[lemonwaterlime]

I’m fairly certain that the difference between the approaches is that the f(x,y) function you mentioned requires limits to represent certain concepts while the eml approach is essentially a tree or a chain of computations meant to represent a model of a system.

[SideQuark]

Computing exp or ln is an infinite series, and vastly more compute. Hiding series behind a name doesn’t make them free to compute.

[AlotOfReading]

They're not series, that's just a convenient way to think about defining and calculating them. I've never found it particularly useful to deal with the series definitions either, and none of the (good) approximation methods I'm aware of actually take that approach.

Moreover, EML is complete in a way that your suggested function isn't: If you take a finite combination of basis functions, can it build periodic functions? Hardy proved over a century ago that real (+,-,/,*,exp,ln) can't do this (and answering the paper's unresolved question about similar real-valued functions in the negative). EML being able to build periodic functions is a lot less surprising for obvious reasons, but still pretty neat.

[scotty79]

EML goes through complex numbers and infinities internally.

Previous commenter meant that there are infinite series inside log and exp.

To achieve a thing like sin(x) from his universal expression, yes you'd need infinite series of those, not a finite set of operations, but to get all 36 basic function you'd need a finite set of different infinite series.

So exp and log just happen to be the labels for two element set of such infinite series that you'd have to use to make 36 functions out of the operator that pervious commenter proposed.

All that said, I still think it's pretty neat too.

[lemonwaterlime]

I understand your point. The paper is more about the depth of the tree to represent and audit a model versus the raw CPU clock cycles. It takes the exponent and logarithm as given since for all practical purposes, in a scientific context, they are.

To represent something like sin(x) with f(x,y) requires infinite steps. Conversely, with eml you get an exact result in around 4 using identities and such.

One could argue that we do Taylor Series approximations on the hardware to represent trigonometric functions, but that highlights the key aspect of the eml approach. You can write a paper with those four steps that describes an exact model, here sin(x). And people can take that paper and optimize the result. This paper is about an auditable grammar that you can compute with.

[imtringued]

You're completely missing the point here.

You can reduce all Boolean logic to NAND, but that doesn't actually mean that semiconductor fabs translate their HDL to NAND gates, because it is possible to build complex gates that directly implement higher level operations in a single gate.

Your "cost of computation" objection can be easily resolved by adding more operators, which makes it boring from a research perspective.

Meanwhile the loss of expressivity can only be compensated by encoding algorithms directly into the expression tree. Your objection that an infinite series is a bad thing rings hollow, since you now introduce the concept of an infinitely sized expression tree. That sounds much more impractical than implementing an algorithm for the exponential and logarithm functions.

[SideQuark]

Show me a way to physically compute exp or ln that is less gates than add. More gates means costlier in $, more energy in compute, and for these functions, higher latency.

You don’t get to make up free ops, claim there is no cost in reality, and hand wave away reality.

There are infinitely many ways to do what the paper did. There’s no gain other than it’s pretty. It loses on every practical front to simply using current ops and architectures.

[lioeters]

> no gain other than it’s pretty

Conceptual elegance is worth something, isn't it? I don't mean just aesthetic pleasure, as in recreational mathematics, but there's often (not always) value in being able to succinctly describe a wide range of phenomena with a small number of primitives. It could open up new ways of understanding or working that wasn't possible before. Not saying this specific discovery fits the description, but it seems too early to dismiss the idea entirely based on its im/practicality compared to existing solutions.

Aren't there examples in the history of mathematics, where a new idea was criticized for being impractical, then later found to have applications or implications, possibly unexpected even to the person who discovered it?

[ageofthun]

I feel sad when pragmatics comes in scientific discussions... that's not what science should be (I think). But I value the discussion this paper is bringing to distinct contexts (even outside academia). That by itself adds value to this work.

[zonked45]

i am outisde of academia, i am told there are significant findings here at monogate.dev . just started vibe coding from the paper.

appreciate any feedback

[Qem]

> Show me a way to physically compute exp or ln that is less gates than add.

IIRC a resistor in series to a capacitor does the trick, for exp.

[SideQuark]

No, it approximates exp poorly over an infinitesimally small interval compared to exp. Resistors and capacitors are no where ideal components, which is why they have spec sheets to show how quickly they diverge.

If we’re making sloppy approximations to a tiny range of exp, then I too can do it with a few terms.

[gyb997]

The feasibility of memristor analog circuits is evident, and I believe this paper represents a valuable early exploration. We've been constrained by Boolean logic for quite some time now.

[SideQuark]

The world has had many types of logic before and after Boolean logic was created, many used in computing. Boolean logic isn’t a constraint; it’s used where it’s useful, and others are used where they’re useful.