/sci/ - Science & Math

Discovered

Invented

>>9984102
Racists say invented. People say discovered. Because nobody knows if it's been discovered before and forgotten or not.

>>9984102
invented

>>9984114
But if our universe is based purely on mathematics, how can you claim you've invented it?

Did Einstein invent e=mc2?

No, he discovered it

Discovered.

>>9984102
Discovered because God came up with it first.

Discunted.

>>9984151
>e=mc2

>>9984155
By god, do you mean the people running the simulation?

>>9984162
>expecting intelligence on 4chan

>>9984151
>e=mc2

>>9984102
Neither. It's described.

>>9984151
Math exists independent from our world. We just defined particular patterns as math and simply describe how it works.

>>9984170
>>9984162
e=mc2 is just as valid model all full equation. They are just models, they are supposed to work only in particular situations.

>>9984102
Math is constructed.

It can't be discovered because axioms are assumptions, not facts.

test

>>9984201
no

Axioms are invented, the consequences of them are discovered as theorems. Theres a third thing that people can argue about, the mapping of mathematical object to to reality, for example the mapping of integers to apples. I'd say the mapping is discovered once you have an invented mathematical object and realise it could model some part of reality adequately.

An argument against this I've heard on sci is that some mathematical objects are used before the axioms are formulated, thus they can't be invented. Like people who can count without knowing the piano axioms, but I'd say you still have some primitive axioms about how addition works if you can count that was invented, it might be inspired by nature by seeing two apples are the same as one and another one, but saying it's thus discovered is like claiming airplanes are discovered because they take inspiration from birds.

>>9984102

Invented, it's completely created by humans, and can only exist with human consciousness.

>>9984351
By this logic we dont discover mental illness, we invented it.

>>9984678
but thats literally true

mental illness, psychology and all of physiology is just humans becoming self aware of thought patterns that are both harmful and useful, and giving them names

>>9984102
Axioms are invented. Theorems are discovered.

>>9984163
>people running the universe
>people
If we're giving "them" names I'd go with Anime Girls.
A universe run by anime girls just seems better.

>>9984102
Discovered imo. I don't really consider invention to be a valid concept.

LMAO, well mathematics is invented.
It's a symbolic language based on logic, another language, that we invented as a small picture to how things work in the universe.
Wittgenstein is my bro
Let's say something wrong implies something wrong for the truth value function.
In the real numbers for the usual arithmetic operations, we have:
1+4 = 0, thus 1+4 = 5

>>9984834
Of course you could see it as a language for a natural science that only applies to natural phenomena that are possible or could be possible BUT that depends on whether our mathematical system is correct and that's not provable

>>9984102
It's discovered. Anyone who says otherwise is a moron.

This argument is just confused. There are aspects of mathematics that resemble discovery and invention. The fact that mathematical rules have deterministic and singular results suggests discovery. The fact that people come up with rules and the number of possible rules is infinite suggests invention. It just has both.

But if I had to pick one I would say "invented". It just makes more sense to me to concede that invented things have non-invented deterministic outcomes then it is to concede that everything anyone could think of is in some way "out there" pre-existing and waiting for be found.

>>9984102
Neither invented nor discovered. Only its notation is at the behest of humans.

Having subjective awareness requires an intrinsic understanding/knowing of "quantity" and separation because you are the awareness of yourself, there is only one, and you are not the awareness of someone/something else.

So the truest representation of 1 is your subjective consciousness, because you intrinsically know you have a consciousness, not multiple. I don't think it's a coincidence that the letter/word 'I' is the same shape as the number 1, since 'I' is the linguistic representation of this singular subjective consciousness.

>>9984102
Who cares

>>9984102
The mathematical truths of our universe are discovered but the formalism used to describe them are invented. Hope that makes sense.

>>9984102
We had this thread before, so please read the answer, understand it, then stop posting old shit topics.

