinity, as I often say, is unimaginably big. You can spend forever traveling to get there, and never arrive. So there is lots of room for an infinitely graduated hierarchy. But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.

Cockiness, then, about how brilliant “we” are is out. Or should be.

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  1. TomTom

    After 2020, I am uncertain whether I am high IQ or whether most people are low IQ,

  2. DAV

    Nor can [a dog] know the power of speech

    Depends on what you mean by “speech”. They don’t talk in words but they do communicate.

  3. Robin

    I understand hypotheticals, recursion and induction. But I’m still struggling with Monads (at least where Haskell is concerned).

  4. Kenan Meyer

    Bonhoeffer’s Theory of Stupidity

  5. RT

    This may not follow the direction of your essay; however, I share this here for “a view from the other side” who still are in agreement with what you write.

    My IQ is said to be significantly over 140, the number at which Mensa membership begins. Education was always a crooked, rocky path starting early on with skipping grades; a teacher declaring my left-handedness was an additional problem; instructors who “rewarded” me with more busy work or the tutoring of fellow students if I completed assignments quickly; advanced coursework over summers repeated slowly again during academic years because the next step was not funded…. Eventually, I “shut down,” content to fall under the radar. I did well enough academically and professionally, but never truly attained the top of my mountains.

    Joining Mensa was a help in young adulthood because I met others with similar stories; attended conventions of international groups; and, especially, followed articles written by some exceptional authors in the Bulletins. I discerned how few of us were truly successful in the grand scheme of things. Many of us had too narrow a focus, or, conversely, too scattered a tale.

    I still find it difficult that others are content with what I see as problems. And I always wonder how my life would be different if I was permitted to attend a trade school to also study to be an electrician, as opposed to the mandated college preparatory high school.

    As an “intelligent” person, choices are really made for me and not by me, the same as the mentally impaired. “It hurts to be smart” is a learned quote that I remember daily.

  6. Hagfish Bagpipe

    So, basically, what you’re saying, Briggs, is that dogs and bees are like angels, because infinite recursive hierarchy.

    Well, yeah, that’s pretty obvious, really…. when you think about it. Dude.

  7. Uncle Mike

    Yeah, well, smartypants, that doesn’t explain why the President is a moron one degree above flatliner.

  8. Mick Jagger Gathers No Mosque

    Catholic man: God created the Honey Bee with the instinct/knowledge to make hexagonal cells to store honey and raise baby bees.

    Darwinian Dude: The construction habits of the Honey Bee evolved because efficiency.. I know there are no examples to be found of square or triangle cells once used to store honey and act as a nursery but trust on this because a billion years.

  9. Rudolph Harrier

    As time goes on, I am starting to realize that the focus on rote memorization in school is not entirely due to teacher laziness. There are many students who simply cannot understand material and thus can only “learn” it by memorization. You can give the false impression that students understand quite a lot more than they actually do, because even many complicated calculus techniques can be fully described in an algorithmic form that can be memorized. But that doesn’t necessarily imply any understanding.

    I’ve seen many situations where students will go through complicated calculations to find all the roots of a degree 4 polynomial. Then you ask a question like “Since x = 3 is a root of the polynomial, what will we get if we evaluate it at x = 3?” and you get absolutely no comprehension that there is a connection between this question and the process of finding roots (unless the class devoted a rote repetition period to this very specific question. What I mean even if the class repeatedly says “roots of a polynomial are the numbers that make it go to 0” many students will still not understand the connection. But if you do multiple examples where you find the roots and then after you find them say that they will make the polynomial equal to 0, then the students will generally get the answer right. But if you swap the question even slightly, such as saying “if (x-3) is a factor of the polynomial, what will happen when we plug 3 into the polynomial?” and you’re back to square one.”

  10. John B(S)

    Rinse & Repeat

    Shampoo companies are counting on understanding of recursion

    Then there’s

    “Pete and Repeat went down the street, Pete went away and who was left?”

