(Thanks. I don’t think this is necessarily significant evidence against my hypothesis (see my comment on GeneSmith’s comment.)
Another confusing relevant piece of evidence I thought I throw in:
Human intelligence seems to me to be very heavytailed. (I assume this is uncontrovertial here, just look at the greatest scientists vs great scientists.)
If variance in intelligence was basically purely explained by mildly-delterious SNPs, this would seem a bit odd to me: If the average person had 1000SNPs, and then (using butt-numbers which might be very off) Einstein (+6.3std) had only 800 and the average theoretical physics professor (+4std) had 850, I wouldn’t expect the difference there to be that big.
It’s a bit less surprising on the model where most people have a few strongly delterious mutations, and supergeniuses are the lucky ones that have only 1 or 0 of those.
It’s IMO even a bit less surprising on my hypothesis where in some cases the different hyperparameters happen to work much better with each other—where supergeniuses are in some dimensions “more lucky than the base genome” (in a way that’s not necessarily easy to pass on to offspring though because the genes are interdependent, which is why the genes didn’t yet rise to fixation). But even there I’d still be pretty surprised by the heavytail.
The heavytail of intelligence really confuses me. (Given that it doesn’t even come from sub-critical intelligence explosion dynamics.)
If each deleterious mutation decreases the success rate of something by an additive constant, but you need lots of sequential successes for intellectual achievements, then intellectual formidability is ~exponentially related to deleterious variants.
Yeah I know that’s why I said that if a major effect was through few significantly deleterious mutations this would be more plausible. But i feel like human intelligence is even more heavitailed than what one would predict given this hypothesis.
If you have many mutations that matter, then via central limit theorem the overall distribution will be roughly gaussian even though the individual ones are exponential.
(If I made a mistake maybe crunch the numbers to show me?)
(initially misunderstood what you mean where i thought complete nonsense.)
I don’t understand what you’re trying to say. Can you maybe rephrase again in more detail?
Suppose people’s probability of solving a task is uniformly distributed between 0 and 1. That’s a thin-tailed distribution.
Now consider their probability of correctly solving 2 tasks in a row. That will have a sort of triangular distribution, which has more positive skewness.
If you consider e.g. their probability of correctly solving 10 tasks in a row, then the bottom 93.3% of people will all have less than 50%, whereas e.g. the 99th percentile will have 90% chance of succeeding.
Conjunction is one of the two fundamental ways that tasks can combine, and it tends to make the tasks harder and rapidly make the upper tail do better than the lower tail, leading to an approximately-exponential element. Another fundamental way that tasks can combine is disjunction, which leads to an exponential in the opposite direction.
When you combine conjunctions and disjunctions, you get an approximately sigmoidal relationship. The location/x-axis-translation of this sigmoid depends on the task’s difficulty. And in practice, the “easy” side of this sigmoid can be automated or done quickly or similar, so really what matters is the “hard” side, and the hard side of a sigmoid is approximately exponential.
Is the following a fair paraphrasing of your main hypothesis? (I’m leaving out some subtleties with conjunctive successes, but please correct the model in that way if it’s relevant.):
“”″ Each deleterious mutation multiplies your probability of succeeding at a problem/thought by some constant. Let’s for simplicity say it’s 0.98 for all of them.
Then the expected number of successes per time for a person is proportional to 0.98^num_deleterious_mutations(person).
So the model would predict that when Person A had 10 less deleterious mutations than person B, they would on average accomplish 0.98^10 ~= 0.82 times as much in a given timeframe. ”″”
I think this model makes a lot of sense, thanks!
In itself I think it’s insufficient to explain how heavytailed human intelligence is—there were multiple cases where Einstein seems to have been able to solve problems multiple times faster than the next runner ups. But I think if you use this model in a learning setting where success means “better thinking algorithms” then if you have 10 fewer deleterious mutations it’s like having 1⁄0.82 longer training time, and there might also be compounding returns from having better thinking algorithms to getting more and richer updates to them.
Not sure whether this completely deconfuses me about how heavytailed human intelligence is, but it’s a great start.
I guess at least the heavytail is much less significant evidence for my hypothesis than I initially thought (though so far I still think my hypothesis is plausible).
