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00:11:25 <oerjan> <shachaf> long time no fet <-- hm cross-language pun?
00:12:04 * oerjan checks omniglot for whether it works in any single one
00:13:47 <oerjan> hm nope. no language has both ja=yes and no=no
00:13:56 <oerjan> (on that list, anyway)
00:18:05 <oerjan> <hppavilion[1]> Remember kids: Chicken may seem fun, but remember to be safe <-- . o O ( UNSAFECOERCED CHICKEN )
00:19:43 <HackEgo> lol stands for laughing out legends
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00:25:28 <oerjan> also, Nofet is presumably Jafet's evil twin.
00:26:32 <oerjan> nemeses don't need to be family hth
00:27:35 <oerjan> hm i suppose evil universe mirror twins aren't technically either.
00:28:13 <oerjan> (exercise: how many ways can you permute evil, universe, mirror and twin there and still make sense)
00:28:26 <shachaf> oerjan: Are they genetic clones?
00:29:00 * boily mapole oerjan en français
00:29:04 <oerjan> shachaf: i thought cloning implied a common substrate.
00:32:03 <shachaf> I used to think "beard" meant "goatee".
00:32:14 <shachaf> I didn't know about the latter word.
00:32:22 <shachaf> I still feel odd about using it.
00:32:40 <myname> as long as you don't think it means goatse
00:33:09 * oerjan points boily at myname
00:34:45 * boily happily mapoles myname with glee
00:35:10 * boily *thwack* *thwack* *thwack* myname
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00:40:17 <boily_> maudit routeur de mes deux m'a te ******* aux vidanges tu vas voir ça sera pas long!
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00:41:19 <oerjan> hey how can i learn proper québécois when you censor the important words tdnh
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00:42:51 <boily> «crisser» was the word.
00:46:15 <boily> there's the French «crisser» (“to screech”, “to squeal”), and Québécois «crisser» (“to do something with violence or suddenly”).
00:49:34 <boily> derived from Christ, commonly pronounced «crisse» /kʁɪs/.
00:52:15 <oerjan> hm apparently "sheesh" is also one
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01:05:01 <boily> random dizziness. not moving much.
01:05:37 <lambdabot> KATL 262352Z 20009KT 10SM FEW075 FEW250 33/17 A3000 RMK AO2 SLP147 CB DSNT S & SW T03330172 10356 20333 55002
01:05:51 <quintopia> that got more mild since last i checked
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01:06:25 <quintopia> so is it true that quebec is less anti-american than anglophone canadia?
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01:08:15 <boily> canadia is anti-american?
01:09:37 <boily> I guess my question supports your point. there's no feeling of animosity here.
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01:34:32 <\oren\> Apparently if no party gets a majority, then the House of Rep.s will pick the president, and the Senate will pick the vice president. that could be fun!
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01:36:15 <\oren\> then you could have Paul Ryan/Tim Kaine! Or Hillary Clinton/Donald Trump
01:36:37 <\oren\> Or any number of horrifying cross-party appointments
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01:37:57 <\oren\> My battery wasn't charging for some reason, so I bought a new laptop charger with more watts
01:38:06 <\oren\> now it's charging up good!
01:39:26 <\oren\> specifically, 90 wats instead of only 65
01:40:56 <lambdabot> Couldn't match expected type ‘Int’ with actual type ‘[Char]’
01:40:56 <lambdabot> In the first argument of ‘replicate’, namely ‘"wat"’
01:40:56 <lambdabot> In the expression: replicate "wat" 25
01:44:01 <\oren\> hehehe this is charging up so damn fast
01:46:56 <boily> European Space Agency hth
01:47:27 <myname> i always have a good eye on my space agencies
01:47:51 <shachaf> the North American Space Agency is better hth
01:48:24 <\oren\> shachaf: it's National Aeronautics and Space Administration
01:48:47 <shachaf> \oren\: no, it's an agency for canada and mexico as well
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01:52:51 <HackEgo> Zekka: Welcome to the international hub for esoteric programming language design and deployment! For more information, check out our wiki: <http://esolangs.org/>. (For the other kind of esoterica, try #esoteric on EFnet or DALnet.)
01:52:57 <lambdabot> Local time for myname is Wed Jul 27 02:52:57 2016
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02:09:57 <quintopia> myname: european speedrunner assembly
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02:30:08 <oerjan> if you run fast enough, you get into space, obviously.
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02:36:17 <myname> yeah, i did that twice
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02:43:45 <tswett> It is not the case that a human can run arbitrarily fast without getting into space.
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02:47:01 <tswett> As an example, I cannot run at 120 miles per hour (200 kilometers per hour) without getting into space.
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02:55:56 <myname> i am wondering wether the sentence is corrext under the assumption that people cannot do arbitrary small turns
02:56:34 <myname> i.e. for every speed you are running, there should be a smallest possible circle you can run in
02:56:46 <myname> and the size of those should increment as speed does
02:57:05 <myname> leading to space at some ridiculously high speed
02:58:21 <\oren\> well at some speed, the ground falls away from your feet and you can't accelerate yourself
02:59:09 <myname> only if you accelerate in steps that are too small
02:59:28 <myname> if i get from 0 to speed of light in one instant, that should work out
02:59:44 <\oren\> but you'll end up in space
02:59:53 <oerjan> SPAAAAAAAAAAAAAAAAAAAAAAAACE
03:00:57 <myname> speed of light should be slightly higher
03:01:28 <\oren\> at horizantal speed v > sqrt(g*r), you fall upward
03:02:10 <\oren\> (where g is earths gravity and r is earth's radius)
03:02:41 <oerjan> the equation might not be quite relativistically correct.
