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00:22:27 <\oren\_> alercah: the way I heard that story, the prof was at yorku. he stated a lemma as being obvious. a student asks: "is that really obvious?" the professor stared at the chalkboard for a minute... two minutes... three minutes. the students also stared at it. some scribbled in their notebooks. after 10 minutes of silence, the professor announced: "yes, it's obvious."
00:24:01 <shachaf> That is a well-known but different story.
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00:50:52 <fizzie> There was also a nice list of different types of proof on one of those humoristic text files that go around and around.
00:51:15 <fizzie> http://www.lel.ed.ac.uk/~heycock/proof.html is the first instance I could find, though I'm sure they vary.
01:20:14 <esowiki> [[Fueue]] https://esolangs.org/w/index.php?diff=54423&oldid=54296 * Oerjan * (+175) /* Kolakoski sequence */ Copy my golfing answer here
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01:30:45 <shachaf> Cale: Oh man, polycategories are obviously the answer here.
01:31:58 <oerjan> . o O ( you have a category problem, and think "i'll use polycategories"... )
01:32:38 <shachaf> oerjan: It gets worse. What I want is a 2-polycategory.
01:33:25 <oerjan> that does sound worse.
01:33:25 <shachaf> But I'll settle for a regular polycategory for now.
01:33:39 * oerjan swats shachaf -----###
01:33:50 <shachaf> what did i do to deserve that
01:34:23 <oerjan> on the joke i was alluding to, no less
01:35:10 * shachaf once punned without noticing it
01:36:35 <oerjan> `le/rn People who've punned without noticing it//People who've punned without noticing it includes: oerjan shachaf
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03:26:14 <esowiki> [[Fueue]] https://esolangs.org/w/index.php?diff=54424&oldid=54423 * Oerjan * (+105) /* Thue-Morse sequence */ Shorter version
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03:42:40 <doesthiswork> Proof by reduction to the wrong problem is pretty funny
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06:19:55 <shachaf> Cale: whoa, tr(ABCDE) = tr(EABCD) etc. is really obvious with string diagrams using cups and caps
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10:01:18 <Cale> shachaf: yeah :)
10:09:38 <Taneb> Future oerjan: very nice re: Fueue golf!
10:12:23 <Taneb> (one of the oerjans for sure)
10:19:20 <shachaf> Cale: To which of the things I said?
10:19:51 <shachaf> Taneb: future oerjan. fuerjan.
10:20:16 <shachaf> obviously fuerjan would be the one interested in Fueue
10:20:45 <Cale> shachaf: That the trace relation is obvious with string diagrams
10:20:53 <Taneb> shachaf: that logic is impecabl
10:22:22 <shachaf> Cale: Representable polycategories are too good
10:23:53 <shachaf> Cale: By the way, do you remember that we talked about generalizing eigenvectors/eigenvalues to other categories?
10:24:04 <Taneb> My typing is also impecable
10:24:35 <shachaf> Anyway there's a clear meaning of scalar multiplication in any monoidal categories, which I didn't realize
10:25:24 <shachaf> Where a scalar is an arrow : I -> I where I is the identity of the tensor product
10:25:38 <shachaf> Sorry, I *am* the identity
10:26:25 <shachaf> Anyway what are some monoidal categories where Home(I,I) isn't trivial?
10:28:03 <esowiki> [[Minim]] https://esolangs.org/w/index.php?diff=54425&oldid=53141 * Thenewcomposer * (+2194) A Simple, Low-Level, Interpreted Language
10:28:31 <esowiki> [[Minim]] M https://esolangs.org/w/index.php?diff=54426&oldid=54425 * Thenewcomposer * (+2) /* Hello World */
10:28:43 <esowiki> [[Minim]] M https://esolangs.org/w/index.php?diff=54427&oldid=54426 * Thenewcomposer * (+2) /* 99 Bottles */
10:30:56 <esowiki> [[Language list]] https://esolangs.org/w/index.php?diff=54428&oldid=54400 * Thenewcomposer * (+12) /* M */
10:38:16 <Taneb> Only thing I can think of is the category of modules over some ring
10:39:41 <shachaf> I was trying to generalize from vector spaces, so that's pretty similar
10:40:13 <shachaf> There's the category of abelian groups with Z as the tensor identity I think
10:40:39 <Taneb> I think that's equivalent to modules over Z?
