←2020-10-24 2020-10-25 2020-10-26→ ↑2020 ↑all
00:04:33 <arseniiv> Snakebird looks like it would make a good esolang, as birds can grow any length, they can stuck and they have great hysteresis, and also one can blow a sleeping bird graphic marker to mean something more
00:06:19 <arseniiv> e. g. imagine a nondeterministic machine where birds move in all possible ways to reach a goal or to go through kind of checkpoints
00:07:56 <arseniiv> one can encode data in a bird’s form like how many squares does it run between turns
00:10:27 <arseniiv> hm this scheme makes addition on ℕ easy: you have a L-shaped bird and you just need it to straighten at the portal
00:14:11 <arseniiv> now we need to specify how the bird is placed at the start, e. g. if it’s the tail square that’s fixed in place or the head square, and which orientation the bird is, and also I now see that we can’t add unbounded numbers if we place the snake and the portal both in predetermined places
00:17:48 <arseniiv> that’s not all that obvious so maybe I’m wrong
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02:48:22 <esowiki> [[User talk:TightOnTime]] N https://esolangs.org/w/index.php?oldid=78140 * TightOnTime * (+0) Created blank page
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04:49:14 <imode> I have my doubts about rot7 + {dup drop compose apply apply!} being turing complete. or I just don't see how the construction can be performed.
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04:55:10 <imode> seeing as you can't push an empty quotation, you would need to duplicate two pieces of data. but duplicating one piece of data means you lose track of another, unrelated combinator.
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12:12:15 <ais523> @message imode if for some reason you need an empty quotation, just compose dup and drop
12:12:15 <lambdabot> Maybe you meant: messages messages-loud messages?
12:12:19 <ais523> @tell imode if for some reason you need an empty quotation, just compose dup and drop
12:12:19 <lambdabot> Consider it noted.
12:13:25 <ais523> a question I've been idly wondering about (that has minor implications for PPCG answers): if I have a matrix where the elements are drawn uniformly from a finite field, is the probability of the matrix being singular exactly 1/n (where n is the number of elements in the field)?
12:13:30 <ais523> or is it just approximately 1/n?
12:13:55 <ais523> err, I guess it's called CGCC nowadays
12:14:50 <ais523> really I need to make a good finite field library, finite fields seem to come up all the time when dealing with anything to do with storing information
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12:15:32 <int-e> The number of non-singular nxn matrices in GF(q) is q^n-1)*(q^n-q)*...*(q^n-q^(n-1)). So your probability is 1 - (1-1/q)*(1-1/q^2)*...*(1-1/q^n).
12:16:06 <ais523> hmm, I wonder if that has a simple closed form; probably not, but it looks like it might
12:16:09 <int-e> (different n, obviously)
12:17:40 <int-e> I think that is the simple closed form (if you write it as a product) ;-)
12:21:17 <ais523> the closed form is apparently the q-Pochhammer symbol
12:21:25 <ais523> which I'm pretty sure I came across recently in another context
12:21:48 <ais523> in this case, (1/q; 1/q)_n
12:22:44 <ais523> because the first two arguments are equal, it collapses to the Euler function as n tends to infinity
12:24:11 <rain1> they come up in partitions a lot
12:29:42 <ais523> I guess what I'm trying to figure out is, is the probability of being singular likely to be small / invertible likely to be large?
12:31:11 <ais523> it does look like it, the Euler function has values near 1 when its input is small
12:33:11 <ais523> OK, and I found a Wolfram Alpha query that explains the behaviour pretty well: https://www.wolframalpha.com/input/?i=minimum+of+QPochhammer%5Bq%5D%2Bq+for+q+in+0+to+1
12:33:45 <ais523> looks like the probability of being singular is a little more than 1/n, but never by all that much
12:34:12 <ais523> so in particular, if we just rely on picking a random matrix and hoping it's non-singular (my use case), we'll normally get away with it when the field is large
12:36:57 <esowiki> [[Entfedern]] M https://esolangs.org/w/index.php?diff=78141&oldid=74960 * PythonshellDebugwindow * (+29) /* See also */ See also
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13:33:11 <b_jonas> zzo38: I don't understand the context. what is snakebird?
