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The answer to these questions is one of those things that are beyond human understanding. It's like asking why does probability work? Why does predicate logic w

The answer to these questions is one of those things that are beyond human understanding. It's like asking why does probability work? Why does predicate logic work? They are axioms. We have never looked beyond these axioms nor will we ever in your lifetime. I mean we may find a deeper mathematical model for quantum mechanics but the question of "why?" will never be answered. It may not even be the right question.

moonchild 5y ago
That is an assumption. We do not currently know of any process by which we might explain these axioms; but: 1. We may still glean insight by reflecting on them, and 2. There may be unknown processes by which we can explain these axioms
- deltaonefour 5y ago
  1. All axioms are assumptions. 2. You mean Logic? The foundation which axioms and theorems themselves rely on? Logic is like a recursive axiom. We assume logic is true (aka an axiom) then, logic allows us to create axioms themselves and build theorems off the axiom. The thing with logic is that it's almost a thought driven endeavor. We don't need to observe the world to go deeper. But we can't. The buck ends here. To answer the question "why?" we have to go deeper, but there's nothing left.
bawolff 5y ago
We may not find the answer, but it seems really different than say predicate logic. It seems easy to imagine a non-quantum world. I can't imagine a world where predicate logic doesn't work.
- deltaonefour 5y ago
  The universe seems to be built in layers. Science, Math, and logic in that order with logic at the very bottom. So logic is always PART of the answer as it's just a layer on the bottom of everything. The thing is, I would imagine the answer to the question "why?" is on some hidden layer below logic. But the buck stops there. Even the very thought of predicting that there's a hidden layer has to involve logic. To get at the hidden layer we have to remove the upper layer of logic and therefore the process of thought itself. How is this even possible? We can't go further. It's beyond us. But I get what your saying. You think the answer exists on the side or the upper layers. Science and beyond.
  - bawolff 5y ago
    Not entirely what my view is. Although arguably much depends on the meaning of the word "why" My original point was: say logic is false. That's hard to concieve of, and if so we basically can't reason. The rules of logic are independent of the physical world in a way the physical world following QM is not. I wouldn't say it is gradual layers but a hard line between physical and non-physical theories. As to your point - i disagree although i think we have different conceptions of "why". We'll never answer it in the sense of some creator saying "because i thought it'd be funny", but we can motivate the choice. We can make arguments that it is the most "natural" or "simple" system that meets requirements. Or most "elegant". Arguably that would probably all be post-hoc justification, but its still an interesting exercise.
    - deltaonefour 5y ago
      Elegance and natural and simple are just attributes of a system. There is no law that says all systems must be elegant. You're saying finding attributes of a mathematical model to be simple or elegant answers this question of "why?". For me such an attribute is arbitrary. If we determine something to be elegant it doesn't mean anything at all. But "why" is it elegant means something.
      - bawolff 5y ago
        I think the underlying (somewhat irrational) claim is that nature prefers to work in elegant ways. Thus if you can show that QM is the most elegant solution under some contraints, it helps explain the "why".
ketralnis 5y ago
Why does a^2+b^2=c^2 for a right triangle? It's just axiomatic, right? Not exactly. It's only true in flat euclidean geometry. If General Relativity holds then we're only in a flat spacetime if the total energy content of the universe is in some range of values, otherwise the universe could be the 3d equivalent of a sphere or it could be a hyperbolic shape. In neither of these configurations do right triangles behave the way you learnt in primary school. So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect.
- deltaonefour 5y ago
  >Why does a^2+b^2=c^2 for a right triangle? It's just axiomatic, right? Pythagorean theorem is not an axiom. It's a theorem. >Not exactly. It's only true in flat euclidean geometry It's a theorem for Euclidean geometry. >So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect. For theorems and the entire concept of math to even work all forms of mathematics from Euclidean geometry to hyperbolic geometry rest on universal axioms of logic. At best we have built higher forms of logic from the universal axioms and mathematics from arbitrary assumptions but we have never delved deeper than the 3 "laws" of logic. The other weird thing that we don't understand, and this is likely connected with logic is probability. We don't know why it works. It seems foundational just like logic but the weird thing is, formally probability is just like another math theory with random axioms at it's foundation and the rest of the theorems built up from logic. >If General Relativity holds then we're only in a flat spacetime... This is part of science. Observed phenomena then statistically matched to a arbitrary mathematical model. The OP's article is talking about something more fundamental... he asks "why?" When you ask that kind of question you have to really deep. Deeper than the science, deeper then the math all the way to the bottom. Everything stops at logic and probability. There is nowhere left to go to even move the needle closer to answering the question "why?"
  - grog454 5y ago
    > The other weird thing that we don't understand, and this is likely connected with logic is probability. We don't know why it works. Can you elaborate on this or provide further reading?
deleted 5y ago
[deleted]

