< 1171584082 0 :SevenInchBread!n=CakeProp@wikipedia/The-Prophet-Wizard-of-the-Crayon-Cake JOIN :#esoteric < 1171584508 0 :kxspxr!n=kxspxr@x1-6-00-0c-41-39-32-8e.k302.webspeed.dk JOIN :#esoteric < 1171585032 0 :sp3tt!unknown@unknown.invalid QUIT :Connection timed out < 1171585671 0 :SevenInchBread!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171585705 0 :SevenInchBread!n=CakeProp@wikipedia/The-Prophet-Wizard-of-the-Crayon-Cake JOIN :#esoteric < 1171585753 0 :_D6Gregor1RFeZi!unknown@unknown.invalid NICK :GregorR < 1171587040 0 :ihope!n=ihope@c-71-205-100-59.hsd1.mi.comcast.net JOIN :#esoteric < 1171587396 0 :kxspxr!unknown@unknown.invalid QUIT : < 1171592727 0 :ihope_!n=ihope@c-71-205-100-59.hsd1.mi.comcast.net JOIN :#esoteric < 1171592985 0 :goban!n=ubuntu@ip68-229-102-1.hr.hr.cox.net JOIN :#esoteric < 1171592987 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :#ps < 1171592993 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :~ps < 1171592993 0 :bsmnt_bot!unknown@unknown.invalid PRIVMSG #esoteric :None < 1171592997 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :Really? < 1171592998 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :ihope < 1171593003 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :Suspicious. < 1171593010 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :? < 1171593012 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :bsmntbombdood: yes? < 1171593013 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :you restarted it < 1171593022 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :When? < 1171593029 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric :#exec dir(self) < 1171593044 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :~ is the command character here, guys :-P < 1171593051 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :er < 1171593063 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :kill everthing < 1171593071 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric :#exec self.raw("MSG #esoteric "+str(dir(self))) < 1171593082 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :PRIVMSG, not MSG. < 1171593089 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :~exec sys.stdout(dir(self)) < 1171593090 0 :bsmnt_bot!unknown@unknown.invalid PRIVMSG #esoteric :['COMMAND_CHAR', 'THREADING', '__doc__', '__init__', '__module__', 'chan', 'commands_running', 'commands_running_lock', 'connect', 'connected', 'disconnect', 'do_callbacks', 'do_ctcp', 'do_exec', 'do_kill', 'do_ps', 'do_quit', 'do_raw', 'errorchan', 'exec_execer', 'get_message', 'host', 'ident', 'ihope', 'listen', 'load_callbacks', 'message_re', 'nick', 'owner', 'pong', 'p < 1171593090 0 :bsmnt_bot!unknown@unknown.invalid PRIVMSG #esoteric :ort', 'print_callbacks', 'raw', 'raw_regex_queue', 'readbuffer', 'realname', 'register_raw', 'save_callbacks', 'socket', 'sockfile', 'verbose'] < 1171593095 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :Or that. < 1171593103 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric :#exec self.raw("PRIVMSG #esoteric "+str(dir(self))) < 1171593114 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :sheesh < 1171593126 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :~exec self.raw("PRIVMSG #esoteric :"+str(dir(self))) < 1171593126 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :it won't work anyhow, you are missing a colon. < 1171593127 0 :bsmnt_bot!unknown@unknown.invalid PRIVMSG #esoteric :['COMMAND_CHAR', 'THREADING', '__doc__', '__init__', '__module__', 'chan', 'commands_running', 'commands_running_lock', 'connect', 'connected', 'disconnect', 'do_callbacks', 'do_ctcp', 'do_exec', 'do_kill', 'do_ps', 'do_quit', 'do_raw', 'errorchan', 'exec_execer', 'get_message', 'host', 'ident', 'ihope', 'listen', 'load_callbacks', 'message_re', 'nick', 'owner', 'pong', 'port', 'print_callbacks', 'raw', 'raw_regex_queue', 'readbuffer', 'realname', 'regi < 1171593152 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric :#exec self.raw("PRIVMSG #esoteric ""+str(dir(self))) < 1171593155 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric :#exec self.raw("PRIVMSG #esoteric :"+str(dir(self))) < 1171593159 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :um... < 1171593172 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :anyone else thinks sgeo is a bit dense today? < 1171593182 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :Sgeo: ~exec, not #exec < 1171593199 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric :Is it the same code on bsmnt_bot and ihope? erm < 1171593205 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :ACTION says this, having misspelled stdout as output for n-1 of the last n attempts < 1171593215 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :Sgeo: what? < 1171593220 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :~ps < 1171593221 0 :bsmnt_bot!unknown@unknown.invalid PRIVMSG #esoteric :None < 1171593227 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric : #exec self.raw("QUIT :") < 1171593227 0 :Sgeo!unknown@unknown.invalid PRIVMSG #esoteric :* DogKing has quit (Active Quit: ) < 1171593232 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :Sgeo: mine was running with # as the command character. < 1171593234 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :ihope is not a bot. I hope this clears things up. < 1171593257 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :I started it with an ~exec on this one. < 1171593258 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :ACTION growls at ihope_  < 1171593264 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :bsmntbombdood: yes? < 1171593277 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :just felt like growling < 1171593280 0 :ihope_!unknown@unknown.invalid PRIVMSG #esoteric :Oh. < 1171593364 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :ACTION giggles at ihope_  < 1171593366 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :hm... < 1171593408 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :a Zoo language, unifying OOK, MOO and various other beastly endeavours. < 1171593609 0 :bsmnt_bot!unknown@unknown.invalid QUIT : < 1171593628 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171593724 0 :bsmnt_bot!unknown@unknown.invalid QUIT :Client Quit < 1171593743 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171593794 0 :ihope!unknown@unknown.invalid QUIT :Success < 1171593842 0 :bsmnt_bot!unknown@unknown.invalid QUIT :Client Quit < 1171593858 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171594170 0 :bsmnt_bot!unknown@unknown.invalid QUIT : < 1171594186 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171594783 