The forum discussion centers on the philosophical debate regarding whether mathematical truths are discovered or invented. Participants argue that while mathematical concepts like Ohm's Law and the Pythagorean theorem may be articulated through human invention, the underlying truths exist independently of human recognition. The conversation references notable figures such as Einstein and Ramanujan, emphasizing that mathematics serves both as a language for describing natural phenomena and as a construct developed by humans to solve problems. Ultimately, the consensus leans towards the belief that mathematical truths are both discovered and invented, depending on the context.
PREREQUISITESPhilosophers, mathematicians, educators, and anyone interested in the foundational concepts of mathematics and its relationship with reality.
I tend to agree with you...but just to play devil's advocate could someone not use a different way (besides mathematics) to describe Ohm's law? In a sense isn't mathematics just a set of invented tool's used to solve a certain problem? Could some civilization in another galaxy have reached the same conclusion (Ohm's law) using a different set of invented tools?Danger said:If they're truths, then they must have always existed, so the former would hold true (in my opinion).
It's like... Ohm's law and all others have always been true, but someone had to realize that and put them to use.
Perplexing viewpoint. I would argue against you only in that mathematics itself (at least the verified parts thereof) consists of truths that also had to be discovered and articulated. It's like asking if water existed before the English called it "water" or the Russians called it "vody" (sorry, PopChar is acting up, so I couldn't use the proper Cyrillic letters)._N3WTON_ said:could someone not use a different way (besides mathematics) to describe Ohm's law?...
...Could some civilization in another galaxy have reached the same conclusion (Ohm's law) using a different set of invented tools?
Good point, also I suppose that even if someone discovered a certain truth using a different set of tools, the truth itself was still always there, giving validity to the belief that such truths are discovered not invented...although after reading a bit about the subject I found out that some guy called Einstein believed that certain truths are invented...Danger said:Perplexing viewpoint. I would argue against you only in that mathematics itself (at least the verified parts thereof) consists of truths that also had to be discovered and articulated. It's like asking if water existed before the English called it "water" or the Russians called it "vody" (sorry, PopChar is acting up, so I couldn't use the proper Cyrillic letters).
Well, he was getting on in years... :p_N3WTON_ said:some guy called Einstein believed that certain truths are invented...
Sure, but If a different method could also work, that doesn't say anything at all about Ohm's law. Ohm's law would still be true._N3WTON_ said:I tend to agree with you...but just to play devil's advocate could someone not use a different way (besides mathematics) to describe Ohm's law? In a sense isn't mathematics just a set of invented tool's used to solve a certain problem? Could some civilization in another galaxy have reached the same conclusion (Ohm's law) using a different set of invented tools?
Why do you feel that way? I'm curious to here your POV because I tend to believe they are discoveredzoki85 said:Invented
Becouse I believe human race has unlimited inventive potential._N3WTON_ said:Why do you feel that way? I'm curious to here your POV because I tend to believe they are discovered
jerromyjon said:Somewhere on several occasions I've heard of math described as the "universal language". Assuming the laws of physics are constant throughout the universe, constants such as pi and c as well as theorems like pythagoras'
Perhaps their existence might be in a pure energy state where our technology imprisons and/or destroys their lifeforms. Our language of mathematics would be terrorism!Pythagorean said:Our attempts to communicate through the physical constants discovered in our set of axioms would be found vulgar and offensive and Earth would be destroyed.
While the Pythagorean theorem is a discovered "mathematical truth," the right triangle it applies to is a pure human invention. The significance of a right angle only exists in the human mind. Humans invented and developed an ideal right angle, not discovered anywhere in nature, on which to perform calculations. Saying mathematical truths are discovered is like saying chess truths are discovered. Both statements ignore the fact you're making discoveries about a human mental invention and falsely imply you're making discoveries about nature._N3WTON_ said:Why do you feel that way? I'm curious to here your POV because I tend to believe they are discovered
Until eaten...Pythagorean said:our cows and corn live a very Orwellian life.
The right angle of geometry has a specific definition that was arrived at in the human mind after defining prior ideal concepts like points and lines and angles. Determining the height of a tree, or using a plumb bob in erecting a house wall, means assuming an ideal horizontal plane we can't actually see. Geometric ideals are worked out in the mind, and then approximately superimposed on irregular nature.jerromyjon said:Right angles do occur in nature... plants tend to grow perpendicular to an open, level, flat plain. .
Nautilus shells, fiddlehead ferns, and many other aesthetically pleasing spirals are not generally Fibonacci spirals. This is an unfortunate side effect of the human brain's ability to match superficially similar patterns that are not truly identical. See http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm for a more in-depth discussion of this phenomenon. As zooby noted, the brain's ability to form a type of "equivalence class" of similar patterns may be the motivation for many abstractions such as right angles, but there is not necessarily any individual physical analogue.Danger said:Until eaten...
Zoob, would you then say that the Fibonacci spiral of a nautilus shell or fiddlehead fern isn't a natural occurrence?
The question to ask is whether Fibonacci learned the sequence from nature or simply invented it by following a simple kind of logic. The formulas for many kinds of spirals were arrived at purely by mathematical experimentation, and later it was discovered similar spirals occur in nature. The fact that what was originally a mere invention happened to describe some natural pattern is interesting, but doesn't change its being an invention.Danger said:Zoob, would you then say that the Fibonacci spiral of a nautilus shell or fiddlehead fern isn't a natural occurrence?
Thanks for that link. I've always thought that spiral and the "Golden Mean" were overrated.slider142 said:Nautilus shells, fiddlehead ferns, and many other aesthetically pleasing spirals are not generally Fibonacci spirals. This is an unfortunate side effect of the human brain's ability to match superficially similar patterns that are not truly identical. See http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm for a more in-depth discussion of this phenomenon. As zooby noted, the brain's ability to form a type of "equivalence class" of similar patterns may be the motivation for many abstractions such as right angles, but there is not necessarily any individual physical analogue.
Does that mean the the universe didn't know how to make objects move properly until Galileo discovered f=ma? Does that mean if I didn't have any math (subtraction) to describe my eating of grapes that eating grapes would make more grapes appear in front of me?zoobyshoe said:Saying mathematical truths are discovered is like saying chess truths are discovered. Both statements ignore the fact you're making discoveries about a human mental invention and falsely imply you're making discoveries about nature.
zoki85 said:Becouse I believe human race has unlimited inventive potential.