00:01:16 <esolangs> [[Brianfuck]] https://esolangs.org/w/index.php?diff=108897&oldid=61557 * Squidmanescape * (+88)
00:02:58 <esolangs> [[Broken Tape]] https://esolangs.org/w/index.php?diff=108898&oldid=101638 * Squidmanescape * (+79)
00:03:38 <esolangs> [[Broken Tape]] https://esolangs.org/w/index.php?diff=108899&oldid=108898 * Squidmanescape * (-1) Every time I don't check, I get an error, huh.
00:04:24 <esolangs> [[Bulgu]] https://esolangs.org/w/index.php?diff=108900&oldid=17374 * Squidmanescape * (+69)
00:04:40 <esolangs> [[Business Offers]] https://esolangs.org/w/index.php?diff=108901&oldid=101804 * Squidmanescape * (+9)
00:05:42 <esolangs> [[BuxRo]] https://esolangs.org/w/index.php?diff=108902&oldid=87983 * Squidmanescape * (+89)
00:06:00 <esolangs> [[C-trice]] https://esolangs.org/w/index.php?diff=108903&oldid=79425 * Squidmanescape * (+9)
00:07:53 <esolangs> [[CATHY]] https://esolangs.org/w/index.php?diff=108904&oldid=98952 * Squidmanescape * (+75)
00:08:36 <esolangs> [[C@/Lol.js]] https://esolangs.org/w/index.php?diff=108905&oldid=101436 * Squidmanescape * (+9)
00:10:09 <esolangs> [[CCS]] https://esolangs.org/w/index.php?diff=108906&oldid=46656 * Squidmanescape * (+23)
00:11:01 <esolangs> [[YoptaScript]] https://esolangs.org/w/index.php?diff=108907&oldid=89248 * Squidmanescape * (+9)
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00:18:39 <esolangs> [[ELVM]] https://esolangs.org/w/index.php?diff=108908&oldid=96953 * Squidmanescape * (+29)
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00:21:10 <esolangs> [[Turing (Joshop)]] https://esolangs.org/w/index.php?diff=108909&oldid=57571 * Squidmanescape * (+8)
00:22:41 <esolangs> [[Snek]] https://esolangs.org/w/index.php?diff=108910&oldid=84483 * Squidmanescape * (+84)
00:24:15 <esolangs> [[SIMPLE (the other one)]] https://esolangs.org/w/index.php?diff=108911&oldid=102012 * Squidmanescape * (+89)
00:25:52 <esolangs> [[Recursoin]] https://esolangs.org/w/index.php?diff=108912&oldid=57154 * Squidmanescape * (+24)
00:26:24 <esolangs> [[CES updates]] https://esolangs.org/w/index.php?diff=108913&oldid=81493 * Squidmanescape * (+29)
00:27:40 <esolangs> [[Cell]] https://esolangs.org/w/index.php?diff=108914&oldid=71304 * Squidmanescape * (+98)
00:29:16 <esolangs> [[Chinese]] https://esolangs.org/w/index.php?diff=108915&oldid=43720 * Squidmanescape * (+92)
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02:50:53 <Sgeo> r/bing told me not to use Balanced. Precise gave a good answer: https://i.imgur.com/JyrVvnd.png
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11:02:22 <esolangs> [[Decleq]] N https://esolangs.org/w/index.php?oldid=108916 * ChuckEsoteric08 * (+520) Created page with "{{Stub}} '''Decleq''' ('''Dec'''rement and jump if '''L'''ess or '''Eq'''ual to zero) is an [[OISC]] by [[User:ChuckEsoteric08]] inspired by [[P1eq]]. ==Command== a b c Means: <code>b=a-1</code> and jump to <code>c</code> if <code>b</code> is less or equal to zer
11:21:35 <esolangs> [[EsoBASIC]] https://esolangs.org/w/index.php?diff=108917&oldid=108824 * ChuckEsoteric08 * (+1809) Added deadfish interpeter
11:26:13 <esolangs> [[EsoInterpreters]] https://esolangs.org/w/index.php?diff=108918&oldid=108809 * ChuckEsoteric08 * (+426) Added deadfish interpeter in EsoBASIC
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16:50:53 <Sgeo> Does f(a, b) = ln(e^a + e^b) have interesting properties? Want to wonder what the next step "below" addition is, if logs turn multiplication into addition, what do they turn addition into
16:53:55 <Sgeo> Doesn't seem to have an identity element, unless -infinity in the extended reals counts.
