/sci/ - Science & Math

the actual calculations are discovered, while the terms we used to define them are created as neccessary. syntax vs. semantics

neither, it's always existed

"Imaginary" numbers were invented and not discovered.

>>5818465
they were one of the necessary definitions to advance mathematics and bridge gaps.

>>5818466
[citation needed]

>>5818468
That is the citation, learn it.

>>5818469
no

The axioms are created, their consequences are discovered.

The answer is to fucking simple:

Systems of logic (i.e. first principles) are invented. Deductions within a system are discovered.

Example: Imaginary numbers were invented; Euler's identity was deduced.

>>5818502
It's the other way around dude. Axioms are the bare essential properties of something. 1 is 1 regardless of what you call it. Regardless of how much you try to deny it.

So math is discovered, how we apply it is created.

it's dead and alive at the same time

>>5818456
I'd say, neither. Mathematics is defined.

Question comes down to whether Platonic ideals exist and guess what no they don't existence is emergent bc godel!

>>5818456

Created. Like literally created in structures known as "brains" which are able to create "arbitrary" axiomatic systems. Arbitrary in quotation marks because "brains" are also pattern recognition systems and the axiomatic systems first created were probably in response to the needs and desires of brains in a natural environment full of exploitable patterns.

>>5818456
discovered

Created.

It is all inductively derived from the axioms on which it is based. Change the axioms, change math.

every day

invented

>>5819714
This

>>5819714
>implying axioms and results, themselves, are math
Surely math is more about the process of deriving and applying results, so it is really too abstract to be "created".

discovered

>>5820207

Think about what you are saying. If what you are observing drastically changes, then the math must also change. Axioms arent facts, they are just operational conditions

it's developed and it's applied

Definitions and axioms(which are arguably definitions) are invented.

Theorems are discovered.

>>5818687
This

>>5820207
Who are you quoting?

>>5818466
>necessary

Could you back this up with evidence? Sure they were useful but were they really necessary?

>>5821980
take the taylor series for e^x, and substitute x -> ix

>>5821983
And how does that answer my question?

>>5821988
it "pulls" apart into an equation unifying algebra and geometry.

>>5821990
>unifying algebra and geometry.

How? And why can't this be done without complex numbers?

>>5821994
Very elegantly, and why work around such a useful tool? i^i is a real number, which is cool as well.

>>5818465

in what way are negative numbers and imaginary numbers different? neither exist in the real world

>>5821998
>Very elegantly
But how? How does it "unify algebra and geometry"?

>and why work around such a useful tool?
That's not my question. You or a poster whose point you're arguing said it was "necessary".

>>5822001
Negative numbers exist. They are just a direction.

>>5822000
essentially by drawing a circle in the imaginary plane, if you pick out n equidistant points you have a regular n-gon.

>>5822003
and imaginary numbers are an orthogonal direction.

>>5822004
What does this have to do with complex numbers? I can draw a circle and polygons without needing or knowing "imaginary" numbers.

>>5822006
An orthogonal direction can described by another real axis. No need for "imaginary" numbers.

>>5822010
go ahead, stick to <span class="math">x^2 + y^2 = r^2[/spoiler]
i'm sure it will make math easier in the future for you.

>>5822016
So you cannot answer my question? I was not saying that complex numbers aren't useful. I was asking you to explain how "imaginary" numbers are "unifying algebra and geometry" and how they are "necessary". These are two claims of yours and I'd like to see your reasoning behind them.

>>5822023
I've already explained both, how about the complex roots of polynomials then? simply nonexistent?

>>5822025
>I've already explained both
No, you didn't. You gave examples of how complex numbers can be interpreted geometrically. You did not explain how they are "unifying algebra and geometry". Neither did you explain how they are "necessary".

>how about the complex roots of polynomials then? simply nonexistent?
Yes. They are only defined to be the roots. Basically that's like saying "the solution is what solves the equation". I might as well define a number x with the property x < x and call it imaginery.

>>5822031
...
i see no point in carrying on further

>>5822035
>i see no point in carrying on further

Neither do I. You could have explained Kähler manifolds and Dolbeault cohomology to me. But you didn't. Apparently you don't know shit about complex geometry and you're just another 14 year old talking out of his ass after seeing Euler's identity for the first time.

>>5822046
well i didn't know about those things but what I said should have made it's importance clear.

