[bsaul]

I wonder if our common expectation that true theories somehow had to be beautiful and elegant is going to survive the coming century. What if "real" nature phenomenon were actually best described by horrible mess of impossible equations, that only machines could actually manipulate and reason about ?

That would be really sad..

[jordanb]

> our common expectation

I think you're going too far with this. Most people understand scientific theories to be an approximation. F=ma is approximately true, in the sense that it's only accurate within the newtonian regime and each of those terms includes so many asterisks that you will only ever measure it approximately.

The latter is the jokes about the physicists "assuming a perfectly spherical cow."

In fact that's kinda the whole point of the "unreasonable effectiveness of mathematics" essay. It is unreasonable that mathematical approximations are so good at describing our world.

[the_af]

> The latter is the jokes about the physicists "assuming a perfectly spherical cow."

Not to detract from your point at all, but I only ever heard this joke about mathematicians!

[try_the_bass]

I've definitely heard a similar joke about economists. It probably applies to most sciences, tbh

[nagaiaida]

do we mathematicians do particularly much work with cows that is made simpler by assuming they're spherical?

[the_af]

At the very least the cow-equations are made simpler!

[iamflimflam1]

I often think this about medicine and the human body. We want to believe that our bodies are some miraculous well oiled machine. But it often seems that it’s a barely held together bag of mess.

[idiotsecant]

Biology is incredibly robust!! I'd say barely held together bag of mess describes something like an internal combustion engine. A primate, on the other hand, is a self-replicating machine capable of self-repair and just about universal fuel sourcing. It has a robust defense network capable of identifying and eradicating a staggering number of foreign replicators. It has holographic design storage, with each cell containing the plan for the whole organisim. It has general cognition based on a world model, and does all this on almost no energy.

Biology is incredibly well oiled!

[paytonjjones]

I think your reply and the parent can both be true, you're just using slightly the same words to describe different things.

The parent is talking more about elegant simplicity vs. sprawling, seemingly haphazard complexity, and you're talking more about durability to failure points and 'completeness'.

Likewise, in code, a lot of the most durable, battle tested software looks extremely inelegant and duct taped, as 90% of the code is dedicated to handling one-off patches and weird edge cases.

[HPsquared]

I think politics and economics work along similar lines.

[nullorempty]

No, you just need to be on a regular good maintenance schedule!

[aeve890]

>I wonder if our common expectation that true theories somehow had to be beautiful and elegant is going to survive the coming century.

That's the layman's idea of physics theories. They are beautiful and elegant only on the surface, that's why they're technically models and approximations of the real world. The standard model renormalization techniques are a mess of patches and ad-hoc heuristics, pretty far from the "this lagrangian literally contains all physics". Generally you just _ignore_ higher order terms and just call it a day. The famous E=mc^2 it's just the first term of a Taylor expansion. The beautiful form of physics it's what you would call "good enough" and often just a pedagogical tool.

[sestep]

> The famous E=mc^2 it's just the first term of a Taylor expansion.

Is this actually true? My understanding was that E=mc^2 is exact for a particle at rest.

[reinitctxoffset]

It would represent a pretty sharp inversion from all the progress of mathematical physics until the present.

Up until the present it has been a nearly uniform march of revealed symmetries, collapsed privileged frames of reference, and other such (in the deepest sense) simplifications in our model of reality that has improved its fidelity to the measurable.

I hang qualifier about these developments being simplifying because the result isn't simple in the details: quantum chromodynamics is a daunting subject! But it's not just an enumeration of details and contradictions, the particle zoo that preceded the Eightfold Way looked like line noise, now in indexed notation the Lagrangian of the entire Standard Model fits on a page (or so I've been told I've never actually seen the page).

It's almost tautological that the frontier where it's still messy involves an unrevealed symmetry or a persistent privileged frame of reference, that's what frontier means, we don't see past it to the seam where it folds up.

Personally I suspect AI systems will be a great deal more inclined to discard the parochial axioms that have every point placed human ego above simplicity.