16:56:50 <ais523> it reminds me a bit of a hyperbolic function, but I think it's different enough to be its own thing
16:57:47 <ais523> it's pretty similar to max(a, b) – obviously not quite the same
16:58:06 <ais523> and + and max are sometimes used to form a semiring in the same way that × and + are
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16:58:40 <ais523> max(a+b, a+c) = a+max(b, c) so you have a distributive law
16:59:21 <ais523> and max(a, -∞) = a, a + 0 = a, a + -∞ = -∞ so you have the identities correct as well
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17:00:21 <ais523> so maybe max fits Sgeo's requirement for a "step below addition"? of course it doesn't quite work with logs in the same way
17:00:33 <ais523> is this just a logarithm with base infinity?
17:01:47 <ais523> max(a,b) = lim(x→∞) log_x(x^a + x^b)
17:03:41 <ais523> and a+b = lim(x→∞) log_x(x^a × x^b) so you have a perfect relationship there
17:04:54 <Sgeo> I don't understand that limit for max (and the limit for a+b is a bit redundant, right?)
17:05:19 <ais523> Sgeo: basically, the higher x is, the closer an approximation log_x(x^a + x^b) is to max(a,b)
17:06:50 <Sgeo> I think I need to try to visualize that more... but it approaching max does make the whole identity-is-negative-infinity thing make sense
17:08:50 <ais523> and yes, the limit is redundant in the +/× case but that doesn't make it incorrect
17:13:03 <ais523> a good search term for information about max/+ as a substitute for +/× is "tropical semiring" but Wikipedia doesn't have much that's useful on the page directly, it's primarily just definitions
17:13:53 <ais523> because pretty much all the relevant identities are the same, if you can prove a statement about +/×, it also often happens that you can use the same proof to prove the same statement about max/+…
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17:43:13 <esolangs> [[SSREPL]] N https://esolangs.org/w/index.php?oldid=108919 * ChuckEsoteric08 * (+832) Created page with "'''SSREPL'''('''S'''imple '''S'''tring-'''R'''ewriting '''E'''soteric '''P'''rogramming '''L'''anguage) is an esolang by [[User:ChuckEsoteric08]]. ==Specification== Initial value Data String is taken from user input. Line numbers are 1-indexed. There is only one i
17:44:52 <FireFly> isn't that log base -inf <=> max also analogous to norms, with the infinity norm being max too?
18:02:27 <esolangs> [[User:ChuckEsoteric08/Interpreters]] M https://esolangs.org/w/index.php?diff=108920&oldid=108811 * ChuckEsoteric08 * (+1)
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19:42:04 <Sgeo> It's interesting to see the crease in the 3d graph
19:42:16 <Sgeo> Although this 3d graphing calculator doesn't seem to want me to use max
19:50:01 <Sgeo> f(a, a) = ln(2*e^a) = ln 2 + a. So... almost like addition is repeated f() but not quite.
19:52:09 <Sgeo> Although weird to think of repeated beyond, 2, since I'm not sure if f(f(x, y) z) = the obvious way to define f(x, y, z) or not
19:53:28 <b_jonas> one step below addition is the successor operation, or, if you wish, a two-argument successor like succ(x,y) = 1+y
19:55:43 <b_jonas> because succ(y,succ(y,...succ(y,succ(y))...)) = x + y where you nest (x-1) succ operations, y+(y+...(y+(y+y))...) = x*y where you have (x-1) additions, y*(y*...(y*(y*y))...) = x↑y where you have (x-1) multiplications, and you define tetration similarly for natural numbers
19:58:14 <b_jonas> this is useful because this is actually one way how you can define addition of natural numbers, such as in Peano arithmetic
19:58:58 <b_jonas> (the alternative is to define cardinal addition from the union of two disjoint sets, and then restrict that to finite cardinalities)
20:05:29 <Sgeo> Oh good, ln(e^(ln(e^a+e^b))+e^c) = ln(e^a + e^b + e^c)
20:05:58 <ais523> in Church numerals, addition is defined as (a+b)x = a(x) × b(x), so I think it's using the distributive law backwards?
