I’m not good at math (or maybe I am but never worked at it), I sort of stopped trying somewhere around algebra. But I am good at arithmetic. I can do addition and subtraction, multiplication and division, decimals, fractions, and percentages in my head fairly quickly and accurately. I even enjoy it. When running on the treadmill I would calculate what percentage of my run was complete, or how much of a mile I covered in a minute. This may have come from being a baseball fan (a bit more on that below.) When I was a big fan, back in the dark ages before the Internet, things like slugging percentage and on-base percentage were not in the sports pages or on baseball cards. So I would calculate them myself. Just to be clear, I’m not a savant – I do have to do the calculation – although every once in a while I do “see” a product or quotient.

So I guess I’m saying, I don’t like math, but I like numbers. Sometimes they have a certain feel for me.

In elementary school, as we were getting a feel for all of this, my mind would wander and I would tell myself stories about the numbers. Westerns were still a thing, so in my mind odd numbers were bad guys and evens were good guys. Eight was the town sheriff, a brave capable guy. With his deputy, six, he could handle the local ruffians (threes) and their ringleader (a seven.) But when a gang of bad fives rolled into town led by a fearsome nine – the good sheriff was overmatched. That’s where 10, the big hero, showed up to save the day.

I recently began thinking about the importance of numbers. We tend to see numbers ending in a zero as significant. The tenth, twentieth, and hundredth anniversaries of events are important. Far more so than the 98^th anniversary. Even within that distinction there are gradations of importance. The 70^th anniversary is less significant than the 50^th, for example. Although this is context dependent, for a marriage the 70^th anniversary will be seen as more significant than the 50^th because a 70-year marriage is simply remarkable. This applies in other realms as well, making $100,000 a year or $1,000,000 is seen as a big marker of success. Having $789 million just makes you another rich guy, but having a billion makes you a celebrity. In baseball, there are numbers with real significance – 500 career home runs, 300 career wins, or 3000 career hits. These are all markers of a Hall of Fame career.

Numbers can also be scary – 100,000 Covid deaths was seen as a particular milestone but then we reached the even more terrible 1 million. In the Great Recession, the Obama administration believed that a trillion-dollar stimulus package was simply too much. I just listened to a podcast saying that given that the U.S. economy is over $20 trillion and the global economy is over $100 trillion we need to “get over” this idea that a trillion dollars is simply an inconceivable amount of money.

Earth-8

The importance of these numbers is socially constructed. Imagine that on the exact opposite side of the sun from us is an Earthlike planet, pretty much the same as ours. But the people are like cartoon characters and only have four fingers on each hand. Just as we use base-10, they would use base-8. So their numbers would be 1-7 and then 10, then 77 and 100, and so forth. Their 10 = our 8, their 100 = our 64. So a home run hitter hitting 500 home runs might not be a mark of true greatness, since it’s only 320 homers (which is really good, but still.) They might assign the significance we assign to 500 to 1000 which in base-8 is 512. Similarly, 3000 hits would only be 1536, while 10,000 hits would be 4096 (a bit too high, only two major leaguers have made this.) But 6000 hits in base-8 is 3072, so that works. I don’t have the energy to think about percentages in base-8. I guess a batting average of .200 in base-8 is equivalent to our .250 and .300 in base-8 is .375 for us. I’m not going to do ERA – they’d count 9 innings as 11 and – look I just can’t.

Let’s imagine that our base-8 counterparts have money that works like ours. Sure their dollars would have 64 cents instead of 100, but we’ll leave that alone. A salary of 8$100,000 would only be equivalent to $32,786 and a base-8 millionaire is only worth $262,144, maybe it isn’t real money until you are worth b8$10,000,000 (which is $2,097,152 in b10).

Because of the relationship between 2, 4, 8 some numbers that we don’t think much about would gain significance. 40 (32 in base10) and 400 (256 in base10) would play the role of 50 and 500. I think 20 (which is 16 in base10) would take on a near mystical significance, since it was also a quarter of the way to base8 100 (64 in base10).

We assign certain numbers unique emotional or cognitive significance. Sometimes this is limiting, but it is also socially useful. But there are also numbers of inherent significance. Squares and cubes for example, but the big ones are primes which are central to mathematical theory. We may change the labels placed on them, but they are inherent. Sure, our 11 is base8 13 and our 13 is base8 15, and our 17 is base8 21. But in terms of mathematical theory they are the same, these numbers are inherently special.

People, Numbers, and Personality

What about us. What if every person were a unique number, that this number somehow was reflected in our soul. Primes, with their special qualities might be the geniuses, or the saints. Squares, cubes, and quads would be the highly accomplished (although Earth8 highlights just how reliant this is on context). The big ten-based and five based numbers with lots of zeroes would be the celebrities, heroes and villains – the one in a million. Most of us are just regular numbers. 1367428. A perfectly good number, the only one of its kind, with a unique combination of factors and characteristics. And in the face of infinity, that’s pretty cool.