> i.e. there isn't a school with 1,000,000 students and many small ones with 10 students each, and, even if that were the case, if all of the small 10-student schools make up for 10,000,000 students, the probability of an individual coming from the "big one" is only 10%. Come on, this is common sense.

Not sure if it's common sense, but you are right, it is basic probability theory...if you assume that you are randomly distributed over those 11 million total students. But that if fundamentally is NOT a scientific IF, it's a philosophical one, in fact it's a unstated philosophical axiom that underlies tons of lines of reasoning on this subject.

What if we are not randomly distributed amongst possible universes? After all, we are not even randomly distributed amongst all humans who have ever lived (100+ billion)--by definition we are only amongst survivors in the present. Cue the anthropic principle, which mops half of these stupid probability theories right out the door. We a.) have survivorship bias and b.) live in a universe that must, no matter how improbable the chain of events that leads up to this present moment, have been capable of and, indeed, did produce this present moment. Considering that our past is littered with extremely improbable survival events, that means we should not really expect that other places in the universe aren't full of stupidly improbable things too.

What I am saying is that I actually do not believe we live in an average universe. In fact, we can't, because in most, we are dead!

I also don't believe that we're randomly distributed over possible intelligent beings, because why aren't we Boltzman brains?

> We a.) have survivorship bias and b.) live in a universe that must, ...

unless we are boltzmann brains.

Hah, fine. But we're Boltzmann brains that believe we evolved from apes on Earth. That's gotta be less probable than regular Boltzmann brains.

Yeah, trying to infer probabilities from a dataset with one sample point is strange. (Especially when all our priors are from philosophical axioms and not observation.)

> For instance: "you are more likely to have attended a school with more pupils than most other schools"

Isn't this statement still true in your example? (Assuming some small variance among the small schools just so it's still possible to order them by size.)

If one school has 1,000,000 students and a million schools had about 9 to 11 students, the median school would have about 10 students. No matter what (ignoring exact ties), 500,000 schools are going have more students than the median school, even if most of those schools just have 10 or 11 students. Sure, most people in your example come from the ~10 person schools, but more students come from the more populated half of those ~10 person schools. There's at least a 54% chance that you "attended a school with more pupils than most other schools" (6 of 11 million students).

(It's fair to ignore exact ties because it's unlikely that many planets have the exact same population.)

Your distribution makes it likely that there is one school with a much larger population than your own, but not that most schools have a larger population.

Yes, but there is no way you can conclude "the typical student should come from school X" from that, which is the main issue with the author's argumentation.

I think the author is saying that if there's no variance (e.g. all schools have 10 students), then our school is as big as all the other schools, and as you increase the variance, the odds of you being in a larger than average school increases. But no matter the distribution, we're never most likely to be in a smaller than average school.

You cut out the context in some of your quotes that makes this clearer. The article says

> imagine that planet populations are distributed in the same pattern as countries on Earth ... in that case, most planets will have a very much smaller population

They're saying, for purposes of illustration, imagine planet populations were distributed like countries on Earth. But that's not the distribution they use in their actual calculation. It's just to help explain.

Precisely. I'm glad you took the time to understand. :)

You put this brilliantly. Especially the last bit about credentials, what a silly, silly person.

This is the "About the author" section that would be hidden behind a click on other websites but all content on the submitted page is on a single page. Where should it have gone instead?

The last part about his titles is sad. It is like preemptively saying "buuut PhD!" when people will point the mess in his math.

I replied the same to a sibling comment already but all the content on this website is on a single page - where should the author have put the "About me" section instead if not at the end?

Try to apply a set of constraints to a problem to reduce the possible set of results is a good thing, provided the constraints are extensive. Two things are universal in the, erm, universe, physics, and by extension chemistry and I don't see any consideration of those.

There's many reasons why the Earth is in the Goldilocks zone. It's just the right temperature for liquid water, we have oxygen in the atmosphere, and the planet doesn't weigh too much.

Without oxygen, creating mechanical work from fuel by burning, is 'tricky' (though maybe not impossible), no mechanical work, no industrial revolution, no technology. There's an argument that cooking food (fire) leads to better diet, more calories, and the evolution of the brain.

Whilst there are types of alternative biochemistry (https://en.wikipedia.org/wiki/Hypothetical_types_of_biochemi...) carbon is by far the most likely.

And lastly, if the earth were slightly more massive, the mass of (chemical) fuel required to propel a rocket becomes too much.

I'm doubtful that we'd see biological 'big aliens', or even 'small aliens', that significantly differ from our size, if they exist.