03:03:11 <tswett> Acceleration is square of speed divided by radius?
03:03:34 <oerjan> in a circular movement, yes
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03:06:58 <myname> so as long as r cannot get as close to 0 as wanted, you will always break out
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04:56:35 <\oren\> Yay, I finally have a laptop charger that can charge while the sytem is powered up!
05:00:08 <shachaf> Does the charger go on your lap?
05:00:59 <\oren\> oerjan: yeah but the obvious question is why did this laptop come with a 65 watt charger when that's inadequate to both charge the battery and run the system at full power
05:01:49 <\oren\> do they expect people to shut off their laptops to charge them? does anyone do that?
05:03:52 <oerjan> i suspect when you bought it, you forgot to check the box where it said to charge extra hth
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05:11:54 * shachaf grabs the swatter and swats oerjan -----###
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07:44:47 <izabera> idea for a new kernel: let people use recv on non socket file descriptors
07:45:48 <izabera> so e.g. you can do non blocking reads without fcntl
07:47:09 <pikhq> Though... recv *already works* on non-socket FDs.
07:47:53 <izabera> pretty sure you get ENOTSOCK
07:48:34 <pikhq> Depends on if you have a non-zero flags argument.
07:48:48 <pikhq> Oh, huh. That's *optional* behavior.
07:49:06 <pikhq> Per POSIX recv may refuse to work on non-sockets as it sees fit.
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07:49:51 <pikhq> Oh, per POSIX it's required to.
07:50:39 <pikhq> izabera: More useful thing: let poll and/or select actually tell if a read request will block or not on a file.
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07:50:53 <pikhq> Clearly I have been up too long and should go to bed.
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09:03:17 <izabera> https://kat.am limited functionality
09:03:28 <izabera> but i'm glad to see it back
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12:34:46 <HackEgo> Now I Know My ABC's \ 1UU \ Enchantment \ At the beginning of your upkeep, if you control permanents with names that include all twenty-six letters of the English alphabet, you win the game. \ UNH-R
12:36:49 <b_jonas> myname: un-cards are almost all the cards from the Unglued and Unhinged M:tG sets, two sets for sort-of self-parody that do things M:tG can't normally do. The cards have a silver outer border, and they're not legal for any sort of serious game or tournaments.
12:37:27 <HackEgo> Vanquish the Foul \ 5W \ Sorcery \ Destroy target creature with power 4 or greater. Scry 1. (Look at the top card of your library. You may put that card on the bottom of your library.) \ THS-U
12:38:05 <FireFly> Ah, UNH-r / THS-U is the set
12:38:36 <b_jonas> `fetch http://www.yawgatog.com/resources/oracle/All%20Sets-2016-07-23.zip share/mtg/AllSets-2016-04-08.zip
12:38:36 <HackEgo> http://www.yawgatog.com/resources/oracle/All%20Sets-2016-07-23.zip%20share/mtg/AllSets-2016-04-08.zip: \ 2016-07-27 11:38:33 ERROR 404: Not Found.
12:38:46 <b_jonas> Firefly: yes. UNH is Unhinged.
12:39:00 <b_jonas> `fetch http://www.yawgatog.com/resources/oracle/All%20Sets-2016-07-23.zip
12:39:08 <HackEgo> 2016-07-27 11:39:01 URL:http://www.yawgatog.com/resources/oracle/All%20Sets-2016-07-23.zip [719795/719795] -> "All Sets-2016-07-23.zip" [1]
12:39:27 <b_jonas> ``` mv -vi "All Sets-2016-07-23.zip" share/mtg/
12:39:34 <HackEgo> `All Sets-2016-07-23.zip' -> `share/mtg/All Sets-2016-07-23.zip'
12:40:15 <b_jonas> ``` cd share/mtg && unzip -l "All Sets-2016-07-23.zip"
12:40:16 <HackEgo> bash: unzip: command not found
12:40:48 <int-e> boo, "Our Market Research Shows That Players Like Really Long Card Names So We Made this Card to Have the Absolute Longest Card Name Ever Elemental" contains only 21 distinct letter (missing fjqxz)
12:41:07 <b_jonas> ``` cd share/mtg && zcat "All Sets-2016-07-23.zip" > allsets-2016-07-23.zip
12:41:35 <b_jonas> ``` wc share/mtg/allsetes-2016-07-23.zip
12:41:38 <HackEgo> wc: share/mtg/allsetes-2016-07-23.zip: No such file or directory
12:41:47 <b_jonas> ``` wc share/mtg/allsets-2016-07-23.zip
12:41:49 <HackEgo> 117206 527886 3165532 share/mtg/allsets-2016-07-23.zip
12:42:01 <b_jonas> ``` ln -svf allsets-2016-07-23.zip share/mtg/allsets.txt
12:42:06 <HackEgo> `share/mtg/allsets.txt' -> `allsets-2016-07-23.zip'
12:43:00 <b_jonas> `card-by-name harmless offering
12:43:02 <HackEgo> Harmless Offering \ 2R \ Sorcery \ Target opponent gains control of target permanent you control. \ EMN-R
12:43:21 <HackEgo> Usage: jar {ctxui}[vfm0Me] [jar-file] [manifest-file] [entry-point] [-C dir] files ... \ Options: \ -c create new archive \ -t list table of contents for archive \ -x extract named (or all) files from archive \ -u update existing archive \ -v generate verbose output on standard output \ -f specify archive file name \
12:43:33 <int-e> there's your unzip ;-)
12:44:02 <b_jonas> int-e: I should just install a 7z
12:44:26 <int-e> `` jar -t share/mtg/"All Sets-2016-07-23.zip"
12:49:20 <HackEgo> Usage: tar [OPTION...] [FILE]... \ GNU `tar' saves many files together into a single tape or disk archive, and can \ restore individual files from the archive. \ \ Examples: \ tar -cf archive.tar foo bar # Create archive.tar from files foo and bar. \ tar -tvf archive.tar # List all files in archive.tar verbosely. \ tar -xf archive.t
12:49:25 <HackEgo> bzip2, a block-sorting file compressor. Version 1.0.6, 6-Sept-2010. \ \ usage: bzip2 [flags and input files in any order] \ \ -h --help print this message \ -d --decompress force decompression \ -z --compress force compression \ -k --keep keep (don't delete) input files \ -f --force overwr
12:49:28 <HackEgo> Usage: xz [OPTION]... [FILE]... \ Compress or decompress FILEs in the .xz format. \ \ -z, --compress force compression \ -d, --decompress force decompression \ -t, --test test compressed file integrity \ -l, --list list information about .xz files \ -k, --keep keep (don't delete) input files \ -f, --f
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13:09:32 <int-e> Is oerjan's hydra still alive?