(Thanks. I don’t think this is necessarily significant evidence against my hypothesis (see my comment on GeneSmith’s comment.)
Another confusing relevant piece of evidence I thought I throw in:
Human intelligence seems to me to be very heavytailed. (I assume this is uncontrovertial here, just look at the greatest scientists vs great scientists.)
If variance in intelligence was basically purely explained by mildly-delterious SNPs, this would seem a bit odd to me: If the average person had 1000SNPs, and then (using butt-numbers which might be very off) Einstein (+6.3std) had only 800 and the average theoretical physics professor (+4std) had 850, I wouldn’t expect the difference there to be that big.
It’s a bit less surprising on the model where most people have a few strongly delterious mutations, and supergeniuses are the lucky ones that have only 1 or 0 of those.
It’s IMO even a bit less surprising on my hypothesis where in some cases the different hyperparameters happen to work much better with each other—where supergeniuses are in some dimensions “more lucky than the base genome” (in a way that’s not necessarily easy to pass on to offspring though because the genes are interdependent, which is why the genes didn’t yet rise to fixation). But even there I’d still be pretty surprised by the heavytail.
The heavytail of intelligence really confuses me. (Given that it doesn’t even come from sub-critical intelligence explosion dynamics.)
If each deleterious mutation decreases the success rate of something by an additive constant, but you need lots of sequential successes for intellectual achievements, then intellectual formidability is ~exponentially related to deleterious variants.
Yeah I know that’s why I said that if a major effect was through few significantly deleterious mutations this would be more plausible. But i feel like human intelligence is even more heavitailed than what one would predict given this hypothesis.If you have many mutations that matter, then via central limit theorem the overall distribution will be roughly gaussian even though the individual ones are exponential.(If I made a mistake maybe crunch the numbers to show me?)(initially misunderstood what you mean where i thought complete nonsense.)
I don’t understand what you’re trying to say. Can you maybe rephrase again in more detail?
Suppose people’s probability of solving a task is uniformly distributed between 0 and 1. That’s a thin-tailed distribution.
Now consider their probability of correctly solving 2 tasks in a row. That will have a sort of triangular distribution, which has more positive skewness.
If you consider e.g. their probability of correctly solving 10 tasks in a row, then the bottom 93.3% of people will all have less than 50%, whereas e.g. the 99th percentile will have 90% chance of succeeding.
Conjunction is one of the two fundamental ways that tasks can combine, and it tends to make the tasks harder and rapidly make the upper tail do better than the lower tail, leading to an approximately-exponential element. Another fundamental way that tasks can combine is disjunction, which leads to an exponential in the opposite direction.
When you combine conjunctions and disjunctions, you get an approximately sigmoidal relationship. The location/x-axis-translation of this sigmoid depends on the task’s difficulty. And in practice, the “easy” side of this sigmoid can be automated or done quickly or similar, so really what matters is the “hard” side, and the hard side of a sigmoid is approximately exponential.
Thanks!
Is the following a fair paraphrasing of your main hypothesis? (I’m leaving out some subtleties with conjunctive successes, but please correct the model in that way if it’s relevant.):
“”″
Each deleterious mutation multiplies your probability of succeeding at a problem/thought by some constant. Let’s for simplicity say it’s 0.98 for all of them.
Then the expected number of successes per time for a person is proportional to 0.98^num_deleterious_mutations(person).
So the model would predict that when Person A had 10 less deleterious mutations than person B, they would on average accomplish 0.98^10 ~= 0.82 times as much in a given timeframe.
”″”
I think this model makes a lot of sense, thanks!
In itself I think it’s insufficient to explain how heavytailed human intelligence is—there were multiple cases where Einstein seems to have been able to solve problems multiple times faster than the next runner ups. But I think if you use this model in a learning setting where success means “better thinking algorithms” then if you have 10 fewer deleterious mutations it’s like having 1⁄0.82 longer training time, and there might also be compounding returns from having better thinking algorithms to getting more and richer updates to them.
Not sure whether this completely deconfuses me about how heavytailed human intelligence is, but it’s a great start.
I guess at least the heavytail is much less significant evidence for my hypothesis than I initially thought (though so far I still think my hypothesis is plausible).