It doesn't resolve all of the open problems in physics if you amputate consciousness, free will, agency persistent identity, and an unambiguous arrow of time.

But it starts looking possible to make progress.

[dnmc]

This has been on my mind lately! Especially in light of the many incomprehensible but machine-checkable proofs we've been hearing about.

Occam's Razor is a useful heuristic, but it biases us towards simpler explanations.

[wonnage]

But those proofs are showing that the fundamental axioms (which are generally simple and elegant) are still enough to build a complex result.

I think of elegance as not having to add epicycles, not that everything in the system has to be simple.

Also, without a working theory the, the space of possible solutions is near infinite. LLMs manage to pluck out the space of comprehensible English strings from n-dimensional hell. Even if this is done with a black box of billions of parameters, it’s still elegance in the sense that such a space even exists and was found

[SOLAR_FIELDS]

Would it be sad? If it’s gnarly and it solves the problem, as an end user I don’t really care. The only people who lose are the mathematical purists

[pitched]

Math is a language to explain systems. Teaching someone that force varies linearly to mass is a helpful first pass. It isn’t exactly linear but is not exponential at all.

Gaining expertise is always the hard part and our new LLM overlords are making that much harder. So the simple “pure” functions as a teaching aid have never been more important.

End users have never cared about how the sausage is made though.

[dmix]

> LLM overlords are making that much harder.

LLMs can explain complex things to humans with tons of specific context that you don’t find in textbooks or even a google search.

It’s probably never been easier to grasp a large codebase than it is today for example. You can probe and ask specific questions without going through a maze of imports and relationships and config files yourself.

Learning things will always be up to the person, it’s still a choice and dedication to a craft can still be taught.

[Planktonne]

> LLMs can explain complex things to humans

I keep meeting people who think this and have enormous understanding gaps in the topics they've had an LLM teach them.

The absolute worst judge of how well someone understands a complex topic is the novice themselves.

[pitched]

The difference now is that the learning is optional (more often but not always) to getting the task done.

When gaining mastery is not a requirement to doing novice-level work, many fewer people will get there. It takes more dedication than it did before.

[ambicapter]

The "common expectation" I think, misses the point. The idea isn't that fundamental theories are simple or elegant (quantum physics equations are pretty darn ugly), it's that, given the choice between a more complicated and a more simple theory, generally the simplest one is the most accurate choice.

[dyauspitr]

I don’t agree with that at all. Maybe for asinine things like human behavior but otherwise nature and physics don’t really follow that rubric.

[folkrav]

Are you thinking of any specific examples? I don't disagree that complex things generally end up having complex explanations, but I'm admittedly drawing a blank trying to come up with things where the most complex explanation ended up being the correct one.

[__MatrixMan__]

There are many marvels of evolution's ability to come up with robust complex distributed systems which work way better than anything we build. The one I've learned about most recently is the https://en.wikipedia.org/wiki/Immunological_synapse in which different kinds of white blood cells gather around a bit of evidence that one of them found and decide whether to shoot the messenger (clonal anergy), or raise a clone army to defeat the invader (T-cell activation).

Imagine that it's maybe the 1800's and you're asking why somebody who has already survived smallpox is not susceptible to becoming infected again. If you offered an explanation involving tiny detectives wandering around and collecting evidence which they present to each other and decide whether to multiply... one in which the tolerance comes from the detectives from the previous fight still hanging around in your lymph nodes ready to spring into action if they run across the right kind of evidence. Well that would probably be a more complicated explanation that anybody at the time would offer, and it would also be correct.

[folkrav]

Incomplete prior knowledge doesn't mean it's simpler, just that it's inaccurate. Would the phenomenon you're describing really accurately be explained by something _simpler_?

[programjames]

You should look into Solomonoff induction. Nature and physics, absolutely, tautologically, have to follow the "shortest explanation is more likely principle".

https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...

[jvanderbot]

My suspicion is that we had a sense that generality and compactness was really neat, so we liked easily-remembered laws like F=ma. Applies everywhere, is clean.