moonchild 5y ago

That is an assumption. We do not currently know of any process by which we might explain these axioms; but: 1. We may still glean insight by reflecting on them, and 2. There may be unknown processes by which we can explain these axioms

deltaonefour 5y ago
1. All axioms are assumptions. 2. You mean Logic? The foundation which axioms and theorems themselves rely on? Logic is like a recursive axiom. We assume logic is true (aka an axiom) then, logic allows us to create axioms themselves and build theorems off the axiom. The thing with logic is that it's almost a thought driven endeavor. We don't need to observe the world to go deeper. But we can't. The buck ends here. To answer the question "why?" we have to go deeper, but there's nothing left.

bawolff 5y ago

We may not find the answer, but it seems really different than say predicate logic. It seems easy to imagine a non-quantum world. I can't imagine a world where predicate logic doesn't work.

deltaonefour 5y ago
The universe seems to be built in layers. Science, Math, and logic in that order with logic at the very bottom. So logic is always PART of the answer as it's just a layer on the bottom of everything. The thing is, I would imagine the answer to the question "why?" is on some hidden layer below logic. But the buck stops there. Even the very thought of predicting that there's a hidden layer has to involve logic. To get at the hidden layer we have to remove the upper layer of logic and therefore the process of thought itself. How is this even possible? We can't go further. It's beyond us. But I get what your saying. You think the answer exists on the side or the upper layers. Science and beyond.
- bawolff 5y ago
  Not entirely what my view is. Although arguably much depends on the meaning of the word "why" My original point was: say logic is false. That's hard to concieve of, and if so we basically can't reason. The rules of logic are independent of the physical world in a way the physical world following QM is not. I wouldn't say it is gradual layers but a hard line between physical and non-physical theories. As to your point - i disagree although i think we have different conceptions of "why". We'll never answer it in the sense of some creator saying "because i thought it'd be funny", but we can motivate the choice. We can make arguments that it is the most "natural" or "simple" system that meets requirements. Or most "elegant". Arguably that would probably all be post-hoc justification, but its still an interesting exercise.
  - deltaonefour 5y ago
    Elegance and natural and simple are just attributes of a system. There is no law that says all systems must be elegant. You're saying finding attributes of a mathematical model to be simple or elegant answers this question of "why?". For me such an attribute is arbitrary. If we determine something to be elegant it doesn't mean anything at all. But "why" is it elegant means something.
    - bawolff 5y ago
      I think the underlying (somewhat irrational) claim is that nature prefers to work in elegant ways. Thus if you can show that QM is the most elegant solution under some contraints, it helps explain the "why".

ketralnis 5y ago

Why does a^2+b^2=c^2 for a right triangle? It's just axiomatic, right? Not exactly. It's only true in flat euclidean geometry. If General Relativity holds then we're only in a flat spacetime if the total energy content of the universe is in some range of values, otherwise the universe could be the 3d equivalent of a sphere or it could be a hyperbolic shape. In neither of these configurations do right triangles behave the way you learnt in primary school. So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect.

deltaonefour 5y ago
>Why does a^2+b^2=c^2 for a right triangle? It's just axiomatic, right? Pythagorean theorem is not an axiom. It's a theorem. >Not exactly. It's only true in flat euclidean geometry It's a theorem for Euclidean geometry. >So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect. For theorems and the entire concept of math to even work all forms of mathematics from Euclidean geometry to hyperbolic geometry rest on universal axioms of logic. At best we have built higher forms of logic from the universal axioms and mathematics from arbitrary assumptions but we have never delved deeper than the 3 "laws" of logic. The other weird thing that we don't understand, and this is likely connected with logic is probability. We don't know why it works. It seems foundational just like logic but the weird thing is, formally probability is just like another math theory with random axioms at it's foundation and the rest of the theorems built up from logic. >If General Relativity holds then we're only in a flat spacetime... This is part of science. Observed phenomena then statistically matched to a arbitrary mathematical model. The OP's article is talking about something more fundamental... he asks "why?" When you ask that kind of question you have to really deep. Deeper than the science, deeper then the math all the way to the bottom. Everything stops at logic and probability. There is nowhere left to go to even move the needle closer to answering the question "why?"
- grog454 5y ago
  > The other weird thing that we don't understand, and this is likely connected with logic is probability. We don't know why it works. Can you elaborate on this or provide further reading?

deleted 5y ago

[deleted]