0 :bsmnt_bot!unknown@unknown.invalid QUIT :Excess Flood < 1171594801 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171594873 0 :ihope_!unknown@unknown.invalid NICK :foobar < 1171594902 0 :foobar!unknown@unknown.invalid NICK :ihope < 1171595111 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :ACTION again advertises nickserv's ghost command < 1171595140 0 :bsmnt_bot!unknown@unknown.invalid QUIT :Remote closed the connection < 1171595148 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171595157 0 :ShadowHntr!i=sentinel@wikipedia/Shadowhntr JOIN :#esoteric < 1171595553 0 :Sgeo!unknown@unknown.invalid QUIT :zelazny.freenode.net irc.freenode.net < 1171595553 0 :puzzlet!unknown@unknown.invalid QUIT :zelazny.freenode.net irc.freenode.net < 1171595577 0 :puzzlet!n=puzzlet@122.46.198.22 JOIN :#esoteric < 1171595655 0 :bsmnt_bot!unknown@unknown.invalid QUIT : < 1171595660 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171597249 0 :crathman!n=chatzill@cpe-76-185-186-143.tx.res.rr.com JOIN :#esoteric < 1171597310 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :fun, we can blow up any combinatory logic program to any size < 1171597315 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :replace I with SKI < 1171597323 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :K with S(KK)I < 1171597354 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :S with S(KS)I < 1171597357 0 :Sgeo!n=sgeo@ool-18bf61f7.dyn.optonline.net JOIN :#esoteric < 1171597461 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :repeat ad nauseuj < 1171597462 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :m < 1171597470 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :*am < 1171597521 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :right < 1171597525 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :ACTION draws his roman soldier sword < 1171597564 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :That is a noun of the FIRST declension, so it's accusative ends in... ? < 1171597572 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :*its < 1171597574 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :huh? < 1171597594 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :You haven't seen Life of Brian? < 1171597611 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :no < 1171597629 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :(Strictly speaking, neither have I, somehow I always miss the middle) < 1171597701 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :S(KI)I < 1171597710 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :There's this hilarious part where John Cleese's Roman character scolds Brian for writing Romans Go Home grafitti < 1171597736 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :But not because of what it says, but because he butchers the Latin grammar < 1171597916 0 :digital_me!unknown@unknown.invalid QUIT :Remote closed the connection < 1171598061 0 :bsmnt_bot!unknown@unknown.invalid QUIT : < 1171598064 0 :bsmnt_bot!i=gavin@abacus.kwzs.be JOIN :#esoteric < 1171598240 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :SSK < 1171598276 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :SSKxy = xyx < 1171598415 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Wait, what's this ghost advertisement stuff all about? < 1171598532 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :about getting back your nisk after being thrown off < 1171598536 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :*nick < 1171598557 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Also, bsmntbombdood, was it you some of us were trying to teach ordinal numbers to? < 1171598561 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :do /msg nickserv help ghost < 1171598563 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :oerjan: how's that relevant to stuff? < 1171598584 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Oh, the... right, yeah. < 1171598588 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :yeah < 1171598615 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :bsmntbombdood: got it figured out yet? < 1171598627 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :haven't read anything since then < 1171598661 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :bsmntbombdood: well, mind if I try one more time? < 1171598666 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :is it time for confusing him more by telling about epsilon? < 1171598673 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :oerjan: nah. < 1171598753 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :basically, ordinals are all about induction. < 1171598786 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :I'd say they're all about well-orderings. < 1171598804 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :That, too. < 1171598807 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Yeah. < 1171598822 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :But well-ordering is what you need for induction to be well-defined. < 1171598839 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :A well-ordering is an ordering of a set such that all subsets of the set have a least element. < 1171598839 0 :crathman!unknown@unknown.invalid QUIT :Read error: 110 (Connection timed out) < 1171598856 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :For example: the positive integers: {1, 2, 3, 4...} < 1171598873 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Any (non-empty) subset of them has a least element. < 1171598883 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :huh? < 1171598893 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :isn't that any set? < 1171598895 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :And that is equivalent to the usual rule of induction. < 1171598902 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Can you think of a set of positive integers that has no least element? < 1171598912 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :...Wait, what? < 1171598931 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Any set of positive integers has no least element. < 1171598939 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :*a < 1171598951 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :...Right, yes. < 1171598970 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Now, an ordinal number essentially expresses one notion of the size of a well-ordered set. < 1171599001 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :{1} has the ordinal number 1, {1,2} has the ordinal number 2, {1,2,3} has the ordinal number 3... < 1171599019 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Then for {1,2,3,4...