For a three particle configuration space, you could imagine tagging each of the three particles as "particle A", "particle B" and "particle C". So for a classical configuration with a particle at each of the positions X, Y and Z, you would have six ways of assigning the particles to the positions -- if we represent them as (particle at X, particle at Y, particle at Z), we've got (A, B, C), (A, C, B), (B, A, C), (B, C, A), (C, A, B), (C, B, A). In general, for n particles, the number of ways is just the factorial n! (the number of permutations of n elements), which you may have guessed by now.

But of course in quantum configuration space there's only one way of having "particles at X, Y and Z", so we cut down the space by 1/(n!).

This series is great. But, I'm having a little trouble understanding the fourth diagram, the one with the folded configuration space.

I sort of get it: the original configuration space distinguished between two particles, which is wrong, so in reality only half of the configuration space's area matters when it comes to information. But I don't get how that means you delete the probability from half of the space. Why is it wrong to make the space symmetrical across the diagonal line? It seems a little arbitrary to me; is there a physical reason, or is this a standard thing to do?

Also, I don't get why "this identity cuts down the size of a 2-particle configuration space by 1/2, cuts down the size of a 3-particle configuration space by 1/6, and so on." What's the relationship from 1/2 to 1/6? What comes after that? Why isn't it 1/2 to 1/4 to 1/8?

It's a shame that I'm not in Phoenix at this time. Maybe in the summer I'll be able to. Anyways, good luck!

Update: Added about 10 more direct PDF links to the original article.

It might also make sense to raise the question as a new topic in the discussion section.

I think it's the way to bet that if you're confused by something here (especially if it's at all technical or about using the site), you aren't the only one.

Hello. Please call me Paul Watcher. Watcher is not my real name, but I do know someone named Watcher, and it is what I've been doing. I'm a medical student.

I've recently finished all the sequences (except the luminosity one still), and my head still hurts. I'm really happy I found them, though. It was painful, but I call myself better now.

I'm now relearning as much as I can. I'm trying to use divia's Anki deck to memorize the sequences: basic things worth memorizing. I still have yet to actually understand lot of what I read here, so I hope that helps.

I registered because I'm still confused about some things, which I hope will get answered in whatever general discussion thread I post them in. I don't really anticipate participating much more (though I'm not too confident on that).

Nevertheless, I am pleased to meet you all.

Edit: I have a question. Let's say that I'm confused about something in, say, Conservation of Expected Evidence. Should I ask my questions on it in comments of the article itself, or in the open thread of this month, or somewhere else?