00:02:53 but isn't the way board game players interact, taking turns to manipulate some state, game theoretical stuff
00:04:12 i guess not really
00:04:45 hmm
00:05:04 A|(B C) = (A|B) (A|C), obviously
00:05:15 but does A (B|C) = (A B)|(A C)?
00:05:23 where A B is common parts and A|B is combination
00:06:16 isn't the study of general properties of game trees an important part of game theory? at least the one book i've read talks about it a lot.
00:08:09 oklopol: winning theory could be your chance to include all the ridiculous ideas you've ever thought of into mathematics
00:08:23 so what's the symbol for A totally winning B?
00:08:31 i'm not sure how that maps to what category theory is to algebra though
00:08:42 Tw(A,B)? TW(A,B)? TwAB? A op B?
00:09:02 as always, A | B = A <==> A > B
00:09:13 or maybe more like >=
00:10:40 of course
00:10:43 but totally winning is about strategy
00:11:17 I think op is the best route as you know, operators are awesome and you can invent symbols for them
00:11:24 doesn't mean we should get too creative when defining the algebra of games
00:11:30 Whyever not.
00:11:38 indeedso iguess not.
00:11:48 or do i mean yes
00:11:55 Circled > would be nice.
00:12:02 i'm not really following any of these conversations
00:12:03 Might confuse with just >, but isn't that a good thing?
00:12:09 :|
00:12:14 yeah!
00:16:34 -!- alise has quit (Ping timeout: 252 seconds).
00:19:16 -!- Oranjer has joined.
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00:30:55 what did i miss since what i last said?
00:32:05 beats me!
00:34:15 alise: < oklopol> yeah!
00:34:27 that is it? :P
00:35:25 well also "02:17… Oranjer has joined #esoteric"
00:35:26 that's sort of relevant to what Oranjer said
00:36:16 what is it with chess ais, you give them a huge amount of time because you don't wanna feel pressure and they just sit about doing nothing
00:36:27 you're a computer. you don't panic. stop wasting my time
00:37:50 chess is too hard anyway
00:38:23 what
00:38:37 lament: i don't care, it's entertaining
00:38:47 -!- Ilari has quit (Ping timeout: 268 seconds).
00:38:58 oh I think i may just have set up the ai wrongly
00:39:01 it just sat there and ran out of time
00:39:06 alise: AIs do use up time
00:39:22 coppro: yes but this one played fine with little time. also, as i said, it ended up not moving at all.
00:39:58 how does it end up not moving
00:40:19 lament: yeah i never learned how knights move
00:40:31 * alise tries a different type of clock
00:40:33 Oranjer: by not moving in the allocated time
00:40:42 I think they do the Kansas City Shuffle, oklopol
00:41:22 two steps this way and then one step this way oh and by the way YOU CAN FLY OVER OTHER PIECES, that's just insane
00:41:59 it's just a game after all
00:42:06 flying horses
00:42:25 -!- cal153 has quit.
00:42:47 Chess: the only playable Allegory of Islam
00:43:31 lament: your responses are really boring today, are you drunk on life?
00:43:54 i'm sober
00:44:00 Oranjer: you are way too postmodern
00:44:11 how so?
00:44:18 lament:
00:44:22 -!- Ilari has joined.