  11. The True Nolan

    @ Rudolf Harrier: “As time goes on, I am starting to realize that the focus on rote memorization in school is not entirely due to teacher laziness. There are many students who simply cannot understand material and thus can only “learn” it by memorization.”

    Physicist Richard Feynman wrote about a period he spent teaching students in Brazil. Asked to give a speech at the end of his course on his experience with his students, he compared the Brazilians with his US students. The Brazilians, he said, were some of the brightest, most hardworking students he had ever encountered. They would wade through dense chapters, memorize formulas, recall exact quotes, etc. etc. — BUT (big “but”) they were terrible at transposing that abstract knowledge into real life, physical examples. They could repeat exactly the laws of refraction, but give them a piece of glass and a measurement of how the light bends going through it, and they were at a loss to connect the law with the example.

    Conclusion? Memorization is a good thing, but only as a vehicle which may be used to transport the student down the road to actually grasp the significance and implementation of his subject.

    At some point, I think all of us must have “studied to the test”, i.e., have memorized just enough salient information to pass the test, but never understood the significance of what we memorized, or even kept the memories past the first year or so. Sadly, I see more and more people who have no realization that all that information, all those concepts, are essentially worthless if they cannot be corelated with the real world. All too often those memorizers and abstract thinkers end up as teachers, and mold their students into images of themselves. We cannot maintain a technological civilization without thinkers who also know how to get their hands dirty.

  12. Incitadus

    Humans with a lifespan of seventy to a hundred years never get out of adolescence
    and poof they’re gone. Imagine the IQ of a being that was a hundred thousand years old
    and still looked like he was forty five; eight or nine feet tall. You might be forgiven for
    thinking he was a god.

  13. Hun

    RT, Mensa cutoff is 130 (not 140). I don’t find that club particularly useful. In my experience it’s mostly people who are proud to have a paper proving their high IQ.

    I am also skeptical of any “solutions” proposed by a group of high-IQ people. IMO, the effect would be the same as rule by Experts. There are other qualities that are necessary for ruling, and high-IQ in isolation is extremely insufficient.

  14. kmann

    “Clever is as clever does”
    -Forrest Gump
    (a paraphrase)

  15. Whilst we may not know what we are not capable of knowing we can try to specify the limits of our knowing. IQ tests can specify these limits. But in other areas examinations can test the level of our understanding by requiring a candidate to show how they achieved their result.
    Shame this demonstration of understanding is becoming increasingly absent when policy is advocated or implemented.

  16. RT

    Hun – I think it depends upon the testing accepted, but I believe you are correct about the 130. As I wrote, I did enjoy the Bulletins, especially the articles about linguistics, recent discoveries, and member authored publications. Since Mensa employees cannot be Mensa members, recent years have seen “cutesy” changes and editorial comments that seemed to me childish. Also, local meetings were always focused on dining, game rooms, and silly contests. Overseas, we did meet in universities and many of the speakers were quite interesting. Intellectuals have always negated the value of Mensa, especially citing, “What have members done?”

  17. swordfishtrombone

    Mick Jagger Gathers No Mosque,

    Catholic man: God created the Honey Bee with the instinct/knowledge to make hexagonal cells to store honey and raise baby bees.

    And God created Onchocerca volvulus, the parasitic worm which causes River Blindness, in his infinite wisdom. Cheers, God!

  18. JohnK

    Not sure it’s defined Catholic dogma that angels are of necessity particularly intelligent, let alone hyper-intelligent, let alone intelligent in hierarchical ranks. But fun to think about. Also fun to think about how we might think about angels about as accurately as — pick a creature: an ant, our dog, etc. — thinks about us.