13:10:56 <myname> you aren't supposed to asl about someone elses penis
13:22:50 <b_jonas> in HackEgo, do we have a directory under the versioned file system that's also in the shared library path? I want to install a binary that uses a shared library. if there's such a directory, I'll install directly. otherwise, I'll create a shell script wrapper that sets LD_PRELOAD
13:24:08 <b_jonas> also, why don't we have a fracking /hackenv/libexec directory?
13:25:27 <b_jonas> oh right, we can't have a user-writable directory in the GLOBAL shared library path, because that would require us writing the system /etc/ld.so.cache
13:25:42 <b_jonas> and there's apparently no LD_LIBRARY_PATH set
13:25:50 <b_jonas> ok, I'll create a LD_LIBRARY_PATH wrapper then
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13:33:21 <HackEgo> myname is not your name. You don't know what they are doing. Or you are doing. Or am I? He is Perl's evil twin brother.
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13:39:51 <b_jonas> `fetch http://russell2.math.bme.hu/~ambrus/pu/p7zip-16.02-linux-bin-only.tar.xz
13:40:08 <HackEgo> 2016-07-27 12:40:03 URL:http://russell2.math.bme.hu/~ambrus/pu/p7zip-16.02-linux-bin-only.tar.xz [1143816/1143816] -> "p7zip-16.02-linux-bin-only.tar.xz" [1]
13:40:12 <b_jonas> ``` tar tf p7zip-16.02-linux-bin-only.tar.xz
13:40:15 <HackEgo> bin/ \ bin/7z \ bin/7za \ lib/ \ lib/p7zip-16.02/ \ lib/p7zip-16.02/7z \ lib/p7zip-16.02/7z.so
13:40:22 <b_jonas> ``` tar xvf p7zip-16.02-linux-bin-only.tar.xz
13:40:34 <HackEgo> bin/ \ bin/7z \ bin/7za \ lib/ \ lib/p7zip-16.02/ \ lib/p7zip-16.02/7z \ lib/p7zip-16.02/7z.so
13:40:38 <b_jonas> `rm p7zip-16.02-linux-bin-only.tar.xz
13:42:01 <b_jonas> ``` perl -pie y/\\r// bin/7z
13:42:03 <HackEgo> Can't open perl script "y/\r//": No such file or directory
13:42:07 <b_jonas> ``` perl -pi -e y/\\r// bin/7z
13:42:23 <b_jonas> ``` perl -pi -e y/\\r//d bin/7z
13:42:32 <HackEgo> 52) <oklopol> if a girl is that cute, i don't care how many penises she has \ 173) <elliott> oerjan: What, can girls aim their penises better?
13:43:00 <b_jonas> ``` perl -pi -e 's/LD_PRELOAD/LD_LIBRARY_PATH/' bin/7z
13:44:16 <HackEgo> /hackenv/lib/p7zip-16.02/7z: 1: /hackenv/lib/p7zip-16.02/7z: Syntax error: "(" unexpected
13:44:25 <b_jonas> what does that error message even come from?
13:45:07 <HackEgo> bash: /hackenv/bin/7za: cannot execute binary file
13:45:52 <b_jonas> this doesn't seem to be working
13:57:20 <b_jonas> might have to compile a new one or something
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14:07:03 <b_jonas> ``` objdump -p bin/7za | grep ^..NEEDED
14:07:05 <HackEgo> NEEDED libpthread.so.0 \ NEEDED libc.so.6
14:07:39 <b_jonas> that's why. it's an x86_32 executable, and we don't have x86_32 libraries, not even libc.so.6
14:08:01 <HackEgo> \ bin/7za: file format elf32-i386 \ architecture: i386, flags 0x00000112: \ EXEC_P, HAS_SYMS, D_PAGED \ start address 0x0804a8f0
14:08:47 <b_jonas> I'd probably have to build a static one for source if I want this
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14:08:56 <b_jonas> or an x86_64 dynamic one from source
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16:56:15 <\oren\> Hmm... are Hungary/hungry puns racist?
16:56:41 <b_jonas> \oren\: I don't think they're racist, but they're kind of boring
16:57:40 <\oren\> How about Turkey/turkey puns?
16:58:39 <myname> what's the difference between racism and asians? ...