00:44:25 Muhammed flys somewhere on a flying ass
00:44:53 Muhammad, sorry
00:45:26 oklopol: empty string
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01:11:51 In which I play Chess extremely shittily:
01:11:52 1. b4 c6 {+0.17/8} 2. Nc3 Nf6 {+0.31/9} 3. Na4 d6 {+0.21/9} 4. c4 g6 {+0.06/8} 5. d4 Be6 {+0.14/8} 6. c5 Na6 {+0.06/9} 7. d5 Nxd5 {+0.79/8} 8. b5 cxb5 {+1.70/10} 9. e4 Qa5+ {+1.61/10} 10. Bd2 Qxa4 {+1.71/11} 11. Qxa4 bxa4 {+1.98/10} 12. exd5 Bxd5 {+2.00/10} 13. a3 Nxc5 {+3.09/9} 14. Ba5 Nb3 {+3.00/9} 15. Rb1 Bg7 {+3.82/10} 16. Bc7 Rc8 {+5.19/10} 17. Ba5 Nxa5 {+5.87/10} 18. g4 Bxh1 {+10.37/10} 19. Nf3 Bxf3 {+13.43/11} 20. Be2 Bxe2
01:12:06 23. Rb4 Rxa3 {+14.69/9} 24. Rb5 Rh3 {+14.96/8} 25. g5 a3 {+17.63/9} 26. f4 a2 {+22.11/9} 27. Rc5 bxc5 {+26.91/9} 28. f5 gxf5 {+27.85/9} 29. Ke1 Rxh2 {+79.98/28} 30. Kd1 a1=Q# {+79.99/28}
01:12:11 Admittedly a few mistakes were due to the mouse slipping.
01:12:27 That probably made the already ridiculous difference in skill vs the computer vastly worse
01:12:38 But hey, it was entertaining. I am awfully bad though.
01:13:48 how does one read this notation
01:13:48 can the computer give an estimate of how much you sucked?
01:16:16 Oranjer: ignore the bits in {}s
01:16:23 and then just google chess move notation
01:16:27 i'm white
01:16:29 obviously
01:16:30 hi
01:16:38 lament: probably, but i don't feel like hating myself that badly
01:17:34 alise
01:17:51 fax
01:18:00 hello
01:18:03 hello
01:18:18 I love finite calculus
01:18:27 ok zeilberger
01:18:34 ceil(burger)
01:18:38 failculus
01:18:47 it isn't really very calculusy tbh :p
01:19:04 it blows my mind that the are so many stiking similarities with the real calculus
01:20:05 it blows my mind that this blows your mind
01:20:23 given that calculus is obviously the limit of finite calculus
01:20:31 well 1 is basically the infinitesimal of the integers :P
01:20:47 finite calculus isn't calculus on integers
01:20:56 i know
01:21:09 i know you know, i just like saying it
01:21:11 it's catchy
01:21:18 ??
01:21:22 it's not calculus on integers?
01:21:28 are you reading the same paper as me? :P
01:21:49 oh well it's calculus from integers
01:22:02 but the functions still go to R
01:22:11 fax: why not on booleans
01:22:12 mine are Z -> Z
01:22:17 boolean calculus, do it now
01:22:24 alise, I am actually reading George Booles paper on this right now
01:22:28 er book
01:22:39 haha man I'm laughing too much at the idea of boolean calculus
01:22:53 * fax frowns
01:23:00 fax: no you /must/ do it on Bool -> Bool where true : Bool, false : Bool and nothing else
01:23:03 well the reason the paper doesn't talk about Z -> R, i think, is that integers always sum to integers, so you can restrict it that way, unlike normal calculus
01:23:11 I guess I'm basically asking for calculus from naturals mod 2
01:23:13 so DO IT
01:23:16 >:3
01:23:34 -!- augur has quit (Ping timeout: 264 seconds).
01:24:01 well it could be Q -> Q also
01:24:03 but that's not as elegant
01:24:12 why are you talking
01:24:17 boolean calculus
01:24:17 now
01:24:28 alise, it's your idea, you do it!
01:24:41 i don't have a cock compiler
01:24:50 just s/Z/Bool/ in your code, job done
01:24:56 um :P that wont do it
01:25:02 i think it's very elegant from Z to R
01:25:06 hey I just realized Bool is a field
01:25:24 what's Bool?
01:25:27 oklopol, why is Z -> R better than Z -> Z?
