Love Story

The geometric fractals of these crystals branch into fans, inches long. Strong mathematical resonance between the ice on the reeds and the feathers on the song birds, who watch me freeze my fingers from their perches in the marsh.

Today, a love story to melt your cold, fractal heart!

I was recently chatting with a friend who divorced a lifetime ago and has since devoted herself to her independence. And yet, life happens. She met a man recently, wonderful in all the right ways. Her heart says yes, but her mind holds back.

“Why?” I ask.

“He’s only 35. So young.”

“And how old are you?”

“41.”

We talk a while, and I hear all the warm and wonderful details. But this one little reservation stays on my mind. It’s not just that we’re all adults and 6 years is small. It’s not only that there are gender dynamics dampening her joy (I bet she’d be comfortable with a 47 year old man). The numbers themselves are arbitrary.

We live in a base-10 world.

It starts with our fingers: 2 hands with 5 fingers each for a total of 10.

There is diversity in digit numbers within our species. I know a precious a little boy who was born with 12 and a colleague who lost one-and-a-half to a lawnmower for a new total now of 8.5, but the commonest configuration is 10.

If you are a budding mathematician from ANY age, stage, or epoch, how do you use these digits of yours? You count with them.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Because of this, we have invented ten DIGITS, or symbols, to represent our entire number system: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 (ZERO). The number ten is actually represented by two digits, 1 (in the “tens place”) and 0 (in the “ones place”). Ten represents our complete set, which is why it bumps us up to the second digit. We made a whole set of ten!

Anything bigger than 99, we count in groups of 100 (ten sets of ten!) Then 1000, then 10000, etc. In fact, any familiar number can be broken down by digit back into its powers of ten. Like so:

Note that I use roman-numeral-influenced symbols as shorthand, c for hundreds place, x for tens place, and a dot for ones place. It’s a handy little notation trick that can help young learners.

What does the BASE mean in base-ten? It means that every decimal position is a power of ten, and in the power expression the base is 10.

So the hangup — a real impediment to a potentially epic love story! — comes down to my friend having lived through 4 sets of ten years, and her lover only gathering 3 sets of ten so far.

But wait. We do not have to build our numbers in sets of ten! In fact, we can use ANY base. The ten is completely arbitrary. Our own preference for our own fingers.

Let’s try HEXADECIMAL, or base-16. It is used a lot in computer science and programming.

In hex, we need 16 digits, because our master number, the number making all of our sets, is 16.

Our hex ones place feels very familiar. It is counting ones, because any number to the 0th power is just 1. So it doesn’t matter what base system you are, all one-digit numbers count ones. But now we count all the way PAST ten up to 16 to make our first set.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, (yeah we use letters to make up the absent digits) and NOW onto the next digit.

The next biggest place counts sets of 16, so the number “10” in base 16 means:

one set of 16 + zero sets of 1 = sixteen things.

Phew. Confused yet? It’s hard at first because of the ambiguity of the numbers. We’re so used to seeing the number 10 and having it mean “one set of ten zero sets of one” that it takes a bit of practice to translate.

In any case, let’s compare the lovers’ ages in base 16:

I texted my friend right away:

You know, in hexadecimal, your man is 23 and you are 29. Furthermore, you have seven whole years until you’re in your hex 30s!

It goes: 28, 29, 2A, 2B, 2C, 2D, 2E, 2F, 30!

She liked it. (Or at least said that she did!)

I don’t know what the takeaway is here.

Is it that math heals patriarchal cultural wounds and opens up opportunities for profound love? Or is it that, if you want to be my friend, expect some deeply nerdy takes on your personal problems.

Why not both!

XO, everybody.