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2020-10-21 23:35:19 <sshine> > (2 + 2) `mod` 3 -- more complex at the math level?
2020-10-21 23:35:21 <lambdabot> 1
2020-10-21 23:35:24 <ski> crestfallen : consider `[0,1,2] >>= \x -> [x^2,-x^2] >>= \y -> []'
2020-10-21 23:35:54 → GyroW_ joins (~GyroW@ptr-48ujrfd1ztq5fjywfw3.18120a2.ip6.access.telenet.be)
2020-10-21 23:35:55 × GyroW_ quits (~GyroW@ptr-48ujrfd1ztq5fjywfw3.18120a2.ip6.access.telenet.be) (Changing host)
2020-10-21 23:35:55 → GyroW_ joins (~GyroW@unaffiliated/gyrow)
2020-10-21 23:36:25 × wroathe_ quits (~wroathe@c-68-54-25-135.hsd1.mn.comcast.net) (Ping timeout: 258 seconds)
2020-10-21 23:36:47 × Tops2 quits (~Tobias@dyndsl-095-033-090-095.ewe-ip-backbone.de) (Read error: Connection reset by peer)
2020-10-21 23:36:55 × GyroW quits (~GyroW@unaffiliated/gyrow) (Ping timeout: 265 seconds)
2020-10-21 23:37:00 <ski> (aka `map (\x -> map (\y -> []) [x^2,-x^2]) [0,1,2]'. or `[z | x <- [0,1,2],y <- [x^2,-x^2],z <- []')
2020-10-21 23:37:08 <sshine> crestfallen, I'm not really an expert at the math level, but I'd think that monoidal composition just yields another member. so if there's any complexity added, it's at the computational level, since you have a bigger expression that needs to be resolved.
2020-10-21 23:37:58 <ski> crestfallen : after we've added the `>>= \y -> []' at the end, we get an empty list. if we add some further `>>= \z -> ..z..', we'll still have an empty list
2020-10-21 23:38:09 <crestfallen> sshine but I thought that the object.. the monad structure, is increased upon, but ski just illustrated that it's not always the case [0,1,2] >>= \x -> [x^2,-x^2] >>= \y -> []
2020-10-21 23:38:49 <ski> so, in this case, adding `>>= \y -> []' makes things "simple" in the sense of getting a plain empty list (that no further use of `>>=' can change to a non-empty list)
2020-10-21 23:38:59 <sshine> crestfallen, at the syntactic level, many >>=s chained together is more complex. upon evaluation, it really depends.
2020-10-21 23:39:02 → wroathe joins (~wroathe@c-68-54-25-135.hsd1.mn.comcast.net)
2020-10-21 23:39:06 <crestfallen> the list is unchanged.. but in the intermediary steps, it "takes on" complexity, I thought
2020-10-21 23:39:30 <ski> compare with multiplying numbers. if you have `a * b * c * ... * y * z'
2020-10-21 23:39:55 <ski> as you multiply `a' by `b', then the result of that by `c', and so on, you'd generally say you get something more complex
2020-10-21 23:40:26 <ski> but if one of the factors happen to be zero, then regardless of what the latter factors you multiply in are, you'll still always get zero
2020-10-21 23:40:45 <crestfallen> exactly. adding 2 + 3 gives us five, which has unique properties
2020-10-21 23:41:01 × AceNovo quits (~chris@67-42-33-191.phnx.qwest.net) (Ping timeout: 264 seconds)
2020-10-21 23:41:02 <crestfallen> exactly two posts back ski
2020-10-21 23:41:04 × alp quits (~alp@88.126.45.36) (Ping timeout: 246 seconds)
2020-10-21 23:41:26 <crestfallen> compare with multiplying numbers ....
