Origin of Mathematics

[hermes_the_thrice_gr (hermes the thrice great)]

@SideShowBob

I am saying that mathematics is simply a language that orders the universe in a certain way. It is not the universe. The order in the universe has no label.

If you define mathematics as merely the symbols that represent quantities and functions then that is a remedial definition of math. The word RED has no color. It represents color. The color red existed prior to the word red. Man created the word red, he discovered the color red. The word red has no meaning in and of itself. It is arbitrary. It has meaning only because we assign it meaning. The color red does have meaning. It is a real property of nature. It does not need man’s understanding or definition to exist.
The relation between quantities and functions exists in nature. If you observe nature then you observe the relation of quantities and functions. The symbols one uses to represent quantities and functions are as arbitrary as the word used to symbolize red. The color red is inherent in nature. Mathematics is inherent in nature. The symbols one uses to represent either are arbitrary.

but the color red isn’t inherent in nature. You need a word to describe that particular part of the light wave spectrum. Otherwise it is an undifferentiated part of the flow of the world. It exists, but only in a network with all the other colors and “stuff”. These quantities and functions that you speak of, to some extent, do exist, but you do need an active, historically rooted interpreting mental apparatus to separate out the strands. This apparatus is mathematics. It is a sorting machine that labels what it sorts. The labels aren’t inherent.

I will admit perhaps we are talking past each other.

[SideShowBob]

Not to beat a dead horse here but lets be clear about one thing. All symbols or “labels” as you call them whether they be words, mathematical equations, musical notation or whatever, all exist for a singular purpose. Which is for one person to communicate a concept to another person. The concept exist independent of its expression. You say,

but the color red isn’t inherent in nature. You need a word to describe that particular part of the light wave spectrum. Otherwise it is an undifferentiated part of the flow of the world

Nonsense. The frequency of light that we define as red does not need to be defined in order to exist it only needs to be defined if we want to talk about it. You are defining math as the symbols that represent quantities and functions which of course is a creation of man. I define math as the relationship of quantities to functions which is inherent in nature.

The second part of antonios question was

Can there be different types of mathematics

Lets do a simple math problem two different ways and examine this. Lets add the numbers fifty five and eighty nine.

In conventional base ten decimal notation fifty five is represented as 55 and eight nine is represented as 89.

55
89
144

The process used to carry out this function is to begin in the upper right corner and work down and to the left. So we add five and nine to get fourteen, drop down the four, carry the one, and add one, five and eight to get 14 which gives 144.

Now lets do the exact same problem using binary numbers. Fifty five is represented as 00110111 and eighty nine is 01011001

00110111
01011001
10010000

In this process we also begin in the upper right corner and work down and to the left but that is where the similarities end.
1st digit - add one and one which is two. Leave zero and carry the one
2nd digit - add one and one which is two. Leave zero and carry the one
3rd digit - add one and one which is two. Leave zero and carry the one
4th digit - add one and one which is two. Leave zero and carry the one
5th digit - add one, one and one which is three. Leave one and carry one
6th digit - add one and one which is two. Leave zero and carry the one
7th digit - add one and one which is two. Leave zero and carry the one
8th digit - add one and zero which is one. Leave one

Now does this look the same? Absolutely not.
Are they the same? Absolutely yes.

Not only are the symbols different but the process itself is completely different. Nevertheless the result is the same. This is because mathematics is not the symbols that represent quantities and functions. Symbols are arbitrary. Mathematics is the relationship of quantities and functions. This relationship does not change. It has always been. It will always be.

[_removed_by_manageme ([removed by management])]

[contented edited by ILP]

[tmminionman]

Just because we weren’t around to understand it doesn’t mean the relationship wasn’t already there. Things in the universe occur in such a way that we can describe them wiht mathematical laws. Again, us not being around to describe it has no effect on it’s existence.

[_removed_by_manageme ([removed by management])]

[contented edited by ILP]

[chanbengchin]

Mathematics exist because of something inherent in the world as we know it, namely structures or relationships between parts in the natural world.

For example the natural numbers, at its most primitive level is based on the notion of similarity and distinction: ie different things are the same but yet distinct and hence there are different numbers of the same thing. Similarly the notion of position and distance is a relationship between a thing in space to everything else. And in general geometry is an abstraction of physical space, in terms of concepts such as points, lines, surfaces and volumes.

Mathematics is the language for describing such inherent natural structures in our common human experiences.

The more interesting question really is why is it that humans are able to ‘see’ such unseen structures, and to translate that, apparently intuitively, to intangible abstract concepts, like a line or number, and to determine the underlying laws governing their relationships.