Orcas have about 43 billion cortical neurons—humans have about 21 billion. The orca cortex has 6 times the area of the human cortex, though the neuron density is about 3 times lower.
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My uncertain guess is that, within mammalian brains, scaling matters a lot more for individual intelligence,
This post seems to assume that a 2x increase in brain size is a huge difference (claiming this could plausibly yield +6SD), but a naive botec doesn’t support this.
For humans, brain size and IQ are correlated at ~0.3. Brain size has a standard deviation of roughly 12%. So, a doubling of brain size is ~6 SD of brain size which yields ~1.8 SD of IQ. I think this is probably a substantial overestimate as I don’t expect this correlation is fully causal: increased brain size is probably correlated with factors that also increase IQ through other mechanisms (e.g., generally fewer deleterious mutations, aging, nutrition). So, my bottom line guess is that doubling brain size is more like 1.2 SD of IQ. This implies that doubling brain size isn’t that big of a deal relative to other factors.
I think this is basically the bottom line—quite likely doubling brain size isn’t very decisive, but I did a more detailed botec to get to a (sloppy) bottom line out of curiosity.
First let’s account for non-brain size differences. My guess is that orcas are (median) around −4 SD on non-brain size differences (aka brain algorithms) with respect to research tasks (putting some weight on language specialization, accounting for orca specialization, etc.), for an overall estimate of −2.8 SD. This doesn’t feel crazy to me?
Where does this −4 SD come from? My guess is that the human-chimp gap in non-brain size improvements is around 2.2 SD[1] and the chimp-orca (non-brain size) gap is probably similar, maybe a bit smaller, let’s say 1.8 SD. So, this yields −4 SD.
I think my 95% confidence internal for the orca algorithmic advantage (on research) is like −8 SD to −1 SD with a roughly normal distribution. (I could be argued into having a substantially lower value for the bottom of the confidence internval; −12 SD doesn’t seem too crazy.)
To get a interval for IQ vs brain size effect, let’s do a very charitable estimate and then use this as a 95th percentile. The maximally charitable estimate would be something like:
Assume the correlation is more like 0.4 and is fully causal.
Assume standard deviation of 8% so 2x is 9 SDs.
This yields 3.6 SD of IQ per doubling.
Using this as a 95th percentile and 1.2 as my median, my 95% confidence internal is like 0.4 to 3.6 SDs per 2xing (putting aside the probability of this whole model being confused). Let’s say this is distributed lognormally.
Now, let’s say 95% interval on ocra brain size as 1.5 to 2.5. (With a log normal distribution.)
This yields ~5% chance of orcas being over 4SDs above humans. And ~10% chance of >2SDs. (See the notebook here.) After updating on our observations (humans appear to be running an intelligent civilization and orcas don’t seem that smart), I update down by maybe 5x on both of these estimates to 1% chance of >4SDs and 2% chance of >2SDs.
Correspondingly, I’m not very optimistic about the prospects here.
I think the chimp vs human gap is probably roughly half brain size and half other (algorithmic) improvements. The brain size gap is 3.5x or 2.2 SD (using 1.2 SD / doubling). So, if the gap is half brain size and half other (algorithmic) improvements, then we’d get 2.2 SD of algorithmic improvement.
Thanks for describing a wonderfully concrete model. I like that way you reason (especially the squiggle), but I don’t think it works quite that well for this case. But let’s first assume it does: Your estimamtes on algorithmic efficiency deficits of orca brains seem roughly reasonable to me. (EDIT: I’d actually be at more like −3.5std mean with standard deviation of 2std, but idk.) Number cortical neurons != brain size. Orcas have ~2x the number of cortical neurons, but much larger brains. Assuming brain weight is proportional to volume, with human brains being typically 1.2-1.4kg, and orca brains being typically 5.4-6.8kg, orca brains are actually like 6.1/1.3=4.7 times larger than human brains. Taking the 5.4-6.8kg range, this would be 4.15-5.23 range of how much larger orca brains are. Plugging that in for `orca_brain_size_difference` yields 45% on >=2std, and 38% on >=4std (where your values ) and 19.4% on >=6std. Updating down by 5x because orcas don’t seem that smart doesn’t seem like quite the right method to adjust the estimate, but perhaps fine enough for the upper end estimates, which would leave 3.9% on >=6std.
