SoylentNews

VLM [soylentnews.org] writes:

Here's one that's been making the rounds:

https://arxiv.org/abs/2603.21852 [arxiv.org]

"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, sqrt, and log has always required multiple distinct operations. Here I 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, pi, and i; arithmetic operations including addition, subtraction, multiplication, division, and exponentiation as well as the usual transcendental and algebraic functions."

Discussion ideas:

1) Yes everyone knows there's not one, but two universal logic gates, anything made of NAND gates can be made of NOR gates and vice versa. So there's possibly at least one other "universal computation" for continuous math.

2) Who's playing with the idea of computer/microcontroller FPUs that use nothing but this operation, super optimized? I think this is funny to think about even if impractical.

3) Ditto analog computation. Analog opamp subtraction ain't rocket surgery, and old fashioned bipolar transistors can output logs and exponentials or you can use single chip devices to calculate logs and exponentials. I'm trying to wrap my head around using the AD633 universal multiplier... This could get expensive.

4) You can do this on a slide rule for educational purposes. You need a rule with LL scales or at least L and C/D. I have to think about this some more.

Original Submission