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/sci/ - Science & Math

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6456467 No.6456467[DELETED]  [Reply] [Original]

Hey /sci/!

Why does mathematics describe the nature so perfectly? Almost everything in the nature can be expressed as series as equations. Why? Is there some underlying cause to this?

>> No.6456469

because we make equations that describe how nature works

>> No.6456473

>>6456469
> because we make equations that describe how nature works

Yet they work so perfectly even on newly discovered phenomena. There's something much deeper to this.

>> No.6456476

Because mathematics is basically logic. (incoming fire from people who know Gödel's incompleteness theorems).

>> No.6456496

>>6456476
^ This guy gets it.
Mathematics is logical. All of math can be reduced to a set of simple logical expressions, definitions, and axioms.

We don't need to worry about Gödel's Incompleteness Theorem, math still works just fine.

>> No.6456507

>>6456476
>>6456496
Which explains nothing, because nature doesn't have to follow your logic in the first place

>> No.6456510

>>6456467
>Why does mathematics describe the nature so perfectly?

It doesn't, we need several mathematical models, there is no mathematical formula that describes the universe in all scales, that's why people are looking for the theory of everything

>> No.6456508

>>6456476
>>6456496
what makes you guys think that nature is logical? It's not.

>> No.6456512

>>6456476
This.

Math isn't numbers. (Numbers happen to fall under math, but not the other way around.) At the broadest level, math is nothing more than: being organized.

Bob is not a mathematician. He gets Wild Idea X. He writes it up like a sci-fi novel, and either ignores or flies into a rage if anybody even tries to argue against it. And even if someone manages to convince him one line of it is flawed, he'll just say that line's not important.

Jim is a mathematician. He gets Wild Idea Y and writes it up in an organized way, with theses clumped together with evidence of those theses, very which things depend on which other things. If you disagree with him, you are free to point out a line that's wrong, and why it's wrong, and he will immediately concede that everything following from that line is now suspect.

>> No.6456514

>>6456507
>>6456508
If nature behaved illogically this would mean nothing else but that contrary states of affairs were possible, such that a particle does both exist and not exist at all points in space, and has and has not a velocity in every direction. And this would apply to all particles. In fact, every particle would and would not be the same particle as every other particle. This would result in an undifferentiated plenum which our universe isn't as is apparent from mere observation.

>> No.6456530

>>6456514
Actually you get this kind of weird stuff happening on the microscopic level, as described by quantum mechanics. That logic allows us to make predictions is one thing, but nature doesn't have to abide to that logic in the first place, it just does, we can't explain why.

>> No.6456533

>>6456507
>nature doesn't have to follow your logic in the first place
that doesn't mean it doesn't

>> No.6456534

>>6456530
Actually, the universe as a whole still behaves deterministically according to quantum mechanics.
The only problem is that we try to view systems in isolation while they are actually coupled to their environment, which is why things like "wavefunction collapse" actually happen.

>> No.6456535

>>6456530
As I understand it, things at the quantum scale don't defy logic by both occupying and not occupying the same point in space. The point they occupy is merely indeterminate, or else the universe switches between a description of their behavior as particle or wave based on context, rather than having one uniform set of rules.

>> No.6456538

>>6456533
which is not what i said

>> No.6456544

Nature works perfectly, and when we assign language to nature that creates mathematics.

Really, all mathematics is is just the logic we derive from nature in the form of language, extended into abstraction.

The universe doesn't fit into our math, our math fits into the universe.

>> No.6456547
File: 107 KB, 400x410, Alice-matrix.jpg [View same] [iqdb] [saucenao] [google]
6456547

I read somewhere that physics can be so successfully described using mathemathics because the most successful physical theories are NOT mathematics approximating physics, BUT mathematics approximating mathematics!

Our universe is mathematical which can mean many different things. Also, pic related.

>> No.6456549

>>6456535
The distributive law fails when you take into account quantum phenomena
http://en.wikipedia.org/wiki/Quantum_logic

Besides it might be impossible to understand the universe completely with logic only

>> No.6456551

>>6456544
>Really, all mathematics is is just the logic we derive from nature
I disagree. You can't arrive at basic axioms like the commutativity of addition by induction; because if you didn't already have the concept you would not be able to observe its expression in nature.