>muh MUH

http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

>>5822001
Wave-functions are complex valued, and observables are Hermitian operators.
The Dirac equation is satisfied by a spinor - a necessarily complex (or Clifford algebra-y) construction. Going further, the local symmetries of field theories are given by (special) unitary groups, which are represented by complex matrices.
Complex numbers are more real than the real numbers.

>>5822239
>quantum mechanics
>real
top lel

I hope you do realize that it's just a mathemtical model, a very faulty one btw. If you educated yourself, you'd know how many commonly unsolved flaws there are in quantum theory.

>>5822064


I literally laughed out loud when I realized that the second "muh" was an actual acronym. You made my fucking day anon.

>>5822248
It's a highly accurate model in its relevant domain and makes use of complex numbers in a fundamental fashion.
Please highlight some of these flaws, and explain how you would resolve them by expunging complex numbers from our description of the universe.

>>5822248
It isn't faulty, it produces incredibly accurate experimental results. But it's not the be all and end all, a better theory might be formulated in the future. The "flaws" are just new questions that come from QM, a "flaw" would imply that there's a problem with the theory.

>>5822239
I'm pretty sure there's a big difference between math that can help explain the real world, and math actually being real. It's hard to explain without getting into a pointless philosophical debate.

>>5822266
>Please highlight some of these flaws

There is no consistent mathematical model of how consciousness arises at the quantum level.

http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/

I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say 'the correct answer is whatever the correct answer is'. Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>>5822013
And the opposite direction can be described by another positive axis.

>>5822474
People like you need to do a complex analysis course. Nothing we can say will convince you of the beauty and utility of complex numbers until you actually see it for yourself

>>5818456
subtle
10/10

>>5822474
"God made the integers; all else is the work of man."
Or not, but if anyone rejects Complex numbers go ahead and reject everything else but integers.

>>5822550
God made the nature, man tries to recreate it's components.

I say created

>>5818460

Then its discovered

>>5818502

There consequences are also invented. As in, the consequences dont exist until we come to them.

>>5818687

Then its created. We do the defining.

>>5821980

'Practical' and 'necessary' over lap to some extent. As in, its necessary that we have i to work with, to do such and such in the real world.

>>5822550

The quote goes 'God made the natural numbers...' integers can be created from the naturals. But I dont know, maybe we can go a step further.

>>5822552

How is math a recreation? If I see something, and then write a symbol down on a paper have I recreated that something?

Math, unlike the world, has no particular refernece. '1' refers to nothing in particular.

>>5822572
see, but it does, 1 will always be the same thing, even if you turn your back.

>>5822574

I mean, if we add two things in the world, we arent adding the objects, we are adding numbers we feel can correspond to those objects in the world. What I mean by having no particular reference, is that I could say there is one chair, or one computer, or one hockey puck. the symbol '1' doesnt refer to any particular thing in the world, although I get what you are saying, that '1' refers to a particular number, ontologically.

>>5822578
no, apparently you defined your symbols wrong your whole life, you see we here actually associate meaning with the symbols we use, we're not just playing around with the keys like you.

>>5822581

Well help me. What do symbols like '1' mean?

first of all, I talked about correspondence, not meaning. But, lets investigate this. What is meaning?

I think meaning is all about use. Meaning isnt a matter of content, as in, the symbol isnt a container for meaning. The meaning is a matter of what the symbol is used to do.

The numeral (number symbol) '1' corresponds to the number, but the number, to be useful, has to correspond to something in the world.

Give me some feedback. Dont just say 'wrong' like an asshole.

>>5822594

the number corresponds to a quantity

wildebeests can count cape hunting dogs

>>5822594
The number is a simple property, and when it's in different contexts (we call dimensions) you get your feet , liters, acres, pounds, etc. This is simple physics.

>>5818460
that would mean they are discovered, dumbass

>>5822597

I dont think it is a property. There is nothing 'two' about two dogs, its the person who labels the dogs as two. The same could be said about color. Yeah, we see a brown dog as brown, but thats because human minds assign color to stuff. There is nothing inherently brown about what is seen as brown.

>>5822596

Elaborate. I suspect there is something circular about saying a number corresponds to a quantity. 'a quantity' is not like an object in the world, so it must be something apriori, or defined in the rules of something else, like mathematics.

>>5822617
>Theres nothing 'two' about two dogs
I hope you realize how pointless your argument is.

>>5822625

I dont.

