Newsletter the Fifty-first

If I were to choose one symbol that best represents mystery — and in particular, the intersection between that which is known and unknown — it would be π (pi). After all, this symbol represents not just a number, but an idea: the geometry and mathematics of circles, which are fascinatingly both measurable and immeasurable at the same time.

Back in the '90s I got really into the number pi, and ended up writing a book about it, called The Joy of Pi. (It's out of print now, but that shouldn't stop you from finding some used copy. Some day I'll revise the whole thing and get it published again.)?

So… for those who don't remember exactly what pi is: Measure the distance around a circle, and then divide it by the width of the circle. The answer is about 3.14, which is represented by the symbol π. However, as it turns out, the number is impossible to measure or calculate exactly, and instead rattles off into an infinitely long string of digits after the decimal point… 3.14159265… and so on.

That's part of the mystery: why would something as simple and straightforward as measuring a circle — literally the simplest, most fundamental shape in the universe — result in an unknowable number??

Of course, with any mystery comes skeptics and conspiracy theorists. So over the past 25 years, I have received over a thousand letters and emails from people insisting they have "squared the circle" (calculated an actual, rational value for pi). I rarely reply, but I've kept almost all of them. Some include esoteric, almost spiritual digrams. Others span pages of equations and explanations.?

I appreciate people's skepticism, but none of them are correct. We know this because mathematicians proved over 140 years ago that pi is both irrational and transcendental — that is, there's no way that any finite equation could ever result in pi. It requires an infinite number of steps.

And yet that doesn't feel right… just as some people feel that a perpetual motion machine ought to be possible, the circle-squarers feel that centuries of mathematicians must be wrong and we should be able to solve the mystery and learn the Truth. When are we going to learn that feeling doesn't make it so?

In today's hyper-scientific world, pi helps us remember that there are truly mysteries everywhere — unknowable, incalculable, immeasurable.

It's Pi Day

I've been thinking about pi because Monday is pi day… that's 3/14. At least that's how we type it here in the USA. In most of the world, the date is written 14/3, which just isn't exciting at all. But 3/14… now that evokes all kinds of amazement because it looks like 3.14, or π (pi).

If you prefer the "date/month" notation, you'll have to wait until July 22 (22/7), which we call "pi approximation day." After all, the fraction 22/7 = 3.142… hey, it's close!

Area 51

As we're on the topic of numbers, I feel obliged to muse, self-referentially, that this is the 51st issue of this newsletter. I love the number 51 because most people think it's a prime number… but it's not. Prime numbers, you'll undoubtedly recall from your school daze, are numbers that are not evenly divisible by anything except themselves. For example, 13 is prime because there are no two whole numbers that, multiplied together, equal 13.

51 seems like it has to be a prime, doesn't it? But once again, how a number feels to us can be misleading.?

Here's a fun math trick: If you add up all the digits in a number, and the result is divisible by 3, then the whole number is, too. Here: 5 + 1 = 6, which is obviously divisible by 3. So 51 is, also! And indeed: 3 x 17. Not prime. (Though because it's the product of two primes, 51 is considered "semi-prime.")

There are a lot of prime numbers… an infinite number, in fact. Here's my personal favorite: 314,159. Yes, π strikes again.

Thank you!

I enjoy sharing my musings… and I enjoy hearing yours! Please share this newsletter with a friend,?follow me on LinkedIn, and send me feedback. You can always reach me at [email protected]