}, the ordinal number is omega. < 1171599061 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Now, for a "bigger" well-ordering of the natural numbers, we could say 1 is greater than the rest: {2,3,4...1}. < 1171599082 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :There are other kinds of sets that _don't_ have least elements, for example the set of all _negative_ integers. < 1171599085 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Look at it as {2,3,4,5...1}, and it seems like it has one extra element. < 1171599089 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Yes, like that. < 1171599118 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Now, this one extra element is expressed by adding one, so this new set has the ordinal number omega+1. < 1171599147 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :{1,2,3,4,5...} is the same as {2,3,4,5,...1} < 1171599153 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Then if you say 1 is greater than everything except 2, and 2 is greater than everything, you get {3,4,5,6...1,2}. The ordinal number for that would be omega+2. < 1171599175 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :As a set, yes, but it's the order they're in that matters here, not the elements themselves. < 1171599177 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Not when you consider the ordering. < 1171599190 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :sets are unordered < 1171599206 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Well, call it an order instead of a set, then. < 1171599281 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :"Ordered set" is really an abbreviation for a set, plus an order relation on that set. < 1171599293 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :k < 1171599294 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :It's the same set, yes, but 1 is greater than everything else in the set--it's an infinity, basic(al)ly. < 1171599338 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :So then if you go do something like {0,2,4,6,8...1,3,5,7,9...}, you have the same set again, but this time you have an infinite number of things, each of which is greater than another infinity of things. < 1171599351 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :This is omega+omega, or omega*2. < 1171599393 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :If it confuses you to change the ordering of the natural numbers, it is possible (for now) to use sets of fractions instead. < 1171599407 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Indeed it is. < 1171599415 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :fractions? < 1171599435 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :How about something like this: {0, 0.9, 0.99, 0.999... 1} < 1171599437 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Say, {0, 1/2, 1/3, ..., 1, 1+1/2, 1+1/3, 1+1/4, ...} also has ordering omega*2 < 1171599450 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :oerjan: but that's still out of order. < 1171599453 0 :SevenInchBread!unknown@unknown.invalid QUIT :Read error: 113 (No route to host) < 1171599453 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :that would be omega+1 < 1171599456 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :whoops < 1171599474 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :{0, 1/2, 2/3, 3/4... 1, 1+1/2, 1+2/3...} < 1171599487 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :right < 1171599497 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :k < 1171599501 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :not sure where this is going < 1171599517 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Then you can still add more to the end: {0, 1/2, 2/3, 3/4... 1, 1+1/2, 1+2/3... 2} would represent the ordinal omega*2+1. < 1171599562 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Go as far as you want, adding as many infinities as you want: {0, 1/2, 2/3, 3/4... 1, 1+1/2... 2... 3... 4.....} < 1171599575 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Go on forever like *that*, and you have omega*omega, or omega^2. < 1171599598 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Now, the nice thing is that the different well-orderings are themselves well-ordered. < 1171599656 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Therefore, you can represent each ordinal as a set of ordinals: instead of {0, 1/2, 2/3, 3/4... 1, 1+1/2, 1+2/3, 1+3/4...}, you can have {0, 1, 2, 3... omega, omega+1, omega+2, omega+3...} < 1171599675 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :omega*2 happens to be the lowest ordinal number greater than all elements of that set. < 1171599715 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :And if you have a "continuous" set like that, it defines an ordinal number. < 1171599752 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :So if you took the unions of the sets corresponding to, say, omega, omega*2, omega*3, omega*4, etc., you'd end up with the set representing omega*omega. < 1171599803 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :The union, I mean, not unions. < 1171600038 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Often, an ordinal number is said to actually be the set of ordinal numbers that goes with it, so ordinal numbers are defined as being sets of ordinal numbers. < 1171600090 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Those are known as von Neumann ordinals, after the inventor. < 1171600225 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :You can add ordinals: < 1171600272 0 :Sgeo!unknown@unknown.invalid QUIT :Read error: 110 (Connection timed out) < 1171600281 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :If you have an ordered set in two parts, first one ordered as the ordinal a and then one part ordered as the ordinal b, then the ordinal of the whole set is called a+b. < 1171600342 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :You can see that in the omega+1, omega+2 etc. above. < 1171600377 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Strangely enough this addition is not commutative. < 1171600390 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :1+omega = omega != omega+1 < 1171600423 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :(It is associative however) < 1171600447 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :(I.e. a+(b+c) = (a+b)+c) < 1171600470 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :I like natural