  19. Rudolph Harrier

    The most relevant bit of Aquinas regarding the intelligence of angels is this one:

    This in particular is relevant to the current discussion:

    “For some people there are who cannot grasp an intelligible truth, unless it be explained to them in every part and detail; this comes of their weakness of intellect: while there are others of stronger intellect, who can grasp many things from few.”

    i.e. the intellectual power of angels lies in a higher power of abstraction. Also relevant is his reply to objection one, where he says that (unlike us) angels do not abstract to universals via induction:

    “It is accidental to the universal to be abstracted from particulars, in so far as the intellect knowing it derives its knowledge from things. But if there be an intellect which does not derive its knowledge from things, the universal which it knows will not be abstracted from things, but in a measure will be pre-existing to them; either according to the order of causality, as the universal ideas of things are in the Word of God; or at least in the order of nature, as the universal ideas of things are in the angelic mind.”

    Later questions make clear that according to Aquinas the knowledge of angels is simultaneous and simple. For example, an angle conceiving the real numbers would conceive all of them at once, together with their union with the set as a whole. As humans we can merely think about single numbers, or sets of finite numbers, or the idea of one infinite set in a very abstract way. But we cannot comprehend truly infinity, while theoretically angels can.

    Aquinas is drawing on his theory of mind to make these statements, but also scripture, Augustine and Dionysius. So this is by no means an official teaching of the Church, but it is strongly based in traditional Catholic theology.

  20. Cary Cotterman

    I was all in until angels came up. I think they’re fun, like fairies, shades, sylphs, willis, and the Ghost Riders in the Sky, but I suppose I’m just not smart enough to believe they’re real. Oh well.

  21. Briggs


    Many such cases.

  22. Jim Fedako

    At what level is IQ a gift or the product of effort? Consider athletics, there are gifted folks who never train or do not train enough to achieve fame. Then there are those who train effectively and sufficiently to achieve success above their assumed potential.

    Looking at recursion … I bet I can do recursion better than most simply because I have years programming recursive code. I would know to use some heuristic technique to organize the recursive dialogue. Does that mean I am a genius … or does that simply reflect my years of experience?

  23. Half of all people are below average intelligence, which isn’t all that bright. I was interested in Mensa as a teen, until I took one of their tests, which was trivially easy, and met some of the members, who were all rather dim.

    I’m smart enough to know how dumb I can be. I recognize many of my blind spots, and accept them. I’ve met smart people. I stand in awe of their intellect. But very few of them have lived decent, productive lives. Academia corrupts.

    I have developed a very practical hierarchy of human intelligence. Note that there are different types of intelligence, and everybody has topics on which they are dumb (not just ignorant) as a bag of rusty hammers.

    Repeatedly and frequently does painful thing.
    Does painful thing several times.
    Does painful thing once or twice.
    Sees others do painful thing, and avoids.
    Hears about others doing painful thing, and avoids.
    Reads about others doing painful thing, and avoids.
    With some thought, determines that doing thing would be painful, and avoids.
    Never thought about doing obviously painful thing in the first place.
    Why the heck would anybody do that?

  24. @Jim – “Does that mean I am a genius … or does that simply reflect my years of experience?”

    It simply means you have surpassed a minimum standard of understanding in that narrow field. Many people will never achieve that goal, despite all the education you could throw at them.

    You can lead a horse to water, but you can’t make it think.

  25. Kneel

    Also: Hierarchies – some people see everything as “flat”, others see them as hierarchies.
    Those who see hierarchies and who can “zoom in or out” to the required “level” make good diagnosticians in their field – whether it be a mechanic or an MD or anything else. As such people gain more experience and therefore more intimate knowledge of each “level”, they become true “experts” in that they are more likely to be asked by the “flat” individuals for advice.

  26. Robin

    @Rudolf Harrier

    “As time goes on, I am starting to realize that the focus on rote memorization in school is not entirely due to teacher laziness. There are many students who simply cannot understand material and thus can only “learn” it by memorization. ”

    Of course there are poor students. But another factor is just bad teachers, many who don’t understand the material themselves; or if they do, don’t know how to teach it.