>> No.6456552

>>6456544
>The universe doesn't fit into our math, our math fits into the universe.

No, see my comment here: >>6456544 Math is at the bottom of it all. Physics itself is not. It's the mathematical structures that give rise to physics.

>> No.6456560

>>6456549
Are you talking about matrix multiplication? Because matrices aren't ordinary numbers.

>Besides it might be impossible to understand the universe completely with logic only
I wouldn't know any other way of understanding something but by means of logic.

>> No.6456564

>>6456551
>ic axioms like the c

"I have three coins in my left hand and 2 in my right. When I put my left hand coins in my right I get 5. If I put my right coins in my left hand, I get 5"

>> No.6456568

>>6456551
>>6456552

I see that as very anthoprocentric. A human construct at the bottom of it all? I think math is something humans made , not something that's part of the universe

>> No.6456569

>>6456560

Intuition

>> No.6456573

>>6456564
And how are you going to appreciate the connection between this pair of observations without the concept of commutativity already available to you?

>> No.6456574

>>6456569
arbitrary, if you still arrive at a logical conclusion

>> No.6456579

>>6456568
Everything human beings could possibly do to formulate the behaviour of the world we inhabit would be vulnerable to the charge of being a mere 'human construct'. There's no conception of the universe that isn't "anthropocentric" in your sense. So what you're saying is bereft of significance because it doesn't get you past "well maybe things are different."

>>6456569
What do you mean by 'intuition'?

>> No.6456583

>>6456551
the same could be said of syntax in sentences.

>> No.6456584

>>6456467
>Why does mathematics describe the nature so perfectly?
It doesn't. Out of all of mathematics, only a very limited number of equations describe ballistics. Think of the uncountable number of theorems that theoretically exist, and the huge (to us) number we'll prove over the next thousand years, and how few of those will have anything at all to do with frictionless collisions.

>Is there some underlying cause to this?
You only noticing the things we describe with mathematics, and ignoring all the things we don't.

>> No.6456585

>>6456560
>I wouldn't know any other way of understanding something but by means of logic.
Just because you wouldn't know means there is not any other way? Humans and their arrogance in believing that they know everything. Everything you think you know come from your sensory perception, we cannot even explain how sensory perception arises in the first place and we experience other things besides that perception. Then who knows what might be the take of aliens who reached our level of technological/intellectual advancement 1 million years ago.

>> No.6456588

>>6456579
Knowledge that is given or reached without justification

>>6456574

What is a logical conclusion? Do you need logic to say you've reached one?

>>6456573

The same way you appreciated that 2 objects joined with 3 objects gets you five objects.

>> No.6456589

>>6456579
I think it's reasonable to say that mathematics is a language, nothing more. The most accurate way of describing the universe, but a language. And so how do we form the language? We observe nature, "one" stick and "one" stick gives you "two" sticks, and you go from there

>> No.6456595

>>6456589
Drive-by here. I agree. Math is the language of certainty.

>> No.6456598

>>6456588
>Knowledge that is given or reached without justification
Sounds like you're talking about some kind of axioms or facts. Logic doesn't deal in these. To understand something logically means to be able to slice it into component parts and reason about their interactions. If somethings functioning is just taken for granted I would hardly call that 'understanding'.

>> No.6456603

>>6456588
>The same way you appreciated that 2 objects joined with 3 objects gets you five objects.
Which is how?

>>6456589
If Mathematics is a language it's unique in that its semantic range is entirely mathematical, whereas the semantic range of English is not itself contained within English (e.g. English sentences underspecify meaning and can only be understood contextually).

You don't observe that one stick and one stick give two sticks unless you already appreciate what that would mean. Remove your genetically endowed capacity for reasoning arithmetically and all that would be apparent to you is a change in spacial relations.

>> No.6456608

>>6456598
Logic itself is based on axioms, science as well. Any logical reasoning begins from axioms that you cannot logically prove by definition. How do you call that 'understanding' then, any more than reaching knowledge without logical justification?

>> No.6456607

>>6456598

If the knowledge that was reached is explanatory to a notion, it seems like its understanding.