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17:26:39 <almightynsx1> does anyone know of any good documentaries about real magic?
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17:29:06 <izabera> and with real you mean not the gathering?
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17:38:22 <Taneb> `welcome almightynsx1
17:38:27 <HackEgo> almightynsx1: Welcome to the international hub for esoteric programming language design and deployment! For more information, check out our wiki: <http://esolangs.org/>. (For the other kind of esoterica, try #esoteric on EFnet or DALnet.)
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18:29:00 <izabera> the opposite of assassin is dickdickout
19:02:17 <Taneb> izabera, I don't think ass has a defined opposite
19:02:37 <Taneb> One could argue that its opposite should be, for example, tits
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19:13:46 <Taneb> Wow, why am I doing this
19:13:57 <Taneb> Why am I nitpicking a joke I actually found rather funny
19:14:08 <Taneb> izabera, apologies, and thank you for the joke
19:29:39 <Elronnd> One might argue that the opposite of ass is philanthropist, but that completely ruins the joke
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19:35:03 <\oren\> Trump openly called for the russians to hack hillary and release her private emails
19:36:11 <\oren\> The entire planet is entering an age of madness
19:38:43 <\oren\> This is going to be hilarious and terrifying at the same time
19:41:41 <int-e> nah, it's just us people who're going mad
19:42:12 <int-e> (mad human disease)
19:45:39 <HackEgo> This wisdom entry was censored for being too accurate.
19:45:51 <HackEgo> <oerjan> le/rn mad/This wisdom entry was censored for being too accurate. \ <oerjan> rm wisdom/mad #this thing has been too damn true lately \ <Bike> revert \ <FreeFull> for x in wisdom/*; do rev "$x" > "$x"a; mv "$x"a "$x"; done \ <oerjan> revert \ <FreeFull> run rm -rf wisdom \ <shachaf> revert 0 \ <shachaf> run rm -rf wisdom/* \ Initial impor
19:47:40 <shachaf> oerjan: Why did you censor that wisdom entry?
19:48:31 <int-e> He could've cited copyright reasons... except they expired, I think: '"But I don't want to go among mad people," Alice remarked. "Oh, you can't help that," said the Cat: "we're all mad here. I'm mad. You're mad." "How do you know I'm mad?" said Alice. "You must be," said the Cat, "or you wouldn't have come here."'
19:49:12 <FreeFull> Caroll died in 1898, there is no way the copyright hasn't expired
19:49:37 <HackEgo> The U are a very mad people.
19:49:49 <HackEgo> wisdom/hydrogen \ wisdom/holy water \ wisdom/welcome.eo \ wisdom/nobody \ wisdom/itidus21 \ wisdom/everyone \ wisdom/\oren\ \ wisdom/pizza \ wisdom/skeleton \ wisdom/sand \ wisdom/the u \ wisdom/madness \ wisdom/vampire \ wisdom/prography \ wisdom/madbr \ wisdom/mroman \ wisdom/alice \ wisdom/marriage \ wisdom/lmt \ wisdom/progres \ wisdom/@ \ wisd
19:50:05 <HackEgo> /home/hackbot/hackbot.hg/multibot_cmds/lib/limits: line 5: exec: skeleton: not found
19:50:07 <HackEgo> A skeleton is an unintelligent undead, similar to the zombie but harder to create, because it's lacking most of the body. The best skeletons are made by groups of people, so-called skeleton crews.
19:50:33 <HackEgo> Hydrogen is what stars are made of. There's a conjecture that at the immense pressures inside Jupiter or Saturn, hydrogen might form a superconducting liquid metal.
19:50:40 <shachaf> `` rgrep -lP '\bmad\b' wisdom
19:50:42 <HackEgo> wisdom/nobody \ wisdom/everyone \ wisdom/the u \ wisdom/alice \ wisdom/lmt \ wisdom/gamemanj
19:50:56 <shachaf> `1 rgrep -P '\bmad\b' wisdom
19:50:59 <HackEgo> 1/2:wisdom/nobody:Nobody killed the cyclops Polyphemos after he tried to eat a shipful of sailors, and this perceived injustice made Poseidon so mad he swore vengeance at him and the gods couldn't calm him down for ten years. \ wisdom/everyone:Everyone in here is mad. \ wisdom/the u:The U are a very mad people. \ wisdom/alice:Alice
19:51:12 <HackEgo> 2/2:doesn't want to go among mad people. \ wisdom/lmt:lmt is insufficiently mad for this channel. \ wisdom/gamemanj:gamemanj is also the mad scientist I. N. Here.
19:52:41 <int-e> shachaf: anyway, good question... it was accurate in a good way.
19:53:11 <HackEgo> Alice doesn't want to go among mad people.
19:53:27 <int-e> some traces remain, apparently.
19:53:47 <HackEgo> <int-e> revert accbc9c5c7ec \ <ais523> echo wisdom/* | shuf | head -n 10 | xargs rm \ <mroman> learn Alice doesn\'t want to go among mad people.
19:56:09 <int-e> I checked the log and indeed this is an offspring of the "mad" entry.
19:58:30 <int-e> Before oerjan *murdered* it.
19:59:32 -!- augur has joined.
20:01:26 <HackEgo> 1/1:wisdom/madness:madness lies thataway. \ wisdom/mroman:mroman is a leading artist in password security (SFW). He also likes black madness. He can design password hashes that are worse than the identity function. He invented the identity function. He's also an artist in unconventional warfare.
