←2018-03-19 2018-03-20 2018-03-21→ ↑2018 ↑all
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02:28:36 <shachaf> Cale: Can the trace/contraction of a linear map/tensor be thought of as connecting its output to its own input somehow?
02:29:04 <shachaf> It's a sum of eigenvaluese, which are related to fixed points, at least.
02:30:40 <esowiki> [[Uyjhmn n]] https://esolangs.org/w/index.php?diff=54419&oldid=54168 * Truttle1 * (-98)
02:31:20 <esowiki> [[Uyjhmn n]] https://esolangs.org/w/index.php?diff=54420&oldid=54419 * Truttle1 * (-98)
02:32:23 <esowiki> [[Uyjhmn n]] https://esolangs.org/w/index.php?diff=54421&oldid=54420 * Truttle1 * (-15)
02:33:09 <esowiki> [[Uyjhmn n]] https://esolangs.org/w/index.php?diff=54422&oldid=54421 * Truttle1 * (+0) /* Video */
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04:10:41 <Cale> shachaf: https://www.twitch.tv/videos/240647581?t=03h04m39s -- mrguy888 playing Prismata with his monitor turned off... and winning
04:10:56 <Cale> His opponent got so mad that he walked away from his computer, lol
04:11:13 <shachaf> How does that work?
04:11:26 <Cale> He's just using sounds to figure out what's going on
04:11:45 <shachaf> Hmm, I've always played with it muted.
04:11:52 <Cale> and he does look at the set of units at the beginning
04:12:02 <shachaf> Oh, he does -- yes
04:12:43 <Cale> "Apooche:i think the other type of blindfolded is legit. but this is like if chess players just put blindfolds on and then moved pieces around themselves, trying to figure out what opponent did by listening carefully to the pieces being picked up and put down"
04:13:09 <shachaf> Do different cards make different sounds?
04:13:14 <Cale> Yeah, they do now
04:13:35 <Cale> There have been some nice updates lately, it just released to Steam Early Access the other day
04:13:54 <Cale> and leading up to that there were some polishing features added
04:14:03 <shachaf> But no Linux support?
04:14:20 <shachaf> I did play through the campaign.
04:14:25 <Cale> They had technical problems with getting native linux to work
04:14:42 <shachaf> Though I think I only did one expert challenge. They're tricky.
04:14:43 <Cale> But Chrome/Pepperflash works fairly well for me now.
04:15:14 <shachaf> It's so ridiculous that they made this game in Flash.
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04:15:35 <Cale> Well, to be fair, they started in something like 2009
04:15:49 <shachaf> Still ridiculous.
04:15:57 <shachaf> Are they going to rewrite it?
04:16:41 <Cale> Doubt there are any specific plans at the moment
04:17:07 <shachaf> whoa, the game has keyboard controls now?
04:17:15 <Cale> It always had keyboard controls
04:17:40 <Cale> In fact, the names of the units were picked so that their first initials were all on the left hand of the qwerty keyboard layout
04:17:47 <Cale> (the base set)
04:17:48 <shachaf> I know that
04:17:53 <shachaf> But I mean clicking units and that sort of thing
04:18:25 <Cale> There's just Q to click drones / defend semi-reasonably / breach semi-randomly
04:18:44 <Cale> and then you can hold shift while clicking to click a whole pile
04:18:50 <shachaf> Ah, OK
04:18:52 <shachaf> I know all those
04:19:21 <shachaf> I think I saw an undo and thought it was a way to unclick a pile
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04:22:33 <Cale> ah
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04:38:31 <Cale> shachaf: also, yes, the trace can be thought of like that
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04:40:21 <shachaf> How?
04:41:06 <Cale> Just looking for a lecture about it...
04:41:11 <shachaf> The other question I had was, can I think of a (2,0) tensor as having "two outputs" in a reasonable way?
04:41:34 <shachaf> 16:05 <shachaf> How should I think of a (2,0) contravariant tensor like A^i^j? A (0,2) covariant tensor as a bilinear form makes sense, it takes two vectors and produces a scalar linearly in each. Can I think of a (2,0) tensor as "producing two vectors" somehow? Certainly it's not just a pair of vectors.
