!!!!!

[tml@mementomori.social]

@MeiLin @mhoye Haha, exactly my reaction. I can't fully believe this until I see a Numberphile (or similar) video about it;)

[mms@mastodon.bsd.cafe]

@mhoye as someone who has not seen a mathematical calculator in over two decades: what can this do? Simplify CPU to only to one logic gate? I see that Andrzej (hey! Cracow!) talks about neural networks, but this gives even less understanding.

[kboyd@phpc.social]

@holdenweb @mhoye True, true. But what about those minecraft people who build calculators and such - will it vastly simplify their lives?

[elizafox@social.treehouse.systems]

@mhoye I expected this to say 1975 or some shit but no it says 2026. Fucking WILD.

[soblow@eldritch.cafe]

@mhoye alt-text:

"""
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, , and log has always required multiple distinct operations. Here we show that a single binary operator,

eml⁡(x,y)=exp⁡(x)−ln⁡(y),

together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as e, π, and i; arithmetic operations including +, −, ×, /, and exponentiation as well as the usual transcendental and algebraic functions. For example, ex=eml⁡(x,1), ln⁡x=eml⁡(1,eml⁡(eml⁡(1,x),1)), and likewise for all other operations. That such an operator exists was not anticipated; I found it [...]
"""

[lykrast@eldritch.cafe]

@mhoye oh shit

[ellie@ellieayla.net]

@mhoye this paper is a shitpost, right?

[jorendorff@federate.social]

@PsySal @mhoye From Euler's formula, sin(x) = (exp(ix) - exp(-ix))/2i.

So you first find formulas for subtraction, negation, multiplication, division, i, and 2, and then it's easy...

I dunno. The paper strikes me as crank. But what do I know.

[f4grx@chaos.social]

@mhoye can you please add an alt so we can retoot this mindblowing article? thank you! you can almost copy paste the abstract as the alt.

[f4grx@chaos.social]

@MeiLin @mhoye some of the formulas could be recalculated by hand.

eg it's obvious that eml(x,1) is exp(x)

[psysal@mastodon.social]

@jorendorff @mhoye ah! I was wondering how you got a cyclic function out of ln and exp. I am not superstrong at math-- I just like it

The core idea does seem pretty cool. The paper is annoyingly wordy in a slop-machine-wrote-this way-- the author discloses as much. Lately I have been thinking about how functions (e.g. sin()) are actually implemented (did some baby level numerical integration stuff lately which made me curius.)

Also wonder: is this idea similar to Taylor polynomials?

[pointlessone@status.pointless.one]

@mhoye This is way over my head but there was this in my feed related to the link: https://www.stylewarning.com/posts/not-all-elementary/