Logic does deal with axioms, in the sense that, it requires them. If you definition of understanding is to be able to explain it with logic, then of course you wont be able to see how you can understand without logic.

>> No.6456611

>>6456603
Are you claiming that mathematical knowledge is innate?

>> No.6456617

>>6456603
I agree that mathematics and our understanding of logic is genetic, that's what enables us to observe and measure the universe like we do

I still hold to the opinion that math is not a trait of the universe, or something, it is something that arose out of the universe, through us, enabling us to understand and measure the universe.

>> No.6456619

>>6456607
>If the knowledge that was reached is explanatory to a notion, it seems like its understanding.

You're dodging the burden of explaining yourself by employing weasel-words. What is 'understanding' if not the ability to slice things into component parts and reason about their interactions?

>Logic does deal with axioms, in the sense that, it requires them.
Yes but it doesn't justify them. That it rains or doesn't rain tells us nothing about the weather.

>If you definition of understanding is to be able to explain it with logic, then of course you wont be able to see how you can understand without logic.

It's not a matter of defining understanding, but naming it. "Logic" is merely the of reasoning about the human capacity to reason and rigorously formulating the principles and common aspects underlying it.

>> No.6456621

>>6456603
Sorry about this:>>6456611

Of course you are.

But, just because we can create abstract systems from empirical observations doesn't mean we had to have previous knowledge of that system.

If we see a stick, we simply call it an object of 1 because we are able to endow it with it being a distinct entity. Then we realize that, no matter what the object, if you place 1 next to 1, you can call it to. Then we realize that we can define this operation as addition.

We didn't need to know about it in order to define it

>> No.6456624

>>6456619

I have a question then. How can you tell if someone understands something?

What must they communicate to you to prove that they understand.

>> No.6456626

>>6456611
The bare minimum you'd need to reach conclusions like Pythagoras' theorem of Fermat's last theorem, yes. Obviously the fact that this inborn knowledge entails Fermat's last theorem is not obvious from childhood - a decompression process is necessary.

>>6456608
You do not understand the axioms, you merely understand their consequences. And that's really what logic deals in - consequences. Axioms are the raw material, similar to how shoe makers deal in shoes, not leather.

>> No.6456631

>>6456617
It would depend on what you mean 'trait of the universe'. It could be a complete description of the universe or a partial one. To claim it's no description of the universe whatever smacks too much of vulgar solipsism to me. Though perhaps you have some sophisticated philosophical argument?

>> No.6456633

>>6456608
see bottom part of >>6456619

>> No.6456637

>>6456621
>we are able to endow it with it being a distinct entity
Because this is how the human brain functions. There might be other ways to look at it, that we couldn't conceptualize with our brain.

>> No.6456642

>>6456637
I agree completely, I dont think we were on the same page.

>> No.6456649

>>6456626
>You do not understand the axioms, you merely understand their consequences
What do you mean you understand their consequences but not the axioms? A consequence is a statement that you consider to be true, an axiom is a statement that you consider to be true. The only difference between the two is that you applied a set of rules (the laws of logic, which are axioms in themselves) in order to consider the consequence to be a true statement.

>> No.6456653

God is a mathematician.

>> No.6456656

>>6456649
It means that you have a definite mechanical process for moving from antecedent to consequent by elementary operations on your given symbols. The axiom isn't considered true, it's assumed to be true. Mathematics and science do not say "A, therefore B" but "if A then B" + "A if anything at all".

>> No.6456677

>>6456631
I don't know if the same type of laws that exists in the universe we came out of is the same as the whole universe or multiverse.

What I was sort of saying, in response to OP, is that I think we only need a few basic abilities, addition and other things, to deduce all of what we know as mathematics. If our methods are correct, which would be dependant on evolution, we could start to see how the unverse operates through our deductions.

We can look at somthing like the inverse square operation, which is something we can apply all over the observable universe. All we need to arrive at the idea of an inverse square are some innate mathematical tools. As with other things.

Now that we are taking our mathematics even farther, deducing things like multiple dimensions with our mathematical tools, I am hoping that everything is somehow connected to everything else, the same way you can reason that someone had been walking in the sand because of some footprints, only applied to logic, so that mathematics can take us farther than our senses ever can.