Answer:
>"Mathematics" is a formal system in which all deductions are ultimately founded on a set of Axioms
>For example, euclidian geometry is a formal system which is characterized of euclid's 5 postulates
>Axioms are presupposed, not deduced. This is a fundamental property of axiomatic/formal systems
>The first axiomatic systems we formulated (like the example above) were usually formulated in terms of experience
>For example, one could establish the natural numbers by assigning specific quantities of objects a certain number
>However, this does not mean Axioms are discovered, it means that their validity was initially presupposed for the pragmatism of their use
>You cannot "prove" or "disprove" an Axiom, you can only show it to be logically inconsistent within the set of Axioms it is supposed in
>In this regard, the foundations on which mathematics is established is fully invented
>However, this is not the full story, as we have yet to consider the theorems which result from these axioms
>For instance, one would not immediately guess from looking at ZFC that Fermat's Last Theorem is correct and deducible from ZFC
>This is because intuition does not always align with the facts
>When a fact is deduced independent (or contrary) of the assumptions (or reasoning) that intuition provided, it is discovered
>In this regard, "Theorems" are necessarily discovered
To summarize: Axioms are invented, the Theorems which result from these axioms are discovered. There is also a footnote to be mentioned, which is that this interpretation is strictly formalist, and rejects the ideas of logicism, as it is not necessary to establish that an axiomatic system need be deduced from basic logic, but instead that the axioms or (arbitrarily or pragmatically) presupposed. Also platonism is retarded

>>9985072
Brainlet here, but couldn't you argue that the thought process going into an invention can be argued to involve discovery ?

>>9985072
Fucking hate platonists and the nihilistic physics approach. Makes me want to vomit.

>>9985072
Mathematics is far more fundamental than "axioms" or "theorems", these things were formed to obfuscate the true nature of mathematics.

>>9984102
Used.

>>9985101
Entirely depends on how you define invention and discovery. As listed in the post, one could take, for example, the natural numbers as being something that is founded on experience. However, this approach to establishing the natural numbers speaks nothing of the validity of their construction. You cannot assign a number to a quantity of objects without supposing the validity of both of the natural numbers and their ability to describe nature. Without diving too much into semantics, when something is invented, that thing must have its properties be established by some means, whether that be on experience or through presupposition. The point of the example and the following deduction is that when an invention is established on the basis of experience the validity of that basis and the laws which are formulated from it have to be presupposed at some level. Therefore, both a formulation on experience and on arbitrary presupposition falls into the same category of invention, as to argue otherwise requires that formulation to be deduced from something other than a fundamental assumption, which is impossible.

>>9985111
no dude we invented 3-space it's just a fictional axiom, also 3 was made up too

>>9984102
Same as asking: is god invented or discovered?

>>9984102
Invented. Mathematicians are platonists because they are bluepilled.

>>9984151
>Did Einstein invent e=mc2?
Yes, he even guessed it.

>>9985119
>we invented 3-space it's just a fictional axiom
Correct. Having a quantity of "dimensions" is silly, it's an infinite regress, because you cannot have 1 dimension without having the 2nd, 3rd, 4th, 5th ad infinitum. It's an arbitrary axiom and should not be taken seriously nor applied to physical reality.

>also 3 was made up too
The notation/symbol representation of 3 was made up, but '3' as a metaphysical quantity is logically consistent with "all other" metaphysical quantities. And certainly an interesting quantity when it comes to metaphysics in general.

>>9984151
Since 1934 it's known that theories in physics are invented. Thank faggots who say that philosophy is irrelevant.

>>9985142
>space isn't 3D because then you need infinitely more dimensions
?

>>9985185
By "space", what are you referring to? A mathematical abstraction, or something physical?

>>9984114
>the manual to how to build cars has been developed, because there was always the possiblillity to build a car.

>>9985221
you honestly believe regular space doesn't have exactly 3 orthogonal axes?

>>9985237
I believe that's an arbitrary metaphysical quantity you have applied to something that doesn't have any finite qualities.

>>9985237
would you say that the 4th dimension is time?
Because like 2d beings in a 3d world, we only see a cross section of time, only a snippet. 2d beings would precieve 3d comparably.

