Multiverse theory and the two die allegory

In my last post, I described an allegory I'd created that illustrates why life on Earth, even if it is extremely unlikely, does not serve as evidence that God exists. (I emphasize "if" because there is actually no empirical data I know of that has established this probability.)

The same allegory can be used to understand a thought experiment which is one of my favorites. I forget where I read it and who it's by, but it serves as a proof of multiverse theory. That's the theory that says that there are infinite parallel universes. At each moment, every decision or random act that's possible happens in one of those multiple universes.

So, here's the thought experiment: Find a reliable pistol, load it, put it to your head, and pull the trigger. There is a high probability that you'll have just killed yourself, but a small probability that the gun will fail. Repeat this several times. For good measure, after you've pulled the trigger a few times, fire it at the wall to make sure that the gun really works; then put it to your head and pull the trigger a few more times.

If the multiverse theory is wrong, you're almost definitely going to die. In fact, you probably died at the first pull of the trigger.

But if multiverse theory is right, then at every pull of the trigger, you die in the vast majority of universes — but live in the very few in which the gun failed. "Very few" of infinity is infinity, so you're still alive in infinite universes. Moreover, you only go on testing out the experiment and analyzing its results in those [rare] universes in which you're alive. (That's where the evolution allegory comes in.)

The result is that, if you're still alive after having tried to kill yourself a couple hundred times, you can be relatively sure that multiverse theory is correct. You'd have a very, very small chance of being alive if it's not correct, but a 100% chance of being alive if it is.

The kicker, of course, is that you can't communicate with any of the other parallel universes. So while you can be fairly sure that multiverse theory is right, that information doesn't help the versions of you that are dead. Also, since outside observers haven't eliminated all versions of themselves in which you're dead, they won't be able to share your knowledge: even if multiverse theory is right, the chance that an outside observer is in the right universe to see you alive is the same as the chance that the gun has failed. So even if they do see you live, there's no way for them to know if that's because multiverse theory is right or if you're just very, very lucky.

Needless to say, for both your sake if multiverse theory is wrong and for your loved ones' sakes even if it's right, I highly recommend not trying this out.

Math puzzle: which station? (part 1)

Whoops, looks like I missed this week's regularly scheduled posting. It's late now and I don't feel like typing anything too involved, so here's a neat little math question I've been wondering about.

Environmentalist that I am (or "greentard," as my girlfriend likes to call me¹), I like to take the T to work as often as I can. My 90-minute trek starts with a walk to the red line, which I take in to Park Street.² There are two T stops, Porter and Davis, roughly equidistant from my house; the train going my direction hits Davis first, then Porter. The question is: does it matter which I take?

Here's my thinking. On the one hand, trains run through each station at the same pace, so it shouldn't matter where I wait. If I have to wait an average of X minutes at Porter, I should have to wait the same X minutes, on average, at Davis.

On the other hand, let's imagine that I walk to Davis and get there just in time to see the train pulling out; I missed it by 30 seconds. It takes a minute or two for the train to get to Porter, so if I'd instead gone to that station, I'd get there just before the train; perfect timing!

My hypothesis is that if my schedule and the trains' schedules were completely random, everything would even out and it wouldn't matter which station I went to. But neither one of them is totally random; the trains are relatively regular (every 7 or 8 minutes), and so am I (I try to leave around 7:45 am). If I assume that my time is somewhat synchronized with the trains' — with some randomization, since neither of us are flawless — I bet Porter is the better station. My time cost for being a bit ahead of the train isn't high (30 seconds or a minute), but if I'm a bit behind, I'll catch a train at Porter that I'd miss at Davis.

I'll run some simulations; stay tuned for the results next week.

Apologies if this post is badly written; the timestamp is my excuse.

[1] She stole this term shamelessly from Fake Steve Jobs.
[2] Sic. Remind me to write about my conundrum regarding "in to" and "into" soon.

Shavitian subprime numbers

In honor of the fact that I'm a bit of a nerd, here's interesting class of numbers I discovered: Shavitian subprime numbers. A number is a Shavitian subprime if it's prime, and every number within it is prime. For instance, for the number 1,234 to be a Shavitian subprime, the following numbers would all have to be prime: 1, 2, 3, 4, 12, 23, 34, 123, 234, 1234.

If you're still reading, you probably have too much time on your hands. As a reward, I'll let you in on a little secret: there's only nine such numbers in all of existence: 2, 3, 5, 7, 23, 37, 53, 73 and 373.

Intrigued? You can read more (including as close to a formal proof as I could come up with) on my GooglePages page on Shavitian subprime numbers. That's not meant as linkbait -- I just don't want to bore you with a big ol' copy-paste.