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prefect posted:is this a religious thing, or was there some guy named church who thought them up? nah its encoding numbers in lambda calculus. i made my list in order of importance btw
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# ? Jun 9, 2013 17:57 |
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# ? May 16, 2024 18:15 |
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wait, what's the difference between p-adic numbers and p-ary numbers except that you get cool algebraic properties from p being a prime like, 13.5 in binary is code:
code:
this poo poo is cool though
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# ? Jun 9, 2013 18:03 |
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I feel like floating point should be higher on the list. Its probs more important than arbitrary precision, since for a lot of common applications arbitrary precision doesn't matter and floating point math is a thing computers do better. Like graphics and poo poo.
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# ? Jun 9, 2013 18:06 |
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OBAMA BIN LinkedIn posted:i knew a guy who at university tried to rewrite jquery for a coursework. instead of using jquery. that's a decent way to learn what's going on in jquery just never, ever use the rewrite you create
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# ? Jun 9, 2013 18:09 |
prefect posted:just never, ever use the rewrite you create well the thing was he wrote it to use in his project, which actually had nothing to do with rewriting jquery at all
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# ? Jun 9, 2013 18:25 |
prefect posted:that's a decent way to learn what's going on in jquery every-javascript-library.txt
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# ? Jun 9, 2013 18:28 |
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if javascript is so great why isnt anything important done with it?
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# ? Jun 9, 2013 18:31 |
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prefect posted:is this a religious thing, or was there some guy named church who thought them up? it's because functional programmers believe in the separation of church and state
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# ? Jun 9, 2013 18:35 |
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nrook posted:wait, what's the difference between p-adic numbers and p-ary numbers except that you get cool algebraic properties from p being a prime 2's complement is just restricting 2-adic integers to a finite number of bits and considering the leftmost bit infinitely many repetitions of that bit. edit: which sounds like a really douchey thing to say but really those are the rules, its how it works, blah blah blah Ronald Raiden posted:I feel like floating point should be higher on the list. Its probs more important than arbitrary precision, since for a lot of common applications arbitrary precision doesn't matter and floating point math is a thing computers do better. Like graphics and poo poo. probably FamDav fucked around with this message at 19:05 on Jun 9, 2013 |
# ? Jun 9, 2013 18:46 |
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tef posted:it's because functional programmers believe in the separation of church and state
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# ? Jun 9, 2013 19:03 |
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tef posted:it's because functional programmers believe in the separation of church and state
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# ? Jun 9, 2013 19:27 |
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FamDav posted:2's complement is just restricting 2-adic integers to a finite number of bits and considering the leftmost bit infinitely many repetitions of that bit. idgi 11111111 = -1 but as a 2-adic number ...11111111 = sum from 0 to infinity of 2^n = +inf ? or, wait, never mind--- it's a limit over two variables, not one, isn't it? a "2-adic number" of arbitrary size can be defined as just the limit of a 2-adic number mod 2^k, where k -> infinity and in all of those guys, the string of all 1s is going to be -1 I think I get it right now but I probably dont, is there a decent paper or something on arxiv I can read to understand this
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# ? Jun 9, 2013 19:45 |
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http://www.madore.org/~david/math/padics.pdf is a paper
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# ? Jun 9, 2013 19:52 |
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i already learned all that stuff and forgot it welp cya later
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# ? Jun 9, 2013 20:02 |
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code:
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# ? Jun 9, 2013 20:26 |
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Socracheese posted:i already learned all that stuff and forgot it welp cya later
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# ? Jun 9, 2013 22:32 |
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vas0line posted:
you didn't declare n idiot
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# ? Jun 9, 2013 22:44 |
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prefect posted:is this a religious thing, or was there some guy named church who thought them up? I think he means Roman Numerals
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# ? Jun 9, 2013 23:34 |
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FamDav posted:if you job a computer these are the representations of numbers you should know 1 well duh 2 this is some sort of nerdy way to say 2s complement? okay i guess 3 lol we're gonna ignore the first 3 3 ieee754 duh yeah i mean dont need it memorized but you should know it exists and vaguely how it works 4 what the gently caress is this poo poo get out
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# ? Jun 9, 2013 23:54 |
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if you do any kind of scientific computing or graphics work, knowing how to write numerically stable code makes you less awful. and church numerals are: 0 = \x.\f.x 1 = \x.\f.f x 2 = \x.\f.f (f x) etc.