01:26:05 gf
01:26:08 true/true = true
01:26:11 true/false = undefined
01:26:17 that's one fucking awesome field xD
01:26:19 "= undefined" *barf*
01:26:26 as in "is undefined"
01:26:27 because if we consider Z a measure space with cardinality as the measure, then sums are just integrals
01:26:29 false/true = false
01:26:32 false/false is undefined
01:26:40 *unbarf*
01:26:41 and with integration we usually have functions from our measure space to R.
01:26:42 so basically X/true = X anything else is undefined
01:27:04 oklopol, wait what
01:27:07 so the multiplicative inverse is
01:27:10 true^-1 = true
01:27:12 that's it
01:27:16 worst field ever
01:27:31 oklopol, ooh I wonder if there's a Z[i] calculus with all the nice harmonic, holomorphic stuff
01:27:31 then again multiplication is boring on booleans anyway
01:27:33 whoa
01:27:38 multiplication is division on booleans
01:27:43 wait no
01:27:49 except for half of it (/false) >_<
01:27:53 alise, unitary calculus!!
01:28:02 fax: the crazy dude's paper talked about discrete analytic functions
01:28:06 for all the cases where / is defined on bools it is identical to *
01:28:15 01:27 < alise> for all the cases where / is defined on bools it is identical to *
01:28:19 oops
01:28:24 oklopol: if you're using his notation you say R but you mean hZ_p
01:28:25 or mentioned them
01:28:26 looked neat
01:28:29 (where Z is a finite set)
01:28:37 do not pervert /our/ discourse :P
01:28:52 tbh addition on booleans is pretty nice, being xor
01:28:57 hmmmm
01:29:18 true - true = false; true - false = true; false - true = true; false - false = false;
01:29:19 heh - = + too
01:29:23 this is the best discovery I have made :))))))
01:29:28 fax: what is
01:29:28 finding this finite calculus
01:29:36 dude it's just some addition and subtraction
01:30:48 hey fax DID YOU KNOW you also have exponentiation on booleans
01:30:54 x^true = x; otherwise undefined
01:31:04 lol
01:31:04 in fact, you can even use the ackermann function on them.
01:31:07 it's clear sums are integrals because every function is simple
01:31:07 from Z, with the usual measure
01:31:07 err wait what
01:31:07 that's bullshit, let me gather myself.
01:31:09 okay maybe it's not completely obvious
01:31:11 "Vladimir Arnold forcefully stated in one of his books that it is wrong to think about finite difference equations as approximations of differential equations. It is the differential equation which approximates finite difference laws of physics"
01:31:12 now you have INFINITE OPERATORS!!!!!!!!!
01:31:39 so fax is now the fifth ultrafinitist i gather
01:35:20 this pleases me
01:35:30 fax: I'll love you if you make a Coq module with ultrafinitist definitions of the following, paramaterised on the rational h and the prime p: Naturals, so that there is no prime greater than p; Integers, presumably with each half of the integers dedicated to a sign; Rationals, divided once more (h must fit into one of these); and Reals, defined as hZ_p.
01:35:48 Along with associated operations, the calculus he defines, and properties.
01:35:51 alise, I will help you do it :)
01:35:54 And by love you, I mean hate you love you.
01:36:06 fax: Well... I started writing it in my language but couldn't be bothered.
01:36:10 alise, I should implement (normal) construtive reals though
01:36:21 those are easy
01:36:30 following the sketch in my constructie functional analysis text
01:37:07 Sigma (f:Q+->Q), Forall (e1,e2:Q+), abs (f e1 - f e2) <= e1 + e2
01:37:08 boring
01:37:19 fax: now do it, ultrafinitistic peon
01:39:53 fax: Actually I suppose that all those sets don't neccessarily have to have the same size because they all coexist.
01:40:19 So having the integers be twice the size of the naturals (minus 1, because there's only one 0...) and having rationals be the size of the naturals plus the integers would be OK.
01:40:31 The reals have to be hZ_p by Order of Zeilberger.
01:42:30 The nice thing is that we don't need any pesky functions or anything to define these because there's a simple, finite number of cases.
