[tptacek]

I hear this argument a lot and I don't know what you think it demonstrates. Put two groups of people on separate islands for 1000 years. Check back up on them. They will be overwhelmingly phenotypically similar. It's not like one of the groups is going to become the X-Men. Really, these analogies mostly seem like a device for smuggling in the premise that innate intellectual ability is less like color vision and more like eye color. Maybe it is, but you have to make and ground that argument.

[medvezhenok]

What is the color vision equivalent of a savant? Surely you don't believe that any person could (given infinite time & training from birth), match the intellectual performance of a savant on, say, multiplying 6 digit numbers in their head?

(I think a clear savant that has a untouchable ability in one small dimension of mathematics is a clearer example than, say, von Neumann - who was equally brilliant but across many domains and in a less obvious way)

[tptacek]

There is certainly variation in innate intellectual capability! There just isn't strong evidence of groupwide variation. Groupwide variation is the point of the "island" story.

[wizzwizz4]

> multiplying 6 digit numbers in their head?

This kind of thing is quite easy. Which mental delay-line caches you exploit depends on how your mind works, but multiplying 6-digit numbers in your head isn't a hard trick to learn, if you care.

There was a time when I cared about such parlour tricks, and I could pick them up quite quickly. I once spent a few days memorising the first 10 digits of pi. Once I'd figured that out, it was the effort of a few hours over the subsequent weeks to memorise to 36 digits. If I had cared, I could have learned twenty new digits a day, using the following scheme:

     3.14159
    265358979
     32384626
     43383
  2795028841
    9716
        93993
     75105820
     97494459
     23078164
     06286208
     99862803
     4825342
    117067
          982
     14808
          65132
       823066
     4...

See how it's lyrical? Just learn the poem. Except… I quickly found I didn't care, and at that point my motivation vanished, and I lost the "savant" ability. (Sure, if I wanted to, I could easily bootstrap the requisite intrinsic motivation – and I suspect I could learn a hundred digits a day thereby – but I don't want to.)

Despite my generally-absent enthusiasm, I'm still capable of aceing IQ tests, scoring highly in measures of cognitive ability that I do not possess, etc, because I have a certain stubbornness towards the idea that these tests truly measure anything important, which means I approach them sideways with the objective of breaking the tests, which means I break the tests. If anything of value hinged on my ability to quickly multiply 6-digit numbers in my head, I expect I could pick it up in… six months?

I do not say these things to brag: rather, the opposite. I don't think I am particularly exceptional: I never learned a thousand digits of pi, would probably take an hour to multiply 6-digit numbers in my head…

I am able to solve problems I've never encountered with computer systems I've never used, after half a second of thought, while concentrating on other things – but from the inside that doesn't feel exceptional at all: it's just a few tricks, well-practised. People who have memorised millions of digits of pi likewise claim to use a few tricks – and while those particular tricks don't always work for everyone, I don't think these people are innately exceptional.

[medvezhenok]

I understand the argument, but I think you're missing the nuance somewhat. There are a series of things that are learnable mental tricks; I have read Moonwalking with Einstein and am well aware about rhyme techniques, memory palace techniques, etc. I memorized ~250 digits of pi in the 6th grade, so I'm also aware of techniques for that. I wouldn't consider either of those a domain of savants.

(sidenote - I would be impressed with the people that could memorize millions of digits of Pi, given that the world record is either 70,000 digits or ~110,000 digits last time I checked (depends on the source), and it takes ~6 hours just to recite that many digits)

I'm talking specifically like things like Hypercalculia: https://en.wikipedia.org/wiki/Hypercalculia , which are documented feats that cannot be explained by "tricks". Usually people with savant syndrome also have co-occurring autism and other neurological conditions like synesthesia.

Here is a an ABC profile of one of these savants: https://abcnews.go.com/2020/autistic-savant-daniel-tammet-so...

I don't think you could learn a "trick" to compute 27^7 in a few seconds.

[wizzwizz4]

Funny you should give 27^7 as an example, because I actually did get good at powers of 2 and 3. 27^7 is 3^21 is 3×81^5, which is easy to calculate in your head if you're good at multiples and powers of 8: it's just binomial expansion with the next row after 1 4 6 4 1, i.e. 1 5 10 10 5 1. (I used to be able to directly recall 1 5 10 10 5 1 and 1 6 15 20 15 6 1, but this is literally the first time I'm doing non-trivial mental arithmetic in a decade.) Multiplying a power of 2 by 5 is the same as halving and multiplying by 10, which reduces the problem to a simple addition of digits of small powers of 2 (^0 = 1, ^2 = 4, ^6 = 64, ^9 = 512, ^11 = 2048, ^15 = 32768), then a multiplication by 3 – both of which are easy to perform in a streaming fashion, if you have a suitable delay line. (I use the auditory processing delay line ("echoic memory"), which would probably work better if I spoke a language like Mandarin, where all digits have the same syllable length – but I got by. Some find the mental abacus more reliable, but I have no training in this approach.)