20:06:34 <ais523> or, hmm, that looks pretty weird, the distributive law has a + there not a ×
20:07:58 <b_jonas> oh, the ln thing. that's based on how addition and multiplication relate, but not really on how they compare to exponentiation or tetration, so it's a different step backwards
20:08:18 <ais523> ^ul (:*)(::*)(:)~*(~)*~*(*)*(a)~^
20:08:39 <fungot> ais523: in that case, the government, although the bill to close the funding gap, to some, the most attractive place to do the investigation, the uk failed to see the point of.
20:08:49 <ais523> oh, I forgot to put in an output command
20:08:51 <ais523> ^ul (:*)(::*)(:)~*(~)*~*(*)*(a)~^S
20:08:59 <ais523> ^ul (:*)(::**)(:)~*(~)*~*(*)*(a)~^S
20:09:16 <ais523> ^ul (:*)(::**)(:)~*(~)*~*(*)*S
20:10:29 <ais523> ooh, application is exponentiation in Church numerals, so the definition is actually x^(a+b) = x^a × x^b
20:10:32 <ais523> that makes so much more sense
20:10:57 <ais523> they basically define addition in terms of multiplication, exponentiation and logarithm
20:12:11 <ais523> (Underload has * and ^ as builtins, but you have to define addition manually)
20:12:30 <ais523> (and because exponentiation is function application, you can define logarithm using lambda)
20:13:15 <ais523> or, hmm, I'm not sure that last comment is quite right, but it seems to be along the right lines at least
20:13:15 <b_jonas> what? why would you define addition in terms of multiplication and exponentiation? wouldn't you define it by applying one of the church numbers on succ and then applying that on the other number?
20:13:57 <ais523> hmm, we can compare the definitions I guess? the definition in terms of multiplication and exponentiation is (:)~*(~)*~*(*)*
20:14:26 <ais523> and in terms of succ is ((:)~*(*)*)~^^
20:14:40 <ais523> ^ul (:*)(::**)((:)~*(*)*)~^^(a)~^S
20:14:49 <b_jonas> sorry, I'm not that fluent in underload
20:15:11 <ais523> the former's much more efficient because you don't need to actually evaluate the number
20:15:28 <ais523> and I think it's the normal definition for Church numerals because successor itself is defined as addition of 1
20:15:39 <ais523> so defining addition in terms of successor would be a circular definition
20:16:42 <b_jonas> er no? successor is defined as \n\r.(r(n r)) isn't it?
20:16:59 <b_jonas> or am I thinking of the wrong kind of church numeral?
20:17:59 <ais523> I don't think successor has a definition that simple?
20:18:06 <b_jonas> let me look up how church numerals work
20:18:14 <b_jonas> I don't like them so I keep forgetting
20:18:18 <b_jonas> https://esolangs.org/wiki/Church_numeral
20:18:39 <b_jonas> yeah, it's slightly more complicated
20:18:57 <ais523> Wikipedia defines successor by substituting in 1 for the argument of an addition
20:19:36 <b_jonas> I think succ = \n\f\x.(f(n f x))
20:19:41 <ais523> which is pretty easy because 1 is the identity function
20:19:58 <ais523> plus = \m\n\f\x.m(f(n f x))
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20:20:46 <b_jonas> true, that should work for addition
20:21:14 <b_jonas> isn't it plus = \m\n\f\x.(m f)(n f x)
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20:21:21 <b_jonas> you associated it the wrogn way
20:21:23 <ais523> err, yes, just realised I got the parens in the wrong place
20:22:06 <ais523> @pl \m -> \n -> \f -> \x -> (m f)(n f x)
20:25:44 <b_jonas> you're right, defining addition from succ is more complicated
20:26:06 <b_jonas> it still works of course, but gives a slightly more complex expression
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22:44:07 <Sgeo> base sqrt(2) makes the addition as repeated whatever happen to work out, but I think it's a cheat. log_sqrt2 (sqrt2 ^ x + sqrt2^x) = log_sqrt2 (2) + log_sqrt2 (sqrt2^x) = 2 + x
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22:44:34 <Sgeo> Having trouble telling Wolfram Alpha to do log base sqrt(2) of 2. It's interpreting it as
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22:44:44 <Sgeo> https://www.wolframalpha.com/input?i=log_%28sqrt%282%29%29%282%29
22:46:05 <b_jonas> Sgeo: just ask it to take base 2 logarithm and multiply it with 2 then