    Mathematics and Physics suffer from this more than others.

    WRT IQ, my measure is whether someone can define a problem with a number of abstractions yet arrive at a concrete solution. Computer programming requires this ability in abundance. So should most higher scientific degrees.

  27. swordfishtrombone

    Now many of you won’t believe, though at this late date it’s hard to see how, in angels.

    Why ‘at this late date’? It would surely have been easier to believe in angels in Old Testament times when they were having sex with humans, or in New Testament times when they were apparently so commonplace the gospel writers couldn’t even agree on how many were loitering near Jesus’s tomb.

  28. 1 – I’ve done some work in AI and can tell you and anyone else interested that you can’t develop what you can’t define.

    2 – I did make up my own definition of intelligence – and sold it to exactly nobody because the team I was supposed to advise split down the middle between old guys who believed in neural networks and younger ones who believe in simple brute force apps like Siri.

    3 – one of the interesting implications of my approach is that it provides a framework within which IQ is seen as species specific. In other words a magpie with a brain the size of small pea can be smarter than a human if the tasks during which it demonstrates this smarterness (hey why not..) are tasks for which magpies have evolved a facility.

    4 – I have not looked at these issues for years – if you wanted, I could put something together for your fans to tear into.

  29. NLR

    Aquinas’s idea about angels is fascinating.

    There some hints of it in Aristotle’s treatise “On the Soul”:

    “Certain kinds of animals posses in addition the power of locomotion, and still another order of animate beings, i.e. man and possibly another order like man or superior to him, the power of thinking, i.e. mind”


    “Lastly, certain beings – a small minority – possess calculation and thought, for (among mortal beings) those which possess calculation have all the other powers above mention, while the converse does not hold – indeed some live by imagination alone, while other hanve not even imagination. The mind that knows with immediate intuition presents a different problem.”

    Aristotle talks about both beings superior to man as well as a mind that knows with immediate intuition. The Medieval thinkers knew Aristotle forward and backward, so I suspect that these hints helped with their idea of angels.

    One view of angels conceives then angels as being in a linear order. The idea is that, according to the Thomistic-Aristotelian view, the only way one angel can differ from another is in the degree of understanding. Hence, the angels are organized in a line, where each one above knows more than the one below.

    But I would disagree with this. First of all, the theory may not capture all that is to be known about angels. But even then, there is nothing in the theory itself that requires degree of understanding to be all that differentiates angels. They can also differ in the quality of understanding. This fits in well with Dionysius’s 9 choirs. Where angels in one choir may know different things but the same degree of things. And angels in a higher choir know more and can do more than those in a lower choir. Then, the angels would form a partial order ( rather than a linear order.

  30. JOy

    Yet again, Briggs, you’re wrong about dogs and speech.
    However, I thought an interesting quiz? test might be to say two objects and see how one can go from one to the other in one stream of consciousness. The other day i was listening to revelations on alexa, and ended up discovering ther’es something called a klein bottle and that therre exists:
    ” certain kind of set, such as those of a topologically closed surface or an analogue of this in three or more dimensions.”
    So what was I thinking ab out?

    That’s how my mind works!!!
    And using the same kind of reasoning I can deduce or infir! that you don’t like dogs.
    Apparently, the Corgis didn’t like Putin, after he left, the Queen is reported to have said that:
    Animals can just tell, they have. a. way of knowing.

    Klein boottles are just toruses with delusions of grandeur

  31. Joy

    ““Pete and Repeat went down the street, Pete went away and who was left?””
    That’s Repeat!
    Since it’s a capital letter, so proper noun, so it’s a Robot parrot called Repeat.
    Repeat was left down the street all on his own.
    (in only works in aural without the punctuation)
    You know the one about Adam and Eve and pinch me?
    went down to the sea to bathe, Adam and eve were drowned, who do you think was saved?

