[bgutierrez]

To me, the most interesting sentence in this essay is: "[H]e, Gödel, had felt that a nuclear chain reaction would be possible only 'in a distant future'."

Gödel was second-to-none in analytic ability and he was paranoid. What made him so certain that nuclear chain reaction was a distant possibility? If it were anyone else, I'd say they were just trying to comfort themselves by not thinking about terrible consequences. I wish I knew what made him come to the conclusion he came to.

[campbel]

The only reason that nuclear energy/weapons are possible at all is because there exists isotopes that release more neutrons than they absorb during fission (the chain reaction). Nuclear fission itself wasn't fully understood until 1938.

I think this is the hard part of analyzing systems. If there exists mechanisms outside of your current understanding, there is no way to predict what is and isn't possible

"It always seems impossible until it's done." - Nelson Mandela

[lainga]

>If there exists mechanisms outside of your current understanding, there is no way to predict what is and isn't possible

See Lord Kelvin on heavier-than-air flight (he was fixated IIRC on the theoretical maximum power-to-weight ratio of a steam engine)

[JadeNB]

> Gödel was second-to-none in analytic ability and he was paranoid. What made him so certain that nuclear chain reaction was a distant possibility? If it were anyone else, I'd say they were just trying to comfort themselves by not thinking about terrible consequences. I wish I knew what made him come to the conclusion he came to.

The universe does not subscribe to rigorous, certain analysis. Being an unparalleled genius in mathematics can make you too certain of the applicability of conclusions deduced from axioms about the real world; in mathematics axioms are true because you decide to work in a model of them, but the real world usually doesn't care to cooperate with the axioms that make sense to you. My suspicion would be that that's what happened here.

[Isamu]

The chain reaction was still speculative. Also physics is math, but math is not physics.

[77pt77]

Physics is not math.

Physics uses math.

[aspenmayer]

Physics is not math any more than the map is the territory.

https://en.wikipedia.org/wiki/Map%E2%80%93territory_relation

[baggy_trough]

Depends on your philosophy.

[aspenmayer]

There are an uncountable number of atoms in the universe. There are nondeterministic occurrences in many natural processes. Even if the universe is a simulation, that doesn’t mean that it’s able to be represented or formalized from within the simulation.

Math is possibly one of the best tools of the scientific method to make logical sense of the universe, but that doesn’t mean that we can compute any given thing due to the scales involved. Gödel was likely familiar with the unknowable nature of the universe given certain hard limits of calculation, computation, and measurement.

Physics is the tool we use to move the world, yet we may never be able to build a lever or fulcrum long enough to actually do so - physics and math only give us a place to stand and means to orient ourselves. Everything else is engineering, I’d say.

> Give me a place to stand and with a lever I will move the whole world.

https://en.wikiquote.org/wiki/Archimedes

I would like to hear your thoughts, however. I think you’re right in a sense, that physics and math are possibly inseparable syntactically, similar to the identity property. If a thing is what it does, physics is math as much as it is logic, or vice versa.

Like math, logic is what we understand it to be, regardless of correspondence to reality. Physics rather seeks to represent and model more than the abstract truths of math and logic, and physics has an element of necessary utility and correspondence to hypothetical or actually existing realities, possibilities, and observable phenomena, whereas math and logic are not burdened by testability, but are rather proven or disproven via internal consistency and formalisms.

Like many tools, their proper usage comes down to holding them correctly, both in hand and in mind.

[baggy_trough]

https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...

[aspenmayer]

Awesome reference! Thanks for that.

To further cite:

On Math, Matter and Mind

https://arxiv.org/abs/physics/0510188

If I’m following your train of thought, I read it like this:

All squares are rectangles, but not all rectangles are squares. All physics is math, but not all math is physics.

As it applies to my understanding of your point and to my understanding of the MUH, Tegmark argues that the universe is necessarily pigeonholed by physics, and must be constrained by and embodies physics, which seems logical and consistent to me.

My point was perhaps a bit more pedantic regarding the distinctions between A: actually existing external reality independent of our understanding of it, and B: our representation of the universe that physics seeks to formally define.

I think it’s reasonable to assume that the universe is internally consistent and rational; that is to say that it’s bounded by so-called laws of physics, but we may not be able to reason about it because we currently lack the tools to make sense of it; that is to say we don’t know how to represent it mathematically.

I think we likely agree - the universe computes itself and proves itself by its essential nature and very existence. I don’t mean to speak for you, but only to find points of agreement.

[genman]

Physics is math, but not all math is physics.

[andrewflnr]

Physics is, optimistically, math plus a whole load of initial conditions that are not findable a priori.

[wizzwizz4]

Physics is the study of reality under the assumption that it's lawful. The real world doesn't run on physics: it just is.

[andrewflnr]

Yes, that's one of the less mathematically optimistic perspectives. :)

[mistermann]

The physical portion of reality.

[wizzwizz4]

No, the causal portion of reality. (Philosophers of metaphysics are still arguing whether acausal aspects of reality are, in any real sense, real, but we don't need to listen to them.) If we discover something non-physical (the usual example being ghosts), that'll just become a new branch of physics.

Physics currently talks about dark energy, the geometry of spacetime, and quantum superposition. I don't think you can get much less physical than that.

[lanstin]

My understanding is that QFT is not axiomatized - it works but there's a bit of hand-waving at the level of actual proofs. There are people working on this, but currently physics is physics and maths is maths.

[SJC_Hacker]

QFT also becomes increasingly unwieldy for large systems. E.g., try calculating bond energies of complex molecules. You can do it for hydrogen and "hydrogen like" molecules, but once you get beyond a few interactions, the differential equation does not have closed form solutions. This is not a total loss as you can resort to numerical solutions in at least some cases.

Science is mostly about producing models that "work" whether this involves reductionism to more fundamental principles or not. At worst however, the model which describes the larger system should not conflict with the description of the smaller one.

[lanstin]

Verseon is doing raw quantum mechanics computations about various potential drugs and various important receptors. https://www.verseon.com/

[aatd86]

Banach spaces looking like lightweight Euclidian spaces (in terms of constraints), and reality being experienced as data and applications, I'm going to try and say that:

Physics is a subset of Mathematics but which subset we don't exactly know.

In a sense, physics is the self-referential discovery of a subset of mathematics.

Makes sense since "existence" is impredicative.

[smj-edison]

Mathematics is perhaps a subset of logic? I'm not very familiar with this space, but I think it's pretty cool that so much of math can be represented with very simple rules building up, especially with things like the Lean proof language.

[lanstin]

I find infinite dimensional spaces even of zero curvature to be a bit creepy. Especially with a vector space structure, that just makes it worse.

[andrewflnr]

You're entirely missing the critical point of my comment, which is the initial conditions.

[aatd86]

I beg to differ. What are initial conditions if not some additional constraints?

[jandrese]

Physics is just applied math.

[isk517]

But not all math can be applied.

[whizzter]

It seems like less well researched hunches on nuclear processes often led programs astray with bad calculations.

The Germans focused on heavy water for their reactors instead of just using graphite, because they miscalculated neutron absorption allegedly because of measuring graphite pieces rich in boron. The entire program was subsequently after the heavy water sabotages in Norways seemingly taking too long and was depriorititzed (Did the world luck out on small happenstances like this and Lenard?).

The Swedish program likewise initially overestimated the required amount of fissile materials needed by an order of magnitude and it wasn't clear until years later, could an accurate figure have made the program progress quicker before public opinion turned? (a lot of complex and expensive designs were worked out to produce at the higher rate)

[marcosdumay]

Oh, right. It "only" took the Manhattan Project.