Digital Roots And Wonder

I posted this. Don’t judge. (I kinda did get judged but whatever. I’m secure, I swear.)

To which I get this mind-blowing reply from resident math genius @quantian.

We learn of “digital roots”. It’s easiest to show by demonstration.

The digital root of 231 is the sum of the digits: 2 + 3 +1 = 6

You can do this for any number, just proceed until the final digital root is a single digit.

So for 489, we go:

4 + 8 + 9 = 21

(then 21 gets reduced)

2 + 1 = 3

So the digital root of 489 is 3.

After reading @quantian’s explanation, I summarized the conclusion:

Any number minus its digital root must be wholly divisible by 9.

So 489 – 3 = 486.

486/9 = 54


Gets better though.

So we can recap the rules:

  • Any number with a digital root of 9 is divisible by 9
  • Any number with a digital root of 3 is divisible by 3
  • Any number minus its digital root is wholly divisible

Add this to any number ending in 5 being divisible by 5 and even numbers being divisible by 2 and you have a playful set of numeric wonders. And as @jadam2122 recommends, your digital clock becomes a fun toy for the kids.

And I’ll address the question some if not many want to blurt out…what’s the point?

The point is wonder.

I have zero doubt that there are readers who know the practical application of these observations (and I welcome them, and will even share the ones you send). But we are pattern-matching machines. Narratives, math, music, concepts. It’s all around us.

It’s true, in this letter, we often talk about how being a pattern bloodhound often leads us astray with confirmation and availability bias. But this ability to match patterns is also a skill from chess to trading to persuasion to self-awareness to diagnosis and to discovery. It’s a power we learn to wield. It uncovers the seams between disciplines.

If every time you saw a pattern, you dismiss it because its application was not-yet-apparent then your mental library of patterns would grow too slowly and the probability that you would match new stimuli to a small library would be tiny. You would deprive yourself of insight but also that feeling of wonder.

And that feeling of wonder is what leads to the next question.

And before you know it…you grow.

That’s why you’re here. Right?

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