For many human traits, it’s perfectly obvious what it means to have twice as much. A six-foot tall man is twice as tall as a three foot tall man. Someone who can lift 300 lbs is twice as strong as someone who can lift 150 lbs. Someone who can run 100 meters in 10 seconds is twice as fast as someone who can run it in 20 seconds.
It becomes more difficult to apply the same logic to IQ. Although we can say a 2000 cubic centimeter brain is twice as big as a 1000 cubic centimeter brain, we can’t necessarily say it’s twice as smart (on average) because we don’t know if the relationship between intelligence and brain size is linear.
I do think the relationship between brain size and IQ is linear (excluding pathological cases) but that’s because brain size is normally distributed and IQ is largely forced to fit a normal curve, however that doesn’t mean intelligence itself is normally distributed.
On the contrary, a member of Prometheus society once claimed that because the human mind works in parallel, complex learning and problem solving speed doubles every 10 IQ points (he later revised to every 5).
To test this fascinating this hypothesis, I imagined people taking the WAIS-R IQ test. Because several subtests (Arithmetic, Block Design and Object Assembly) awarded bonus points for super fast performance, it was possible to imagine a person perfectly solving all the items within the time limit, but using 100% of the allotted time.
Such a person would have an Arithmetic IQ of 105, a Block Design IQ of 100, and an Object Assembly IQ of 90.
Then I asked what would happen if the same person had only used 50% of the allotted time: Arithmetic IQ 105, Block Design IQ of 105, and Object Assembly IQ of 90.
25% of the allotted time: Arithmetic IQ 110, Block Design IQ 120, Object Assembly IQ 100.
12.5% of the allotted time: Arithmetic IQ 135, Block Design IQ 145, Object Assembly IQ 125.
6.25% of the allotted time: This speed takes you beyond the ceiling of all subtests except Object Assembly for which you would score an Object Assembly IQ of 140
It’s hard to draw strong conclusions because David Wechsler arbitrarily decided how much speed was needed for a bonus point, but on balance it looks like a doubling of speed on a particular subtest, equates to a jump of 10 or 15 IQ points (on that subtest)
But how do we reconcile such an explosive distribution with the popular notion of a bell shaped IQ curve, which Jensen assumed IQ likely had given the fact that linear regression predicts IQs of one’s relatives and biological correlates of IQ like brain size enjoy a bell curve.
And indeed some psychometric tasks really do enjoy a true curve (without test takers having to force one). The number of digits you can repeat from memory, or the number of abstract symbols you can copy in 90 seconds or even in the number of words in your vocabulary (when randomly selected from a dictionary) all increase in a linear way with IQ, which means all must form the same bell curve.
So my guess is that the building blocks of intelligence (brain size, memory, raw neural speed) are all normally distributed yet actual complex problem solving and real world adaptive behavior show huge inequality, perhaps because a few extra units of data can double the number of interrelations between them, so the amount of information we can process is normally distributed, but the output of that data is explosively distributed.
So what does it mean to be twice as smart? Well, if you define intelligence as the cognitive capacity for problem solving or goal directed adaptive behavior, then being twice as smart means either the ability to solve twice as many problems or the ability to solve the same amount of problems twice as well.
If we assume most problems in the universe are complex problems, then I’d say an extra 13 math IQ points makes you twice as smart mathematically, an extra 13 spatial IQ points makes you twice as smart spatially etc.
But since different cognitive abilities are imperfectly correlated, I’d say it takes 19 overall IQ points to be twice as smart overall (all domains averaged together).
So assuming mature apes have an IQ of 14, we can very tentatively conclude the following (for young adults):
IQ 14: 1 times smarter than an ape
IQ 33: 2 times smarter than ape
IQ 52: 4 times smarter than an ape
IQ 71: 8 times smarter than an ape
IQ 90: 16 times smarter than an ape
IQ 109: 32 times smarter than an ape
IQ 128: 64 times smarter than an ape
IQ 147: 128 times smarter than an ape
IQ 166: 256 times smarter than an ape
IQ 185: 512 times smarter than an ape
IQ 204: 1,024 times smarter than an ape
So instead of asking people their IQ, you can ask them their MiQ pronounced My Cue (monkey intelligence quotient). A MiQ of 16 to 32 (16 to 32 times smarter than an anthropoid monkey) implies average intelligence for young adults in developed countries. A MiQ below 8 implies impairment in a young adult but would mean gifted in a toddler.
So even though the average human brain is roughly 4 times bigger than the average ape’s, the human mind is roughly 20 times bigger.