>>5822628
you might just very well be the one exception, we've been looking for a counterexample

>>5822629

I mean, its not pointless. Analyzing our own language is extremely important. I think all problems of math and logic come down to confusions regarding our own language. Its actually the opposite of pointless, its crucially necessary.

It might seem absurd, or pseudo-philosophical, but it would be unfair to expect anything less than a tiresome analysis. Thats where the real work is to be done.

Actually, just hastily throwing out words like 'pointless' is exactly what will get you in trouble in the long run. Again, thats exactly why its so purposeful to re-examine what was supposedly not pointless, like the meaning of the word 'pointless'.

>>5822622

are you suggesting wildebeests have complicated rules of mathematics?
they can count to about five

>>5822658

Well I dont know anything about wildebeests aside from what you tell me, but there must be some understood counting rules in order for wildebeests to count at all.

As to whether to understand what it means for them to understand counting is a separate matter entirely.

>>5822645

I am in complete agreement with you.

But 4chan is judgmental and edgy, and it would rather call you a faggot who needs to die than admit you have a point which might help humanity in the long run.

Don't cast your pearls before swine. Your subtlety is lost on these assholes. Sounds pretentious, but it's true.

>>5822662

If you have a pile of stones.
There is a certain quantity of stones in the pile.
It is not a quality of one stone, but of the pile.

>>5822248

Are stupid assholes who say "top lel" created or discovered?

>>5822677

teh internetz created them

>>5822677
they're neither, they have no significance to any measurement.

>>5822677
Stop bullying me.

Mathematics have been completely discovered.
However, the ability of Mathematics to describe reality has been discovered.

One thing's for sure.
If whatever created/discovered in place A can just as well be created discovered in place B. Absolutely, exactly the same "object".
It doesn't matter how you get there, or if you get there, or when you get there. Theorem's are always there.
I say discovered.

The amount of people who say created surprised me but it's fine.

>>5822046
Which facts of mine do you disagree with?

>>5823299
all of them.

The answer is yes. Mathematics is created or discovered.

mathematics is a social constuct

>nobody has reported OPs post for being a horsefucker image
>>>/out/

>>5823966
nobody but you gives a fuck about the image while people try to discuss

>>5823956
Postmodernism is a social construct.

>>5823966
...so you're saying you pay enough attention to mlp to recognize that image?

>>5823966
You must be new here.

>>5818456
Is your mom fucked or banged?

>>5824315
don't continue, that was a fucking knockout. Way to go.

>>5823966
>reporting mlp
>on board filled with horsefuckers

Mathematics unlike most subjects is predefined. It can only be discovered and not created, even if you take imaginary numbers, they have always been there, we simply gave them a name and discovered the results of manipulating them. This applies to all areas of maths, you cannot create what is already there but you can discover more things about it.

Is the universe continuous or is it discrete

>>5824409
But the results wouldn't have existed if we hadn't "discovered" them. Ergo, math is created

>this non-stop trolling and shitposting

Is this question ontological or semantic in nature?

>>5824422
Would never happen if no one bumped the threads.

>>5824421
What nonsense! The result will exist and have always exist. Just because we haven't observed them happening and/or recorded it does not make it not exist.

>>5824430
This is a deep ontological question, and I'm just going to have to disagree with you, unless you can offer a convincing proof.

>>5824439

What I'm saying is that something that we haven't discovered is not therefore non-existent, It does I will agree; open the potential of non-existence. To simply say that something doesn't exist because we haven't discovered it, would be the same as saying the world was flat before it was traveled round, or a planet isn't there before we find it. The results MAY not exist.

I'm new to using boards and stuff, by proof do you mean some form of report or paper on the subject or just an argument that appears logical and lacking is counter argument?

>>5824439
In the current context, 1 + 1, irrelevant of weather it has been discovered, or what you would name it will always and has always been equal to 2. In what possible way could this or any other mathematical concept not be the same (as in the result previously not exist) before we "discover" the result our self.

>>5822046
>you're just another 14 year old talking out of his ass after seeing Euler's identity for the first time.

Damn I love how /sci/ talks shit.

>>5822046
>cohomology
>the study of co-homos
dat 1 made me giggle m8

>>5824512
lol 10/10

Hey guys, what's your favorite kind of math?

>>5825350
linear equations

>>5825350
Arithmetic.

>>5825357
>>5825358

Those are very nice types of math. You guys must have a lot of fun working on them.