20:02:09 <myname> i am curious to see such a hash function
20:02:31 <HackEgo> identify function? ¯\(°_o)/¯
20:02:50 <int-e> myname: take any constant function
20:03:10 <myname> yeah, that's what i thought of, too
20:03:12 <shachaf> Someone once gave me a puzzle: Find two periodic functions whose sum is the identity function.
20:03:15 <int-e> (it may be hard to do worse than that)
20:03:21 <myname> but i wouldn't say it's worse
20:03:41 <myname> it is easy to login as someone else
20:03:53 <myname> but it is impossible to get the original password in case of a leak
20:04:14 <int-e> myname: hmm, true. so it depends on what you're trying to defend against
20:09:39 <int-e> shachaf: is it okay to work in Z/6Z? (I guess you want R -> R, but you didn't specify that)
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20:10:13 <shachaf> I think it requires the axiom of choice.
20:11:41 <int-e> thanks I'll ponder that on my way home
20:12:36 <int-e> (involving the axiom of choice isn't much of a surprise)
20:44:56 <\oren\> hmm... something to do with interference patterns
20:48:41 <\oren\> the periods definitly have to be different
20:49:46 <\oren\> and in fact, at least one of them has to be irrational
21:01:57 <\oren\> hmm, could you not just take the fourier series and divide it into two?
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21:06:37 <\oren\> suppose the period of f is a, and the period of g is b
21:12:39 <int-e> shachaf: okay, you don't have to be overly creative for that problem (no transfinite induction required)
21:12:56 <int-e> shachaf: (only a straightforward application of the AoX)
21:12:57 <\oren\> hmmm so you really need only find a single function g, and then prove that there exists an a, such that for all x, 0 = g(x) + a - g(x + a)
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21:14:15 <\oren\> oh, and also prove that there exists b such that from all x, 0 = g(x) - g(x + b)
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21:19:02 <\oren\> int-e: axiom of choice? hmmm well what if you turned the real numbers into a cartesian product
21:21:17 <\oren\> one periodic function that might help is the modulo function
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21:23:09 * \oren\ looks through thing equivalent to the axiom of choice. there are a lot
21:23:37 <int-e> shachaf: http://sprunge.us/BWCV (spoiler)
21:24:46 <\oren\> what if you made the real numbers into a vector space and found a basis
21:25:45 <\oren\> for example the basis (...,10,1,0.1,...)
21:26:20 <\oren\> every real number can be represented as a linear combination of those
21:26:34 <\oren\> with integer coeficints too
21:27:18 <int-e> \oren\: but not uniquely, which is potentially a problem
21:27:19 <\oren\> but it isn't really a good basis because they aren't linearly indepeted
21:27:59 <\oren\> int-e: right so what we need is a basis where they're all primes or inverted primes or something
21:28:09 <int-e> I'm not ruling out that such a vector space construction works but... it has to be over some field, and if you want to obtain the usual addition in R as vector space addition, the field must have characteristic 0. Q is probably the natural choice in that case.
21:28:53 <\oren\> the coeficints would be rationals? ok
21:29:15 <int-e> "if you want to obtain the usual addition in R as vector space addition"
21:30:49 <int-e> Anyway I didn't find vector spaces useful here.
21:30:57 <shachaf> int-e: The person who gave me the puzzle used the vector space of R over Q.
21:31:01 <\oren\> int-e: well I do, because we need to have the end result two functions that add together
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21:35:19 <\oren\> shachaf: ok well that vector space must have a basis by the
21:35:52 <\oren\> so suppose it's some set of numbers A={a,b,...}
21:36:08 <\oren\> defiantly an infinite set
21:37:01 <\oren\> can we show that f_a(x) = the coeficient of x for a is periodic?
21:37:12 <int-e> shachaf: okay, I can make that work but it seems to be an unecessary complication to me.
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21:39:14 <\oren\> if we can, then all that remains is to prove that there exists some other number z, such that for all x, f_a(x) + z - f_a(x + z) = 0
21:41:27 <FreeFull> \oren\: Aren't real numbers already a vector space
21:41:46 <\oren\> hmm f_a(b) = 0 for any b in A\a
21:42:02 <int-e> FreeFull: sure, but not in a useful way for shachaf's puzzle
21:42:22 <\oren\> and f_a(x+b) = f_a(x) + f_a(b) = f_a(x)
21:42:39 <FreeFull> I'm thinking the two periodic functions aren't continuous
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21:43:03 <FreeFull> Also you only have to find one periodic function
21:43:13 <int-e> FreeFull: you can rest assured that they are not; their graphs are both dense in the real plane
21:43:32 <\oren\> FreeFull: and prove that x-f(x) is also periodic
21:45:31 <\oren\> and I think f_a(a^2) = a
21:46:23 <\oren\> hmm I wonder what the period of x - f_a(x) would be?
21:46:50 <\oren\> FreeFull: it certainly does, you need it in order to prove that it's periodic
21:47:21 <FreeFull> Hm, I assumed the periods have to be equal, but maybe not
21:47:29 <int-e> FreeFull: they can't be equal
21:48:03 <FreeFull> I bet it'd be best to use a fourier transform somehow
21:48:07 <int-e> FreeFull: otherwise the sum of the two functions would be periodic (with the same period, and potentially shorter ones), and f(x) = x isn't periodic.
21:48:54 <FreeFull> Means that the periods can't be a rational multiple of each other either
21:49:29 <int-e> FreeFull: in fact the two periods have to be incommensurable, as the Pythagoreans would say.
