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sonicelectron
Hi everyone, I'm new here so, hello. I guess for my first thread, I'd like to ask whoever thinks math is invented, how do they define "invented"?
sonicelectron said:Hi everyone, I'm new here so, hello. I guess for my first thread, I'd like to ask whoever thinks math is invented, how do they define "invented"?
berkeman said:Welcome to the PF.
What is your background in math? What year are you in school? Are you familiar with Peano's Axioms?
http://en.wikipedia.org/wiki/Peano_axioms
That's a good place to start to understand the basis of mathematics IMO.
In this context "invented" means created by humans for humans, but based on principles existing in nature.sonicelectron said:Hi everyone, I'm new here so, hello. I guess for my first thread, I'd like to ask whoever thinks math is invented, how do they define "invented"?
zoobyshoe said:In this context "invented" means created by humans for humans, but based on principles existing in nature.
The simple act of counting is an invention. Things aren't counted in nature, they aren't assigned a number between zero and whatever upper limit is operative. The whole notion of keeping a tally is a human one.
sonicelectron said:Thanks for the response. Is there a context in which you think "mathematics" leans more towards discovery than a human creation?
Well, your opening post asks for responses from people who think it's an invention.sonicelectron said:So basically, correct me if I'm wrong (it's late), what I'm seeing here so far is that math is merely a set a tools and curiosities created by humans.
zoobyshoe said:Well, your opening post asks for responses from people who think it's an invention.
Medicol said:Mathematics was "invented".
http://en.wikipedia.org/wiki/History_of_mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics
I don't think it's an exercise in semantics. It's very easy to feel that Nature is built on mathematics, that the fundamental relationship of everything to everything else is mathematical. I believe it was Galileo who concluded (something like): "God is a mathematician!" Newton seemed to agree.phinds said:I think your attempt to categorize math as discovered or invented is just an exercise in semantics and not particularly helpful. Those words tend to get very fuzzy sometimes.
http://en.wikipedia.org/wiki/PythagorasThe so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.
—Aristotle, Metaphysics 1–5 , cc. 350 BC
zoobyshoe said:I don't think it's an exercise in semantics. It's very easy to feel that Nature is built on mathematics, that the fundamental relationship of everything to everything else is mathematical. I believe it was Galileo who concluded (something like): "God is a mathematician!" Newton seemed to agree.
My post was about what semantics has to do with feeling, not mathematics.mal4mac said:What does mathematics have to do with feeling?
phinds said:I think your attempt to categorize math as discovered or invented is just an exercise in semantics...
homeomorphic said:Think about tic-tac-toe. The rules are made up, but initially, it might not be obvious that the first player can always win or draw if the opponent plays right. You DISCOVER that you can always draw because you didn't know it at first. It doesn't make sense to me to say that we invented the fact that you can always draw.
So, we invent the axioms, perhaps, we invent the rules of deduction, but theorems are discovered, if you are going to use the terms invented and discovered in a way that makes sense to me, at least.
SteamKing said:IMO, all knowledge is a human creation.
What if the guy who invented tic-tac-toe started out by trying to invent a game in which optimal players would always draw? Subsequent players might discover they can only draw, but this "feature" was actually invented.
I guess that a theist could argue that theorems are invented by God. Atheists suggest that in an infinite multiverse all possible theorems are created. So no human inventor is needed. But then you might say, speaking a bit loosely, that "the universe" invented the theorems. But it took humans to disover them. So they are invented and discovered!
So, I disagree. The universe invented the axioms, rules of deduction, and theorems. But we discovered them.
Earlier when I said "...Edison discovered sound could be recorded," I would hope everyone realized this was a strained use of the word "discover". Of course, he had to make some sort of discovery about the physics of sound before he could invent a sound recording machine, but his accomplishment lies in inventing a practical way to do it. Since his time many more practical ways of recording sound have been invented. It's been recorded optically, magnetically, and now digitally. These are human inventions because there is no digitally recorded sound out there to be discovered in nature. Recorded sound was invented by man for man.homeomorphic said:Invention suggests freedom to choose. If that's what invented means, no, it's not completely invented. But maybe you allow for some restrictions, as with inventing a new gadget, in order to get it to work properly. Discovery is a term that evokes comparisons with scientific discoveries. In spirit, I think it's more like discovery, to my mind.
zoobyshoe said:The simple act of counting is an invention. Things aren't counted in nature, they aren't assigned a number between zero and whatever upper limit is operative. The whole notion of keeping a tally is a human one.
OK, but do humans count things because they observed DNA keeping track of the number of fingers we have? Is counting something we discovered in nature and copied?PeroK said:One could argue that the number of fingers is encoded in DNA and, although there is no conscious counting going on, nature is in a sense keeping track of how many fingers we have. And, recording this in the DNA.
There are some amazing mathematical patterns found occurring naturally. This is excellent fuel for the thinkers who conclude math is the foundation of Nature/The Universe, and that we merely discover it.And, of course, the Fibonacci numbers tend to crop up in nature.
I look at the sky at night once in a while and have never observed an ellipse up there. It took man thousands of years of observation and measurement to realize the shape of an ellipse is implied in orbits and to invent the tools whereby that implication can be treated as a static geometric fact, and the motion analyzed: "Equal areas are swept in equal times," and so on. IMO it's invention to make use of models for things we can't directly observe.And, the planets orbit in ellipses. Even if the precise, mathematical definition of an ellipse is a human invention; the underlying shape is found in nature.
zoobyshoe said:There are some amazing mathematical patterns found occurring naturally. This is excellent fuel for the thinkers who conclude math is the foundation of Nature/The Universe, and that we merely discover it
Math is a language made to simplify the physics around us, and to make trading an easy job.In addition to this, math does exist by nature but we are who conclude it; between parenthesis WE INVENT.sonicelectron said:Hi everyone, I'm new here so, hello. I guess for my first thread, I'd like to ask whoever thinks math is invented, how do they define "invented"?
I'm confused. The "language" is being spoken by whom or what? Are you saying Nature is speaking when a fibonacci sequence turns up in a plant seed pod?Pythagorean said:If we take mathematics to be a highly accurate language (and the system of rules for interpreting that language) the patterns are themselves just semantic representations of the thing they describe. Much like the word "organism" is not actually an organism.
zoobyshoe said:I'm confused. The "language" is being spoken by whom or what? Are you saying Nature is speaking when a fibonacci sequence turns up in a plant seed pod?
So, you're saying math is neither invention nor discovery. It's language.Pythagorean said:Humans. Humans use the fibbonacci sequence as one way to represent what turns up in nature.