10:41:34 <shachaf> Is there a notion of the "trace" of an abelian group homomorphism? Maybe it gives the rank of the group when applied to the identity or something?
10:41:59 <shachaf> So that's not anything new
10:42:37 <shachaf> Well, I'd settle for something where Hom(I,I) has more than one element. Even just two.
10:48:03 <Taneb> My gut is telling me that if it has more than one it must necessarily have an infinite number
10:48:19 <Taneb> But my brain isn't convinced
10:49:43 <shachaf> Yes, Rel is monoidal with the usual Cartesian product
10:51:57 <shachaf> Where composition behaves like and, I guess, if the empty set is false
10:52:34 <shachaf> What does scalar multiplication on a relation do?
10:52:47 <shachaf> I'm in bed failing to sleep and typing this on my phone
10:54:22 <Taneb> You've got a (*0) and a (*1) there basically
10:54:25 <shachaf> I guess 1*f is f, and 0*f takes every relation to the empty relation
10:54:49 <shachaf> But can you define a "trace"?
10:55:11 <shachaf> Does it maybe measure the diagonal?
10:56:18 <Taneb> What properties should the trace have, here?
10:56:46 <shachaf> I guess one good property is traveling(AB) = tr(BA)
10:58:28 <shachaf> Actually, I guess Rel has a dagger thing, so you can define trace through that presumably
11:00:17 <shachaf> I think tr(f) is 1 if (x,x) is in f for any x
11:00:40 <shachaf> Which makes sense gives how relation composition works, right?
11:01:14 <shachaf> Say you have f : A -> B and g : C -> D
11:01:57 <shachaf> Say you have f : A -> B and g : B -> C
11:02:22 <shachaf> You have be fxg : AxB -> BxC
11:02:47 <shachaf> And if you trace on that B you want to end up with the composition g.f
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11:11:49 <shachaf> Oh, I should've just looked it up
11:12:05 <shachaf> There are at least two possible tensor products and each one of them gets a trace
11:17:14 <shachaf> But you can represent this as vector spaces too apparently
11:25:23 <Taneb> ...is Rel isomorphic to GF(2)-Vect?
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11:39:25 <fizzie> So odd: there's wifi on this plane..
11:40:52 <Taneb> That's just plane weird
11:43:33 <Taneb> ...you know, I think Rel is isomorphic to GF(2)-Vect
11:46:06 <Taneb> Which suggests a trace being hte parity of the diagonal
11:47:47 <Taneb> shachaf: does this sound concievable?
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11:59:25 <Taneb> (trace in general does not have the property tr(AB) = tr(BA))
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12:14:57 <FireFly> fizzie: heh, all Norwegian flights offer free wifi apparently, it was a nice surprise when I flew a while ago
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13:01:40 <danil> ^ul (1)S((0)(1))(~:^:S*a~^*a*~:^):^
13:01:40 <fungot> 110101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101 ...too much output!
13:01:58 <danil> ^ul (1)S((0)(1))(~:^:S*a~a^~*a*~:^):^
13:02:10 <danil> ^ul (1)S((0)(1))(~:^:S*^~*a*~:^):^
13:02:37 <danil> ^ul (1)S((0)(1))(~:^:S*~a~^~*a*~:^):^
13:02:56 <danil> ^ul (1)S((0))(~:^:S*a~^*a*~:^):^
13:03:05 <danil> ^ul (1)S(0)(1)(~:^:S*a~^*a*~:^):^
13:03:13 <danil> ^ul (1)S((0)(1))(~:^:S*a~^*a*~:^):^
13:03:13 <fungot> 110101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101 ...too much output!
13:03:25 <danil> ^ul (1)S((0)(1))(~:^:S*~^*a*~:^):^
13:03:32 <danil> ^ul (1)S((0)(1))(~:^:S*a~^*^*a*~:^):^
13:04:18 <fizzie> FireFly: So I've heard, but this is my first time. It's a BA flight, they're slowly rolling it out so you never know if there will be wifi until after takeoff.
