What’s your favorite number? I think that can say a lot about a person. Personally, my favorite natural number is 7, because it’s somehow inherently funny, don’t you think? Whenever someone asks me a question that requires a numerical answer- anything from “how many of those did you eat?” to “how many stars are in the sky?”, before I actually answer, I say “seven.” It’s just a fun, random number! I wonder why that is. Some of it is that it is the first two-syllable number, I think. Also, it’s prime, so you can’t split it down into smaller, equal groups to picture it. I can easily, instantly picture six, because it’s two threes, and I can instantly picture eight because it’s two fours, but I struggle a tad with seven. There’s seven pennies. See what I mean?

My favorite irrational number is tau. Tau is equal to two times pi, and some mathematicians think we should use it instead of pi, because most equations that have pi in them at all, have two pi. When you have ‘tau times the radius’ instead of ‘pi times two times the radius’, it makes the equation for circumference much cleaner and more beautiful.

My favorite not-really-a-number-but-pretty-close concept is countable infinity. I feel like I relate to it because yeah, it’s infinity, but it’s the smallest infinity. If countable infinity was a person, I bet they’d have an inferiority complex.

Really, though, lots of numbers are interesting for all different reasons. 42, 69, and 101 are interesting for cultural reasons. Graham’s number, googol, and Avogadro’s constant are interesting for math-related reasons. 13.8 billion, 7.4 billion, and 9.8 are interesting for what they represent in the physical world. This can make you wonder- are there any uninteresting numbers?

Before we get into the paradox, let’s try an experiment. Right now, go to a random number generator, get a number, then tell me in comments if you can find anything interesting about it. I just tried this, and I got 385. Google informed me that 385 is the area code for Salt Lake City, which is interesting to me because I have a good friend who lives there. I checked, and sure enough, her phone number starts with 385.

Ok, paradox time. If you tried to split numbers into two groups- interesting and boring, then the smallest or first number to be boring would be interesting, because it was the first! Then that number, whatever it was, would be moved to the interesting category, and the next boring number would be the real first one… but wait, isn’t that interesting, too? This is one reason that you can’t group numbers into interesting and boring. Another reason is our world is just too big. People have come up with too many sequences, and done too many things. Even if you find a number you find uninteresting mathematically, that number is probably the number of stars in an interesting galaxy, or atoms in an interesting object. It would be very interesting if you had a number that was only interesting because of this paradox!

Advertisements