“So… what’s your major?”
“Math.”
“…Oh.”
‘Oh’ is pretty much all I say; I think it would be rude of me to point and laugh and yell, “WHY STUDY SOMETHING THAT DOESN’T EVEN EXIST!?” Yet for all the people studying it, for all the uses we’ve found for it, and all the faith we placed it in, the concept of mathematics is based on a suspiciously shaky foundation: numbers.
Numbers are so normal, so ordinary, so ingrained that nobody thinks to question their existence; and yet I wonder: do numbers exist? When you count three dogs, the dogs exist and the number is an adjective. When you write ’3′ the numeral exists there on your paper. But what of the actual number three? Two? One? There is no such thing as a one.
Yet here people would protest that it exists as a concept; it may not be tangible, but then, what ideas are? Clearly math cannot be an arbitrary set of rules and principles, else it wouldn’t be so universal. So it exists in our minds. Descartes’s famous ‘cogito ergo sum’ seems appropriate;we think it, therefore it exists. But what if there was no human life left to think numbers into existence?
Many thinkers, more well-known, qualified, and intelligent than myself, have pondered the existence of numbers without coming to a satisfactoy conclusion. To me this crisis of identity, although worrisome to some of us who think too hard. stands as a testament to the power of the human consciousness. Mathematics as a self-existent field of study is uniquely manmade, of equal parts necessity and innovation. By virtue of its basis in nothing but itself, it intrinsically gains the freedom of being bound only by itself.
And therein I find at least one fiber connecting the realms of math and art. Art is aesthetics; aesthetics are independently defined, with no laws to govern right from wrong. While it is true the attractiveness is partially biological–we seek traits in mates that are advantageous, for example–that is simply one schematic of appraisal. Just as geometry can break free of its Euclidean roots, the evolution of artistic appreciation beyond the ‘norm’ is the essence of the similarity between art and math.
This perhaps is why I don’t regard math as a ‘regular’ science. The sciences concern themselves with sets of rules and laws to govern the world. For those worlds that exist, this creates a natural limitation. For the world of numbers, imaginary as they are, there is no such barrier. This places mathematics into a sort of intersectional limbo, with both roots and branches so far-reaching, its ubiquity transcends that of any other language. It is clearly present in the other realms of science; field theory, for example, is nearly purely mathematical. Equally is it present in the artistic world, where even aesthetics will recognize the significance of phi.
Who needs a third culture when you have math?
Here’s some people who are a lot smarter than me discussing math. It’s really quite interesting:
http://www.blackwell-synergy.com/doi/pdf/10.1111/1467-9213.00079
http://www.math.hawaii.edu/~lee/exist.html
http://platosheaven.blogspot.com/2005/12/do-numbers-exist.html