>>9984102
I would say "codified". It is a codification of principles and patterns that exist in the universe.

>>9985258
How are you seeing "time"?

>>9985237
How the fuck do you know this, experiments have only narrowed it down to between 2.995 and 3.005, it would be a massive coincidence if it's exactly 3.

The axioms are invented and then the applications are discovered

>>9985258
Lol fucking brainlet

>>9985276
Surely axioms are discovered. We don't invent the principles of maths. The principles already exist out there in the world, and all we do is try and codify them as best we can.

>>9985291
No, we literally invent them.
Math isn't the language of the universe no matter how much you will hear this, its our language made to describe whatever the universe is actually doing.

You have these pebbles but you don't know how to count them yet.
With a language you came up how to count these rocks.
Invention or discovery?

>>9985272
how are you seing 3d?

>>9985295
>something can be invented that then becomes true forever before and after it everywhere

>>9985309
I don't see "3D", that is a metaphysical concept. I see physical reality.

>>9985072
>To summarize: Axioms are invented, the Theorems which result from these axioms are discovered.
>mfw mathematics is literally a social construct

>>9984102
discovered

>>9984772
No it's not "literally true". Humans provide a landscape for it to occur naturally and thus be discovered. It's like saying that electricity is invented because humans became self aware of lightning and gave it a name.

You're stretching definitions, and trying to argue that just because something occurs naturally due to the random creation of life that it means we invented it. We did not invent schizophrenia we discovered the illness.

This may be one of the dumbest things I have ever read on the internet

>not realising math is just a logic-based language we use to describe meaning
>not invented since logic doesn't need consciousness
>not discovered since logic doesn't really exist
this conversation is meaningless and absurd.

>>9984102
The numbers and variables themselves are invented, but the patterns represented in formulas are discovered.

>>9985934
You’re a brainlet

>>9985258
We have 3 dimensional space and one dimension of time. 4 dimensional spacetime in total. It's not hard to figure out.

>>9985291
We invented axioms. You can freely discard them and come up with new ones as long as they don't cause paradox. We just picked ones that are most practical.

>>9984102
Invented, please consult Plimpton 322 tablet and mesopotamian and greek maths as a whole-- constructed reasoning based on the provisional needs of what needed to be expressed. New maths are constructed for what isn't contained within the grammar/logic of previous maths.

ex. Euclidian vs non-Euclidian geometry-- the maths didn't fit up with reality, so a new math was invented for the purpose of approximating the phenomenon before us.

Fucking essentialists need to leave even a gigantic theoryfag like me realizes that

>>9984102
the universe was created, not discovered

>>9986654
Math is independent from the universe.

>>9986674

>>9986674
you can't discover maths until there is a universe.
no universe = no maths
create universe = create maths

>>9984163
God is writing the story.

>>9986654
'the universe' (our perception of it) is a result of our minds

>>9986611
Ahh yes, Plimpton 322, now *that* was a tablet

>>9986701
You can't exists until there is your mom.
no mom = no (You)
fuck your mom = create (You)

>>9986825
amerigan retard

>>9984175
>Math exists independent from our world. We just defined particular patterns as math and simply describe how it works.
The maths we use now is not but there might be mathematics that are capable of describing reality with complete accuracy, in which case the universe runs according to existing mathematics regardless of whether we have discovered it or not.

>>9986611
this

>>9987008
That's just physics with the theory of everything.
It's still math under hood, but so is every other universe we don't live in and can be described using math.

Invented means discovered in the mind.

>>9984102
Some of it was invented and some of it was discovered

>>9984175
Wrong.
Math is apriori. Ie not necessarily mind-independent.

>>9986611
dubs of truth also sick plimpton ref will forgive the reddit spacing for this

>>9985072
>hurr durr

Inventions are discoveries.

Wow it's fucking nothing!

>>9984341
Very thot provoking.

>>9984102
We create initial conditions in the form of axioms and definitions, than we try to discover what happens when they interact in various ways.

So... both?

>>9985315
https://en.wikipedia.org/wiki/Problem_of_induction

>>9984102

Invented a model to describe a phenomena which was discovered previously.