21:50:09 <int-e> (well, as you just pointed out yourself)
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21:51:47 <FreeFull> You do need an infinite number of discontinuities, but does the function have to be discontinuous everywhere, or can you get away with some continuity?
21:52:20 <int-e> FreeFull: and the point of viewing R as a vector space, as far as I can see, is to make the two periods part of the basis of the vector space. So R as vector space over R doesn't help.
21:52:31 <wob_jonas> oh, a calculus question. let me look at the logs (though I probably can't solve it, I'm bad at calculus)
21:52:44 <int-e> FreeFull: no, continuity anywhere would contradict denseness of the graph in the plane ;)
21:52:49 <\oren\> wob_jonas: more like an algebra question
21:52:57 <FreeFull> int-e: Ah, right, you already proved it's dense
21:53:16 <int-e> (smiley because it's a sledgehammer argument)
21:53:41 <int-e> wob_jonas: finding two periodic function (R -> R) whose sum is the identity function
21:53:42 <FreeFull> Damn, it's actually really difficult to come up with functions that are continuous nowhere
21:54:03 <int-e> FreeFull: f(x) = 1 if x in Q, 0 otherwise.
21:54:04 <wob_jonas> int-e: oh... I think I heard that, but I don't know a solution off-hand. hmm
21:54:07 <\oren\> oh, wait, we have to use g(x) = f_a(x)a
21:54:25 <wob_jonas> oh, isn't that a set theory question actually? or at least one solution is
21:54:28 <\oren\> which means that g(x) still has period b
21:55:08 <\oren\> and also, g(x + a) = g(x) + g(a) = g(x) + a
21:55:31 <wob_jonas> let me think, I think there might be a construction using the well-ordering theorem
21:56:04 <\oren\> means that x + a - g(x + a) = x + a - g(x) - a = x - g(x)
21:56:15 <\oren\> so x - g(x) has period a.
21:56:17 <int-e> wob_jonas brings out the big guns.
21:56:37 <\oren\> int-e: I already solved it
21:56:39 <wob_jonas> int-e: I doubt there's a simple algebraic solutino
21:57:01 <\oren\> except that I have no idea how to construct a basis for R over Q
21:57:01 <int-e> wob_jonas: shachaf has a solution; I have one at http://sprunge.us/BWCV; \oren\ is stumbling around, I think; I don't know about FreeFull.
21:57:05 <wob_jonas> as in, I think you need axiom of choice for it
21:57:12 <FreeFull> I don't even have any idea how to do it, really
21:57:15 <int-e> wob_jonas: well, the Axiom of Choice will play into the solution in some form.
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21:57:20 <wob_jonas> int-e: I want to think about it without reading a full solution for a little bit
21:57:33 <int-e> wob_jonas: but well-ordering may not be the best form :)
21:57:53 <wob_jonas> int-e: sure, it might be the theorem that every vector space has a basis (was mentioned above)
21:58:01 <int-e> wob_jonas: sure, I'm just stating it's there and summarizing what's happing, since you didn't look at the logs.
21:58:05 <FreeFull> int-e: Does it matter that it's sqrt(2) in particular?
21:58:12 <wob_jonas> just not enough to see the question
21:58:18 <int-e> FreeFull: no, it's just convenient.
21:58:31 <int-e> FreeFull: I mean, name an irrational number!
21:58:46 <wob_jonas> by the way, do you know my other favourite maths question? not the Chameleon one, but the one that has a LOT of different ways to solve, which is why I like it
21:59:01 <\oren\> if you have such a basis A, then f_a(x)a where a is a member of the basis and f_a(x) is the coeficient of a in x, has period b where b is any other member of A, and x - f_a(x)a is periodic with period a
21:59:30 <wob_jonas> I would guess you can start with any two periods whose quotient is irrational
21:59:46 <wob_jonas> it's not likely that there's a further restriction
21:59:46 <FreeFull> Another irrational number: 1 + 1/(2 + 1/(3 + 1/(4 + ...)))
22:00:06 <wob_jonas> FreeFull: hmm, does that have a closed form?
22:00:20 <wob_jonas> I could check in plouffe's but I'm lazy
22:02:03 <\oren\> I found an article online that uses this approach
22:02:51 <\oren\> except they call f_a(x) instead (x,a)
22:03:23 <\oren\> they also have x^2 as a sum of periodic functions
22:03:54 <wob_jonas> hmm, indeed maybe it would be worth to use a vector space basis (of the reals over rationals), which can help because we know it's countable
22:03:55 <\oren\> A polynomial of degree n is the sum of n+1 periodic functions
22:04:22 <\oren\> wob_jonas: and the coeficints are each periodic
22:04:45 <wob_jonas> \oren\: I don't see why that's important
22:04:52 <wob_jonas> I mean, I don't see why that's necessary
22:05:00 <wob_jonas> it might simplify the construction, but I don't see why
22:05:35 <\oren\> suppose a and b are two of your basis numbers
22:05:52 <\oren\> f_a(x) is the coeficint of a in x
22:06:18 <\oren\> (or else they aren't independent)
22:06:36 <\oren\> f_a(x + b) = f_a(x) + 0
22:07:40 <wob_jonas> \oren\: ok, now I don't get what you're talking about. what coefficients of what?
22:08:08 <\oren\> well if x is in R, and A is a basis for R over Q
22:08:32 <\oren\> that means there exist functions f_a, f_b,.... for each a,b.... in A
22:08:55 <\oren\> such that f_a(x)*a + f_b(x)*b +.... = x
22:09:39 <\oren\> these rational coeficients are used to add up rational multiples of the basis numbers, to create each number in R
22:11:40 <FreeFull> wob_jonas: ISC says it might be Besl(0,2)/Besl(1,2)
22:12:37 <\oren\> so then, the expansion of a in A would be (1,0,0,....)
