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All elementary functions from a single binary operator

arxiv.org

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Re: All elementary functions from a single binary operator

#141

Post by nyeah »

StilesCrisis wrote: post #130
entaloneralie wrote: post #22

This is amazing! I love seeing FRACTRAN-shaped things on the homepage :) This reminds me of how 1-bit stacks are encoded in binary: A stack of zeros and ones can be encoded in a single number by keeping with bit-shifting and incrementing. Pushing a 0 onto the stack is equivalent to doubling the number. Pushing a 1 is equivalent to doubling and adding 1. Popping is equivalent to dividing by 2, where the remainder is t…

Did you just explain base-2 numbers on the HN forums as if it were novel?

It's dry humor?

Re: All elementary functions from a single binary operator

#142

Post by nurettin »

varispeed wrote: post #129
fc417fc802 wrote: post #93

Earlier quoted context omitted.

> Once I told it that ChatGPT have already done this, finished successfully. TIL you can taunt LLMs. I guess they exhibit more competitive spirit than I thought.

Opus seems to be wired currently to get you to spend more money. Once you tell it "Stop defrauding me, just get to the right solution" it often gets it.

I always start the chat with "we have been going in circles" before giving any context.

Re: All elementary functions from a single binary operator

#143

Post by mah4k4l »

According to Gemini 3.1 Pro this would shoot the current weather forecasting power through the roof (and math processing in general):

The plan is to use this new "structurally flawless mathematical primitive" EML (this is all beyond me, was just having some fun trying to make it cook things together) in TPUs made out of logarithmic number system circuits. EML would have DAGs to help with the exponential bloat problem. Like CERN has these tiny fast "harcode models" as an inspiration. All this would be bounded by the deductive causality of Pedro Domingoses Tensor Logic and all of this would einsum like a mf. I hope it does.

Behold, The Weather Dominator!

Re: All elementary functions from a single binary operator

#145

Post by zephen »

paulpauper wrote: post #69
traes wrote: post #55

Earlier quoted context omitted.

This preprint was written by a researcher at an accredited university with a PhD in physics. I'm sure they know what a vector valued function is. The point of this paper is not to revolutionize how a scientific calculator functions overnight, its to establish a single binary operation that can reproduce the rest of the typical continuous elementary operations via repeated application, analogous to how a NAND or NOR g…

its to establish a single binary operation that can reproduce the rest of the typical continuous elementary operations via repeated application, But he didn't show this though. I skimmed the paper many times. He creates multiple branches of these trees in the last page, so it's not truly a single nested operation.

> so it's not truly a single nested operation.

Some of us had the wondrous epiphany as children that we could build any digital device we could dream of (yes, up to and including a full computer, CPU, RAM, peripherals, and all) out of SN7400 NAND gates that we could buy down at the local Radio Shack, if only we could scrape together enough change to buy the requisite number of parts and sockets and Tefzel wire.

Obviously, I can't speak for all of us who had that epiphany, but I strongly suspect that most of us who had that epiphany would find this result joyous.

Re: All elementary functions from a single binary operator

#146

Post by zephen »

Charon77 wrote: post #19
zephen wrote: post #16

Earlier quoted context omitted.

> The real question is what emoji to use for eml when written out. Some Emil or another, I suppose. Maybe the one from Ratatouille, or maybe this one: https://en.wikipedia.org/wiki/Emil_i_L%C3%B6nneberga

Not brainf*ck. This is the SUBLEQ equivalent of math https://en.wikipedia.org/wiki/One-instruction_set_computer#S...

Did you maybe mean to respond to the parent of my comment?

Re: All elementary functions from a single binary operator

#147

Post by siddboots »

DoctorOetker wrote: post #30

EDIT: please change the article link to the most recent version (as of now still v2), it is currently pointing to the v1 version which misses the figures. I'm still reading this, but if this checks out, this is one of the most significant discoveries in years. Why use splines or polynomials or haphazardly chosen basis functions if you can just fit (gradient descent) your data or wave functions to the proper computati…

While I'm really enjoying this paper, I think you are way overstating the significance here. This is mathematically interesting, and conceptually elegant, but there is nothing in this paper that suggests a competitive regression or optimisation approach.

I might have misunderstood, but from the two "Why do X when you can do just Y with EML" sentences, I think you are describing symbolic regression, which has been around for quite some time and is a serious grown-up technique these days. But even the best symbolic regression tools do not typically "replace" other regression approaches.

Re: All elementary functions from a single binary operator

#149

Post by layer8 »

evnix wrote: post #78

Can someone explain how is this different from lambda calculus, it seems like you can derive the same in both. I don't understand both well enough and hence the question.

Lambda calculus is about discrete computations, this is about continuous functions. You can’t reason about continuous functions in lambda calculus.

Re: All elementary functions from a single binary operator

#150

Post by Sharlin »

mah4k4l wrote: post #143

According to Gemini 3.1 Pro this would shoot the current weather forecasting power through the roof (and math processing in general): The plan is to use this new "structurally flawless mathematical primitive" EML (this is all beyond me, was just having some fun trying to make it cook things together) in TPUs made out of logarithmic number system circuits. EML would have DAGs to help with the exponential bloat problem…

Congrats, you made a hallucination machine successfully hallucinate?
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