addition. < 1171600483 0 :Sgeo!n=sgeo@ool-18bf61f7.dyn.optonline.net JOIN :#esoteric < 1171600511 0 :ShadowHntr!unknown@unknown.invalid QUIT :"End of line." < 1171600548 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :To multiply: < 1171600702 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Make a set containing a subdivision into segments, all with the same order a, and such that the set of segments themselves have order b. Then that whole set has order a*b. < 1171600727 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :So omega*2 consists of two subsets, each with order omega. < 1171600738 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :This is not commutative either. < 1171600791 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :But it is associative, and there is distributivity: a*(b+c) = a*b + a*c < 1171601146 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :That distributivity hold only rightwards. < 1171601151 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :*holds < 1171601229 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :For powers, we need to use induction. < 1171601263 0 :goban!unknown@unknown.invalid QUIT :"Leaving" < 1171601281 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :a^1 = a, and a^(b+c) = a^b*a^c. < 1171601304 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Except that doesn't help us reach infinity, so: < 1171601362 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :a^b = union of a^(b_l) when b = union of b_l. < 1171601369 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :omega. < 1171601374 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :There, I've reached infinity! < 1171601377 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric ::-P < 1171601388 0 :alex-4!n=alex@c-71-231-132-227.hsd1.or.comcast.net JOIN :#esoteric < 1171601394 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Good, now you can explain omega^omega :) < 1171601545 0 :oklopol!unknown@unknown.invalid PRIVMSG #esoteric :oerjan: i don't hate any languages :) < 1171601559 0 :oklopol!unknown@unknown.invalid PRIVMSG #esoteric :but i don't know swedish that well < 1171601562 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :that's good, neither do i < 1171601568 0 :sp3tt!n=sp3tt@80-162.cust.umeaenergi.com JOIN :#esoteric < 1171601578 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :then you can explain oko here :) < 1171601593 0 :oklopol!unknown@unknown.invalid PRIVMSG #esoteric :okoing is a way of life :) < 1171601600 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :omega^omega: the union of omega^n where n < omega. < 1171601780 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Now then, epsilon = union of omega^(omega^(omega^...))) nested n times when n < omega < 1171601871 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :omega, omega^omega, omega^omega^omega, omega^omega^omega^omega... < 1171601881 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :omega^epsilon = epsilon, incidentally. < 1171601907 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :epsilon = omega^^omega, no? < 1171601909 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :If I remember right. < 1171601939 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :I suppose so. < 1171601954 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :I am not sure of that ^^ notation. < 1171601969 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Tetration? < 1171601980 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :And omega^^^omega would be epsilon_1. < 1171601987 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :I think. < 1171602002 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Well, maybe not. < 1171602013 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :(omega^^omega)^^omega? < 1171602026 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :I think we just went past what I remember :) < 1171602098 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Except one huge step more: < 1171602164 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :omega_1 = the union of all ordinals of reorderings of the natural numbers. < 1171602197 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :(I hope omega_1 is the right name. The first ordinal of cardinality aleph_1.) < 1171602348 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Yes, omega_1 is the first ordinal of cardinality aleph_1. < 1171602359 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :omega_n has cardinality aleph_n, in general. < 1171602366 0 :oklopol!unknown@unknown.invalid PRIVMSG #esoteric :wtf are you talking about :O < 1171602375 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Ordinal numbers < 1171602388 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :there's only two numbers < 1171602392 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :zero and one. < 1171602402 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :lament: what about... uh... hmm. < 1171602433 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :lament: is that algebraically closed? < 1171602441 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :I mean, surely not. < 1171602458 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :x^2 + x + 1 = 0 < 1171602461 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Solve that. < 1171602471 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :{0,1} form a field if that's what you're asking. < 1171602479 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Algebraically closed. < 1171602487 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Polynomials all have solutions. < 1171602508 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :x*x = x and x+x = 0, so that equation up there is equivalent to 1 = 0. < 1171602531 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Also, it's Friday over here. Less than ten minutes ago, it was Thursday. < 1171602539 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :I think I should be getting to bed. < 1171602545 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :so what if it's not algebraically closed? < 1171602558 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Then it cannot be all numbers. < 1171602566 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Then... uh... say, why don't we define CK_n for all ordinal numbers n? < 1171602587 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :okay, let's close it then < 1171602587 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :What is CK? < 1171602633 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :The smallest ordinal number that can't be enumerated