  32. Joy

    “It is certain your dog, which is an intelligent creature, as long as we’re being loose with “intelligent”, cannot do recursion.”

    They can certainly learn that repeating the same operation will produce the same effect. They can be induced to display signs of depression and demoralisation n experiments, cruel ones. So memory and association is all that’s required for recursion in a non linguistic sense.
    They have memory and they also have ability to plan. Often to trick or con owners.

    It doesn’t have the intellect man does. It cannot know what it is like to be a man and have this power. Nor can it know the power of speech, a form of intellection, and all that flows from it.

    There is evidence though, that dogs have an understanding and a sense of the meanings of speech. I had one dog which used, on occasion, to mouth at me rather than bark, she used to do a “mime’ of a bark, opening and closing her mouth.
    One dog can enunciate “no”
    But only when in a temper! (jack Russel). She is also exceedingly jealous of the African grey parrot who talks and definitely understands meanings in conversations. So they know that speech has power just as you know that Newton’s intellect had power even if not experienced first hand. Parrots don’t just

    And then even a bee knows how to find its way back to the hive. And it has almost no kind of mind at all.

    Be careful!
    So you now concede that there is a spectrum of intellect?
    Except your spectrum is vertical and is merit based. That’s okay until you consider the evil genius, as your article implies intellectual superciliousness is shown up. Everybody’s definition of intellect is different and almost never declared beforehand.
    Assume endlessly, for arguments sake, but then in response, never give the opponent the benefit of the doubt and misquote their premises, reframe their argument to death! It’s not a sign of great intellect. Definitely a sign of human nature at play

  33. PatchedBrain

    I really enjoyed reading that and taking the “tests”! Thanks!

    I have to admit, however, that I almost didn’t make it beyond “How would you have felt if you didn’t eat lunch?”

    My teeth clenched and my brain blew. It would have been easier to proceed, had it been correctly written, instead of just written as-is-now-usual. So, with “How would you have felt if you had not eaten lunch?” firmly patching my brain, I could then proceed onward.

    Thanks again for the great post!

  34. Joy

    Re patched brain’s comment and an observation of that part of the article:

    It’s always the other’s fault for being dumb, even when deliberate misleading, misuse of grammar and punctuation hide the true intension of the question.

    In case of convicts, they are used to being interrogated or being in the wrong and so accused of having “done something” So they jump to the defensive position.

    Not very bright, of the person writing the questionaire and drawing conclusions about intellect from the responses.

    The other way to look at the question, is it’s typical of a con or a scam

  35. DEEBEE

    In the original Pfizer study of about 20,000 people in each leg of the RCT, 9 infection in vaccine and 169 infections in unvaccinated. No deaths in either. Thus came the the 95% efficacy against infection. The goalpost got moved to mortality after “breakthroughs”. If mortality cessation was the goal, then both vaccine and non-vaccine were equally good as no one died of Covid in either leg.

  36. Joy

    Aren’t all conditionals hypotheticals?

  37. neon

    You say “it’s well documented”.
    How about this:
    “Most people (95%+) with less than 90 IQ can’t understand conditional hypotheticals”

    There is no other “documentation” than screenshot from 4chan on reddit.
    There is no actual research about that, or is it?

  38. JasonM

    @neon I’ve been Googling to find actual research, and haven’t (so far)…

  39. Anonymous

    “But I did eat breakfast”

  40. David Beckham

    There is no other “documentation” than screenshot from 4chan on reddit.
    There is no actual research about that, or is it?

    That’s my thought too. So much memes and things made of this, and all from an anon story that could fake news for all we know. Also, someone on Twitter have a theory that since the whole thing was happening in prison, it could very well that “But I did eat breakfast” is not so much a low-IQ dumbo moment but rather the prisoners being defensive at being asked such a weird question.

  41. Apollo

    For you, maybe. I know things I shouldn’t know. My thinking is beyond your standard “genius”

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