04:41:43 <shachaf> 16:24 <shachaf> I guess what I mean is that a (2,0) tensor is like a vector whose components are vectors.
04:41:49 <Cale> Well, effectively, yes. Are you familiar with string diagrams?
04:41:56 <shachaf> I came to some other conclusions but they're all kind of vague.
04:42:12 <shachaf> Yes, string diagrams are how I started thinking about all this.
04:42:22 <shachaf> https://twitter.com/shachaf/status/974811286474129408
04:46:13 <shachaf> Normally, a (0,2) tensor is a bilinear form, i.e. something that bilinearly takes two vectors and gives you a scalar.
04:46:49 <shachaf> But you can also contract it with a (2,0) tensor, even though in general that's not expressible as the product of two vectors. So that's the sense in which it behaves like it's "producing two vectors"
04:47:01 <shachaf> (That and the variance, of course.)
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04:51:58 <shachaf> Hmm. Even when V is one-dimensional, V⊗V is different from V? It can be contracted with a bilinear form.
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05:04:09 <Cale> shachaf: Finally found something reasonable. I can't find any of the references that I learned this from http://www.math.zju.edu.cn/wjd/TN/nutshell.pdf
05:04:26 <Cale> It uses physicsy notation, hopefully it's all right :)
05:05:45 <shachaf> Physicists have some pretty clever notation. Among all the other notation.
05:06:29 <shachaf> Can the Levi-Civita symbol be basis-free?
05:12:31 <Cale> shachaf: That is an interesting question, but I'd have to even figure out what it means first :D
05:12:49 <shachaf> So I see that theye're saying to use the Kronecker delta to join up an input to an output
05:13:03 <shachaf> But can't trace be defined even when you don't have that?
05:13:51 <shachaf> Anyway I'm looking for an idea of what the trace "means"
05:14:21 <shachaf> I know how to compute it but what does it mean to connect a function's output to its input? Something related to fixed points?
05:15:59 <Cale> Well, it might also be worth looking at what happens when you wire a linear operator up the wrong way around
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05:19:10 <Cale> I've never really seen this particular bunch of stuff entirely extricated from basis-dependent descriptions. Usually you do the basis-dependent thing, and only later prove that various widgets like the trace are basis independent.
05:19:33 <Cale> I think this cup and cap might be basis dependent... obviously the identity map isn't
05:20:26 <shachaf> But trace isn't.
05:20:44 <shachaf> Ah, I found https://www.sciencedirect.com/science/article/pii/S0723086913000790 which talks about trace in various contexts
05:21:21 <shachaf> Though I'm not sure it answers my question exactly
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16:03:54 <danil> hi
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16:33:54 <danil> ^ul (Anyone here)S
16:33:54 <fungot> Anyone here
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16:35:55 <danil> ^ul (1)S((0)(1))(~:^:S*a~^~*a*~:^):^
16:35:55 <fungot> 111010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010011001011001101001011010011001011001101001100101101001011001101001011010011001011010010110011010011001011001101001011010011001011010010110011010010110100110010110011010011001011010010110011010010110 ...too much output!
16:36:09 <int-e> noone
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16:38:26 <danil> ^ul (OK.)S(YES.)S(NO)S
16:38:26 <fungot> OK.YES.NO
16:39:06 <danil> I ain't got a Underload interpreter, so why not use FUNGOT?
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18:36:03 <int-e> . o O ( The phrase "undermining bitcoin" wanders around in your mind in search of something to connect with. )
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18:58:07 <\oren\_> v3. lolo, lolere, lololli, loltum
18:58:15 <\oren\_> so they loled would be "lolollerunt"
18:58:23 <\oren\_> and a lolcow would be a "vacca lolta"
19:07:06 <\oren\_> vaccas loltas lololli
19:10:15 <\oren\_> do you like this?
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19:49:04 <int-e> `?
