1776041222 341903 :amby!~ambylastn@host-81-178-153-130.as13285.net QUIT :Quit: so long suckers! i rev up my motorcylce and create a huge cloud of smoke. when the cloud dissipates im lying completely dead on the pavement
> 1776043970 306373 PRIVMSG #esolangs :14[[07OPRBCM14]]4 M10 02https://esolangs.org/w/index.php?diff=179575&oldid=179542 5* 03PkmnQ 5* (-1) 10it(')s
> 1776047939 705610 PRIVMSG #esolangs :14[[07Kolakoski sequence14]]4 10 02https://esolangs.org/w/index.php?diff=179576&oldid=175130 5* 03PkmnQ 5* (+496) 10/* ZOWIE */
< 1776049342 37519 :lisbeths!uid135845@id-135845.lymington.irccloud.com JOIN #esolangs lisbeths :lisbeths
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< 1776050518 91794 :aadenboy!~aadenboy@172.56.104.200 PRIVMSG #esolangs :goodnight
< 1776050521 213321 :aadenboy!~aadenboy@172.56.104.200 QUIT :Quit: goodbye for now! back another day
> 1776052760 179891 PRIVMSG #esolangs :14[[07DisFuck14]]4 10 02https://esolangs.org/w/index.php?diff=179578&oldid=160030 5* 03Tpaefawzen 5* (+89) 10/* Overview */ +1
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> 1776060492 516879 PRIVMSG #esolangs :14[[07User:Yayimhere/RBCL14]]4 10 02https://esolangs.org/w/index.php?diff=179581&oldid=179580 5* 03Yayimhere2(school) 5* (+2) 10/* Semantics */
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> 1776069090 800739 PRIVMSG #esolangs :14[[07Talk:Emanator14]]4 N10 02https://esolangs.org/w/index.php?oldid=179585 5* 03Yayimhere2(school) 5* (+216) 10Created page with "I think it's generally nicer to leave a proof of turing completeness on the page. like just why not? --~~~~"
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< 1776085238 111843 :ais523!~ais523@user/ais523 JOIN #esolangs ais523 :(this is obviously not my real name)
< 1776085283 363969 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :there's a paper (found via lobste.rs) that claims that f(x,y) = e^x - ln(y) is ELEMENTARY-complete: https://arxiv.org/abs/2603.21852 (the paper itself is terrible but the result is interesting)
< 1776085310 185702 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :err, that function + constant 1
< 1776085328 714880 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :if I were writing that paper I would have written out a basis for ELEMENTARY in terms of the new operator
< 1776085357 904631 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :but the paper doesn't actually do that, just puts a lot of detail into explaining how it was found
< 1776085593 729063 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :that said, the claim itself seems very plausible to me: I think the construction starts with f(x,1) = e^x and f(1,x) = e - ln(x), f(1,f(1,x)) = e - x, f(1,f(1,f(1,x)) = e - (e - ln(x)) = ln(x)
< 1776085663 167355 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :err, typo, I meant f(1,f(x,1)) = e - x, f(1,f(f(1,x),1)) = e - (e - ln(x)) = ln(x)
< 1776085698 97721 :int-e!~noone@int-e.eu PRIVMSG #esolangs :yeah and f(ln(x),e^y) = x - y so you can bootstrap stuff like x^2 = e^(ln(x) + ln(x))
< 1776085733 414226 :int-e!~noone@int-e.eu PRIVMSG #esolangs :then multiplication from 2xy = (x+y)^2 - x^2 - y^2
< 1776085777 399560 :int-e!~noone@int-e.eu PRIVMSG #esolangs :(such a cute trick, well-known of course from working with inner products and norms)
< 1776085789 415959 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :so this is the bit I'm unsure about, because ln(e^x) = x but e^(ln x) has the issue that x might not be in the domain of ln
< 1776085824 634745 :int-e!~noone@int-e.eu PRIVMSG #esolangs :oh I'd restrict to R^+
< 1776085826 484671 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :I think the paper is mostly disregarding that issue
< 1776085862 505552 :int-e!~noone@int-e.eu PRIVMSG #esolangs :well. you'd have to jump back and forth between reals and positive reals quite a bit
< 1776085878 204270 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :the paper itself seems very "AI-influenced", not necessarily AI-written but it makes a mistake common among AIs where it focuses too much on less important details and not enough on the important ones
< 1776085879 357704 :int-e!~noone@int-e.eu PRIVMSG #esolangs :but I don't think it gets out of hand, just a bit tedious
< 1776085955 666344 :int-e!~noone@int-e.eu PRIVMSG #esolangs :But I haven't written anything down, so it's possible that I'm underestimating the complication.