2020-10-21 23:41:47 <ski> so, you could say, that in general, you get more complexity (where "more" really means "more, or else the same" (that is "not less")). but in special cases, you could get something simpler
2020-10-21 23:41:53 → dwt joins (~dwt@c-98-200-58-177.hsd1.tx.comcast.net)
2020-10-21 23:44:01 × wroathe quits (~wroathe@c-68-54-25-135.hsd1.mn.comcast.net) (Ping timeout: 264 seconds)
2020-10-21 23:44:01 × stefan-__ quits (~cri@42dots.de) (Read error: Connection reset by peer)
2020-10-21 23:44:22 → AceNovo joins (~chris@67-42-33-191.phnx.qwest.net)
2020-10-21 23:44:23 → stefan-__ joins (~cri@42dots.de)
2020-10-21 23:44:49 <crestfallen> yeah. so ski in category theory, I've read that the object can literally expand, change dimension, once morphisms are applied. isn't what this is about?
2020-10-21 23:45:10 <ski> i don't know what you mean by that
2020-10-21 23:45:11 <crestfallen> in the case where they become more complex..
2020-10-21 23:45:26 <ski> in category theory, morphisms are not applied to objects
2020-10-21 23:45:40 <crestfallen> they are applied to sets, right?
2020-10-21 23:45:48 <ski> what's called "objects", there, is the possible domains and codomains of morphisms
2020-10-21 23:45:51 <ski> no
2020-10-21 23:45:55 <ski> they aren't applied at all
2020-10-21 23:45:58 <ski> they're composed
2020-10-21 23:46:09 <crestfallen> right, actually I meant that..
2020-10-21 23:46:30 <crestfallen> so monad is a composition, because the structure changes
2020-10-21 23:46:39 <ski> in category theory, if you have `f : A >---> B' and `g : B >---> C', you can compose them as `g . f : A >---> C'
2020-10-21 23:46:52 <ski> but there is no application like `f(x)'/`f x'
2020-10-21 23:47:04 <ski> objects, like `A', doesn't have "elements"
2020-10-21 23:47:17 → merijn joins (~merijn@83-160-49-249.ip.xs4all.nl)
2020-10-21 23:47:23 <crestfallen> no, but 'A' has structure, right?
2020-10-21 23:47:30 <ski> "so monad is a composition, because the structure changes" -- sorry, dunno what this means
2020-10-21 23:47:43 → alp joins (~alp@2a01:e0a:58b:4920:b176:4a05:144c:cd70)
2020-10-21 23:47:54 <crestfallen> (>>=) is a form of composition is what I meant
2020-10-21 23:48:28 <ski> from the point of view of category theory, the "structure" of an object like `A' is given in terms of knowing which morphisms compose to which morphisms
2020-10-21 23:48:47 <crestfallen> yes!
2020-10-21 23:49:27 <ski> but when you "implement" a category, you can choose to implement the objects as some sort of set/type, commonly with some extra "structure" (like having a binary operation, and a neutral element, which could give us a monoid)
2020-10-21 23:49:31 <crestfallen> category theory applies to monadic actions, because the object is changing
2020-10-21 23:49:33 × darjeeli1 quits (~darjeelin@122.245.123.118) (Ping timeout: 260 seconds)
2020-10-21 23:49:33 × falafel quits (~falafel@71-34-132-121.clsp.qwest.net) (Ping timeout: 256 seconds)
2020-10-21 23:49:57 <crestfallen> the structure of the object, is what I was led to believe.
2020-10-21 23:50:02 <ski> `(>=>)' corresponds to composition (in "the Kleisli category"), `(>>=)' does not
2020-10-21 23:50:25 → LKoen joins (~LKoen@lstlambert-657-1-123-43.w92-154.abo.wanadoo.fr)
2020-10-21 23:50:30 <crestfallen> one moment pls
2020-10-21 23:50:30 → darjeeli1 joins (~darjeelin@122.245.123.118)
2020-10-21 23:50:34 <ski> i don't understand "category theory applies to monadic actions, because the object is changing" either
2020-10-21 23:51:10 <monochrom> I'm pretty sure this word game is getting nowhere.
