[ldb]

I am not a mathematician either and only read the “Quick Intro” but that left me with the following question: What happens if I replace the Earth’s populations with that of France and the Earth’s countries with the French cities? If I do that and then follow the logic in the Quick Intro then it makes sense to me that it is likely that I would be born in Paris, but I do not understand how I can follow from this that France is a high population country. What do I miss?

[nearbuy]

Incidentally, France is a pretty high population country. It's ranked 22 out of 195 in population.

If you chose Iceland and used this logic to conclude you're in a high pop country, you'd be wrong. But of course, most people don't live in Iceland. You probably don't live in Iceland. If you pick a random person on Earth, odds are very good that they live in a high pop country like France, the US, China, India, etc.

If you pick a random country, there's a 50% chance you'll pick a country with a lower population than the median country. But not if you pick a random human from Earth.

[ldb]

Yes, I do understand that. So there is a certain probability that my “i am a high population country” conclusion is wrong (e.g. if I am from Iceland). As already asked below: Do you know a way to quantify the likelihood of me making the wrong conclusion (without knowing the population numbers of the other countries)?

[nearbuy]

The author of the article makes some assumption about the distribution of alien animal sizes to come up with their estimate. But they use loose bounds, saying intelligent life can probably vary in size at least as much as the great apes (50kg - 160kg), but probably not to tens of millions of kilograms.

So it seems you need at least some guess of what the distribution might look like to quantify the likelihood of guessing correctly that you're in a high population country. But your guessed distribution doesn't have to be perfect. If you knew the exact distribution, you could compute the exact chance that a random individual is from a high pop country (just take the integral of the distribution). But if you don't know the exact distribution, you can abstract one level up, try to reason about the range of possible distributions there could be, and come up with a probability based on your more limited knowledge. At least, that's what I understood from the article.

For the actual calculations, the author links to them in the article, but I haven't looked at them myself.

[simiones]

There is no way to do it from statistics alone, which is why the whole argument is useless.

Instead, the whole thing depends critically on other arguments about the possible distributions, which are much weaker and than the initial ironclad statistical argument.

[srcreigh]

You would be wrong, but lots and lots of people following the same logic from China, India, USA would be right.

[notahacker]

I think the main problem is piling up the estimates. If I use anthropic reasoning to conclude that I am from an extremely populous country like India, I am wrong, but 2 billion Chinese and Indian people would be right, and the majority of people making the estimation would in fact be from larger than average countries

But if someone starts drawing conclusions like "due to the correlation between population size and landmass, it is therefore unlikely any country is more than 20% larger than mine", there is a 98% chance they are not Russian and therefore incorrect (and there is a 100% chance that their country is dwarfed by either population or landmass by some other country). The probability of them being the largest country is roughly the same as the probability of them being from a small island group like the UK or Japan

If the principle falls apart when applied to the human populations whose population density relationships its estimated from, how can we assert 95% certainty that the circumference of planets supporting very different civilisations will be no more than 20% greater than Earth?

[brabel]

> "due to the correlation between population size and landmass, it is therefore unlikely any country is more than 20% larger than mine" there is a 98% chance they are not Russian and therefore incorrect

Your mistake was to stop using statistics to refer to groups forming a distribution, and referring to ONE particular country, Russia.

The argument only works when you keep things in the realm of statistical distributions. An argument that works should be:

"due to the correlation between population size and landmass, it is unlikely most other countries are more than 20% larger than mine".

You would be right almost every time! Yes, it's a weaker argument but still extremely interesting.

[notahacker]

It's a weaker and more plausible claim, but it's also a different claim from the one advanced by the author "we can say with 95% confidence that another planet with intelligent life, such as our nearest neighbour, will have a circumference no more than 20% greater than that of the Earth".

As far as I can see we can't even predict that for distributions of individuals on earth (the article suggests the median human lives in a country as populous as Pakistan; a random other human has an 18% chance of being Chinese which is quite a bit more than 10x the size of Pakistan by landmass) and that's long before we add ancillary assumptions like alien species' size distribution matching earth's and their tolerance for population density being no greater than mean human population density (which requires them to be less tolerant of dense populations than many self-sufficient human regions!)

[brabel]

The correct claim should be:

"we can say with 95% confidence that another planet with intelligent life will have a circumference no more than 20% greater than that of the Earth".

The author shouldn't have added "such as our nearest neighbour" as that just adds confusion.

The fact that this prediction is not 100% accurate when considering Earth's countries does not invalidate the argument. I see a lot of people doing this: showing one practical example where it doesn't work and calling it BS.

Please try to do as the author suggested: plot your own data against many world statistics... you will see that while yes, some of those statistics fail for you (e.g. you might be 90% taller than everyone else) when taken all together, they should all indicate you're pretty close to the middle in the majority of them... and knowing this, hopefully you can see how, yes, this prediction by the author might be BS, but given what we know, it's the only prediction we can make which has a good chance of being true.

[notahacker]

> The fact that this prediction is not 100% accurate when considering Earth's countries does not invalidate the argument.

I mean, it does , because he's moved from making general applications of the anthropic principle to very explicit claims about confidence intervals, relationships between variables and shapes of the distributions which don't match even the figures for the part of reality that actually is observable. I'm not just saying "but there are exceptions". I'm saying "given actual human population/landmass distributions, it appears obviously wrong to say that a random person has a 95% probability of living in a country no more than 20% larger than the home country of a randomly selected person from another country, and so a claim the confidence interval is that narrow for planets and alien species is quite extraordinary"

(it's moot that much of my own data also works pretty badly for anthropic reasoning, and I'm almost convinced that the applicable version of the anthropic principle for some of those stats is "if an individual is willing and able to make observations about the anthropic principle, the probability they are exposed to Western culture and in the top decile for access to education, cash and free time is ~1" :-) )

[ldb]

Thanks, that makes sense. Do you know if there is any "mathematical trick" to quantify the likelihood of me being wrong (without knowing the population numbers of the other countries)?