[goldenkek]

Mathematics is the study of objective truth in a universe that has certain rules. How could knowing the universe in all its glory be boring? Wish they taught this rather than calculation at school. It's very uninspiring to not realize this and do math.

In fact, natural numbers are the basis for almost all of mathematics. And natural numbers are a manifestation of counting. Information theoretically, to count, one needs two dimensions (or degrees of freedom.) Space for storage of the number. And time to increment the storage medium, again and again, at different points. You could use two dimensions of space instead, and you'd just draw two orthogonal lines..and say the area inside the rectangle is the product.

So if counting is fundamentally related to the relationship between two dimensions, then so is addition since addition is repeated/recursive counting. And multiplication is repeated/recursive addition.

Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe.

Multiplication and addition are related in the way that f(x) and repeat(f(x), y) are related. They distribute over eachother and have certain properties.

See: https://en.wikipedia.org/wiki/Ring_(mathematics)

So..the primes, the chaotic relationship between the modularity of addition over multiplication and the modularity of multiplication over addition, is due to the relationship between our universe's dimensions.

Want to study the universe at the most raw level? Mathematics. Want to study it a little higher? Physics. Want to study it at a higher level..maybe closer to the phaneron? Biology/neurochemistry.

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

Want to study it at the thinking level? Zen buddhism.

Choose your pick. The causal chain of human to universe doesn't discriminate. The whole chain could be the "real" reality. Pick your choice. It's all beautiful. It's all mystifying and enigmatic. Just do it.

[posterboy]

>Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe.

But space and time are natural, ie. you mention a physical interpretation. And a paradox one at that, because you are explaining counting (numbers) by counting (dimensions).

> Want to study the universe at the most raw level?

I'd rather offer that mathematics is about formalization of what you know, while physics is about exploration of what you don't know. Maths is intrinsic, abstract and relies on intuition. Physics is extrinsic, concrete and relies on experimentation. These separations are arbitrary and not useful, if they don't serve a purpose. Why divide like that at all? If you talk hierarchy, I'd say logic is higher up there.

To wrap it up, what's that got to do with bad teaching? I'd suppose that deductive reasoning cannot be taught, because it is learned before language is acquired, then used to acquire language. Maybe, memory can be trained, and curiosity can be stimulated, but school is hardly the right setting to inspire creativity, when most of the time there talking is forbidden.

> Zen buddhism

Sure, nihilism, or religion overall, is like an escape when you abandon all hope and try to recollect new hope. It is admitting you don't know anymore and going back to square one.

[mathperson]

if you think mathematics relies on intuition..you haven't done much mathematics unfortunately. the field is deeply paradoxical once you get into it deeply

[armitron]

If there exists an absolute reality it only make sense to be non-objective [nirguna brahman in advaita] nothingness, in contrast to objective nothingness which conceptually is nihilism.

Mathematics can be used to study the universe at the objective level but do not make the mistake of treating numbers as ineffable, existing in some platonic realm outside of space/time/causation or talk about the "real" reality and mathematics together. Through mathematics we learn more about the limits of our own model building/cognition than any secrets of the universe.

[posterboy]

> [don't] talk about the "real" reality and mathematics together

That stopped me just at the right moment, but then you went and still did it:

> Through mathematics we learn more about the limits of our own model building/cognition than any secrets of the universe.

This is illogic, assuming we are part of the universe. Ignoring that last part, as you wanted, I get the reference. It comes down to saying, through learning about models we learn more about models. I agree if the stress is on learning, because to learn is part of the root of the word mathematics.

The real kicker nowadays is learning about learning, the mind, neurology, etc. directly.

[mannykannot]

I first came across an alternative view in Godel, Escher, Bach, where Hofstadter was writing about Euclid's parallel postulate and the development of non-euclidean geometry. The latter could have been accepted sooner, he suggests, if people were not hung up on the idea that geometry was about physical space, rather than a derivation from axioms. Ironically, it turned out later that physical space is not euclidean.

[posterboy]

I believe our ideas are formed in our brain, that is part of the physical word. So I think the schism you presented would be void.

[justinpombrio]

It's not very helpful to study the ideas that form in human brains, though, since so many of them are nonsense. It would largely be a study of misconceptions and biases.

I think you could just as well have said "I believe our ideas are often formed on paper, when we write therm down. And that writing is part of the physical world. So I think the schism you presented would be void."

[posterboy]

It would well be notable which ideas are wrong, no?

Sure I could've said, writing is physical. I just did, in another comment.