13:04:53 <fizzie> (But I'm trying to work, so I can probably expense it.)
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15:24:50 <esowiki> [[Hatemath]] M https://esolangs.org/w/index.php?diff=54429&oldid=54409 * Sane theinsane * (+11) /* External sources */
15:28:38 <esowiki> [[Hatemath]] M https://esolangs.org/w/index.php?diff=54430&oldid=54429 * Sane theinsane * (+51) /* External sources */
15:28:56 <esowiki> [[Hatemath]] M https://esolangs.org/w/index.php?diff=54431&oldid=54430 * Sane theinsane * (-51) /* External sources */
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15:38:11 <esowiki> [[Haddock]] https://esolangs.org/w/index.php?diff=54432&oldid=54360 * Singingbanana * (+27)
15:40:50 <esowiki> [[Haddock]] https://esolangs.org/w/index.php?diff=54433&oldid=54432 * Singingbanana * (+8)
15:41:31 <esowiki> [[Hatemath]] M https://esolangs.org/w/index.php?diff=54434&oldid=54431 * Sane theinsane * (+1) /* Examples */
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15:46:06 <esowiki> [[User:Sane theinsane]] N https://esolangs.org/w/index.php?oldid=54435 * Sane theinsane * (+197) Created page with "== Myself == Hi I am Saketh. I am a python programmer that likes to make esoteric languages.<br /> == The langs I have made == I am the creator of hatemath and LML(it's made..."
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18:15:51 <zzo38> I will be transporting this computer for repair today, so the server will be unavailable during that time. Is there any considerations that should be made when transporting it?
18:17:46 <shachaf> Taneb: I think it's not GF(2) but a ring where 1+1=1
18:18:16 <shachaf> Trace doesn't in general have that property? When doesn't it?
18:18:26 <zzo38> Do you know anything about considerations when transporting a computer?
18:18:46 <shachaf> I mean for endomorphisms A,B
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18:19:47 <shachaf> @tell zzo38 Remove the disk first?
18:20:01 <fizzie> I'm afraid that computer is now being transported inconsiderately. :/
18:21:43 <shachaf> zzo38 did not leave us much time for consideration
18:21:48 <fizzie> fungot: How do you like to be transported?
18:21:49 <fungot> fizzie: if you had to choose one above the yellow block device, and talk fnord over it, and apply on an arbitrarily long integer math program somewhere that uses the list of constants is smaller in overall volume.
18:22:54 <fizzie> Didn't zzo38 live somewhere in Canada? Wonder if I'm near that computer.
18:23:23 <alercah> I believe zzo38 lives *at* canada
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19:02:05 <\oren\_> AAAAAAAAAAAA stupid global variable initialization order
19:02:27 <shachaf> Are they initialized before smart global variables?
19:03:23 <\oren\_> specificly, for some reason a global std::string gets compiled into CODE not data
19:06:48 <\oren\_> shachaf: well it's a const std::string. I think it should be compiled into data representing the string. but instead code gets generated which allocates and fills the string up
19:07:43 <shachaf> How would you make that work in C++?
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19:08:14 <shachaf> I thought you meant that «std::string s = "blah";» would somehow put "blah" into the code section.
19:09:20 <\oren\_> it would somehow put {5,"blah"} or hoever the string is represented after initialization, into the code section. because it's a const
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19:10:05 <\oren\_> the same thing happens to const int i = 5;
19:10:28 <shachaf> But std::sring is just a class.
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19:15:12 <\oren\_> not sure why that matters?
19:16:07 <shachaf> I mean, are you saying the compiler should special-case this class, or that any string class should be able to do this?
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19:21:13 <shachaf> By having const std::string not copy its argument in this context or something like that?
19:22:19 <\oren\_> yeah. it shoudl just compile to the memory layout of a fully initialized std::string, in read-only memory
19:22:40 <shachaf> I know what you want it to do. But how should it achieve it?
19:23:17 <\oren\_> well it already knows how to run arbitratry code at compile time, so jsut run the initializer at compile time
19:23:31 <shachaf> std::string, even const std::string, allocates memory
19:23:52 <\oren\_> and when it allocates memory, allocate it from the code section
19:24:21 <shachaf> How do you make that work?