by a computer of order n, where a computer of order n is a Turing machine, except able to solve the halting problems for computers of orders less than n. < 1171602640 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Close it, eh... < 1171602654 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Let's say B*B + B + 1 = 0. < 1171602661 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :That means B*B + B = 1. < 1171602689 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :So B(B + 1) = 1, if that matters at all. < 1171602708 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Hey, why don't we call it 2? < 1171602715 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :2*2 + 2 = 1. < 1171602720 0 :crathman!n=chatzill@cpe-76-185-186-143.tx.res.rr.com JOIN :#esoteric < 1171602738 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Then we could say 1 + 2 = 3. < 1171602746 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Eventually, you end up with all the nimbers. < 1171602752 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :;-) < 1171602758 0 :ihope!unknown@unknown.invalid PRIVMSG #esoteric :Fun. Bye! < 1171602952 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :well no < 1171602980 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :? < 1171603042 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :that doesn't sound right < 1171603083 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :What doesn't sound right, and by the way nimbers was probably not a misspelling. < 1171603111 0 :lament!unknown@unknown.invalid PRIVMSG #esoteric :oh, well, okay then < 1171603854 0 :ihope!unknown@unknown.invalid QUIT :Connection timed out < 1171605500 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :can K be made with S and I? < 1171605529 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :no, S and I cannot remove variables < 1171605565 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :They are in the subset called lambda_I calculus < 1171605588 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :where in \x.E, E has to contain x < 1171605599 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :right < 1171605630 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :is lambda_i calculus turing complete? < 1171605642 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :I vaguely recall yes < 1171605665 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :church numeral 0 doesn't work < 1171605685 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :something about simulating K for a large enough subset to make it work for numerals < 1171605687 0 :Sukoshi!unknown@unknown.invalid PRIVMSG #esoteric :Is this Unlambda fun? < 1171605702 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :combinatory logic < 1171605703 0 :Sukoshi!unknown@unknown.invalid PRIVMSG #esoteric :Is this (Unlambda fun) ? < 1171605721 0 :Sukoshi!unknown@unknown.invalid PRIVMSG #esoteric :Ah. Is he creating the Church numerals? < 1171605730 0 :crathman!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171605738 0 :crathman_!n=chatzill@cpe-76-185-186-143.tx.res.rr.com JOIN :#esoteric < 1171605740 0 :crathman_!unknown@unknown.invalid NICK :crathman < 1171605743 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :no we were discussing whether K is necessary for Turing completeness < 1171605795 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :i guess S and I might not be enough, to get lambda_I you need also B and C < 1171605823 0 :Sukoshi!unknown@unknown.invalid PRIVMSG #esoteric :Ah. < 1171605826 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :B and C don't get rid of variables though < 1171605846 0 :ShadowHntr!i=sentinel@wikipedia/Shadowhntr JOIN :#esoteric < 1171605884 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :s/variables/arguments/ < 1171605909 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :i don't know the construction for a "simulated" K for numerals, however < 1171605949 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :it was either Church or Curry's work, I guess < 1171606039 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :wikipedia: The constants of CLI are: I, B, C and S, which form a basis from which all CLI terms can be composed (modulo equality) < 1171606068 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :thought so < 1171606083 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :under "lambda calculus", I found the quote: < 1171606096 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Note that in Church's original lambda calculus, the formal parameter of a lambda expression was required to occur at least once in the function body, which made the above definition of 0 impossible < 1171606200 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :but they don't tell you what it is < 1171606262 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :where did you find that CLI quote? < 1171606328 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :http://en.wikipedia.org/wiki/Combinatory_logic#CLK_versus_CLI_calculus < 1171606676 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :heh, searching for lambdaI gives an article with the title "Proving PSN after ruining a perfectly good calculus" < 1171606684 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :*googling < 1171606684 0 :Sgeo!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171606771 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :PSN? < 1171606837 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :preservation of strong normalization < 1171606844 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :i think it was < 1171606857 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :it was the rest of the title i found funny :) < 1171607029 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :remember iota from the other day? < 1171607036 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :yes < 1171607064 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :If we use a different combinator, \x.xKSK, the definitions of S and K are shorter < 1171607085 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :x=\x.xKSK < 1171607091 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :i may have read that somewhere < 1171607096 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :K = (xx)x < 1171607129 0 :ShadowHntr!