Maybe you meant “brain size” as only an approximation to “number of cortical neurons”, which you think are the relevant part. My guess is that neuron density is actually somewhat anti-correlated with brain size, and that number of cortical neurons would be correlated with IQ rather at ~0.4-0.55 in humans, though i haven’t checked whether there’s data on this. And ofc using that you get lower estimates for orca intelligence than in my calculation above. (And while I’d admit that number of neurons is a particularly important point of estimation, there might also be other advantages of having a bigger brain like more glia cells. Though maybe higher neuron density also means higher firing rates and thereby more computation. I guess if you want to try it that way going by number of neurons is fine.)
My main point is however, that brain size (or cortical neuron count) effect on IQ within one species doesn’t generalize to brain size effect between species. Here’s why: Let’s say having mutations for larger brains is beneficial for intelligence.[1] On my view, a brain isn’t just some neural tissue randomly smished together, but has a lot of hyperparameters that have to be tuned so the different parts work well together. Evolution basically tuned those hyperparameters for the median human (per gender). When you now get a lot of mutations that increase brain size, while this contributes to smartness, this also pulls you away from the species median, so the hyperparameters are likely to become less well tuned, resulting in a countereffect that also makes you dumber in some ways.
So when you get a larger brain as a human, this has a lower positive effect on intelligence, than when your species equilibriates on having a larger brain. Thus, I don’t think within species intelligence variation can be extended well to inter-species intelligence variation.
As for how to then properly estimate orca intelligence: I don’t know.
(As it happens, I thought of something and learned something yesterday that makes me significantly more pessimistic about orcas being that smart. Still need to consider though. May post them soon.)
I initially started this section with the following, but I cut it out because it’s not actually that relevant: “How intelligent you are mostly depends on how many deleterious mutations you have that move you away from your species average and thereby make you dumber. You’re mostly not smart because you have some very rare good genes, but because you have fewer bad ones. Mutations for increasing sizes of brain regions might be an exception, because there intelligence trades off against childbirth mortality, so higher intelligence here might mean lower genetic fitness.”
Number cortical neurons != brain size. Orcas have ~2x the number of cortical neurons, but much larger brains. Assuming brain weight is proportional to volume, with human brains being typically 1.2-1.4kg, and orca brains being typically 5.4-6.8kg, orca brains are actually like 6.1/1.3=4.7 times larger than human brains.
I think cortical neurons is a better proxy than brain size and I expect that the relation between cortical neurons and brain size differs substantially between species. (I expect more similarity within a species.)
My guess is that neuron density is actually somewhat anti-correlated with brain size
This might be true in mammals (and/or birds) overall, but I’m kinda skeptical this is a big effect within humans. Like I’d guess that regression slope between brain size and cortical neurons is ~1 in humans rather than substantially less than 1.
that number of cortical neurons would be correlated with IQ rather at ~0.4-0.55 in humans
I agree you’ll probably see a bigger correlation with cortical neurons (if you can measure this precisely enough!). I wouldn’t guess much more though?
Overall, I’m somewhat sympathetic to your arguments that we should expect that multiplying cortical neurons by X is a bigger effect than multiplying brain size by X. Maybe this moves my estimate of SDs / doubling of cortical neurons up by 1.5x to more like 1.8 SD / doubling. I don’t think this makes a huge difference to the bottom line.
Yeah I think I came to agree with you. I’m still a bit confused though because intuitively I’d guess chimps are dumber than −4.4SD (in the interpretation for “-4.4SD” I described in my other new comment).
When you now get a lot of mutations that increase brain size, while this contributes to smartness, this also pulls you away from the species median, so the hyperparameters are likely to become less well tuned, resulting in a countereffect that also makes you dumber in some ways.
Actually maybe the effect I am describing is relatively small as long as the variation in brain size is within 2 SDs or so, which is where most of the data pinning down the 0.3 correlation comes from.
So yeah it’s plausible to me that your method of estimating is ok.
Intuitively I had thought that chimps are just much dumber than humans. And sure if you take −4SD humans they aren’t really able to do anything, but they don’t really count.
I thought it’s sorta in this direction but not quite as extreme:
(This picture is actually silly because the distance to “Mouse” should be even much bigger. The point is that chimps might be far outside the human distribution.)
But perhaps chimps are actually closer to humans than I thought.
(When I in the following compare different species with standard deviations, I don’t actually mean standard deviations, but more like “how many times the difference between a +0SD and a +1SD human”, since extremely high and very low standard deviation measures mostly cease to me meaningful for what was actually supposed to be measured.)
