On The Symmetry and Calculus of Post-Secondary Education

Here is a concept I have been thinking of for a while now. The basic concept is that the humanities (history, language, etc.) correlate directly when reflected over some imaginary axis to a similar topic in the science/mathematics field (defined for our purposes to include the basic branches of science, mathematics as a whole, and general engineering). In addition, the term "applied" may be used as analogous to the derrivative: ie a method of simplifying a curve or function.

Let us start with what we shall take as our basic functions and what the axis is. The axis, or the line upon which all of this falls shall be the overarching field of philosophy, as is is vague and all-encompassing enough to include all the fields of knowledge. The "functions" that will lie upon this axis are mathematics and language, which may be English or whatever happens to be the lingua franca in the location we are analyzing.

I believe that these fields are in fact asymptotic reflections of each other over some imaginary axis that divides the field of philosophy; that is that these two general, generating functions are relflections that each only inhabit one half of the philosophy axis, never crossing to the other side. This is because these fields form the basis upon which the rest of the fields of study rest, or the language of their related fields of study. Yes, mathematics is a language; it does possess grammer/syntax, sentences (formulas, equations, expressions, inequalities, etc.), and paragraphs or longer works composed of these constituent parts (proofs).

The next step, then, is to ask what happens when one or both of these base "functions" undergoes differentiation. I believe that this is analogous to when the word "applied" is positioned in front of the base field of study. Therefore, the first derrivative of mathematics should be science, as it may be referred to as "applied mathematics" in some circles. It uses mathematics as the language it is described in, but is less concerned with the rigor of proofs in than pure mathematics. This same criteria would then make social studies the first derrivative of language; the social sciences make use of language to convey ideas but do not concern themselves with the workings of language, focusing solely on its use to form and prove an arguement and display facts relating to historical events. Social studies is "applied language."

Now, the question becomes what of the second derivative? What is "applied applied mathematics?" The answer seems obvious: engineering. It is referred to as "applied science" and again focuses on the use of science to design or construct products of some sort. Although science plays a large part in engineering, there is no need for as deep a knowledge in science for engineers; a general or somewhat basic understanding appears to be all that is needed.

This then means there must be a symmetrical second derrivative "applied applied language" on the other end of supposed line dividing philosophy? It may be something such as journalism or communications, but I find this simple conjecture. I claim insufficient knowledge of these fields to make a definitive answer, but I believe they may be the joint second derrivatives of language.

This of course leaves some fields out of the model. I therefore refine my original concept to include an imaginary plane, the arts. Being neither totally in the realm of language or mathematics, the arts would lie on a plane that is related to mathematics and language, but not a part of either and not wholly separate. The list of topics included on this plane could include media/film studies, studio art, music, drama, poetry, etc. I do not claim this to be an exhaustive list, but I do believe it to be a partial list that outlines what would exist in this plane.

With this, I complete my survey of the symmetry and calculus of post-secondary education.