Abstract pyramid of mathematical expressions

Abstract Pyramid of Mathematical Expressions
and Their Techniques of Solution

Pyramid of organizations is basic to all phenomenas:its the only pattern in which complexities occurred,even in idealized,abstract mathematics.Particles,molecules etc also takes this pyramid form,although in a rough,fuzzy pattern,which approximate the idealized version of mathematics.For the purpose of understanding,it suffices that the pattern exist,one can deduce/guess the rough outlines from the idealized,abstract case.

Without such correlation between the abstract and the empirical cases,one is reduced to a mapless treatment of each and every empiricalcase by itself:the world of particles by itself,the world of molecules by itself,the world of circuit by itself etc.One has to learn each field without carry over to other fields,rather treating each field as mere empiricalcases of the idealized,abstract case.

Thus for the purpose of simplicity,onemust assume,even forceably,that each empirical case is merely a rough form of the abstract,general case of mathematics.
Mathematical espresssions can be organized into a pyramid–an idealized grand ultimate of abstract elements–whose apex is the set of positive and negative intergers.More complex expression lower on the pyramid hierachy is systematically build up from the four operations of addition,substraction,multiplication,division perfromed upon the polar/binary number/integers and up to (x,y) class of unknowns in equations of infinite degree and numbers.And further complexities integration/differentiation performed upon equestions of unknowns to even more complex expressions of matrix of intgral/differentil equations.Such a pyramid of mathematical expressions,whose apex is zero,next lower the positive/negative integers and so on to more complex ones build up by the 4 operations of addition etc,and the binary integration/differentiation to matrix form,should encompassed,exhaust all possible know expressions.Any future mathematical operations should also fall ino this pyramid scheme.
If such a pyramid of mathematical expresions expressions exist,what use is it?For one,it certainly help to have things organized,each in its place.more important,one can generate any complex expressions from the most basic elements-integersusing the 4 operations of addition etc.Generation of complexities-expressions has its polar form of destruction....generation/destruction...What is destruction mathematically?Its normally called solution or solving a expression of equation;or moving up toward the apex of the pyramid where the simpler form exist,wwhich is consider the solution to a equation:preferably some integer,or a simpler form of expression.Generation is fro simple/basic to complex,destruction or solution is from complex to simple:moving up and down the pyraamid of mathematical expressions.
If all these sound like hogwash,its sstill a superb mnemonic device not to be ignored.Besides its so mystical,fascinating order.one has to keep this orderly arrangement like it or not.Exact mathematical proofs await the professional.
Solving an equation,or destruction of complex expression,or techniques of solving equations as normally called.Various methods of solution to any expression or an attempt to move toward the apex or climbing the hierachy of expressions toward the simplest or a numerical form.Example;a second degree equation has as one method the com[leting the square,or replacing decond degree expression with a product of two one-degree expression.Climbing the rungs of the pyramid of simpler expression and finally toward a numerical solution near the top apex,so to speak.This is done by the identity o,1 or its equivalents in expressions.
Since the empirical cases of molecules,circuits seemed analogous to the abstract mathematical,ideal case;does these manipulation of solving equations have analogous counterpart in the empirical cases?That is,what meaning is there to ask,”What is the equivalent of solving equation in chemistry?”or in circuit?Climbing up and down the pyramid of expression seem like a nice idea.Is there similar climbing up and down the pyramid of chemical table,of polar acid/base,if circuit analysis?
Written ‘84 yama
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