[justinpombrio]

Do you agree that the probability of an event depends on your knowledge? For example, what is the probability that the bottom card of a shuffled deck is an ace? Peek at the top card, it's an ace of spades, now what is the probability?

Would you agree that something is determined iff its probability is zero or one? I'm guessing the disagreement is here - what definition would you use?

[jamesrcole]

There's two kinds of probability in question.

One concerns a lack of knowledge, like in your cards example. In that case, the probability is an expression of your state of understanding of the deck, and is not a property of the deck itself. The physical details of the deck and the situation it is part of could be entirely deterministic and we could still talk about this kind of probability. In this case your knowledge is independent of whether it is probabalistic or not.

The other is whether the universe contains fundamental randomness, such that you could say it is literally "probabalistic". And in this case whether that is true or not is independent of our knowledge of the probabilities.

[justinpombrio]

There's a third kind -- indexical randomness, or not knowing who you will be -- that appears in many-worlds. Many worlds is in some sense completely deterministic. Yet with indexical uncertainty you still cannot possibly ever know which way you will see a photon go in a half-silvered mirror. Is that fundamental randomness or not?

http://lesswrong.com/lw/jlb/logical_and_indexical_uncertaint...

[jamesrcole]

> Is that fundamental randomness or not?

I would say, not. There's no actual randomness from an objective point of view, it's just a lacking in your understanding of things.

I think that map/territory confusions are the source of so many problems and should be rigourously avoided. I think it would be a map/territory confusion to consider it a kind of actual randomness.

[justinpombrio]

> I think it would be a map/territory confusion to consider it a kind of actual randomness.

Even though it makes perfect sense to apply probability theory to it? We found a perfect coin, one that we know that you can't predict in advance even in principle, and you want to avoid considering it a kind of randomness? Why does the mechanism by which the universe implements randomness -- in this case via determinism -- matter?

[jamesrcole]

The many worlds case I was responding to is different to the coin case you are taking about. In the MW case we know enough to see that the situation is not at all random. In your example you're postulating a coin that may well actually be random.

[matt_kantor]

I don't understand what you mean here. I think "the many worlds case I was responding to" in your comment is justinpombrio's "which way you will see a photon go in a half-silvered mirror", but that's functionally identical to the "indexical coin flip" referred to by the LessWrong article, where the coin flip causes a bifurcation, landing heads in universe A and tails in universe B. From within the multiverse it is impossible to know ahead of time which universe you will observe, same as the photon example. It's "random" in the sense of being absolutely unpredictable (otherwise MWI would not be experimentally equivalent to alternative interpretations of quantum physics).

So, does indexical randomness fit your definition of "fundamental" randomness? And what did you mean when you said "a coin that may well actually be random" if it wasn't the indexical kind of coin?

[justinpombrio]

By "a prefect coin", I was referring to a half silvered mirror.

[Qwertious]

Or to give a slightly better example, suppose you're playing russian roulette with a six-shot revolver. You empty the revolver of bullets, then put one bullet in, spin the barrel, point it at your head and fire.

What is the chance that you're shot? Is it 1/6? What about if you open it up and look in the barrel to see if there's a bullet there?

[jamesrcole]

Nothing about the location of the bullet has changed.

Are you suggesting this example somehow shows that changing knowledge/probabilities determine whether what's going on there is deterministic or not, as is the issue under discussion?

[cool_shit]

You are right, according to quantum mechanics. If you have a pair of electrons in a product state and measure the spin of one of them, you instantly know what the "other particle's" spin is going to be (if you knew what the initial state was). When you "peek at a card", you "make a measurement" and alter the system.

For anything that exists outside of a light-cone around the first electron, a measurement of the second electron will be truly random from the measurer's perspective.