I still think −4.4SD is overestimating chimp intelligence. I don’t know enough about chimps, but I guess they might be somewhere between −12SD and −6SD (compared to my previous intuition, which might’ve been more like −20SD). And yes, considering that the gap in cortical neuron count between chimps and humans is like 3.5x, and it’s even larger for the prefrontal cortex, and that algorithmic efficiency is probably “orca < chimp < human”, then +6SDs for orcas seem a lot less likely than I initially intuitively thought, though orcas would still likely be a bit smarter than humans (on the way my priors would fall out (not really after updating on observations about orcas)).
This post seems to assume that a 2x increase in brain size is a huge difference (claiming this could plausibly yield +6SD), but a naive botec doesn’t support this.
For humans, brain size and IQ are correlated at ~0.3. Brain size has a standard deviation of roughly 12%. So, a doubling of brain size is ~6 SD of brain size which yields ~1.8 SD of IQ. I think this is probably a substantial overestimate as I don’t expect this correlation is fully causal: increased brain size is probably correlated with factors that also increase IQ through other mechanisms (e.g., generally fewer deleterious mutations, aging, nutrition). So, my bottom line guess is that doubling brain size is more like 1.2 SD of IQ. This implies that doubling brain size isn’t that big of a deal relative to other factors.
I think this is basically the bottom line—quite likely doubling brain size isn’t very decisive, but I did a more detailed botec to get to a (sloppy) bottom line out of curiosity.
First let’s account for non-brain size differences. My guess is that orcas are (median) around −4 SD on non-brain size differences (aka brain algorithms) with respect to research tasks (putting some weight on language specialization, accounting for orca specialization, etc.), for an overall estimate of −2.8 SD. This doesn’t feel crazy to me?
Where does this −4 SD come from? My guess is that the human-chimp gap in non-brain size improvements is around 2.2 SD[1] and the chimp-orca (non-brain size) gap is probably similar, maybe a bit smaller, let’s say 1.8 SD. So, this yields −4 SD.
I think my 95% confidence internal for the orca algorithmic advantage (on research) is like −8 SD to −1 SD with a roughly normal distribution. (I could be argued into having a substantially lower value for the bottom of the confidence internval; −12 SD doesn’t seem too crazy.)
To get a interval for IQ vs brain size effect, let’s do a very charitable estimate and then use this as a 95th percentile. The maximally charitable estimate would be something like:
Assume the correlation is more like 0.4 and is fully causal.
Assume standard deviation of 8% so 2x is 9 SDs.
This yields 3.6 SD of IQ per doubling.
Using this as a 95th percentile and 1.2 as my median, my 95% confidence internal is like 0.4 to 3.6 SDs per 2xing (putting aside the probability of this whole model being confused). Let’s say this is distributed lognormally.
Now, let’s say 95% interval on ocra brain size as 1.5 to 2.5. (With a log normal distribution.)
This yields ~5% chance of orcas being over 4SDs above humans. And ~10% chance of >2SDs. (See the notebook here.) After updating on our observations (humans appear to be running an intelligent civilization and orcas don’t seem that smart), I update down by maybe 5x on both of these estimates to 1% chance of >4SDs and 2% chance of >2SDs.
Correspondingly, I’m not very optimistic about the prospects here.
I think the chimp vs human gap is probably roughly half brain size and half other (algorithmic) improvements. The brain size gap is 3.5x or 2.2 SD (using 1.2 SD / doubling). So, if the gap is half brain size and half other (algorithmic) improvements, then we’d get 2.2 SD of algorithmic improvement.
Thanks for describing a wonderfully concrete model.
I like that way you reason (especially the squiggle), but I don’t think it works quite that well for this case. But let’s first assume it does:
Your estimamtes on algorithmic efficiency deficits of orca brains seem roughly reasonable to me. (EDIT: I’d actually be at more like −3.5std mean with standard deviation of 2std, but idk.)
Number cortical neurons != brain size. Orcas have ~2x the number of cortical neurons, but much larger brains. Assuming brain weight is proportional to volume, with human brains being typically 1.2-1.4kg, and orca brains being typically 5.4-6.8kg, orca brains are actually like 6.1/1.3=4.7 times larger than human brains.
Taking the 5.4-6.8kg range, this would be 4.15-5.23 range of how much larger orca brains are. Plugging that in for `orca_brain_size_difference` yields 45% on >=2std, and 38% on >=4std (where your values ) and 19.4% on >=6std.
Updating down by 5x because orcas don’t seem that smart doesn’t seem like quite the right method to adjust the estimate, but perhaps fine enough for the upper end estimates, which would leave 3.9% on >=6std.