>> No.6456694

>>6456621
You need at the very least the capacity for induction and some kind of mental operation which can apply to itself. Say you have the empty set {}, and you realize that may be contained within another set {{}}, and that in yet another {{{}}} etc. and decide to call these sets 0, 1, 2. In a sense your understanding of arithmetic comes from 'observation' but it's observation that has been filtered and made sense of by means of your ability to conceive of recursive operations. You will never be able to reach to conclusion that there are an infinite amount of numbers from the mere observation that two sticks are distinct from one, you need a small mental toolkit for conceptualizing mathematics already baked in.

>> No.6456695

>>6456656
Indeed, but then can you really claim to understand B while it is only true provided A is true, which you cannot prove?

>> No.6456702

>>6456624
There's nothing that could prove it. The only observation you can make is that you seem to understand their behaviour or speech and couple this with the assumption that they operate in basically the same way you do.

Perhaps with some materialist assumptions you could argue that it can be done via some high-resolution brain-scans and a solid understanding of the brain too.

>> No.6456709

>>6456695
To put it as precisely as I can: you only understand that B is decompressed statement which was embedded in A.

>> No.6456714

>>6456709
Also we should draw a distinction between understanding a fact and knowing that it's true.

>> No.6456719

>>6456649
Axioms are things which are taken to be self-evident and irreducible in cause or portion. We are said to have fully understood a thing (event/process/idea) if we know the steps to reproduce it from our axioms.

Using that other anon's shoemaker example, we take the leather for granted, it simply exists and we can reduce it no further: we call it the Axiom of Leather. A shoe, however, can be made from leather and we cannot claim to truly understand this shoe until we know how to produce it from our axioms; for what if it were truly impossible to recreate a specific shoe from the known axioms? What if we discovered that this new shoe cannot be produced simple from leather, but required the Axiom of Rubber?

Such an event would revolutionize our understanding of the world, it would open up multitudes of new avenues for shoe production. Ideas that were previously only possible in the realm of fiction suddenly become reality, and then in the blink of an eye those Chuck Taylor's you had dreamt of are on your feet.

>> No.6456737

>>6456709
Embedded in A and in the axioms of logic that you used to make that decompression. If you don't assume for instance that a statement is either true or false then most of the time you couldn't decompress "B is true" from "A is true".

>> No.6456739

>>6456737
As I said:
Mathematics and science do not say "A, therefore B" but "if A then B" + "A if anything at all"

>> No.6456742
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6456742

>>6456719
Someone understands!

>> No.6456761

>>6456719
>Axioms are things which are taken to be self-evident
And these things are self-evident to our human brain. Everything that is self-evident only appears so because our brain processes them in such a way as to make them seem evident to us. Logic is dependent on our axioms, which are dependent on the way our brains are wired. On many different levels there is a limit to what we can know through logic. And so we can't claim to be able to understand nature completely with logic alone, when logic cannot make us know all there is to know.

>> No.6456806

>>6456761
I beg your pardon, but you're begging the question. You are asserting that we cannot fully understand nature based on the assumption that we cannot fully understand nature, are you not?

>Logic is dependent on our axioms, which are dependent on the way our brains are wired. On many different levels there is a limit to what we can know through logic.
Says who? Maybe our system of logic is perfectly sufficient to understand everything about the universe, and we'll find nice, neat solutions to all those problems in quantum mechanics (the horror!).

>And so we can't claim to be able to understand nature completely with logic alone, when logic cannot make us know all there is to know.
I will admit the possibility that logic is fundamentally insufficient to understand the natural world, but your argument isn't based on anything concrete. You cannot know that logic is insufficient in our quest to understand all there is to know unless you know of a counterexample to our system of logic (you don't actually happen to have one, do you? Because it would be mighty interesting and I'd love to hear it!).

Your arguments from biology are mere speculation. Unless you have some fascinating new study, there's no justification for supposing arbitrary limits on human understanding.

>> No.6456900

>>6456552
Math is used to describe physics. That's it. Math is a tool of physicists.

If you think mathematical structures give rise to physics go watch this video which is 100% mathematically sound and shove it up your goddamn "math is magic and divine!" ass.

http://www.youtube.com/watch?v=BVVfs4zKrgk

>> No.6456903

>>6456900
What's the vid supposed to demonstrate?