19:49:54 <HackEgo> ​? ¯\(°​_o)/¯
19:50:06 <int-e> `'
19:50:07 <HackEgo> 174) <ais523> I love the way zzo38's comment was cut off after the f of brainfuck <ais523> that's just the most hilarious place to cut it off in a discussion about censorshi
19:52:18 <int-e> `^
19:52:19 <HackEgo> ​/home/hackbot/hackbot.hg/multibot_cmds/lib/limits: line 5: exec: ^: not found
19:52:35 <shachaf> Is that a hat of wisdom?
19:53:13 <int-e> I thought `mkx bin/^//quote|rev;quote
19:53:44 <int-e> or perhaps the opposite way.
19:53:59 <int-e> ``
19:54:00 <HackEgo> 168) <tswett> elliott: just to bring you up to speed, you are now my baby nephew. <olsner> wtf, elliott is a nephew and his uncle is here? <nooga> what <tswett> Heck yes I'm elliott's uncle.
19:54:14 <shachaf>
19:54:15 <HackEgo> ​/home/hackbot/hackbot.hg/multibot_cmds/lib/limits: line 5: exec: ´: not found
19:55:05 <int-e> But I guess it's more annoying an idea than a funny one anyway.
19:55:34 <shachaf> Yep.
19:55:43 <shachaf> Which does mean it fits right in.
19:56:06 <int-e> `wElCoMe
19:56:14 <HackEgo> 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.)
19:57:05 <int-e> `annoy
19:57:06 <HackEgo> ​/home/hackbot/hackbot.hg/multibot_cmds/lib/limits: line 5: exec: annoy: not found
19:59:01 <int-e> `` w # is this the random wisdom thingy?
19:59:04 <HackEgo> fish//Come and dance and love the fish! Mister Disco summoned it.
19:59:14 <\oren\_> `WelCome
19:59:17 <HackEgo> ​/home/hackbot/hackbot.hg/multibot_cmds/lib/limits: line 5: exec: WelCome: not found
19:59:23 <shachaf> `# it is//w
19:59:24 <HackEgo> Usage: `# <comment>//`<command>
19:59:29 <shachaf> curses
19:59:36 <shachaf> `# let's try this again//`w
19:59:40 <HackEgo> btw//btw is short for "bury the weasel"
20:00:51 <int-e> `? wtf
20:00:53 <HackEgo> WTF means Welcome To Finland.
20:01:06 <int-e> . o O ( "Want To Forget" )
20:02:16 <\oren\_> I don't know why but I really like idea of perfect form of "lol" being reduplicated like "curro, cucurri"
20:02:45 <\oren\_> ego lololli
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21:16:53 <shachaf> FireFly: HireFly
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22:36:08 <shachaf> Cale: Looking at that paper again now
22:36:16 <shachaf> "Some readers familiar with relativity will note similarities with the metric tensor—here we will always work in a flat Euclidean space, meaning the metric tensors are trivial"
22:37:05 <shachaf> I feel like this isn't quite a satisfying explanation of trace.
22:56:57 <\oren\_> augh
22:57:16 <shachaf> hell\oren\_
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23:14:46 <boily> hell\oren\_
23:15:02 <boily> helloochaf.
23:15:37 <boily> why the fungot is everything “trivial” in math papers. it's not trivial. it's never trivial.
23:15:37 <fungot> boily: what he claims is inconsistent is not the language itself could well be much worse than ghc's simplified expressions.
23:21:22 <pikhq> You get the feeling that "trivial" is math speak for "I just don't feel like proving it"
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23:33:52 <alercah> this reminds me of a great story I'm going to butcher
23:34:04 <alercah> a prof is teaching a class, and states a lemma is obvoius
23:34:10 <alercah> one of the students says it isn't
23:34:31 <alercah> the prof checks his notes, there is no proof
23:34:34 <alercah> he stares at it
23:34:45 <alercah> doesn't see it
23:35:00 <alercah> tells his students he'll dig up the proof and tell them next class
23:35:08 <alercah> he goes back and does some searching to figure out where he copied it from into his notes
23:35:14 <alercah> the original paper states the lemma with no proof
23:35:19 <alercah> it is written by him
23:35:35 <alercah> leading to a very sheepish return to class the next lecture
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←2018-03-19 2018-03-20 2018-03-21→ ↑2018 ↑all