Today is Pi Day! It’s pi day because in the US dates are notated in the order of month-day, so the date is 3/14. Those are the first three significant digits of π, 3.14. It’s not the only pi day, though. Pi can also be (approximately) expressed by the fraction 22/7, so in places where dates are notated in the order of day-month, the 22nd of July is 22/7 — and that’s another pi day. June 28 is yet another one, because (we’re back in month-day order now) it’s 6/28 and 6.28 is 2π, also called tau (𝜏). If that isn’t enough, November 10 is also Pi day. Before you go nuts trying to fit the 11 and the 10 into something that represents π, that’s not it. November 10 is the 314th day of the year…one additional way to arrive at 3.14.
You might be thinking that this is an awfully indeterminate for a day celebrating some aspect of math. After all, isn’t math supposed to be precise and provable? Well…not quite. For one thing, the number π is an infinitely nonrepeating decimal. It keeps getting closer and closer to the actual value, but it never gets there, no matter how many decimal places you calculate. Or remember. Although you can mathematically prove that you can’t specify pi exactly; it’s always an approximation. Slightly indeterminate, that is.
Remembering the digits of pi seems to become an obsession for some people. There are several different record holders. Rajveer Meena recited 70,000 digits of pi from memory in 2015 to earn the Guinness World Record. The Limca Book of Records is a publication of records in India, and lists a different record holder: Suresh Kumar Sharma, who recited 70,030 digits, also in 2015. And Akira Haraguchi made a claim of surpassing 100,000 digits, but his claim wasn’t certified. It’s not entirely clear to me why anybody would want to memorize that many digits of pi (or anything else), but clearly they do.
A much more accessible way to celebrate the day is by simply eating some pie, since in English, “pie” sounds exactly like “pi.” Maybe you’ve noticed that all of these pi-related events are particularly localized to either a customary date order, or a language, or — and this isn’t strictly local, but I think it’s important — what base you’re using to calculate numbers. Because if you memorize thousands of digits of pi in base 10, you still don’t know anything about the digits of pi in some other base. For instance, in base 3, pi is 10.01021101222201. In base 9 it’s 3.12418812407442. But the weird thing about pi is that it’s an “irrational number”, so it’s going to be a repeating decimal in any whole-number base. Um, I think it would be, anyway. Hey, it’s been a long time since I did any serious math. And for any students in the audience, that stuff they tell you about things like calculus being “something you’ll use all the time when you’re an adult?” Not so much, unless you become a math teacher. Although now that I think of it, memorizing a lot of digits of pi might get you something in the occasional bar bet.
But how do people memorize all those digits? That’s an interesting enough question that it’s spawned it’s own field of study: piphilology. It’s the study of the memorization systems people invent and use to memorize digits of pi — and that might be generalized to memorizing other things. One popular approach is to write a piem — that’s a poem that represents pi because the length of each word, in order, corresponds to the digits of pi. Here’s a short one: How I wish I could recollect pi easily today! When you get to a zero, you use a ten-letter word.
Some people have gotten a bit obsessive about this, too (pi seems to bring this out in some folks), because there’s a short story called Cadaeic Cadenze that’s 3834 words long, and the length of each word represents a digit of pi, in order. But of course somebody else didn’t stop there, and wrote the novel Not A Wake. It does the same thing, but it’s 10,000 words long. Of course, then you have to remember a whole novel word for word, so I’m not sure how much of an advantage that gives you.
A memorization system that works for pi and for practically anything else is called the method of loci. This dates back to ancient Greece, where it was supposedly used to memorize long speeches. It’s also called the memory palace technique. You visualize a real place, ideally someplace you’ve actually visited and know pretty well. It could be a large building, or a street with a lot of shops, or really any location that has a lot of discrete locations (“loci”) you can recall easily. When you’re trying to memorize something, you visualize yourself walking around to these various locations and storing one thing you want to remember in each place. Then to remember, you visualize yourself retracing your steps. It sounds like it would be more work to do it this way, but the human mind works in strange ways, and people are still using this method to remember astonishingly long lists of pretty random things. As often as not, of course, they’re using the memorization technique in order to demonstrate using a memorization technique. I mean, paper and a pencil are generally not that hard to find.
The memory palace technique is, in a way, a sort of “thought experiment.” You try to visualize something in such a realistic way that you can actually use the visualization. You imagine storing a fact in a particular room or shop, and then you can go back and get it. The thought experiment is a way to do physically impossible experiments, too, like traveling on a train at the speed of light. If that sounds vaguely familiar, it’s probably because Albert Einstein popularized the use of thought experiments to formulate his theories of special relativity and general relativity. There’s a myth about Einstein that he didn’t do well in math at school — but it’s just a myth. He taught himself both algebra and geometry during a single summer break. And he started teaching himself calculus when he was 12. How he celebrated his early birthdays wasn’t recorded for posterity, so we really only know one thing about them: they fell on March 14. That’s right, Albert Einstein was born on Pi Day. Except that it wasn’t Pi Day for him — he was born in Germany, where they notate dates in day-month order.
Einstein came to the US, of course, in 1940, where he may or may not have noticed the backwards way dates are notated. But he still wasn’t exposed to Pi Day, because there was no such thing (at least as a formal commemoration) until 1988. Nevertheless, we can still end on a high note (or, well, at least this very old note, which I think I first heard decades ago):
The smartest guy ever on Earth
Was Einstein! We can’t know the worth
All his theories comprised.
So I’m not that surprised,
Pi day’s the date of his birth.