>> No.6456907

>>6456900
>Math is used to describe physics. That's it. Math is a tool of physicists.

hmm.. it's the other way around. physics is just a manifestation of some mathematical structure that composes the universe.

>> No.6456909

>>6456903
That while mathematically sound, it does not in any way describe an event that could happen in reality.

>> No.6456914

>>6456907
There is no "mathematical structure that composes the universe".

Math is our incredibly human yet incredibly useful approximation of the universe.

Math arose because we wanted to be able to count a lot of things without spending 10 hours doing it.

Why is this so hard to understand that the whole idea of math is to solve problems.

Physics uses math. It is not a manifestation of math it is a manifestation of experiment.

Why did I even bother to come to this board.

>> No.6456917

>>6456909
>That while mathematically sound, it does not in any way describe an event that could happen in reality.

that's ridiculous. it's like saying that complex numbers do not happen in reality. they do. all of modern physics is based on them.

>> No.6456918

>>6456900
Ever hear of Noether's Theorem? It's the idea that because a frame of reference doesn't matter, in other words, no matter what you set as your system of coordinates, the laws of physics are the same. It's similar to the idea of both rectilinear and polar coordinates for the complex numbers, but when you construct it mathematically, you get some surprising results. From this idea, you get Newton's laws of physics as well as all the conservation laws. In fact, every symmetry corresponds to a conserved quantity (time -> energy, space -> momentum, rotation -> angular momentum) Perhaps it may seem to be a mathematical trick, but it yields amazingly consistent results.

>> No.6456921

>>6456909
Why couldn't it happen in reality?

>> No.6456923

>>6456584
>You only noticing the things we describe with mathematics, and ignoring all the things we don't.

Ignoring what things?

Math describes all therefor there is nothing to ignore.

>> No.6456927
File: 119 KB, 900x768, amplituhedron.jpg [View same] [iqdb] [saucenao] [google]
6456927

>>6456914
>There is no "mathematical structure that composes the universe".

But there is. Everything in universe is based on something that is akin to platonic solids.

>Math is our incredibly human yet incredibly useful approximation of the universe.

Yes but it works too good which means that math is not an invention but a discovery. It's what underlies our reality.

>Math arose because we wanted to be able to count a lot of things without spending 10 hours doing it.

So? I fail to follow this line of reasoning. Origin of something has very little relevance. It's the same as debating origin of human mind.

>Why is this so hard to understand that the whole idea of math is to solve problems.

That's just idiotic.

>Physics uses math. It is not a manifestation of math it is a manifestation of experiment.

No, it tells us something about the universe we live in.

>Why did I even bother to come to this board.

Don't let the door hit you in the ass. So long.

>> No.6456929

>>6456917
It is nothing like that. Complex numbers arise in order to make calculations easier. Turning a sphere inside out with the established rules in the video is simply a bit of fun I guess you could call it for mathematicians.

>>6456921
Solid spheres do not pass through themselves.

I started to ramble. My main point is that physics does not derive from math. Physics derives from experiment. If it derives from math, it is not physics. Physics is SOLELY an experimental science.
(it's a hypothetical mathematical model of a physical system)

>> No.6456932

>>6456914
>the whole idea of math is to solve problems.
There are useless maths. The idea of maths is just, as one anon said, logic. Thats slightly simplified but still.
Its possible that being part of the universe leads to our sense of logic coinciding with the physically 'true' one of the universe, or its possible that the consistent nature of logic means it can always be used to describe consistent systems(such as the universe.)
That still, indeed, does not make math itself the universe.
But hey, mathematicians are known to be crazy. Platonism, mang.

>> No.6456935

>>6456927
>No, it tells us something about the universe we live in.
No, experiment tells us something about the universe we live in. A mathematical model is all well and good but it means absolutely nothing if you can't corroborate it with reality.

You can derive equations until the cows come home but whether or not they're in sync with reality is an entirely different story. There is an enormous amount of math that is 100% mathematically sound but has absolutely no basis in reality.

>> No.6456936
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6456936

>>6456929
>Solid spheres do not pass through themselves.