>>9986363
Like any idea, logic can exist only in consciousness.

>>9984102
I'd say invented. Mathematics is something humans created to explain the world around us. It's just like taxonomy - objectively speaking, there are no such things as kingdoms, phylum, classes or whatever - they're just terms we invented to segregate life into something we can study systematically.

>>9989553
that's irrelevant to psychologism being false and Platonism being real, but nice try

>math is discovered
>implying axioms are discovered
the absolute state of /sci/tards

>>9989570
sweet jesus. think about what you just said more

>>9985113

inventions are made using discoveries and discoveries are made using inventions.

Mathmatics systems are invented. For example set theory was an invention. Inside of those systems, theorms are discovered. For example, using standard set theory, it was discovered that the set of integers has a one to one mapping to the set of rationals.

Scientific theories, like special relativity, are invented. New phenomenon and experimental results, like finding the Higgs Boson, are discovered.

>>9984341
>piano axioms

Is this might sound very unpopular but i think everything is theoretical after the four basic mathematical operations and numbers.

>>9984102
>invent counting
>everything else is a trivial implication
Therefore, invented.

>>9984102
I would say a bit of both.
Much of the fundamentals are axioms, which are invented. But what maths is really about is what happens as a result of these rules, and that part is largely discovered.

That's what math is. Creating a bunch of rule and seeing what happens. Most of the work is in finding out what happens. Rules are easy to make. But rules that are consistent and don't break anything are not. So a large part of the rule-making has to be learned (discovered) as well.

We invent the axioms, we discover what follows

>computer programs are just huge numbers that always existed, therefore developers are really just discovers with a map

>>9992307
That's not what map means.

>>9984163
No, they themselves are just a within the mind of the one true GOD.

>>9984102
we invented math as a tool to describe processes we discovered

>>9984102
Both. You invent the axioms and discover what they entail.

>>9984151
>e=mc2
Kek

>>9984102
it's an invention that we discovered.

>>9984102
Both

>>9984107
>>9984109
Off to a good start.

>>9984151
>einstein
>e=mc2

>>9984102
I would say invented, because like language it was used to describe the world.

>>9984102
'twas invented and they used that to make artificial discoveries inside their little pocket universe which is bretty cool

>>9984102
Invented...

Philosophically, to discover something, also means to have it in its entirety. If we had discovered math, we would know everything from the beginning.

Also, we still don't know how the universe fundamentally works. We still have theories and can't see or verify everything. For that reason only, everything you do to describe this functionality will be a mere approximation, as you are not able to clearly see the mechanics behind it. You invent it.

The reason mathematics grow and seem right, is because we keep on researching and proving based on the rules we started with, but these are not necessarily the ones nature works with.

>>9984102
As far as man is concerned, is there a difference between the two?

>>9984341
in 4000 years people will look back and have the argument
>were airplanes invented or discovered

>>9984163
The angels

Is even assigning maths (or axioms) a "discovered" or "invented" meaning something well defined? I mean we can all coincide in that theorems are discovered given a list of axioms, so lets suppose that this current list of sufficiently definable axioms is invented. We could then construct (invent duh) another model which supports some kind of semantic meaning, for example a complex enough language with their axioms to make it have sense, such that it is possible to represent our original axiomatic system in it. Then all maths, and perhaps any similar systems would be contained as "truths" in the new model, thus waiting to be discovered. That includes de original list of axioms and of course their theorems. I.e. that very list of axioms is actually discovered.
Although we still would need some kind of invented system just to support it, but we can always keep going if we wanted.
And of course, an axiomatic system could contain itself, I guess ZFC admits enough logic-like objects to define its own axioms within itself.

obviously discovered

>>9985071
THIS.

>>9984102
It's discovered if it ends up being a correct formula or method but invented if not so

Guy who showed modern mathematical axiomatic theory (Kurt godel) believed that in mathematical platonism. Surely he saw it as discovered.

>>9984102
Most people who study math (including myself) are Platonists.