When you attempt to hyper-optimize, even with humans in the loop, you end up a mess. You're lucky if you can find clean guiding principles anywhere. If you can hyper-optimize hyper quickly, you end up with an extra layer of mess.

[YurgenJurgensen]

Or that tractable models are just more useful than intractable ones even when the latter are more accurate.

[slopinthebag]

How would nature be best described as a horrible mess of impossible equations? They would be best described as elegant and beautiful no?

I think your point is more that we might be able to initially describe complex phenomena as messy, horrible complex equations, that doesn’t mean we shouldn’t work to simplify them and make them more understandable to us.

[lomlobon]

Look up diagrams for cell signaling cascades sometime. It's emblematic.

[slopinthebag]

In some ways it's like a smalltalk system haha. I think you can find some elegance there. The system is overall complex, but with simple primitives.

[dyauspitr]

It would be really cool. We already know everything at the lowest levels is a probability cloud. There’s beauty and contentment in not really being able to nail anything down for eternity…

[goatlover]

That's a result of the Copenhagen Interpretation. There are other interpretations of the math which don't rely on reality fundamentally being a probability cloud/wave/field.

[dyauspitr]

I’m not well versed in this but if fundamental particles are probability clouds, the future is not deterministic.

[NopIdoN]

Why not? Every cloud that matters is resolved. What's to say a different resolution to any cloud can be possible?

[kurthr]

All theories are wrong.

Some are useful.

Having theories that only give answers, but you can't reason about is not as useful. Having a theory where you don't know the limits of it's applicability, can be very dangerous.

At least in the physical realm there is not yet anything that combines relativity with QM so they can only be approximations. Even in math so far there seem to be similar challenges using programatic and "AI" driven solutions and proofs.

Still, I know that LLMs will be useful for Verilog/VHDL and particularly with verification, where they are already heavily used. Defined outputs and complete test coverage is already such a big part digital/asic design, I'd be surprised if it isn't used a lot more. Many software people would say that hardware is badly written copy-pasta, as it is. That said, higher velocity slop and hardware "technical debt" isn't something you can fix with an update. And no matter how fast you "ship", you won't get parts back in less than a few months. Poorly used, it will lead to expensive failures.

[csomar]

Hallucination, when it succeeds, is the intelligence.

[programjames]

That is very unlikely due to Solomonoff induction...

[vlovich123]

Solomonoff induction doesn’t concern itself with what is truth and reality. It just says which theory to prefer and how to determine so objectively when multiple are equally precise in making predictions of observations. It’s a formal description of Occam’s razor.

OPs argument is that reality is expressed by very complex equations and interactions; by definition this is outside of Solomonoff induction because it’s easy to imagine this accurate model by definition is the shortest algorithmic explanation, it’s just orders of magnitude more complex than our current approximations.

[programjames]

You should include the error correction code length in the description length. This means Newtonian mechanics was a much longer theory to describe Mercury's orbit than general relativity. It was only the shorter theory before they had the data showing a discrepancy. Which is the correct approach to describing your reality, because until you see a discrepancy, the extensional properties all follow the shorter rules.

I guess the argument from OP would look like: "Yes, now imagine we poke and extend our universe as far as we can. How much bigger do you think our final 'shortest description' would be? I imagine it may be orders of magnitude more complex."

Well, I can imagine a squared circle... doesn't mean the math checks out. I would reply that you do not have to imagine, you can go about looking at different mathematically possible universes in Tegmark IV and find the expected number of bits for the one you actually exist in. Which is ~0 bits more complex than the shortest description based on the data you currently have.

Also, note that Newtonian mechanics is not actually a very short theory for building a universe, because you have to instantiate every object in the universe. You actually get a lot more of the structure for free with general relativity (re: Wigner's classification of the particles). An observer in a presumed-Newtonian universe calling it a simple theory would be like saying, "I compressed Wikipedia to one byte, just by putting it all in the decompiler!"

[akomtu]

Does the nature look like a horrible mess to you?

[dyauspitr]

If you’re not being facetious, then the answer is very much a yes.