Are you a Mandel-bro?

in mandelbrot •  last month 

Humans seem to do this thing where they create explanations for the unexplained, and like to see patterns in nature. Often, these explanations, while quite creative, are built on many often untested assumptions. The Mandelbrot set is a perfect demonstration of this phenomenon.


source: https://www.publicdomainpictures.net/en/

What is the Mandelbrot set, you may ask? Well, imagine a graph with an x and y axis where the x axis depicts real numbers and the y axis depicts imaginary numbers. Then, you're given an equation with which to chart points on the graph but you only chart them as solutions to the equation if the outputs tend to hover around a number as opposed to continuing on forever. I'd give the equation here, but it is not really relevant to the point at hand. So, you graph these points, and some eye-catching siren of mathematics has now been discovered. Now, instead of dancing around a wooden totem, the Mandel-bro dances around a fractal totem. Problem? Well, maybe. One can easily attempt to derive meaning in a concept that is built upon mathematical principles that are actually quite presumptive in nature. Imaginary numbers (which the Mandelbrot set depends on), are built upon a strange assumption: the existence of negative numbers. The negative number is a concept that, while useful in mathematics, is logically impossible. Don't think so?

How can one be said to be in possession of -3 apples? If -3 apples cannot exist, then its square root (an imaginary number) cannot exist either. Some will claim that negative numbers are important in order to indicate debt, or obligation. The quantities argued in a debt still exist somewhere (if I have gone into debt, then I am either in possession of the money owed to the other [which means it is not negative money], or I have given it to someone else). As far as the system is concerned, the money still exists and the negative number is being used to imply obligation. What about in the case where a thing is actually destroyed? Say, instead of loaning an individual money, I just burn it. Now there are fewer dollars in circulation indeed. The change in the money supply from before to after the burning could be measured, but why should we denote it with the negative sign and differentiate it from other quantities? It is fairly arbitrary that we have chosen to assign the expression of debt or loss as being indicated with a negative sign in front, though it provides utility. Loss occurs in quantities, and we have assigned loss the quality of being negative. Does nature appear to operate according to these principles? If it does not, then the Mandelbrot set is not a very useful or accurate representation to describe our natural world at all. What other concoctions have we devised to derive divisive distinctions from in an attempt to placate the mind's wanderings? Are we all doomed to be Mandel-bros attending the fractal frat party of muscle-bound assumptions?

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That is one branch of interpreting this piece, and a valid one. Nice insight.

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