13:39:28 <b_jonas> ais523: re matrix with coeffs uniformly chosen from a finite field: ah, int-e already answered, anyway the probability is much less (if n is large), there's a well-known result that counts the number of matrices over a finite field with nonzero determinants
13:41:11 <b_jonas> ais523: https://en.wikipedia.org/wiki/General_linear_group#Over_finite_fields
13:42:13 <b_jonas> hmm, maybe I'm wrong and the probability is not all that small, unless n is small? hmm
13:42:24 <b_jonas> I mean unless the field is small
13:42:31 <b_jonas> for GF(2) the probability is quite small
13:42:45 <b_jonas> I guess it depends on which direction you take the limit in
13:42:57 <b_jonas> I think for a fixed q, it's always much smaller than 1/n
13:43:05 <b_jonas> I mean for a fixed field
13:43:18 <b_jonas> oh well, you can ask a more precise questoin if you want
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14:06:40 <rain1> snakebird is a cool puzzle game
14:06:43 <rain1> I recommend it!
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14:20:23 <myname> yeah, it's awesome
14:20:26 <myname> i suck at it, though
14:22:35 <rain1> it's pretty hard
14:24:28 <myname> the play store recommended it to me for months and i always looked over it because it looks like a game for children
14:24:31 <myname> but boy was i wrong
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14:38:06 <ais523> b_jonas: it seems that the larger the (square) matrix is, the more likely it is to be singular, but the probability tends to a limit of (1/q; 1/q)_n which is slightly larger than 1/q but not by much (especially if q is large)
14:38:16 <ais523> here, q is the size of the field, n the size of the matrix
14:38:27 <ais523> so the limit is _∞, _n is for a specific size of matrix
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14:56:20 <b_jonas> ais523: I see
14:57:44 <esowiki> [[]] M https://esolangs.org/w/index.php?diff=78142&oldid=75389 * PythonshellDebugwindow * (+1) /* Commands */ Fix command
14:58:04 <esowiki> [[]] M https://esolangs.org/w/index.php?diff=78143&oldid=78142 * PythonshellDebugwindow * (+10) /* Commands */ Fix commands
14:58:44 <esowiki> [[User:PythonshellDebugwindow/(Unnamed language)]] M https://esolangs.org/w/index.php?diff=78144&oldid=75789 * PythonshellDebugwindow * (+1732) First draft of ++**p;
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15:48:12 <esowiki> [[Detrovert]] N https://esolangs.org/w/index.php?oldid=78145 * Hakerh400 * (+6701) +[[Detrovert]]
15:48:16 <esowiki> [[Language list]] https://esolangs.org/w/index.php?diff=78146&oldid=78103 * Hakerh400 * (+16) +[[Detrovert]]
15:48:19 <esowiki> [[User:Hakerh400]] https://esolangs.org/w/index.php?diff=78147&oldid=77146 * Hakerh400 * (+16) +[[Detrovert]]
15:56:02 <b_jonas> ais523: is that limit proportion zero for q=2 but greater than zero for q=3 ?
15:59:05 <ais523> b_jonas: the limit proportion is never zero
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16:59:28 <b_jonas> yay, the wonders of the internet! a second person who knows biology has confirmed the answer I got to my shark identification question
16:59:54 <b_jonas> you can get expert opinions on topics you know nothing about (like fish, in my case)
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18:50:41 <arseniiv> b_jonas: yeah that’s great, though still it doesn’t happen too often
18:58:09 <arseniiv> <b_jonas> zzo38: I don't understand the context. what is snakebird? => that wasn’t exactly zzo38 :D Snakebird is a puzzle game in which you are given birds in the form of snakes on a square grid. A bird can usually move in cardinal directions step at a time as a regular snake from the snake game does, but after each step it experiences gravity and may fall on something sharp or out of the map, which means you need to undo. As the regular snake, a bi
18:58:09 <arseniiv> rd can block its movement and this means a dead end too. In the game, you need to touch every bird’s head to a portal, and they are sucked into it, presumably to the next level
19:01:57 <arseniiv> I’m not finished the game yet, it’s definitely a good level of hard, a bit more than I’m capable of :D agree with myname and rain1
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21:04:45 <esowiki> [[User:PythonshellDebugwindow/(Unnamed language)]] M https://esolangs.org/w/index.php?diff=78148&oldid=78144 * PythonshellDebugwindow * (+165) /* Specification */ Comments
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22:31:35 <esowiki> [[5D Brainfuck With Multiverse Time Travel]] M https://esolangs.org/w/index.php?diff=78149&oldid=76501 * RocketRace * (+219) Some clarifications regarding backwards time
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←2020-10-24 2020-10-25 2020-10-26→ ↑2020 ↑all