I just started a new job, in the 14^{th} floor of a building. As you know, buildings skip the number 13 when they number their floors because it’s unlucky. But it just got me thinking. As a mathematician, you’d think we’d be above number superstition. But we actually get that much worse about it.

Namely, in this case, is my floor still unlucky since it’s really the 13^{th} floor?

But it gets that much worse. Here’s some other neuroses that come out: is 13 only unlucky in the realm of integers? Or does it apply to real numbers too?

If it applies to real numbers too, what’s the range of real number that are unlucky? Anything that rounds to 13, meaning anything from 12.5 to 13.49? Is it precisely 13 on the dot that’s unlucky? Is there an envelope where things get more unlucky the closer numbers get to 13?

In the realm of integers, is it only the number 13 that’s unlucky? Is 1300 unlucky? 13,000? Are only powers of 10 unlucky, or any number with a factor of 13?

What about a number with a 13 in it? Say, 2134… is that unlucky? Should we avoid following any 1 with a 3 in that case?

But you see, there is method to this madness. Because it begs the question of the character of numbers. And that’s ultimately why we got into mathematics in the first place. Even when talking about something as fickle as luck (or lack thereof), it’s a great thought experiment.

See, numbers have character. Indeed they are a reflection of existence itself, which breaks down into quanta. And when you discuss numbers like this, you discuss existence. Indeed when you get into advanced mathematics you find out that the biggest figment of our imagination is the set of real numbers. They exist only to describe abstract things where we have no idea what’s actually going on.

Oh and for the record, the answers are: Yes, applies to reals, no, no, yes, no, yes, yes, only powers of 10 (or 101, 1001, etc in diminishing amounts), no, no.