Heh. That depends on the magnitude of your view. Strange things happen when you look deep. Manifolds intersect in many dimensions. But I guess your puny brain will never realize that.

>> No.6456938

>>6456935
>No, experiment tells us something about the universe we live in. A mathematical model is all well and good but it means absolutely nothing if you can't corroborate it with reality.

And what are experiments? Just a manifestation of underlying mathematical principles. This is like debating what came before: chicken or the egg.

Well, it's math all the way down.

>> No.6456939

>>6456936
You can call me and make fun of my puny brain when you get some physical proof of higher dimensions a la string theory.

Until then keep conjecturing pointless garbage.

>> No.6456942

>>6456938
Our structure of math as it is today is a human construction. Do not even pretend that experiment verifies "underlying mathematical principles" of the universe because that is so horribly naive and egotistical.

>> No.6456943

>>6456927
>Everything in universe is based on something that is akin to platonic solids

Turn that around and its true, platonic solids are based on everything in [our observable] universe.

>> No.6456947

>>6456939
Do you accept that we're all made of atoms? What about that atoms are made of quarks? They're just mathematical structures that we've named and made them "real". Multiple dimensions are just as real as other dimensions that are familiar to us. Do you believe there is a 4th dimension, time? Have you seen it? How do you know it's real? We use it all the time "in order to make calculations easier" as you said. But you have not seen it. Multiple dimensions are EXACTLY THE SAME thing.

>> No.6456945

>>6456473

Not really. New equations have to be invented for some new phenomenon. Scientists didn't know how the fuck gravity worked until someone came up with a model for it.

If all of the equations and models we already have don't work then someone just makes up an equation that does work. It's just that most phenomena have already been discovered and analyzed to hell and back so there's not much more room for equation inventing unless you start getting into seriously high-level physics.

>> No.6456949

>>6456719
>>6456806
Axioms shouldn't be taken to be self-evident in the sense that they obviously describe anything in nature. One of the problems the ancients had with math was that they assumed simple axioms would easily describe their reality. Math isn't supposed to have anything to do with reality, it's just a collection of statements which boil down to axioms, which are unexplained human language nonsense, and a set of somewhat-explicable rules of inference. It's just ordered concepts without any underlying meaning. That's all math has ever been - structure.

>> No.6456955

>>6456945
>Not really. New equations have to be invented for some new phenomenon. Scientists didn't know how the fuck gravity worked until someone came up with a model for it.

Just because we don't know how gravity combines with QM doesn't mean we don't know what it is. We know perfectly well what it is.

And to prove your first part wrong, all you need to look at is the history of Maxwell equations and what they've predicted. It's incredible how much was modeled with them even though they were meant to describe just few results. So there is a deeper structure that Maxwell discovered.

>> No.6456953

>>6456507

The "logic" in math follows nature. 1+1=2 because that's what we see in nature in this universe. Take one object, then take another of the same object, and now you have two of those objects. Math was invented to make sense of the universe. Math doesn't exist as some abstract deity that nature bows to.

If nature doesn't follow what current mathematical models predict then that means the models are wrong and need to be amended. That's how experimentation works.

>make observation in nature
>create model that you think accurately describes observation
>test model in isolated conditions
>observe outcome
>repeat
>if model outcome matches natural outcome consistently, you now have a theory

>> No.6456957

>>6456507
if we define nature as something outside of all of our possible experience, or thought processes, that's meaningless

>> No.6456958

>>6456929
>Complex numbers arise in order to make calculations easier.
One could say the same for negative numbers, can you conceive of a negative number of apples? Imaginary numbers are no more special than other extensions and completions of the natural numbers.

>> No.6456963

The reason why people speculate that the universe is a mathematical object is because any detailed description we make of the universe is going to be a mathematical object. Since scientific models of nature are what we think of as describing something arbitrarily close to reality, people conclude that reality is a mathematical structure.

This isn't surprising, since structure is how we relate the ourselves and the world. It's basically what we are, so whether or not the universe is a mathematical object falls into "you can't know nuffin'" territory.

>> No.6456967

>>6456955

>Just because we don't know how gravity combines with QM doesn't mean we don't know what it is. We know perfectly well what it is.

