Topic: Serious Discussion / The most beautiful equation / Math-reality connection

Originally posted byLaxaria:Since you do not have a significant answer, let me try to speculate. :)

With my general distaste and dislike of Mathematics, I primary consider Math to describe reality (a physical reality) rather than to explain it. As far as I am aware, Mathematics concerns itself with patterns and equations, many of which are used to describe a situation rather than to explain the occurrence. For example, the sine and cosine functions describe relationships of right-angled triangles, but do not necessarily explain why these relationships exist. Mathematics could explain why these relationships exist, but the utilisation of Mathematical proof to explain Mathematical proof does not provide the best means of explanation; it might be more effective to use a different medium, which is extremely difficult given the abstract nature of Mathematics.

Furthermore, Mathematics itself tends to base itself on pre-set axioms and acceptances, on which the framework Mathematics as a field depends on. The abstract nature of Mathematics makes it more adequate as a descriptive language rather than an explanatory one. It could easily describe patterns, fractals, population growth and probability, but it is not as capable of explaining why any of these things happen. Mathematics can describe the occurrences of Fractal Patterns in Nature, even providing Mathematical means of replicating them, but can Mathematics explain the origin of these Fractal Patterns?

As far as I am aware of, Mathematics probably does a better describing reality than explaining it. I suppose one of the underlying differences between Physics and Mathematics is that Physics tries to go beyond Mathematical proof to explain an occurrence. The Newton Laws of Forces could be described Mathematically, but would require some Physics to explain how it works. Numbers can elaborate on the interactions and relationships between forces, but is it able to explain why the interactions exist? I am less inclined to believe it can.

My perception is not set in stone, but heavily influence by my dislike of Mathematics. I have no doubt it is a beautiful thing, but I am not as impressed by its beauty as Music or Art, which, I suppose, as any Mathematician would say, both Music and Art depend on mathematics.

On a side note, I would be interested in understanding how to derive Euler’s equation. I’m definitely not a professional Mathematician, nor one trained beyond rudimentary Mathematics compared to the professionals, but I have been interested in the idea, having come across it in my IB Portfolio work.

You say that Physics attempts to explain an occurrence, however what the laws of physics are just the same as the laws of mathematics, only in Physics they generally have an application that is less theoretical than that of mathematics.

For example, Pythagoras’ law explaining the relationship between the angles and lengths of a right angled triangle is merely an observation that all triangles follow a certain law.

Newton’s Second Law of Motion, F=ma, or rather the acceleration of an object is equal to the quotient of the applied force and mass of the object, is also merely an observation of a law that nature appears to follow. I don’t believe that this really explains /why/ this law exists, it’s just the relation between these quantities.

Anyway, as for the equation itself, my Euler’s is a little rusty. I can see this equation describes the unit circle of the imaginary plane, but I feel that that description does the equation no justice.