Hi Joseph,
*Mathematics works only in perfection, i.e., the concept of a perfect circle or a perfect square, or a perfect two (2+2=4). For example, a perfect circle (C = 2PiR) nowhere exists outside of the human construct. Every circle in nature fails to be "perfect" at some degree of measurement, be it atomic or subatomic.*
I'm having some trouble understanding how you define 'perfect'. At first it appears that your definition of 'perfection' is that which conforms to the rules of a formal system, however fractals can be derived from mathematical formal systems and so can many different shapes other than circles. So, given a sufficiently complex enough algorithm, one should be able to derive a fractal that looks 'real-life' and could perhaps even fool many of us as to whether it was picture taken by a bystander or generated by a computer. In fact, if I understand it correctly, many of the realistic simulation programs now being developed by software companies use fractal equations to develop 'real-life' scenes.
Which raises the question, what does it mean for something to be perfect in a mathematical sense. Perhaps it means to be more simplistic, governed by formal rules? For example, a line is simplistic, and governed by formal rules, and has a sense of 'perfection' to it. What about that idea?
*Therefore mathematics, modeling the universe with "perfect" concepts, is a faulty tool for describing an imperfect universe.*
The problem here is an extension of the good software simulation tools. That is, if simulation tools can simulate a world that looks like ours using rules of mathematics (or rules of computer programs), then at what point does the perfection of mathematics give way to 'imperfect' standards that more accurately describe our world?
I think the term perfect probably is one of those univocal terms that cannot be used to cover all aspects of perfection. Rather, perfection means many things at many times, and perhaps it is an idealized state of the way things appear, but I don't know if we can take it so far as to say that it stems from mathematics, etc. I think the only valid answer is that it stems from the human mind in terms of idealizations of things that seem 'close to perfect' but are still lacking. |