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19:25:41 <\oren\_> when new is called during compile-time, you special case that to allocate from the code section instead of the heap
19:26:07 <\oren\_> new and new[] are already builtin
19:30:18 <fizzie> Would you be okay with just a const std::string_view? AIUI, it's a literal type (has a constexpr constructor), so maybe it handles like that already.
19:30:53 <shachaf> Oh, string_view would be the best C++ answer to this of course.
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19:34:49 <fizzie> People have also done all kinds of workarounds using facilities that actually exist in C++, like https://github.com/akrzemi1/static_string
19:39:11 <\oren\_> hooray, this time it DIDNT crash before the start of main()
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19:56:17 <shachaf> fizzie: Sure, if you use a separate class that's for this purpose.
19:56:38 <shachaf> I guess maybe std::string could do something different in the const constexpr case?
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20:30:00 <esowiki> [[Bitter]] M https://esolangs.org/w/index.php?diff=54436&oldid=54330 * DMC * (+2)
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20:31:28 <esowiki> [[Bitter]] M https://esolangs.org/w/index.php?diff=54437&oldid=54436 * DMC * (-2) /* Description */
20:35:27 <shachaf> Taneb: See http://www.inf.u-szeged.hu/actacybernetica/edb/vol23n1/pdf/actacyb_23_1_2017_18.pdf
20:35:58 <shachaf> Which is about a different monoidal category but mentions that one too.
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20:49:17 <wob_jonas> boily: yes, totally true. There was some algebraic topology result that Kozlov claimed without proof in an introductory paper, spending only a few lines to even state it, and we really wanted it to be true. At first we thought it was a mistake, then after thinking about the whole paper for over a month with my advisor, we figured that it was indeed
20:49:17 <wob_jonas> a trivial result that Kozlov could have seen as so obvious that he didn't include a proof.
20:49:37 <wob_jonas> I'm not sure it was actually Kozlov, may have been some other mathematician.
20:51:16 <wob_jonas> Oh, this started from a quote with the other meaning of "trivial".
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20:55:56 <wob_jonas> fizzie: for a string_view it can be done, yes, and there are very likely two interfaces that do that, both just calling the constructor with a string literal (since then the string_view will point into that literal, and the literal will likely be in a mapped read-only section of the exe), or using a certain user-defined literal that later versions
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20:58:00 <wob_jonas> And yes, I think you usually can't do it for a std::string, because (except possibly for a short string) that simply assumes that the contents is stored in an array allocated with the allocator (by the default new function in an ordinary string) and will try to free it if you destroy the string. And even a const string will typically be destroyed i
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22:43:14 <izabera> do you guys know the hex game?
22:49:03 <shachaf> Do you mean the one where you make a path from one side of the board to the other?
22:52:42 <izabera> you know that the game isn't over yet, and red makes a move
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22:53:12 <izabera> is there a fast way to tell if this move wins?
23:14:40 <quintopia> boily: did you get your registration in?
23:16:15 <boily> I tried to, but it bugged :/
23:16:22 <boily> like, broken error messages and shit.
23:22:08 <Cale> izabera: You could keep track of which sides of the board each stone is connected to, and propagate it as stones are added
23:22:26 <Cale> izabera: and then you only need to check the neighbours of newly added stones
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23:23:14 <izabera> that's a really good idea!
23:24:56 <shachaf> But note that the naive way of keeping track of that can involve updating a lot of stones in a single move.
23:25:20 <shachaf> The fancy algorithm for it is a union-find thing.
23:35:05 <shachaf> I must say I didn't expect https://en.wikipedia.org/wiki/Monoidal_category to be protected.
23:40:10 <quintopia> yeah i assume it closed within an hour of opening on the 10th
23:40:46 <shachaf> Do you know whether there's an efficient online algorithm for strongly connected components in a directed graph?
23:45:30 <quintopia> i mean i guess the obvious thing wouldn't be too inefficient
23:49:00 <boily> quintopia: weekend of the...
23:49:09 * boily does hard mental arithmetic
23:49:36 <boily> 7-8 April I can game.
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