Marvelous Arithmetics of Distance

I must have missed p-adics in school. This was a fun, interesting, and clear read.

I was hoping for something on metric spaces, I was completely wrong but not disappointed. Great post.<p>Edit: Arguably there is a weird kind of metric in that, so not completely wrong I guess...

Shameless promotion of a blog post I made a few years ago connecting 2-adic numbers with computationally fast exponentiation: <a href="https:&#x2F;&#x2F;kevinventullo.com&#x2F;2020&#x2F;12&#x2F;21&#x2F;2-adic-logarithms-and-fast-exponentiation&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;kevinventullo.com&#x2F;2020&#x2F;12&#x2F;21&#x2F;2-adic-logarithms-and-f...</a>

&gt; Likewise, if you start with a positive integer that ends in 6 and repeatedly raise it to the fifth power, you converge digit by digit toward the strange number<p>&gt; b = ···743740081787109376<p>No you don&#x27;t. Trying with 6, 16, 26, any number, you don&#x27;t converge.

For another accessible introduction to p-adic numbers, check out Eric Rowland&#x27;s overview [1].<p>[1]: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=3gyHKCDq1YA">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=3gyHKCDq1YA</a>

&gt; It seems a + b = 1.<p>I&#x27;ve seen this before, and it makes no sense. Is it common to ignore that you are carrying a one?

I like the subject matter, but I find the writing much too long-winded for my taste, with all the “you” and “we” and “let’s” and so on. That conversational style might work in a video, but as written text I find it exhausting.

Yeah, I admit the title is a bit click-baity. But I got the word “marvelous” from the Audre Lourde poem, so it’s not completely gratuitous.

there must be a rule that bans using “marvelous, magic, mysterious, never seen before, miraculous, genius, shocking …” words used in math posts. There’s nothing marvelous about any of this—it’s just math. Imo it’s better to let people face math head on than try to sugar coat it and click bait them into liking math.