The 4 elements and magical work

[Aion]

What I think most all of these systems are is simply a breaking down of an infinite spectrum into more finite and workable bite sized chunks. For example, you can define an infinite range of frequency of light or sound or thought, but it is a lot for the mind to deal with. So we have a rainbow of seven basic colors to concentrate on which makes it a bit more manageable and comprehensible. Same goes for the system of elements, it is just a breaking down of an infinite continuum into some core metaphysical ideas and concepts. Perhaps similar to the idea of "primary colors" by which by understanding the interaction of such can produce the other colors.

So is any analogy necessarily wrong? No, there are various advantages and disadvantages to any conceptualization no matter how well thought out. It is like a metaphysical system of math (which is less specifically defined than real math), by which you can roughly deduce or calculate another implied manifestation given a certain interaction. This is my understanding of the tarot, astrology, and tree of life.  
I think this topic is of a similar nature.

Pretty close to my own thoughts although I would actually argue it can be MORE specific than 'real math' since it can venture in to qualities more easily than regular mathematics.

My analogy would be that of chemistry. The elements are the elements and can be mixed in many ways. Some will find they come to the same results but maybe through a different process or maybe someone creates an 'isotope' or modified version of what is almost the same but a little different. I think the whole process of creating magical 'formulae' is to mix and match all the elements of the self together in order to achieve or realize certain balances between them and thereby allow them to grow. Just like in chemistry, however, I think that if you hit certain combinations they are "non-reversable" and these are the acts of initiation that magic, meditation and prayer work towards realizing. So, just finding the right formula for yourself is a process of self-refinement because you are the formula.

As the alchemists would say, 'the greatest experiment is the alchemist themselves'.