I only memorised my powers of 2 up to 2^16, powers of 3 up to 3^5, and powers of 5 up to 5^5, because the part that made it fun was only memorising things I'd calculated myself, in my head, and this was only an occasional game. If my goal had been "develop the skill of quick arithmetic", I would've memorised the first 12 powers of every prime below 12, and my times tables up to 100×100 – but I resented times tables, so never really memorised them until I (briefly) got really into division.

[medvezhenok]

I'm not going to make a scientifict argument about innate intellectual ability - I don't consider myself qualified enough for that.

I can only speak to my own observations. I have taught a lot of people to juggle. Juggling is an interesting discipline because it's pretty distinct from any other activity that most people have participated in in their life. It also has lower risk of "contamination", since people are unlikely to lie if you ask them if they've juggled before. You can also run this experiment with young kids, etc - you will still see very different rates of skill acquisition. I would bet that any other environmental arguments also fall flat - there are no big pro-juggling or anti-juggling cultures out there.

When you get a group of people together and instruct them to juggle, people will pick it up at very different rates. If you have enough of a sample size of observations, you can see extreme variability - some pick it up after 10-15 minutes, others still can't juggle after a year of trying (believe me, I've seen both). I've also observed brothers, both professional jugglers from a young age and both having invested identical amounts of time and passion into the activity (again, have no incentive to lie), progress at very different rates with acquisition of the skill.

From observing hundreds of people learning to juggle, I strongly believe that there is an "innate aptitude for juggling" in every person. Even people without this innate aptitude can learn to juggle and get to a certain level at the skill, beyond which progress will be so slow as to represent a de-facto "ceiling" on their juggling skill.

If you were to make this same argument in intellectual domains (i.e. chess, as an objective example), the argument gets more muddied in that you could make valid arguments that environment has played a role in "predisposing" someone to more rapid skill acquisition. However, I like to think of skill acquisition as more of a y = mx + b equation (not that all skill aquisition is linear). Every person has a certain rate (slope) at which they can aquire a given skill, and a certain intercept (predisposition) towards the acquisition of that skill. This model also works since someone that acquires skill more slowly can expend more time and achieve the same level of competence, but their ultimate ceiling of skill aquisition is lower (since time is finite).

I can make similar arguments about other domains, having spent time with IMO medalists, IOI medalists and other "outliers" in the intellectual domains. The same examples I showed above still apply, but the data is a lot more messy because it's hard in those cases separate the environmental/cultural effects from the genetic effects. That's why I reach for the juggling example as a clearer argument for that.

[tptacek]

I'm not claiming that there's no variation in innate ability, only that one island won't be innately better at juggling than the other (certainly one island will be better at juggling, because they will care about juggling more, pass down more juggling, push forward the juggling sciences, &c. But those won't be innate, biological differences).

In other words: if, 1000 years later, you somehow stole an infant from bad-juggling island and had them raised on good-juggling island, they'd likely behave as you'd expect a good-juggle-islander to behave, despite their provenance. (Stipulate that there aren't outwardly evident signs of which island you're from, like inherited skin tone or whatever, which would alter your interactions with your environment).

[medvezhenok]

I think if we agree that there are individual differences in predisposition towards juggling aptitude, and that the predisposition is mediated genetically somehow, and if juggling (in this hypothetical) is biologically advantageous for survival/reproduction on one of the islands (really stretching the analogy here) - then I don’t see a way how my 1000 years experiment doesn’t produce actual, population level genetic drift in juggling predisposition between the population on island A and island B (unless we could somehow prove that juggling predisposition is not heritable)

[wizzwizz4]

This is the crux of the issue. You assume, in the absence of evidence, that juggling aptitude predisposition is mediated genetically, in such a way that it is variable among humans; and you place the burden of proof on "somehow prove[ing] that [it] is not heritable" (emphasis mine). But it's far easier to prove the positive (in a world where the positive is true) than prove the negative (in a world where the positive is false), so the appropriate perspective to adopt if you want to investigate via experiment is "try to prove it true, and if we honestly fail, that's an argument that it's false".

If you don't intend to run the experiment, then different considerations dominate: you should justify this bias. Maybe you're drawing an analogy to something similar, which you know to work this way? Bias isn't the same thing as wrong, after all: but unjustified bias often is.