01:46:53 p would be what? The largest known* mersenne prime (* known by http://coqprime.gforge.inria.fr/ )
01:47:10 p and h are parameters to the module
01:47:43 they are universal constants like physical ones but we don't know what they are (zeilberger says that the True Value either p or h - i forget which - is unknowable so uh whatever)
01:47:50 so we just plug in values we like.
01:48:10 -!- augur has joined.
01:48:22 Time for a nick change.
01:48:39 -!- uorygl has changed nick to uorygl[hireMe].
01:48:43 :P
01:48:45 fax: if you have an awful lot of cpu time on your hands the largest mersenne prime would be a good choice for p, yes.
01:49:03 h would be the result of pressing 0., holding down 0 for a long while, then pressing 1, probably.
01:49:23 shouldn't h come from a physical/science experiment
01:49:28 like the fine structure constant or something
01:49:43 Zeilberger claims they are separate to physical constraints and that he is a platonist.
01:50:01 Since we are following his school of ultrafinitism, not the usual physical-constraints one, that is not required.
01:50:14 1/p is a good value for h if you have that in your system.
01:50:26 What is hZ_p?
01:50:30 p is a natural and rationals = size of naturals + size of integers, so
01:50:36 1/p should always be acceptable
01:50:42 uorygl[hireMe]: Z is the integers
01:50:44 _p is subscript p
01:50:54 And h is an h?
01:50:57 Zeilberger, an ultrafinitist that believes no infinite sets exist, defines the reals as hZ_p
01:50:59 That explains so much.
01:51:06 where h is a very, very small number
01:51:09 and p is a very, very large prime
01:51:22 lol
01:51:24 01:50 < uorygl[hireMe]> That explains so much.
01:51:26 ^^^^ lol
01:51:39 So what does hZ_p mean?
01:51:50 It means hZ_p. :-P
01:52:04 That is not a definition!
01:52:23 Or, if it is a definition, then your mom is a perfectly good model of hZ_p.
01:52:27 Since your mom is your mom.
01:52:29 'Tis true
01:53:37 Z_p = Z/Zp I guess?
01:53:49 Galois field
01:53:51 Yeah, I figure Z_p is the integers modulo p.
01:53:57 I have no idea what the h is supposed to be.
01:54:13 F_p = Z/pZ
01:54:27 h is the fundamental mesh constant, it's smaller than 1
01:54:42 so hZ_p = {...-h,0,h,2h,3h,...}
01:54:56 h: It's Smaller Than One.
01:55:04 So you multiply each number by h?
01:56:08 lol
01:56:20 alise you should make slogans
01:56:22 so if h is the fundamental mesh constant, what's the cool name for p
01:56:39 uorygl this is my interpretation, but I am by no mean an expert on this
01:57:41 it doesn't actually do anything
01:57:42 Hmm, ultrafinitists don't even let you have a type of types.
01:57:54 After all, it's infinite.
01:58:00 Unless you have a finite number of sets, which would be cool.
01:58:03 oklopol: what doesn't?
02:00:01 I guess the best thing is to have the integers be of size p.
02:00:43 Which means that the naturals are of size (p+1)/2.
02:00:58 What does let you have a type of types?
02:01:05 So the rationals are of size p+((p+1)/2).
02:01:11 I know of... not many systems under which that's possible.
02:01:12 uorygl[hireMe]: Anything?
02:01:14 Nat : Set.
02:01:27 Yes, but Set !: Set.
02:01:38 Obviously.
02:01:43 But Set is still infinite.
02:02:08 So, the reals have the same size as the integers.
02:02:16 Which means that the reals are smaller than the rationals.
02:02:23 This Makes No Sense (not that ultrafinitism does); start over.
02:02:41 The naturals are of size (p+1)/2.
02:02:44 The integers are of size p.
02:02:52 your mom
02:02:52 The rationals are of size p.
02:03:06 Half negative, half positive.
02:03:11 also the h
02:03:19 So (p-1)/2 each.
02:03:26