[HN Gopher] Marvelous Arithmetics of Distance
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Marvelous Arithmetics of Distance
Author : mathgenius
Score : 89 points
Date : 2023-10-22 19:42 UTC (13 hours ago)
(HTM) web link (mathenchant.wordpress.com)
(TXT) w3m dump (mathenchant.wordpress.com)
| itjustisthough wrote:
| I must have missed p-adics in school. This was a fun,
| interesting, and clear read.
| wging wrote:
| They are typically not taught in school, at least in the US but
| probably elsewhere too. I don't even know of a commonly taken
| undergrad-level course that I'd expect to cover them.
| dividendpayee wrote:
| They're often -- but not always -- touched on in advanced
| undergraduate classes, e.g. after real analysis and abstract
| algebra. Not every math undergraduate takes number theory
| these days.
| wging wrote:
| Which classes are you thinking of?
| behnamoh wrote:
| 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.
| pavel_lishin wrote:
| I will continue to marvel at it, though.
| Koshkin wrote:
| > _just math_
|
| I don't know what this is supposed to convey. Modern
| mathematics is one of the most amazing, marvelous, beautiful
| etc. achievements of the mind. I wish more people could
| appreciate that.
| galaxyLogic wrote:
| The marvel of Math is in its non-obviousness. Obvious truths
| are not marvelous but non-obvious ones are.
|
| "Magic" is also a word we can use about Math because we know no
| true magic exists. Therefore when something is said to be
| "magic" we know it means something "looks like magic".
|
| For the Magician (/Mathematician) it of course doesn't look
| like magic because they clearly understand and see how it
| works.
|
| So, you are perhaps the Mathematician/Magician for whom it
| doesn't look like magic but for the rest of many of us it does.
| We are even willing to pay for the ticket to see magicians
| perform their "magic" and to marvel at it.
| jamespropp wrote:
| 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.
| jxf wrote:
| For another accessible introduction to p-adic numbers, check out
| Eric Rowland's overview [1].
|
| [1]: https://www.youtube.com/watch?v=3gyHKCDq1YA
| krackers wrote:
| It's also not a full introduction, but for those who want to
| have a taste of p-adic numbers, see 3b1b's video
| https://www.youtube.com/watch?v=XFDM1ip5HdU which motivates
| 2-adic numbers. There's also a neat connection between twos
| complement and 2-adic numbers.
| kevinventullo wrote:
| Shameless promotion of a blog post I made a few years ago
| connecting 2-adic numbers with computationally fast
| exponentiation: https://kevinventullo.com/2020/12/21/2-adic-
| logarithms-and-f...
| xeyownt wrote:
| > 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
|
| > b = ***743740081787109376
|
| No you don't. Trying with 6, 16, 26, any number, you don't
| converge.
| LodeOfCode wrote:
| 6^5 ends in ...76
|
| 6^25 ends in ...376
|
| 6^125 ends in ...9376
|
| 6^625 ends in ...09376
|
| and so on
| BlackFly wrote:
| I was hoping for something on metric spaces, I was completely
| wrong but not disappointed. Great post.
|
| Edit: Arguably there is a weird kind of metric in that, so not
| completely wrong I guess...
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