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Microcosmic example. Take 3 people - a newborn (A), a professor of biology (B) and a professor in philosophy (C).
You're easily able to argue that both professors are more intelligent than the newborn (A<B and A<C). However, you're unable to establish (in any meaningful way) whether B<C, or C<B; even B=C is out. This is because both professors have knowledge the other does not, so trying to meaningfully equate or order them in relation to one another is an act of futility.
This is a fun example of a partial order that most of us see every day (in a less extreme form).
My money's on the biology professor.
I say we let them fight to the death to see which one is smarter. I'm putting extra money on the Philosophy Professor going on a rant about how physical combat has nothing to do with intelligence - and getting struck down in the midst of his soliloquy.
Biology Professor: "Survival of the fittest!"
That's also part of the reason why IQ scores are deeply flawed. Using a single number to measure intelligence implies there is an absolute order.
Fun fact: Richard Feynman, one of the greatest physicist of the 20th century and legendary physics educator (author of the Feynman Lectures), was invited to join Mensa after he won the Nobel Prize in physics. He declined however, because he didn't meet the IQ score of 130 normally required by Mensa.
It's similar with the ASVAB (multisection test for determing qualification for military service). I scored the highest score available, a 99, because it seemed in each section they moved on once they established competence.
The few people who saw my score (I don't go around telling people) have asked if I was super smart or something (the recruiter called me "professor" and asked if I had a Masters), and I said no, I am just competent at anything I could do in the military. I'm honestly not excellent at any particular thing, and in any given task I'm unlikely to be the best one there for it. But I'm capable of doing any task adequately. As my old trombone instructor used to say, I'm a "jack of all trades, master of none."
But the test doesn't care if you're amazing at anything. It just wants to see if you're capable of doing anything.
looky here we got us a man who earned a 99 in cleaning out the shithouse. Grab a shovel, "Professor".
I mean, yeah, I can very competently clean out a shithouse as well as I can competently fix a helicopter. I probably won't be exceptional at either one (though I absolutely kill it on written tests, I guess).
Gardner’s “multiple intelligences” model is a nicer way to think about intelligence, but it’s not really quantifiable in the same way. (How would you measure how “ecologically” intelligent someone is?)
It’s very appealing to think that we have some sort of “int” stat like a Dungeons and Dragons character, but I don’t think it’s really that valuable. If the IQ/the “g factor” measures anything, it’s probably something about being able to quickly process visual information. I have a relatively high IQ and think that’s the trait I have that is being measured (from the testing they did in the teen torture facility I spent my adolescence in - my high IQ meant that I was a dangerous, manipulative liar of course.)
If you have two and a half hours to spare, I think this Shaun video is a masterwork of science communication.
Put another way: like so may things, knowledge is multidimensional. If you just compared them on knowledge of chess openings, or how many digits of π they could recall, you could rank them more confidently on that axis.
But general intelligence is such a slippery fish compared to isolated trivia.
I didn't know there was a term for this! Thank you! I try to convey this concept all the time, especially for intelligence and skills, so having a word for it is immensely helpful.