2020-10-21 23:51:17 × deadk quits (e@freenode/staff/spy.edk) (Quit: edk)
2020-10-21 23:51:30 × conal quits (~conal@ip-66-115-176-174.creativelink.net) (Quit: Computer has gone to sleep.)
2020-10-21 23:51:35 <MarcelineVQ> lol deadk
2020-10-21 23:51:43 → wroathe joins (~wroathe@c-68-54-25-135.hsd1.mn.comcast.net)
2020-10-21 23:52:07 <MarcelineVQ> ghoulguy: your good natured antics have gone too far!
2020-10-21 23:52:11 <crestfallen> buzz wreckers enter
2020-10-21 23:52:14 × stefan-__ quits (~cri@42dots.de) (Read error: Connection reset by peer)
2020-10-21 23:52:41 → stefan-__ joins (~cri@42dots.de)
2020-10-21 23:52:43 <ski> crestfallen : fancy moving to #haskell-overflow ?
2020-10-21 23:52:45 <ghoulguy> MarcelineVQ: I'm just a willing participant; edk got me into it
2020-10-21 23:53:14 <MarcelineVQ> man, what am I supposed to do, I'm intrinsicly themed already
2020-10-21 23:53:25 → olligobber joins (olligobber@gateway/vpn/privateinternetaccess/olligobber)
2020-10-21 23:53:35 <monochrom> I want to participate too, but can't think of a spooky mutation of my nick.
2020-10-21 23:53:49 <MarcelineVQ> spookochrom
2020-10-21 23:54:15 <crestfallen> sure ski.
2020-10-21 23:54:15 <MarcelineVQ> monomoooaaannnn
2020-10-21 23:54:24 <monochrom> Apart from "joseph" which is an obscure reference to "joseph and the technocolor dream coat" which is the opposite of "monochrome".
2020-10-21 23:54:59 × crestfallen quits (~john@128.32.176.159) (Quit: Leaving)
2020-10-21 23:55:45 × darjeeli1 quits (~darjeelin@122.245.123.118) (Ping timeout: 240 seconds)
2020-10-21 23:55:45 <MarcelineVQ> heartbreak boy, you can just type /join #haskell-overflow :(
2020-10-21 23:55:47 → crestfallen joins (~john@128.32.176.159)
2020-10-21 23:56:00 <monochrom> or "monodome" or "thunderchrom" in reference to "mad max ... thunderdome"
2020-10-21 23:56:13 <MarcelineVQ> monomax: beyond the thunderchrome
2020-10-21 23:56:39 → darjeeli1 joins (~darjeelin@122.245.123.118)
2020-10-21 23:57:31 × veverak quits (~squirrel@ip-89-102-98-161.net.upcbroadband.cz) (Ping timeout: 246 seconds)
2020-10-22 00:00:01 → edk_ joins (e@freenode/staff/spy.edk)
2020-10-22 00:01:00 → polyrain joins (~polyrain@58.161.83.164)
2020-10-22 00:01:05 × cr3 quits (~cr3@192-222-143-195.qc.cable.ebox.net) (Ping timeout: 265 seconds)
2020-10-22 00:03:37 × tinwood quits (~tinwood@general.default.akavanagh.uk0.bigv.io) (Ping timeout: 260 seconds)
2020-10-22 00:03:59 → tinwood joins (~tinwood@general.default.akavanagh.uk0.bigv.io)
2020-10-22 00:05:33 → conal joins (~conal@ip-66-115-176-174.creativelink.net)
2020-10-22 00:05:34 × codygman quits (~codygman@47-184-107-46.dlls.tx.frontiernet.net) (Read error: Connection reset by peer)
2020-10-22 00:05:43 → codygman joins (codygman@gateway/vpn/privateinternetaccess/codygman)
2020-10-22 00:06:29 <sshine> is this a halloween thing?
2020-10-22 00:06:52 <monochrom> yes
2020-10-22 00:07:04 monochrom is now known as morphochrom
2020-10-22 00:08:34 <morphochrom> I think this will do this year. :)
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