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.
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.
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.
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.
You are welcome to make an assertion that causal forces lie only in the physical realm, but declaring something to be true does not necessarily make it true, though at scale it can certainly make it seem true.
>> An ideology is a set of beliefs or philosophies attributed to a person or group of persons, especially those held for reasons that are not purely epistemic...
>> The illusory truth effect (also known as the illusion of truth effect, validity effect, truth effect, or the reiteration effect) is the tendency to believe false[1] information to be correct after repeated exposure.
[1] The "false" designation here is unnecessary and flawed imho (or better: a fine example of how ubiquitous this problem is).
> (Philosophers of metaphysics are still arguing whether acausal aspects of reality are, in any real sense, real,
What meaning do you assign to the symbol "real" in this context?
Is it flawless?
> ...but we don't need to listen to them.)
In an absolute sense, no you don't. But to achieve certain desires you may have to. Like the saying goes: "You may not be interested in metaphysics (or truth, etc), but it might be interested in you".
But it's even more interesting: not only do you not have to listen to or seek truth, you can engage in mass collective story telling on the internet, confusing the population at scale. Don't believe me? There's a search function right here on HN, the evidence is there for the viewing!
> If we discover something non-physical (the usual example being ghosts), that'll just become a new branch of physics.
a) Science does like their Motte and Bailey.
b) I doubt you can actually see the future. If you disagree, please explain, using only physics, how you can.
> 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.
Do you believe that aggregate reality is constrained by your cognitive abilities, or are you perhaps more so describing your opinion about "reality"?
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.
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.
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.
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.
Physics uses math.