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171607274 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :S = x(xx) < 1171607280 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :much shorter than iota < 1171607344 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :as short as you could possibly get them < 1171607373 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :or could you get one of them to be xx? hm. < 1171607408 0 :ShadowHntr!i=sentinel@wikipedia/Shadowhntr JOIN :#esoteric < 1171607445 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :S = Kx is impossible < 1171607558 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :K=Sx would mean y = Kyz = Sxyz = xz(yz), but yz cannot determine y for all y and z so that is impossible < 1171607660 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :S = xK and K = xS seem harder to analyze < 1171608037 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :I think that's pretty darn good < 1171608075 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :`x`xx, 5 chars < 1171609009 0 :goban!n=whyso@ip68-229-102-1.hr.hr.cox.net JOIN :#esoteric < 1171610606 0 :goban!unknown@unknown.invalid QUIT :"Konversation terminated!" < 1171610739 0 :goban!n=whyso@ip68-229-102-1.hr.hr.cox.net JOIN :#esoteric < 1171610872 0 :helios_!i=helios@item.n1.helzilla.de JOIN :#esoteric < 1171610888 0 :helios24!unknown@unknown.invalid QUIT :"Leaving" < 1171610919 0 :helios_!unknown@unknown.invalid NICK :helios24 < 1171611470 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171611652 0 :goban!unknown@unknown.invalid QUIT :Remote closed the connection < 1171611873 0 :goban!n=whyso@ip68-229-102-1.hr.hr.cox.net JOIN :#esoteric < 1171612095 0 :goban!unknown@unknown.invalid QUIT :Client Quit < 1171612141 0 :crathman_!n=chatzill@cpe-76-185-186-143.tx.res.rr.com JOIN :#esoteric < 1171612164 0 :crathman!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171612187 0 :crathman_!unknown@unknown.invalid NICK :crathman < 1171612199 0 :goban!n=whyso@ip68-229-102-1.hr.hr.cox.net JOIN :#esoteric < 1171612799 0 :clog!unknown@unknown.invalid QUIT :ended < 1171612800 0 :clog!unknown@unknown.invalid JOIN :#esoteric < 1171613176 0 :Arrogant!i=Paragon@244.orlando-06-08rs.fl.dial-access.att.net JOIN :#esoteric < 1171613780 0 :oerjan!unknown@unknown.invalid QUIT :"leaving" < 1171615164 0 :crathman!unknown@unknown.invalid QUIT :Read error: 110 (Connection timed out) < 1171615968 0 :ShadowHntr!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171616014 0 :goban!unknown@unknown.invalid QUIT :"Konversation terminated!" < 1171616115 0 :goban!n=whyso@ip68-229-102-1.hr.hr.cox.net JOIN :#esoteric < 1171617096 0 :Arrogant!unknown@unknown.invalid QUIT :"Leaving" < 1171626430 0 :ihope!n=ihope@c-71-205-100-59.hsd1.mi.comcast.net JOIN :#esoteric < 1171626543 0 :ihope!unknown@unknown.invalid QUIT :Client Quit < 1171631341 0 :nazgjunk!n=htitan@wikipedia/Nazgjunk JOIN :#esoteric < 1171632008 0 :voodooattack!unknown@unknown.invalid QUIT :Read error: 110 (Connection timed out) < 1171632450 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171632727 0 :voodooattack!unknown@unknown.invalid QUIT :Nick collision from services. < 1171632737 0 :voodooattack|!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171632777 0 :voodooattack|!unknown@unknown.invalid NICK :voodooattack < 1171633283 0 :voodooattack!unknown@unknown.invalid QUIT :Nick collision from services. < 1171633297 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171634148 0 :voodooattack!unknown@unknown.invalid QUIT :Nick collision from services. < 1171634162 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171635186 0 :nazgjunk!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171635197 0 :UpTheDownstair!n=htitan@wikipedia/Nazgjunk JOIN :#esoteric < 1171635209 0 :UpTheDownstair!unknown@unknown.invalid NICK :nazgjunk < 1171636995 0 :ooooo!n=cccc@c911fdbe.bhz.virtua.com.br JOIN :#esoteric < 1171637520 0 :crathman!n=chatzill@69.15.198.171 JOIN :#esoteric < 1171640791 0 :nazgjunk!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171640806 0 :UpTheDownstair!n=htitan@wikipedia/Nazgjunk JOIN :#esoteric < 1171640861 0 :UpTheDownstair!unknown@unknown.invalid NICK :nazgjunk < 1171641335 0 :nazgjunk!unknown@unknown.invalid QUIT :Read error: 131 (Connection reset by peer) < 1171641344 0 :UpTheDownstair!n=htitan@wikipedia/Nazgjunk JOIN :#esoteric < 1171641529 0 :UpTheDownstair!unknown@unknown.invalid NICK :nazgjunk < 1171642572 0 :FabioNET!i=500@217.201.35.234 JOIN :#esoteric < 1171644253 0 :voodooattack!unknown@unknown.invalid QUIT :Nick collision from services. < 1171644267 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171645088 0 :voodooattack!unknown@unknown.invalid QUIT :Nick collision from services. < 1171645102 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171645316 0 :voodooattack!unknown@unknown.invalid QUIT :Nick collision from services. < 1171645330 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171646863 0 :sebbu!n=sebbu@ADijon-152-1-6-183.w83-194.abo.wanadoo.fr JOIN :#esoteric < 1171646876 0 :goban!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171646894 0 :goban!n=whyso@ip68-229-102-1.hr.hr.cox.net JOIN :#esoteric < 1171647382 0 :kxspxr!n=kxspxr@x1-6-00-0c-41-39-32-8e.k302.webspeed.dk JOIN :#esoteric < 1171647392 0 :kxspxr!unknown@unknown.invalid QUIT :Client Quit < 1171647532 0 :voodooattack!unknown@unknown.invalid PRIVMSG #esoteric :print "hi" < 1171647671 0 :UpTheDownstair!n=htitan@wikipedia/Nazgjunk JOIN :#esoteric < 1171647682 0 :nazgjunk!unknown@unknown.invalid QUIT :Read error: 104 (Connection reset by peer) < 1171647750 0 :UpTheDownstair!unknown@unknown.invalid NICK :nazgjunk < 1171648277 0 :voodooattack!unknown@unknown.invalid QUIT :Nick collision from services. < 1171648291 0 :voodooattack!n=voodooat@217.54.5.58 JOIN :#esoteric < 1171649169 0 :FabioNET!unknown@unknown.invalid QUIT :Read error: 145 (Connection timed out) < 1171650216 0 :FabioNET!i=500@217.201.26.44 JOIN :#esoteric < 1171650564 0 :sebbu2!n=sebbu@ADijon-152-1-42-120.w83-194.abo.wanadoo.fr JOIN :#esoteric < 1171651035 0 :sebbu!unknown@unknown.invalid QUIT :Read error: 60 (Operation timed out) < 1171651126 0 :FabioNET!unknown@unknown.invalid QUIT :Read error: 145 (Connection timed out) < 1171652076 0 :sebbu2!unknown@unknown.invalid NICK :sebbu < 1171654413 0 :FabioNET!i=500@217.201.3.245 JOIN :#esoteric < 1171655548 0 :ShadowHntr!i=sentinel@wikipedia/Shadowhntr JOIN :#esoteric < 1171657276 0 :_FabioNET_!i=500@217.201.2.221 JOIN :#esoteric < 1171657280 0 :FabioNET!unknown@unknown.invalid QUIT :Read error: 110 (Connection timed out) < 1171658354 0 :voodooattack!unknown@unknown.invalid QUIT : < 1171660847 0 :oerjan!n=oerjan@hagbart.nvg.ntnu.no JOIN :#esoteric < 1171660993 0 :SevenInchBread!n=CakeProp@wikipedia/The-Prophet-Wizard-of-the-Crayon-Cake JOIN :#esoteric < 1171661007 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :hi crumby one < 