Knowing what something IS and knowing HOW something works are two different things. We know how gravity works on a very superficial level, but there's still no known mechanism for how it's observed to work in nature.

I will read up on Maxwell's equations though, because I don't know a lot about them. We're just covering this in my physics lecture so it seems like good timing.

>> No.6456972

>>6456467
Symmetries in nature are intimately connected to the existence of conservation laws.
This is one the big discoveries of the 20th century, discovered by Emmy Noether.
She should be as famous as Gödel, and actually is, among theoretical physicists

http://en.wikipedia.org/wiki/Noether's_theorem

>> No.6456973

>>6456958
>>Complex numbers arise in order to make calculations easier.
>One could say the same for negative numbers, can you conceive of a negative number of apples? Imaginary numbers are no more special than other extensions and completions of the natural numbers.

That's not quite right. The extension to complex numbers isn't quite the same as the extension to integers. I'll explain in my next post.

>> No.6456978

>>6456963
>The reason why people speculate that the universe is a mathematical object is because any detailed description we make of the universe is going to be a mathematical object. Since scientific models of nature are what we think of as describing something arbitrarily close to reality, people conclude that reality is a mathematical structure.

>>6456967
>Knowing what something IS and knowing HOW something works are two different things. We know how gravity works on a very superficial level, but there's still no known mechanism for how it's observed to work in nature.


No, the reason why we know that universe is a mathematical structure is because we use things that are developed from purely abstract mathematical forms into something that perfectly describes reality later on.

For example, 60 years after Riemannian's geometry was developed, Einstein used it to describe gravity. There's so many examples like that that they tell us that our universe truly is a mathematical object.

>> No.6456988

>>6456978
I don't disagree that you can go around treating reality as some convoluded unknown mathematical object and not have any problems, but that doesn't mean that there aren't parts that don't obey the rules you come up with or any other rules. It is literally impossible for us not to see structure, so of course you see it everywhere, but that doesn't mean that unstructured parts of reality don't "exist" is some sense. We just can't interact with them in any meaningful way.

>> No.6456999

>>6456988
But almost all of them do! The issue is that we haven't figured it out all just yet. We see bits and pieces of a much larger structure. And the pieces we have fit perfectly.

>> No.6457023

Ok, what you guys have got to understand is that the term "Mathematics" is vague and overloaded with meaning. Number Theory, Calculus, Statistics, Physics equations, Abstract Algebra, Information Theory, Logic, etc. etc... all of these things are "Mathematics" despite dealing with very different topics. Although everyone thinks that "math" -- this "manipulation of numbers"-- is one entity that works the same way in every field: you work with numbers to produce equal numbers. However that isn't accurate. The common thread throughout all of these topics is the MANIPULATION OF KNOWLEDGE & INFORMATION ITSELF (I wish this board had italics). What you're really doing with math is finding out more information from the information you have by using truth-preserving operations.

My point, is that although it would seem that all of these mathematical operations are the same, and that you can just do math on numbers willy-nilly, you MUST consider the context in which you're working. A mathematical result may WORK in multiple contexts (that is, preserve the truth), but it doesn't MEAN the same thing over different contexts. That is why some people say that "math directly corresponds to reality" and others say "math is entirely human-made" and people argue about it so much.

Some parts of math directly correspond to reality: the natural numbers are an ontological necessity because they exist as soon as there is any kind of differentiation between quantities, time, or space in the universe; they correspond to Order. Other parts of math are human constructs: imaginary numbers exist to solve the question "x^2 = -1, what is x?" Imaginary numbers do not correspond to anything in reality, and only exist because someone created a contradictory problem and demanded an answer for it. However, they are a logical tool for reasoning with equations we otherwise could not work with and so they have proven to be quite useful.

>> No.6457036

>>6457023
Is zero real? How about -1 or -10? Heh. See how vacuous your whole argument is?

>> No.6457042

>>6456958
>>6457023
>>Complex numbers arise in order to make calculations easier.
>One could say the same for negative numbers, can you conceive of a negative number of apples? Imaginary numbers are no more special than other extensions and completions of the natural numbers.

