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was math invented or discovered?
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Does it have to be one or the other? Consider prime numbers. We invent the idea of a number that can be divided only by itself and 1 but we discover that 43019 is such a number.
All math is constructed.
Discovered.
The decimal counting system where we end at 9 is not discovered at all.
The raw logic of 0 and 1 is in the truest coding of reality and even God is enslaved to be incapable of breaking apart 0 and 1 into a simpler level. there has to be 0 to 1 and 1 to 0 otherwise your system is not numerical. A system of only 0 is not going to be able to calculate anything.
discovered
It was definitely discovered. This is proven by the existence of fundamental constants in physics, for example the universal equation for gravity. Wherever you go in the universe this equation will still work. There might be infinite ways to express the equation, but the equation itself -- and hence the relationship between the symbols used to express it -- is always going to be the same.
I think we should start by trying to idetify what the word 'mathematics' refers to. I would suggest it is the study of numbers in the abstract. For example mathematics defines an operation on two numbers ('multiplication')that produces another number called the 'product'. Mathematicians are busy discovering relationships between numbers.
At some point in ancient pre-history it was noticed that if the numbers are, for example, the lengths of a rectangular patch of ground the their product is a useful value, ie its 'area'.
What is not obvious is whether the idea of using multiplication to obtain the area of field of corn is an invention or a discovery. That is, did someone invent a method of getting the area of a field by multiplying the length of its sides or did they discover that you can get the area of a field by multiplying those lengths? (Is there a difference?)
To solve a real-world problem using mathematics, what has to happen first is the problem must be translated into a set of numbers and mathematical operations and finally the result has to be translated back into a real world property.
There is a right way and a wrong way to do that. If you want the area of a field it is no good adding the lengths of its sides. If the field is 3 miles by 2 miles then the sum (3+2) is 5, but that isn't the area. The world is such that the correct mathematical abstraction involves mutiplication, not addition, so inventing a method of calculating the area of a field involves discovering you need to multiply, not add!
The world is as it is. If we are clever enough we can invent/discover a method to convert properties of the world into numbers ('take meaurements'), then use some mathematical operations to get a new number which matches a measurement we could make of some other property.
What is surprising is that it possible to do that! That means properties behave somewhat in the same way that abstract numbers do!
The must-read classic work on this id by Eugene Wigner;
Ok, help a Brotha out.... I'm under the assumption that Math is tool created to help humans create/ invent/ evolve.
This is a good article on the subject imo
7 days later
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@Fallaneze
Agreed Falleneze and J6 have it correct. 10 points each.
Humans do not invent the five, and only five, regular/symmetrical and convex polyhedra of Universe.
They discover their existence. Humans discover what is possible and apply that to construction, sometimes called invention.
They did not invent cosmic laws, principles or sets of number associated with all occupied space , geometric patterns.
At best humans invent words to convey concepts.
23 days later
Was the word "red" invented or discovered?
I think it was invented to describe the property we collectively agree to be the hue "red".
Just like "Rosa" was invented.
Math is the same way. It's a collection of axioms used in a system of rules to perform functions, manipulations of input data to arrive at conclusions we all agree are properly performed mathematical conclusions. These conclusions are helpful in describing real events and other phenomenon where quantities are relevant.
But it is a language invented to describe the relationship of quantities, coordinates, ratios, sets. To say it was discovered would be to assert that the number "one" is some real, yet abstract entity that exists. (Sounds border line theological, which I'm okay with)
While I might say the number "1" is an existing abstract entity, the system Math would still be a collection of rules and statements invented to describe such an entity and it's relationship, comparison to other such entities.
New relationships are being discovered. New properties of these entities are being discerned. But all within the context of a system created to describe them.
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@Mhykiel
Of course red was discovered and agaomg at best humans invented word to communicate that red to self and others.Was the word "red" invented or discovered?
People walk around and see red, blue pink yellow and then assign a conceptual label to identify, catagorize and put into orderly numercal sets.
Frequency of visible light red exists and humans discover that ftequencey, they do not invent that frequency.
Metaphysical-1, mind/intellect/concepts ;
1{ harvest information objectively, discovers paterns and princi
2} sorts the incoming chaos into orderly numerical catagories,
3} discovers patterns and principles,
4} applys those patterns and principles in techological ways in support of humans existence on Earth the integrity of Universe. Thank you B. Fuller
You got two rocks. One rock and one rock. One plus one equals two right?
But wait, closer examination reveals that this rock is not the same as the other rock... so if these two rocks are different, doesn't that mean that one rock doesn't equal one rock? If one rock doesn't equal another rock, how can one plus one equal two?
MATH IS A LIE!
Just kidding. We deal with representations of reality rather than reality itself. That is the lesson.
1 + 1 = 2 or as O + o = set of two objects of disimilar size. Obvious truth and relativity is involved.
Both involve common sense.
1 2D triangle + 1 2D triangle = 4, 2D triangles the same size as the original two via geometric synergy and resultant 3D tetra{4}hedron.
Arguing against truth makes humans look foolish at best and at worst _____________?
Of course red and the tetrahedron was discovered and at best humans invented words/lablels to communicate that special-case color to self and others.
People walk around and see red, blue pink yellow and then assign a conceptual label to identify, catagorize and put into orderly numeriocal sets.
Frequency of visible light red exists and humans discover that ftequencey, they do not invent that frequency.
Metaphysical-1, mind/intellect/concepts ;
1{ harvest information objectively, discovers paterns and princi
2} sorts the incoming chaos into orderly numerical catagories,
3} discovers patterns and principles,
4} applys those patterns and principles in techological ways in support of humans existence on Earth the integrity of Universe. Thank you B. Fuller
No 2 people are the same, but you still have people.
Math when applied to reality is fuzzy. No two 1s are actually the same in nature.
That isnwhy not long after they broke everything down to atoms, it wasn't long after that the atoms were broken down further into isotopes, and then even smaller pieces.
No 2 atoms. Even of the same isotope are truly the same.
Math is definitely a huge part of how we experience things though. Math reveals creation in a very profound way. You can't make sense of anything without having something else to compare it to.
Binary was mentioned earlier in this topic. Duality is the nature of creation. Relativity. Compare this to the singularity.
11 days later
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@Mopac
Please explain how "1" is different in nature and provide examples?Math when applied to reality is fuzzy. No two 1s are actually the same in nature.
it wasn't long after that the atoms were broken down further into isotopes, and then even smaller pieces.
Isotopes ARE atoms. LOL!
Even of the same isotope are truly the same.
Nope, isotopes are atoms with a different value of electrons or neutrons.
Binary was mentioned earlier in this topic. Duality is the nature of creation. Relativity. Compare this to the singularity.
Meaningless drivel.
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@Goldtop
I was demonstrating that no 2 atoms are truly the same.
I know what isotopes are.
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@Mopac
Why do you lie about that, your words are above just there showing that you have no clue what isotopes are. Why is everything you say a lie?I know what isotopes are.
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@Goldtop
I see you have nothing to add to this topic.
Exposing you as a liar and fraud on the topic is plenty of additional. If anyone has nothing to add, it's you.I see you have nothing to add to this topic.
Note: Further evidence - irrational conflation, after alleging claim to be made in ignorance, with dishonesty. "Fraud" "Liar" Opinion: Symptoms are repeating along related circumstances across time-Testing warranted.
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@Plisken
You seem to have conveniently disappeared when a number of questions were posed to you a while back, what happened? Are you here to answer them or more hit and runs?