1171662300 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :x=\x.xSKS < 1171662304 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :S = xx < 1171662315 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :not sure if K is possible yet < 1171662322 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :hm... < 1171662388 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :I = x(xx) < 1171662520 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :how do you get that last one? < 1171662547 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :xS = SSKS < 1171662593 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :erm < 1171662677 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :SSKS = SS(KS) < 1171662699 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :I goofed < 1171662709 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :easy to do < 1171662832 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :I get x(x(xx))=S as well < 1171663052 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :x(xxx)=SS(SKS)=SSI < 1171663402 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :x(x(xxx))=S < 1171663435 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :xx(xx)=SS, x(xx)x=SxS, xxxx=Sxx < 1171663449 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :SSxy = Sx(xy) < 1171663469 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :you mean Sy(xy) < 1171663470 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :Sx(xy)z = xz(xyz) < 1171663515 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :what? < 1171663524 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :SSxy=Sy(xy) < 1171663524 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :i was just using x as a variable < 1171663541 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :i realized that < 1171663557 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :crap < 1171663559 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :yeah < 1171663637 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :i seem to be always getting back to S: x(xx(xx))=S too) < 1171663685 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :yeah < 1171663697 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :think this is a dead end < 1171663731 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :maybe, maybe not. at least getting S cuts many search branches short quick < 1171663755 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :because SKS = I < 1171663794 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :darn you are right < 1171663826 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :well not quite < 1171663833 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :but it's still \x.(((xS)K)S) and not \x.x(SKS) < 1171663897 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :none of the four-x versions actually contain K < 1171663938 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :or wait < 1171663958 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :well x itself is still in there so there might be a chance < 1171664200 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :...DNS is some weird, chaotic stuff... < 1171664217 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :but then again... that kind of applies to networking in general. < 1171664262 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :x(x(xx)x)=SK=KI eventually < 1171664680 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :x(xxxx)=SKS=I < 1171664724 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :cool < 1171665298 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :x(x(x(xx)x))=KS, I have a feeling of getting closer... < 1171665318 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :i've gone on to other combinators < 1171665318 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :(That was the first with 6 x's < 1171665321 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :) < 1171665336 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :fine then we aren't duplicating work < 1171665346 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :i'm going for shortness of S and K < 1171665365 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :indeed this x has been a disappointment in that respect < 1171665366 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :hmm... I'm really interested in the idea of an "anonymous decentralized server"... for lack of a better term < 1171665417 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :but then, if it really was shorter then since the combinator is the same size as the known one it would certainly have been used instead < 1171665438 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :i've got one with a short S and I < 1171665441 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :no K yet < 1171665446 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :hmm.. it'd be like a P2P network acting as a single virtual server... all the data would be partitioned amongst all the peers in the network... and so there would be no real "server". < 1171665479 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :...would be great for illegal stuff. :) < 1171665528 0 :GregorR!unknown@unknown.invalid PRIVMSG #esoteric :Uh, DHT you mean? < 1171665554 0 :GregorR!unknown@unknown.invalid PRIVMSG #esoteric :If you took any ol' DHT system, then connected to it without actually joining the DHT, you have exactly what you're looking for. < 1171665618 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :It would be great for free web hosting too... < 1171665646 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :since everyone being hosted is chipping in some process cycles and hard disk space of their own... there's no need to charge anyone for the service. < 1171665688 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :freenet < 1171665735 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :indeeed < 1171665750 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :without the kiddy-porn though, I hope < 1171665760 0 :GregorR!unknown@unknown.invalid PRIVMSG #esoteric :IIRC, there are no non-participating clients in FreeNet. < 1171665761 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :or maybe bittorrent < 1171665771 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :freenet sucks because it's written in java < 1171665774 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :GregorR: you could write a selfish client if you wanted to < 1171665793 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :nah... you could have kiddie porn. < 1171665796 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :bsmntbombdood: how so/ < 1171665803 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :SimonRC: resource hog < 1171665817 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :maybe < 1171665845 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :Some non-virtual instance methods might be nice in Java. < 1171665850 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :I ran freenet for a while untill I got tired of it using half my memory and all of my cpu < 1171665858 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :Or sealed classes. < 1171665870 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :they would speed up method calls a fair bit I ssupect < 1171665882 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :bsmntbombdood: and all your network connection < 1171665883 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :bsmntbombdood, you can't give it a maximum? < 1171665899 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :This is apparently about networking water coolers, from the looks of slide 2: http://www.dur.ac.uk/tom.friedetzky/local/par/pc14-4up.pdf < 1171665922 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :gargh < 1171665926 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :what? < 1171665929 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :X=\x.xSKSK < 1171665934 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :S = XX < 1171665941 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :what is this for? < 1171665969 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :I = X(XX) < 1171666013 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :SimonRC, trying to find a single combinator to have the shortest S and K < 1171666031 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :best we have so far is X=\x.xKSK < 1171666377 0 :SevenInchBread!unknown@unknown.invalid PRIVMSG #esoteric :hmmm... so freenet doesn't die down on its process cycles when it doesn't need them and/or when there's other stuff that needs them on your computer? < 1171667583 0 :nazgjunk!unknown@unknown.invalid QUIT :"i need to sleep ffs" < 1171668061 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :hmm http://ling.ucsd.edu/~barker/Iota/ < 1171668087 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :yeah < 1171668089 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :yes, that's where we started < 1171668111 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :but \x.xKSK is shorter than iota < 1171668160 0 :crathman!unknown@unknown.invalid QUIT :"Chatzilla 0.9.77 [Firefox 2.0.0.1/2006120418]" < 1171668454 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :oh wow < 1171668463 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :http://www.cs.uu.nl/people/jeroen/article/combinat/combinat.ps < 1171668465 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :? < 1171668495 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :Darn postscript < 1171668525 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :X = \f.fS(\xyz.x) < 1171668527 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :K = XX < 1171668531 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :S = X(XX) < 1171668553 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :ok that's the final word then < 1171668565 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :yeah < 1171668691 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :the worst is i am sure i have seen that URL before < 1171668775 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :it was on the iota page < 1171668909 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :it is considerably more complicated though < 1171668960 0 :sebbu!unknown@unknown.invalid QUIT :"@+" < 1171669305 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :\f.fS(S(S(KS)S(KK)(KK))(S(KK)I)) < 1171669356 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :crazy long < 1171669370 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :i think you have missed some optimizations < 1171669389 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :probably < 1171669397 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :\xyz.x = \x.K(Kx) = S(KK)K < 1171669413 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :uh...yeah < 1171669415 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric ::P < 1171669429 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :i'm stupid < 1171669529 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :\f.fS(S(KK)K)=SI(S(KS)(K(S(KK)K))) < 1171669538 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :wait < 1171669548 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :too late :) < 1171669562 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :whoops < 1171669584 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :\xyz.x = S(KK)(S(KK)I) < 1171669584 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :*S(SI(KS))(K(S(KK)K)) < 1171669590 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :not S(KK)K < 1171669602 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :S(KK)I=K < 1171669618 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :oh duh < 1171669659 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :follows from eta-reduction: \x.fx = f < 1171669692 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :yeah < 1171669757 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :ACTION goes... < 1171669762 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :silly me < 1171669824 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :I wonder if there's a shorter I than SKK < 1171669855 0 :SimonRC!unknown@unknown.invalid PRIVMSG #esoteric :no: S, K, SS, SK, KS, and KK are all not I < 1171669905 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :...so? < 1171669919 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :in iota, I is shorter than both S and K < 1171669938 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :oh you mean with that X < 1171670004 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :actually there is < 1171670017 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :because SKX is shorter than SKK :) < 1171670121 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :oh right < 1171670129 0 :bsmntbombdood!unknown@unknown.invalid PRIVMSG #esoteric :but there still could be a better one < 1171670171 0 :_FabioNET_!unknown@unknown.invalid QUIT :Read error: 110 (Connection timed out) < 1171670350 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :XX=K, X(XX)=K, XXX=KX, X(X(XX))=XK=KS_=S, X(XXX)=X(KX)=KXS(\xyz.x)=X(\xyz.x)=(\xyz.x)S(\xyz.x) < 1171670377 0 :oerjan!unknown@unknown.invalid PRIVMSG #esoteric :eh, wait...