To answer this a bit better now that I've elaborated, negative numbers are a direct, logical extension of natural numbers, which as I said before are an ontological necessity. Negative numbers are exactly the same anywhere across the universe simply by virtue of the universe existing. They close the natural numbers for subtraction (i.e., moving downwards in order).

After natural numbers, we came up with the idea of equations; that performing equal operations on two equal quantities yields still equal quantities, and that by using this method we can uncover the true value of a variable which is initially unknown. This "Algebra" is a form of logical argument for human benefit so that we can deduce more information.

Complex/Imaginary numbers are a direct, logical extension of our base Algebra to allow it to answer the question "x^2 = -1". There is no grand, universal reason why our algebra should be the way it is, that's why you have the field of Abstract Algebra. Although imaginary numbers are necessary for OUR algebra, there's nothing forcing us to use the operations we use and hypothetically there could be aliens out there somewhere just as advanced as us but having never needed to create imaginary numbers because their algebra works differently.

>> No.6457046

>>6457036
You're the vacuous one here. -1 and -10 are integers, not natural numbers.

0 has been debated for a while, and for good reason. Technically, there is no such thing as the order/place of 0. You must have one of something to begin counting; that's why "first place" is written "1st". However, you can include zero without really losing anything as long as you think of it more as a location or threshold rather than an actual position/place/order; in that case zero would just be a place holder for "no place".

Personally, I'd use zero as the first natural number to stay consistent with how computer scientists do array arithmetic: array indices start at 0.

>> No.6457427
File: 98 KB, 630x473, 1.14328.jpg [View same] [iqdb] [saucenao] [google]
6457427

Universe is a holographic projection.

http://www.nature.com/news/simulations-back-up-theory-that-universe-is-a-hologram-1.14328

Imagine you take a 3D object, say a cube and you put it in front of a lamp. What kind of shadow does it cast? It's a 2D shape, right?

Same goes with our universe. It's a projection of high-dimensional structure. Most probably we're inside of a black hole from a high-dimensional, different, universe.

So yes, universe is a mathematical in nature. It's just a projection of some mathematical object.

>> No.6457452

>>6457427
I agree with your conclusion, but what the fuck are you smoking?

>> No.6457462

>>6457452
not smoking anything. I'm just inhaling knowledge.

everything I said are valid scientific hypotheses promoted by some of the greatest minds in physics.

http://news.nationalgeographic.com/news/2014/02/140218-black-hole-blast-explains-big-bang/

>> No.6457464

>>6456589
>>6456595
It's a language constructed by humans, yes, but it's just as much of a language as English would be considered -- it is a human-constructed tool that has bases in something objective in the sense of man-made things. What I mean by this is that math is definitely something created by humans, for humans, but the logic, meaning, and reasoning behind and within mathematical processes is almost a translation of a *real* construct (something natural).

>> No.6457467

>>6457462
Brilliant any more related links?
Ironically I'm writing a research paper suggesting that we live in a holographic universe

>> No.6457471

>>6457467
that's awesome. make sure to support the fuck out of your thesis.

>> No.6457470

>>6457464
>almost a translation of a *real* construct (something natural).

That is correct. if we started mathematics all over again, symbols and names could change but the overall relations would come out exactly the same.

>> No.6457474

>>6457470
Just as geometry, a subcategory of general mathematics, could have been explained any way (i.e a triangle is now a four sided figure with equal lengths -- ignore the prefix and suffix of the word *triangle*, this is also something with roots in a given language or languages).

>> No.6457475

>>6457467
>Brilliant any more related links?
>Ironically I'm writing a research paper suggesting that we live in a holographic universe

Read some of the stuff that's coming out of Perimeter Institute (see Lee Smolin). They're the ones always coming up with some of the big ideas.

The holographic universe and black-hole theory of the universe mesh perfectly. It's actually amazing how well the results from one translate to the other.

>> No.6457478

>>6457462
>nationalgeographic

>> No.6457482
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6457482

>>6457478
Yes, natgeo reporting on a paper from PRL. You must be really slow when the thing you criticize is the site where something's posted to and not the idea itself. back on short bus, kid.

>> No.6457483

>>6457475
Yes I find it fascinating as well, thank you I will read into it

>> No.6457488

>>6456496
yeah you are basically an idiot