22:13:11 <FreeFull> wob_jonas: Yeah, that seems to be actually the case
22:13:15 <\oren\> so then , we know that f_a(b) is 0, just as f_b(a) is 0
22:13:57 <\oren\> and f_a(x + b) = f_a(x) + f_a(b) = f_a(x)
22:14:09 <\oren\> therefore f_a is periodic with period b
22:14:28 <\oren\> (as well as other periods, but it is enoght to have one)
22:14:39 <FreeFull> wob_jonas: https://www.wolframalpha.com/input/?i=BesselI(0,2)%2FBesselI(1,2)
22:15:02 <FreeFull> It even gives a continued fraction
22:15:18 <shachaf> "(1,0,0,....)" -- the basis can't be countable, can it?
22:15:37 <int-e> Oh the point for the polynomials of degree n is that p(<sum of n+1 terms>) splits into a sum of n+1 functions with only n arguments each.
22:15:40 <\oren\> shachaf: maybe not, but so long as we can choose two elements out of it
22:15:58 <FreeFull> Lower down, it says that 1.433127... = 1/2 for some reason
22:16:16 <wob_jonas> I said some really stupid things about this math problem above, so ignore almost all of it please
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22:16:37 <\oren\> then I think what I said work
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22:21:19 <\oren\> x - f_a(x)*a defiantly has period a
22:21:31 <int-e> \oren\: uhm how do you define a sum of uncountably many terms? besides, the problem asked for a sum of only two periodic functions.
22:21:46 <int-e> and can you please stop using "defiantly" instead of "definitely"
22:21:57 <\oren\> int-e: we're not defining it
22:22:00 <shachaf> \oren\ defiantly continues to use words int-e doesn't like
22:22:18 <int-e> shachaf: that was okay
22:22:25 <\oren\> int-e: we're just using the fact there exists a basis for R over Q
22:22:39 <int-e> shachaf: despite the fact that "definitely" also fits there...
22:22:56 <\oren\> and that we can select two numbers a and b out of said basis
22:23:10 <shachaf> int-e: Presumably all but a finite number of components are 0.
22:23:37 <\oren\> such that the coefficent of a in x, f_a(x), has certain properties
22:24:09 <\oren\> specifically, f_a(x + y) = f_a(x) + f_a(y)
22:24:39 <int-e> \oren\: so f_a has period b, great... what now?
22:24:46 <int-e> \oren\: what's the other function?
22:24:55 <\oren\> now, x - f_a(x) has period a
22:25:02 <\oren\> now, x - f_a(x)a has period a
22:25:22 <\oren\> the functions are f_a(x)a and x - f_a(x)a
22:25:38 <int-e> hmm. right, sorry.
22:25:44 <\oren\> which looks a lot less confusing written of paper
22:28:30 <int-e> (sorry, I got lost in the false attempt and irrelevant remarks... I missed the line where you wrote out x - f_a(x)*a, because I was too busy complaining about the word.)
22:28:54 <wob_jonas> I seriously think I should rather solve this problem with the well-ordering theorem than with vector space basis
22:29:16 <alercah> What's the original problem?
22:29:54 <wob_jonas> alercha: prove that the identity function on the reals can be written as the sum of two periodic functions on the reals
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22:30:24 <\oren\> yeah I would prefer a constructed solution as opposed to my hypothetic existence proof
22:31:07 <int-e> the followup problem (simplified version: write f(x) = x^2 as the sum of three periodic functions) will not work with the vector space approach, since that can only produce additive functions. (f(x+y) = f(x) + f(y))
22:31:55 <int-e> Well the axiom of choice very much seems necessary. (Though I have no proof of that.)
22:32:02 <wob_jonas> I mean, I understand if you want to factor the reals to equivalence classes of numbers whose difference is a sum of integer multiply of the two periods (let's call them 1 and sqrt(2) for simplicity)
22:32:14 <wob_jonas> but that doesn't need choice, I don't think I need a complete vector space basis
22:32:50 <wob_jonas> I do think the AC is necessary, but I'd not like to use it through a vector space basis, but through the well-ordering or something similar
22:33:06 <int-e> how about plain AC.
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22:47:16 <int-e> sketch for the simplified followup question: http://sprunge.us/DdKC
22:50:34 <int-e> hmm, I missed some terms there...
22:51:24 <wob_jonas> Anyway, my favourite maths problem is at http://mathoverflow.net/a/90201/35417 :
22:51:39 <int-e> correcting: http://sprunge.us/ALEN
22:51:54 <wob_jonas> There exists a set $ A $ that is everywhere dense on the square $ [0, 1]^2 $, but such that for any real number $ x $, the intersections $ A \cap (\{x\} \times [0, 1]) $ and $ A \cap ([0, 1] \times \{x\}) $ are both finite.
22:52:13 <wob_jonas> I love that problem because there are so many different approaches for it that lead to a proof.
22:52:31 <wob_jonas> So everyone you ask gives different proofs.
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22:58:10 <int-e> tooo many degrees of freedom.
22:58:14 <izabera> http://www.kylem.net/stuff/zero_computer.html
22:58:53 <wob_jonas> int-e: yes, too many different sets $ A $ too.
23:00:19 <int-e> wob_jonas: how about the obvious bijection of rational numbers in [1,2) with powers of two as denominators to themselves: reverse the bits.