Maybe you meant “brain size” as only an approximation to “number of cortical neurons”, which you think are the relevant part. My guess is that neuron density is actually somewhat anti-correlated with brain size, and that number of cortical neurons would be correlated with IQ rather at ~0.4-0.55 in humans, though i haven’t checked whether there’s data on this. And ofc using that you get lower estimates for orca intelligence than in my calculation above. (And while I’d admit that number of neurons is a particularly important point of estimation, there might also be other advantages of having a bigger brain like more glia cells. Though maybe higher neuron density also means higher firing rates and thereby more computation. I guess if you want to try it that way going by number of neurons is fine.)
My main point is however, that brain size (or cortical neuron count) effect on IQ within one species doesn’t generalize to brain size effect between species. Here’s why:
Let’s say having mutations for larger brains is beneficial for intelligence.[1]
On my view, a brain isn’t just some neural tissue randomly smished together, but has a lot of hyperparameters that have to be tuned so the different parts work well together.
Evolution basically tuned those hyperparameters for the median human (per gender).
When you now get a lot of mutations that increase brain size, while this contributes to smartness, this also pulls you away from the species median, so the hyperparameters are likely to become less well tuned, resulting in a countereffect that also makes you dumber in some ways.
So when you get a larger brain as a human, this has a lower positive effect on intelligence, than when your species equilibriates on having a larger brain.
Thus, I don’t think within species intelligence variation can be extended well to inter-species intelligence variation.
As for how to then properly estimate orca intelligence: I don’t know.
(As it happens, I thought of something and learned something yesterday that makes me significantly more pessimistic about orcas being that smart. Still need to consider though. May post them soon.)
I initially started this section with the following, but I cut it out because it’s not actually that relevant: “How intelligent you are mostly depends on how many deleterious mutations you have that move you away from your species average and thereby make you dumber. You’re mostly not smart because you have some very rare good genes, but because you have fewer bad ones.
Mutations for increasing sizes of brain regions might be an exception, because there intelligence trades off against childbirth mortality, so higher intelligence here might mean lower genetic fitness.”
I think cortical neurons is a better proxy than brain size and I expect that the relation between cortical neurons and brain size differs substantially between species. (I expect more similarity within a species.)
This might be true in mammals (and/or birds) overall, but I’m kinda skeptical this is a big effect within humans. Like I’d guess that regression slope between brain size and cortical neurons is ~1 in humans rather than substantially less than 1.
I agree you’ll probably see a bigger correlation with cortical neurons (if you can measure this precisely enough!). I wouldn’t guess much more though?
Overall, I’m somewhat sympathetic to your arguments that we should expect that multiplying cortical neurons by X is a bigger effect than multiplying brain size by X. Maybe this moves my estimate of SDs / doubling of cortical neurons up by 1.5x to more like 1.8 SD / doubling. I don’t think this makes a huge difference to the bottom line.
Yeah I think I came to agree with you. I’m still a bit confused though because intuitively I’d guess chimps are dumber than −4.4SD (in the interpretation for “-4.4SD” I described in my other new comment).
Actually maybe the effect I am describing is relatively small as long as the variation in brain size is within 2 SDs or so, which is where most of the data pinning down the 0.3 correlation comes from.
So yeah it’s plausible to me that your method of estimating is ok.
Intuitively I had thought that chimps are just much dumber than humans. And sure if you take −4SD humans they aren’t really able to do anything, but they don’t really count.
I thought it’s sorta in this direction but not quite as extreme:
(This picture is actually silly because the distance to “Mouse” should be even much bigger. The point is that chimps might be far outside the human distribution.)
But perhaps chimps are actually closer to humans than I thought.
(When I in the following compare different species with standard deviations, I don’t actually mean standard deviations, but more like “how many times the difference between a +0SD and a +1SD human”, since extremely high and very low standard deviation measures mostly cease to me meaningful for what was actually supposed to be measured.)
I still think −4.4SD is overestimating chimp intelligence. I don’t know enough about chimps, but I guess they might be somewhere between −12SD and −6SD (compared to my previous intuition, which might’ve been more like −20SD). And yes, considering that the gap in cortical neuron count between chimps and humans is like 3.5x, and it’s even larger for the prefrontal cortex, and that algorithmic efficiency is probably “orca < chimp < human”, then +6SDs for orcas seem a lot less likely than I initially intuitively thought, though orcas would still likely be a bit smarter than humans (on the way my priors would fall out (not really after updating on observations about orcas)).