Real numbers is just a name, even positive integers are not real. Just like rational numbers are neither more nor less rational than irrational ones. Have you ever met a "2" in real life? I haven't.

When you create something, you have the authority.
If you don't have the authority, you are not creating.

After settling on ZFC and standard definitions (we created a list of axioms and definitions), you no longer have the authority to declare whether a given integer is a prime number or not; instead you are required to discover whether that integer is a prime number or not.

You are only able to decide so much before you begin to discover what is or is not consistent with what you have already decided.

Created, the axioms are thought up, they are not lying anywhere, you must for yourself make them.

People who say math was discovered are trolling most likely.

Is this thread saged or saged.

>>5825400
Sage is not a downvote function.

>>5824424
It is a question of science..

No, mathematics can be neither created nor destroyed. But then some dipshit figured out that if you squeeze it hard enough it turns into fucking mayonnaise.

>>5825370
>Have you ever met a "2" in real life? I haven't.

I did. Being a 10 myself I said "2/10 would not bang".

>>5826286
>missed the point

>>5818462
/thread

>>5818506
/thread

>>5819671
Duh
>missed the point entirely

>>5822456
Thank you, this was elucidating.

>>5818460
That would imply that mathematics is discovered, fucktwat.

>>5818687
DEFINITIONS ARE CREATED.
YOU DENSE MOTHERFUCKER

>>5818525
Axioms are sentences that mimic structures that we already know. So they're invented. Idiot.

>>5827941

Not really because it takes consistent flows of logic (and therein creative neurological structures) in order "follow" any 1+n rules.

There's a difference between natural pattern recognition and explicating rules of neurologically created logics and axiomatics.

>>5828006
Well, I certainly see how someone could profess otherwise. If a definition describes some natural aspect of reality, then the only construct involved is the language in which we express that truth.

axioms/fundamental definitions/whatever are created, everything else is a discovery/deduction

>>5823309
Best answer, hands down.
/thread

>>5824430
>The result will exist and have always exist
This is outright wrong. Unlike counting (and with it, other mathematicall models), measurements do not have any answer set in stone. They depend on how well-defined the question is. As a statistician, this is very clear for me. For instance, let's say I'm asking you about the weight of 1 m^3 wood. I'm not interested in THE exact measurement of any piece of wood of that exact volume -- granted, provided "weight", "wood" and "meter" are well-defined enough, the result will converge to some value, but this will only be because we set the parameters in stone to make our simulation of the answer. This is however a replica of what is being asked about and this is not necessarily what I am interested in. I risk being deluded if I take it to be the real thing. It would be like using graphs and pictures as proofs in mathematics instead of seeing them as an intuitive help. Rather, I'm most likely interested in the weigh of some particular piece of wood or perhaps weigh as a mean value of what I take to be wood in the world. I probably don't care if you're off by a few mm and grams, because what I asked for was to get a general idea of some occurence in the world. And it is a property of general ideas of occurences in the world to not have any definite answers, due to time and more specifically the way in which we as entities in time need to make it so that we can make these ideas appear to us clearly. They are the images of said world.

>>5818456
Emilia, is that you?

Guys, this thread is over 4 days old, and was a troll to begin with.
Don't you think it might be time to just let it die?

>>5828102
Erase it! Don't you have the powers to di that?

>>5828102
Nobody is trolling. Please read the thread. There is still meaningful discussion at hand.

>>5828766
then how did this occur?

Top lel

>>5818456
Mathematics are invented, not discovered. There is no such a thing as a magical place in which ideas reside and wait to be discovered. Basically, it boils down to that.

>>5829889
So, this means that we can create a new math when 2 + 2 = 5?

Everyone is wrong. Discovery is an invention and invention is a discovery. Mathematics doesn't exist.

>>5829968
Insightful. Thanks.

>>5829916
We created a new math, so that 1 + 1 could equal 1, so I don't see why not.

>>5830833
[citation needed]

>>5831076
See Single Bit Binary Addition.
Binary Arithmetic
Binary Mathematics

>>5831120
But in binary 1+1 doesn't equal 1.

>>5819714
When the axioms are set into place, everything else is only discovered. The only 'created' part involves creating the axioms themselves. So yes, mathematics at its base is created, but from there comes infinitely many discoveries.

/thread

>>5832490
in a 1-ring it is 0 though.

>>5828775
Inappropriate O-ring material.

>>5832736
Trivially. But >>5830833 said "1 + 1 could equal 1".