< 1776085999 452942 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :this basis can't obviously compute modulus, I suspect that it could if you go into the complex numbers and use some sort of construction for arcsin or arccos
< 1776086024 630432 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :actually, even regular sin or cos could work if you ensure that the input is an integer times an appropriate fraction of pi
< 1776086103 909603 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :or, no, that works for mod-2 but not obviously for mod-x
< 1776086144 336845 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :the paper is assuming that you're operating on complex numbers but really glosses over the branch cut
< 1776086207 152536 :int-e!~noone@int-e.eu PRIVMSG #esolangs :You can use polynomial interpolation on n-th roots of unity (aka DFT) to do modulo stuff for n > 2 too.
< 1776086226 768667 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :oh, that's clever
< 1776086246 227334 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :as long as the factors you need are constructible
< 1776086248 834421 :int-e!~noone@int-e.eu PRIVMSG #esolangs :maybe just for fixed n?
< 1776086286 778641 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :right, doing it for varying n would mean some sort of automatic construction and I think that would involve an arcsin
< 1776086296 724244 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :but arcsin seems likely to be possible to build out of this operation
< 1776086607 878845 :amby!~ambylastn@host-81-178-153-130.as13285.net JOIN #esolangs * :realname
< 1776087109 662808 :int-e!~noone@int-e.eu PRIVMSG #esolangs :Hmm you have an opportunity to use sin(x) = 2t/(1 + t^2), cos(x) = (1 - t^2)/(1 + t^2) where t = tan(x/2).
< 1776087149 627597 :int-e!~noone@int-e.eu PRIVMSG #esolangs :Just for cuteness; |sin(x)) = sqrt(1 - cos(x)^2) gives you about the same thing
< 1776087193 998145 :int-e!~noone@int-e.eu PRIVMSG #esolangs :either way you can then target e^(ix) = cos(x) + i sin(x), and take the logarithm of that, and hope that the function picks the usual principal value for logarithms.
< 1776087216 169102 :int-e!~noone@int-e.eu PRIVMSG #esolangs :(so the x you get is reduced modulo 2pi)
< 1776088969 774548 :ais523!~ais523@user/ais523 PRIVMSG #esolangs :yes, the details of the branch cut in the complex logarithm are super-relevant if you do this with complex numbers, I think
< 1776090796 867458 :korvo!~korvo@2604:a880:4:1d0::4d6:d000 PRIVMSG #esolangs :ais523: TBH the paper tastes like it was written by a Wolframite; they've always been AI-curious, but when they need to ask the computer for questional numerical results they're using Mathematica rather than ChatGPT.
< 1776090857 403195 :korvo!~korvo@2604:a880:4:1d0::4d6:d000 PRIVMSG #esolangs :Because complex numbers are required, I'm not really convinced that they've given a good method for computing or representing pocket calculations. The hint at the end about using gradient descent seems more interesting TBH.
< 1776091038 606932 :korvo!~korvo@2604:a880:4:1d0::4d6:d000 PRIVMSG #esolangs :This reminds me of a recent paper about generalizing orders of magnitude to the complex numbers: https://arxiv.org/abs/2510.03426
> 1776093838 340101 PRIVMSG #esolangs :14[[07Arbitrary memory emulation14]]4 10 02https://esolangs.org/w/index.php?diff=179596&oldid=175209 5* 03Aadenboy 5* (-654) 10replacing most of the