Scenario A: You’re transported to another world. Based off some quick calculations/experiments you perform (you’re lucky you had a near magically powerful laser and telescope on you, plus your pockit), it seems to be roughly similair to earth in geological features. You then come across what looks like a building, human sized. Outside are a giant (3.5 m tall) and a humanoid (around 1.5 m tall). Shape wise, they’re similair, but they’re covered up. What’s the probability that they’re off the same race, and their species is not significantly polymorphic? How’d you update your evidence on seeing a bunch more of each size wandering around the forest?
One of the things probability-sight tells me is how constraining my models are. One of the benefits of learning more fields is being able to extract sharper likelihood ratios from the same evidence. Here, my likelihood ratios are pretty unsharp. And also, I can feel I’m entering an unrefined conditional distribution of my beliefs, where conditioning on world transport and also earth-similarity produces something pretty strange.
My gut tells me that such large variation in size is rare. And I have cached thoughts about the stress which extreme height places on bones?
However, what are the alternatives? The probability of convergently evolving the same shape in parallel is small. If they could genetically modify themselves or even just customize their morphology using more exotic tech, it seems even less likely that they would stick to two morphologies (which I see wandering around the forest). (I’ve recently updated my thinking on how evolved advanced minds generally will work, and that model suggests that their preferences would probably be very compatible with variety, even though they probably aren’t human preferences.)
Of the hypotheses predicting they are of the same species, extreme sexual dimorphism seems to have the highest posterior probability. Something about this seems wrong to me, or rare, which suggests that there’s some gut evidence I haven’t yet consciously incorporated. There are also more conjunctive possibilities like “they have culture and also exotic morphology modification tech but there are ~two acceptable morphologies”, but this basically feels like a garbage just-so story that I’d need way more evidence to properly elevate to attention.
I think maybe if I had sharper models of evolutionary history, I’d see a sharper (perhaps Gaussian) form like you do. My other hypothesis is that this conditional distribution is really weird and I’d be surprised if you could narrow down to that shape so quickly.
Scenario B: You are transported to another world with your technical doodads. Looking around you, you find yourself in a plain stretching as far as the eye can see. You walk around for a couple of days and nothing changes. You’re terrified of vast expanses of water. Unfortunately, you are unmoored from the digital sea and can’t just check how far fast they’re rising, the tidal range or even where they are. What’s the probability that you’re x-meters above sea-level, supposing this planet even has oceans?
(Written before reading your answer) Ah, another area I don’t know much about. Time for more qualitative reasoning. I think that I’m most curious about what is on the plain. Is there life? Presumably since I’m walking for days, there is some level of humidity, which suggests a water cycle, I think? And in that case, there are probably oceans. And if I can eyeball the soil composition, I could estimate the expected last time where a flood / rainfall occurred, and so that will give me some information about the altitude.
I don’t know how altitude affects rain frequency (supposing the atmospheric dynamics are even remotely similar to Earth’s), but under the flooding-is-possible hypotheses, observing “water has not touched this soil in a long time” represents a weak-to-moderate likelihood ratio against close-to-sea-level hypotheses. (With the weak-to-moderate from the unknown variance of sea level and of storms in this part of the world.)
One of the things probability-sight tells me is how constraining my models are. One of the benefits of learning more fields is being able to extract sharper likelihood ratios from the same evidence. Here, my likelihood ratios are pretty unsharp. And also, I can feel I’m entering an unrefined conditional distribution of my beliefs, where conditioning on world transport and also earth-similarity produces something pretty strange.
My gut tells me that such large variation in size is rare. And I have cached thoughts about the stress which extreme height places on bones?
However, what are the alternatives? The probability of convergently evolving the same shape in parallel is small. If they could genetically modify themselves or even just customize their morphology using more exotic tech, it seems even less likely that they would stick to two morphologies (which I see wandering around the forest). (I’ve recently updated my thinking on how evolved advanced minds generally will work, and that model suggests that their preferences would probably be very compatible with variety, even though they probably aren’t human preferences.)
Of the hypotheses predicting they are of the same species, extreme sexual dimorphism seems to have the highest posterior probability. Something about this seems wrong to me, or rare, which suggests that there’s some gut evidence I haven’t yet consciously incorporated. There are also more conjunctive possibilities like “they have culture and also exotic morphology modification tech but there are ~two acceptable morphologies”, but this basically feels like a garbage just-so story that I’d need way more evidence to properly elevate to attention.
I think maybe if I had sharper models of evolutionary history, I’d see a sharper (perhaps Gaussian) form like you do. My other hypothesis is that this conditional distribution is really weird and I’d be surprised if you could narrow down to that shape so quickly.
(Written before reading your answer) Ah, another area I don’t know much about. Time for more qualitative reasoning. I think that I’m most curious about what is on the plain. Is there life? Presumably since I’m walking for days, there is some level of humidity, which suggests a water cycle, I think? And in that case, there are probably oceans. And if I can eyeball the soil composition, I could estimate the expected last time where a flood / rainfall occurred, and so that will give me some information about the altitude.
I don’t know how altitude affects rain frequency (supposing the atmospheric dynamics are even remotely similar to Earth’s), but under the flooding-is-possible hypotheses, observing “water has not touched this soil in a long time” represents a weak-to-moderate likelihood ratio against close-to-sea-level hypotheses. (With the weak-to-moderate from the unknown variance of sea level and of storms in this part of the world.)