[HN Gopher] Marvelous Arithmetics of Distance
       ___________________________________________________________________
        
       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...
        
       ___________________________________________________________________
       (page generated 2023-10-23 09:00 UTC)