Mathematics is discovered, nothing that humans have invented competes with the depth and beauty of mathematics, those who say that mathematics is invented might as well say we invented the milky way, because we observe the milky way through our eyes and through telescopes.

>>9992529
>>9985072
Idiots claiming we "invented" axioms, even when they acknowledge we observed in nature ahead of time.

We did not invent any of the axioms of mathematics. Either we observed them, or they were innate ideas we were born with.

>>9996244
No, airplanes were discovered. Show me the person who completely thought up, as an original idea, the design of a working airplane.
You can't, obviously, because they couldn't. All they could do was tinker with stuff until discovering what works.

>>9996336
>you have to define every word you use, hmm can't do it? checkmate retard.

Reminder that if your observations contradicted a mathematical proof, you'd be more likely to doubt the proof than your observation.

>>9984102
Both.

Natural math would be whole numbers, if you put ten fish in a basket there are ten fish, see!

But the higher levels of math that get into conceptual numbers or that require agreements In order to solve are fictitious and invented.

>>9998389
Absolute bullshit, the naturals are no more "real" than the other sets of numbers gtfo with your finitism shit.

>>9998398
It’s not bullshit. Simple pure math can be seen and felt, while invented maths need you to agree before you start that some “numbers” or expressions are equal to an imaginary term.

>>9998385
>Idiots claiming we "invented" axioms, even when they acknowledge we observed in nature ahead of time.
Idiots who think axiomatic systems have anything to do with nature.

lmao physics brainlets have no business talking about mathematics

>>9998385
dis·cov·er
dəˈskəvər
verb
1.
find (something or someone) unexpectedly or in the course of a search.

in·vent
inˈvent
verb
create or design (something that has not existed before); be the originator of.

>Show me the person who completely thought up, as an original idea, the design of a working airplane
https://en.wikipedia.org/wiki/Wright_brothers
>You can't, because all they could do was tinker with stuff until discovering what works
You are just playing with semantics, how can something be invented without considering the asbtract and practical preliminaries to invent it?
>We did not invent any of the axioms of mathematics. Either we observed them, or they were innate ideas we were born with.
How do you observe an axiom in nature, and how do you know - from experience - that these deduced axioms exist in nature? Would you likewise argue that an artist observed his paintings (and not invent their image) because he might have taken inspiration from (if not artistically bounded to) his experience? Notice how there exists a crucial semantic division between inspired and observed, which is needed in a discussion about this supposed natural existence of Math. On another point, would you argue that since we only observe Math from nature, then "Math" is subject to our experience? In order to answer yes to that, you would need to argue that Math is a posteriori and not a priori, yes? As for intuition, I need clarity on what you mean by "innate" and "born with." Do you mean that we possess the capacity to understand Math? Do you mean that Math (in accordance of it existing in nature in a platonic sense) is implanted in us just as with our senses? With the former, it can just as argued that we only possess the "capacity" to grasp Math, we do not "possess Math" itself. As with the latter, refer to the first question about observing an Axiom. Just as Chess only exists as it is supposed, pondered, and described, so is the existence of Math.

>>9998385
>bruh, i just discovered this How to build an Airplane Manual.

It's neither invented or discovered and yet it is both.

>>9998866
I have the Trips dubs dubs to confirm

>>9984102
Are dimensions invented or discovered?

>>9999058
Is history invented or discovered?

i guess the brainlets are semi right in that the arbitrary symbols and notation are inventions
maybe that's what they're thinking of

>>9999077
Everyone knows that symbols and notation is invented.

>>9984802
Considering that this is what they came up with, I doubt that it is much better.

>>9984102
Neither. It's constructed.

>>9984102
The constructionfags are correct. 'Constructed' is a much better term for what happens. You can argue to what extent anyone really invents anything... All invention relies on previous observation and experience of the world (such as apparent consistency). Even what appear to be self-contained mathematical systems are built upon basic mathematics, which are abstractions upon how the concrete world appears to behave. The lines are often blurrier than our default terms suggest.

The language is constructed, the properties/configurations it describes are discovered.