[mannykannot]

Does this get us into the question of whether anything mathematical exists before anyone (or anysomething) first thought of it, and exists even when no-one is currently thinking of it? If you answer yes, then mathematics has an existence independent of thought. If you answer no, then that conditional existence presumably extends to physics as well, especially if Max Tegmark is right about math being the reality of physics. In that case, then it seems to follow that the universe only exists when it is being thought about, a conclusion that appears to have a bootstrap problem...

I think I can avoid the whole issue by observing that I can imagine things that do not physically exist, and they are not made to physically exist by dint of a conceptual representation of them physically existing in my brain.

[posterboy]

>Does this get us into the question of whether anything mathematical exists before anyone (or anysomething) first thought of it

No, because you can't ask for it's existence, before you thought of it.

>exists even when no-one is currently thinking of it

Again, who cares, it's by definition undefined, null, niente, the inbetween state of a ternary logic.

>I can imagine things

You can't will a pot of gold into existence by mere imagination, but you can't imagine an idea without it's inherint structure being real.

I'll admit, that's a simplistic outlook, but I wasn't encouraging a complicated discusion.

[zeroer]

Yea, mathematics is more fundamental than physics, in the sense that it would be possible for different universes to exist with different physics, but it's not clear at all that universes could exist with different mathematics. What would that even mean? You may like Max Tegmark's idea that the universe is math: https://arxiv.org/abs/0704.0646

But it's nonsense that the natural numbers require two dimensions. Time appears nowhere in the Zermelo–Fraenkel axioms: https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

[posterboy]

Do you know what the uni~ i universe means? It means only (one-ly). How could there be multiple? That's just non-sense.

The parent implied counting, not the natural numbers, need two dimensions. But even in Set Theory you need at least one level deep nested sets to build the natural numbers. Qunatification is the (a?) difference between zero and higher order logic, I suppose.

[TeMPOraL]

> Do you know what the uni~ i universe means? It means only (one-ly). How could there be multiple? That's just non-sense.

Do you know what "atom" in "atom" means? "Indivisible". But somehow we've been dividing them for power for quite some time.

Arguments from etymology are invalid, because words are not obliged to be backwards compatible.

[posterboy]

> Arguments from etymology are invalid, because words are not obliged to be backwards compatible.

That's how you end up with loads of confusing homonyms, which the parent almost admited to. I mean, sure an etymologic argument can be insufficient or even wrong.

[TeMPOraL]

My point is, words are only labels - pointers to concepts. You can't prove facts about objects from just their labels, nor do the labels have causal power over reality. Universe being derived from "uni" doesn't force the concept of universe to be a singleton.

Proliferation of homonyms is another topic altogether; it is an issue, but it's about creating barriers to communication.

[posterboy]

So, extending the analogy, we've as well been dividing the universe? If you go with quantum mechanics, you also have to consider the Entanglement that, if I understand correctly, posits non-locality, so your argument of spacial division is still nonsense to me. To be fair, quantum theory might as well be nonsense to me. I wouldn't know, it's over my head. But multiverse is stuff of sci-fi and theoretical physics. Theoretical physics is mostly maths, indeed. So I agree to a point, I just contest the schism that's between maths and physics, because it's not constructive.

[zeroer]

In my particular comment, I meant that THE Universe (proper noun) could have different physics. Max Tegmark uses the term a bit differently, but he's quite clear about what he means.

As for your second paragraph, I really don't have any idea what you two are on about.

[posterboy]

I'm not really interested in metaphysics, hence my opposition to the claim.

>As for your second paragraph, I really don't have any idea what you two are on about.

I didn't quite understand the parent, but he clearly related to Computational Complexity of operations on Countable Sets. I happen to study that subject at the moment, so I am taking this discussion as an opportunity to test my understanding.

[deleted] apparently I need to learn a bit more.

[posterboy]

>Max Tegmark uses the term a bit differently

>he's quite clear about what he means.

but I didn't read him and it's pretty arrogant to assume I had to. Sure, I hadn't to butt in on the discussion, but I had to read the comment to find out I didn't want to read it, first. So I felt I had to say something. I mean, I thought it was informative, but obviously I didn't hit the right tone.

[goldenkek]

If you actually read my post more closely you would see I said any two orthogonal dimensions, that could be two spatial dimensions..not necessarily including time.

[Ar-Curunir]

This is pseudoscientific crap. Mathematics does not concern itself with physical reality.

[goldenkek]

Haters gonna hate ;-)