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# ? Jun 10, 2013 00:20 |
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FamDav posted:if you do any kind of scientific computing or graphics work, knowing how to write numerically stable code makes you less awful. what the gently caress is this do you really consider that a valid explanation lmao
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# ? Jun 10, 2013 00:52 |
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Bloody posted:what the gently caress is this how about they are an embedding of the integers into the lambda calculus using the properties of function application lets describe the number N as the result of N applications of a function f to a value x. so 0 = λf.λx.x 1 = λf.λx.f x 2 = λf.λx.f (f x) i even looked up the lambda symbol so it looks nice lets write another function λa.λb.λf.λx.a f (b f x), which is plus. this works because if a is f applied A times and b is f applied B times, then this applies f A+B times. wow, whoa we can write multiply by λa.λb.λf.λx.a (b f) x because this is the application of b (which is the application of f B times) A times i leave exponentiation and subtraction as an exercise to the reader
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# ? Jun 10, 2013 01:15 |
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FamDav posted:how about they are an embedding of the integers into the lambda calculus using the properties of function application
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# ? Jun 10, 2013 01:29 |
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lol if you've never seen Church numerals before
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# ? Jun 10, 2013 02:09 |
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i wonder how many people have seen both church numerals and the genitalia of the opposite sex??
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# ? Jun 10, 2013 02:20 |
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uG posted:i wonder how many people have seen both church numerals and the genitalia of the opposite sex?? Lots, usually on the same monitor
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# ? Jun 10, 2013 02:22 |
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Jerry SanDisky posted:Lots, usually on the same monitor Nice!
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# ? Jun 10, 2013 02:38 |
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Jerry SanDisky posted:Lots, usually on the same monitor
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# ? Jun 10, 2013 07:13 |
Jerry SanDisky posted:Lots, usually on the same monitor
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# ? Jun 10, 2013 07:20 |
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Jerry SanDisky posted:Lots, usually on the same monitor
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# ? Jun 10, 2013 07:31 |
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Jerry SanDisky posted:Lots, usually on the same monitor NICE
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# ? Jun 10, 2013 09:26 |
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FamDav posted:how about they are an embedding of the integers into the lambda calculus using the properties of function application and this is useful because
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# ? Jun 10, 2013 10:51 |
Bloody posted:what the gently caress is this lmao if you can't figure this out on intuition alone oh wait im in the wrong thre\d
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# ? Jun 10, 2013 10:55 |
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Church encoding (Unary basically) is sort of useful in theorem proving systems since they're naturally inductive and so are linked lists They're are really useful for type level naturals to allow safe indexing and the like. p-adic numbers are exotic to most mathematicians so lol if you think joe programmer needs to know them the correct list is 1. Binary numbers in 2's complement 2. IEEE 754-2008 and its algebraic properties 3. Church numerals if u really need them
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# ? Jun 10, 2013 13:18 |
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qntm posted:and this is useful because It's been a while since I've read on that so I might be wrong, but Church numerals are basically equivalent to Peano arithmetics, which are proven to be complete and undecidable and also mean that you can express pretty much any logical system you want with it. It basically yells you lambda calc can be equivalent to any other similar logical system (ZF set theory and whatnot). It's fairly important to guys like Douglas Hofstadter who love that poo poo, and mathematicians that used it in whatever proof system they wanted to make stuff progress, I guess.
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# ? Jun 10, 2013 16:04 |
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The correct answer is to make a blog post about it and throw it up on Hn.
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# ? Jun 10, 2013 16:57 |
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Before knowing all that, programmers should first learn to shower at least once every other day. But that's not gonna happen so onwards with the masturbatory number conversions. I think hex is pretty cool and also make pretty colors.
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# ? Jun 10, 2013 17:02 |
MeruFM posted:Before knowing all that, programmers should first learn to shower at least once every other day. at least once a day or get out
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# ? Jun 10, 2013 19:46 |
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look its obviously 1. reasonable suggestion 2. extended learning 3. lol wacky poo poo from my discipline that im too blind to look above also count hex on your fingers and make logical operations e-z
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# ? Jun 10, 2013 21:31 |
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# ? May 16, 2024 18:15 |
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if this is the case I recommend that being able to implement peano numbers or the equivalent of church-numerals from pi-calc is a good basic requirement in order to be good at concurrent/distributed/actor stuff.
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# ? Jun 10, 2013 22:00 |