Particle/Wave

At the end of my previous post, I made a claim that was simply outrageous:

I invented the question mark.

No, wait...that wasn't me. This was me:

The longer you flip a fair coin, the closer it runs to 50% heads, 50% tails. And you still don't know a goddamn thing about what the next flip is going to be.

Calvino: My god, do I still exist? I hadn't heard from me in months. I thought I had been replaced.

The Stoat: Yet here you are. And I too. I suspect this happens every time the author is about to propose something radical, and it's just been that long since he's done so.

Calvino: Interesting theory. And indeed, suggesting that one knows nothing about the result of the next flip of a fair coin seems pretty radical. And also demonstrably false. You know 50% of the time it will come up heads, and 50% of the time it will come up tails. That's not nothing.

The Stoat: Well, he could merely have been talking about the fact that a million coin flips don't give you any new information about what the next flip is going to be. That is, he could be talking about the well-discussed fallacy that if you flip heads a hundred times in a row, the odds of flipping heads again are....

Calvino: 50/50. And not 1 in 2¹⁰¹. Yes, I know. I believe that the author might point out that this is a problem of language, not probability. Anyway, he didn't say that. He said you know nothing about the next flip.

The Stoat: Yes, and I'm going to propose that it's entirely possible that he indeed believes one knows nothing, that the appearance that one can make a discrete inference about this next flip being heads or landing tails is entirely illusory, and that there exists a more illuminating model. I'm also going to propose that he hasn't entirely formalized this theory, and that perhaps someone has goaded him into presenting this theory now, before it's been formalized, in the name of radicalism.

Calvino: I am bored by your propositions. I want to know why I can't say the next coin flip is going to be heads half the time and tails the other half.

The Stoat: Yes, I suspected that you might.

Coin flips are just about the perfect probabilistic event. A flip could result in the coin falling off the table and getting lost and thus you'll never know what the result was, or it could land perfectly on its side because it's 1961 and you work in a bank and suddenly can hear everybody thinking because you're the guy in that one episode of The Twilight Zone. But you can pretty much just throw those results out--any sane person would aver that if you flip a coin, 50% of the time it'll land heads and 50% of the time it'll land tails.

Go through this thought experiment with me: you've flipped the coin--it's turning over and over in the air, and now it's at it's peak before it starts coming down. Let's stop time and ask a few questions.

The Stoat: Is the outcome of the flip now pre-determined? That is, if time continues from this point on, would the outcome always be tails?

Calvino: My first impulse is to say yes, and in fact to claim that the outcome was fixed as soon as you gave the coin an initial upward velocity and spin with your thumb. But on second thought, we know thanks to 20th century physics that we don't live in a deterministic universe--the Heisenberg Uncertainty Principle and all that. More concretely, I guess that you could reasonably predict that in some universes the atmospheric pressure where the coin is falling will change slightly just before the coin hits the table, such that it bounces funny and lands on a different side than it otherwise would have.

The Stoat: Yes, I agree. By the way, don't you think "Heisenberg Certainty Principle" is a totally awesome name for a rock band?

Calvino: Yes?

The Stoat: I'm just saying, if you go and start, like, a math rock band and name it that, you have to give me credit for having thought up the name.

Calvino: Yeah...sure, whatever. We were talking about probability?

The Stoat: Yes, sorry. Look, before we go any farther--well, you just mentioned above the idea that "in some universes things change and the coin flip comes out differently." It's a nice way to talk about the possibility that the coin can end up heads or end up tails, and I'm now going to take it away from you. The idea of many universes, splitting off from this one is crap, and I will now debunk it.

Calvino: Just like that? A model favored by many famous Physicists who are incredibly much smarter than you? I suppose also you are also going to explain away wave-particle duality at the same time?

The Stoat: Well, yes, I will. But not yet. One coin flip vis a vis many coin flips is in fact an excellent metaphor for particle and wave. But I'll get to that. Firstly, the many worlds interpretation of events states that where you have a quantum event (an atom of carbon, e.g., which will either decay or not decay in a particular time period), that two deterministic universes are created--one in which the particle decayed and one in which the particle did not decay. We also know, in fact, that you don't know in which of these universes you live unless you actually go and measure that particular carbon atom and see if it decayed.

Calvino: You are talking about the collapse of the Schrödinger Wave Function--that a particle actually doesn't have one state or the other until it is observed.

The Stoat: Yes--the many universes theory explains this by saying, no, it did have one state or the other, the universe split into two realities at the moment of the quantum event and you-the-observer landed in one or the other. My objection is this: can you imagine how much memory it would take to run the universe if near-infinite numbers of splits of reality are happening at every instant? Even if most of those universes eventually peter out into non-existence, you're still splitt ing off unimaginable numbers of copies.

Calvino: What, we're in the Matrix? The universe is a computer simulation?

The Stoat: I'm not claiming that, what I'm making is an argument using Ockham's Razor. Which is more likely: a universe that has a nearly infinite number of states, with more states splitting off every instant (many universes), or a universe that is kind of "fuzzy", where there's no fixed reality unless you force there to be one by making an observation (that is, via the collapse of a wave functions)? From a strictly design point of view, the second is utterly less complex to manage. Not only do you not have to keep track of the states of all possible universes, you don't even have to have to keep track of the state of the one--only when somebody's looking do you have to decide whether, e.g., the carbon atom decayed or not, or the coin flip came up heads or tails.

Calvino: Either you're insane or I'm totally lost.

Moderator: ...

Calvino: There's a moderator?

Moderator: Yes, and I'm going to end the discussion here for today, as the author is violating all reasonable laws of blogging by going on endlessly. We'll pick it up here tomorrow.
Tags: Probability,Statistics,Humor