Is the world mathematical?
20:53
If you’ve done high school trigonometry and high school physics, you probably have heard of the sine function. For those of you don’t know, it is a function, which takes in an angle as a parameter and returns the value of the opposite side divided by the hypotenuse in a right triangle amongst other things. In a right triangle with an angles A, B and C, sin (A) = BC/hypotenuse. Like other functions, this function can be plotted on a graph of sin(x) against x. The resultant graph would be a wave. A curvy, mundane looking wave. Look closely, and it may look familiar. It’s the exact same as the graphical representation of a particles displacement against time. Triangle ratios and light seem completely arbitrary, yet have the same representative function. How? Well, as statements get more and more specific, their monumentality diminishes. If a statement affects a large group of people, it is important. If it is too specific, it’s not. The sine problem may sound eerily crazy, until you question its foundation. Look at the graph. It is most likely a Cartesian plane with linear x and y axis scales, with unit increments. Fine, on a 2 dimensional plane with linear scales on the axes, the sine function has these characteristics. This does not sound all that amazing anymore, because linear scales are just one of the many out there. Logarithmic, exponential, and the ones we haven’t even discovered yet. There could be ones that aren’t even compatible with our numbering system.
This brings up the question, what is mathematical? What makes something mathematical? With the right numeral system, anything can be possible. A sine function on a graph with a linear y axis and exponential x axis creates a strange irregular wave. So if math can be bent willfully, what is left? Well, that’s hard to tell. Math, in my opinion, is a fruit of abstract thought. Where it does draw inspiration from nature, it is an independent entity, whose sheer flexibility, makes it unsurprisingly ubiquitous. So in conclusion, yes, the world is mathematical, but no, that’s no mind blowing.
On the flipside, the number system, that seems to align itself so well with nature, has a major chink in its armor. Pi, a value essential to the mensuration of the circle, remains irrational*.
*probably
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