23:01:47 <int-e> (additional constraints: no choice; all the intersections should have size at most 1; high school level)
23:02:18 <wob_jonas> int-e: yes, that works. it's another version similar to the first solution I give in the node, where I define the set without powers of two
23:02:51 <wob_jonas> it's probably the solution that needs the least mathematical prerequisites
23:03:03 <wob_jonas> which means that normal mathematicians don't usually give that, they know too many advanced stuff for it
23:03:36 <int-e> Oh if I wanted a hammer I'd use transfinite induction on the cardinality of the continuum.
23:03:40 <wob_jonas> I list the solutions in 8 bullet points ordered from most elementary to least elementary prerequisites.
23:04:42 <wob_jonas> int-e: yes, that's how the 6th solution works, it's a big hammer, at least for mathematicians like me who learned of set theory somewhat late
23:04:45 <int-e> so, the 6th bullet point.
23:06:08 <int-e> (countable topological bases need extra work)
23:06:58 <wob_jonas> just take all the rational squares
23:08:13 <int-e> That's too Borel. (I have not done much topology so I usually want circles with arbitary real diameter.)
23:08:39 <int-e> and then it's continuum sized.
23:09:06 <wob_jonas> int-e: I mean, you don't really need to know what a "topological base" is for this
23:09:20 <wob_jonas> that's just the way a topologist describes it
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23:09:42 <wob_jonas> you just need to know basic real calculus, that every disk contains a rational circle
23:09:45 <int-e> Anyway, except for the random one these are all good proofs to my mind.
23:11:04 <wob_jonas> or, in what sense is the random one not a good proof
23:11:04 <int-e> Err, sorry, I don't understand the last one.
23:11:08 <alercah> I like set-theoretic structures like topologies, sigma-algebras, and filters. They lead to very weird properties
23:11:26 <wob_jonas> yes, the last one was hard to understand, it took a LOT of time for my friends to convince me that it probably works
23:12:17 <wob_jonas> the problem there is that that set is easy to come up with, and easy to conjecture that it works, but we didn't find an easier proof to prove that it works
23:12:50 <wob_jonas> so once you fixate on that set, you're sort of screwed
23:13:32 <alercah> int-e: I love using the transfinite induction hammer for analysis proofs
23:13:41 <alercah> because they tend to be excessively direct
23:14:00 <wob_jonas> alercah: what's your favourite problem with such a proof?
23:14:03 <int-e> I guess I'm not very good with measure theory, which you need to make the probabilistic argument rigorous.
23:14:31 <alercah> wob_jonas: That every closed real interval is compact
23:14:54 <wob_jonas> int-e: yes, so if you know a lot of set theory but not much of advanced calculus, then the set theory proofs seems more natural to you
23:15:24 <wob_jonas> alercah: doesn't that have a more elementary proof too?
23:15:25 <alercah> (Heine-Borel theorem, basically)
23:15:49 <wob_jonas> because I remember I read the proof first in a book that uses elementary maths only
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23:16:48 <wob_jonas> iirc even the version that every bounded closed set in R^n is compact has an elementary proof there
23:16:58 <alercah> The elementary proof is basically that, given an open cover, if you need infinitely many members to cover a closed & bounded set, you can assume it's an interval, then subdivide it to get a smaller set.
23:17:10 <alercah> or multiple smaller sets, more accurately
23:17:15 <alercah> at least one of which requires infinite cover
23:17:26 <alercah> you can do this indefinitely to get an ever-decreasing sequence
23:17:38 <wob_jonas> right, so using the completeness of reals
23:18:19 <int-e> wob_jonas: btw, the *construction* in the last proof makes perfect sense, but I would have a much more elementary approach to establishing density.
23:18:40 <alercah> eventually, the set gets small enough that it can be covered by a single member, which is the contradiction
23:18:44 <wob_jonas> int-e: does that give a working proof? if it does, I'd be interested
23:18:52 <alercah> the transfinite proof I came up with is hilarious
23:19:49 <alercah> if you're trying to cover [a, b], let I_0 = (i_0, j_0) cover a, I_1 = (i_1, j_1) cover j_0, and so on
23:20:34 <alercah> if you don't cover the entire interval, let I_{\omega} = (i_{\omega}, j_{\omega}) cover sup_{\alpha < \omega} j_\alpha
23:21:12 <alercah> repeat this process transfinitely until it does cover the entire interval [a, b], which must happen because you have an open cover and there are more ordinals than intervals
23:23:54 <alercah> then for each limit ordinal \alpha you used, you can build a finite cover of [a, i_{\alpha}] by taking the previous limit ordinal's finite cover and adding successive intervals until you pass i_{\alpha}, which must happen after finitely many steps since the upper bounds converge to j_\alpha > i_\alpha
23:24:46 <alercah> and just repeat this until you cover [a, b]
23:25:53 <alercah> if you visualize it, what you're basically doing is finding the ordinal-like strucure in the upper ends of the intervals, you might try a bunch and find that they convege, and then try more and find that they converge, and then try this infinitely many times and find that *those* upper bounds converge, etc.
23:26:18 <alercah> but you can always cover the limit point and cut off all but finitely many previous intervals
23:28:32 <alercah> (the argument I gave above doesn't, technically, work, because "previous limit ordinal" isn't well-defined. But it shows you the point of the argument.
23:28:56 <alercah> it's a transfinite induction on "there is a finite subcover of [a, i_{\alpha}]"
23:37:10 <wob_jonas> alercah: I think it's late and I'm too tired to think of math now
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