If someone has a desire to understand some physical realities such as the reality of electric charge or the reality of matter, energy, and force. How does one begins?(adsbygoogle = window.adsbygoogle || []).push({});

One can start by using simple operations of addition and subtraction. By the use of experimentation, one finds that these realities can be quantified by the use of just simple addition and subtraction. Further, one finds that addition can be applied to scalar quantities and vector quantities but subtraction can only be applied to vector quantities. It is the inherent directional property of vector that makes them subtractable.

The reason why scalar quantities with the exception of the numeral "zero" can be added is the existence of a smallest quantum. This is the unity of all unities of numbers.

Then it turns out that nature is much more complex than what was originally thought. Because different realities can also be put into a comparison of relativeness. The introduction of fractions is a way of doing comparison between the different realities. But the ratio of two identical reality is a unitless or, properly, dimensionless quantity called a pure number and again, this is just the return of the good old scalar quantities. When numbers are ratiod, the creation of more varieties of number: algebraic, the transcendental, trigonometric, etc.

Then later the fractions turn out that they can be approaching values of zero and infinity and in-between the rationals and the irrationals, leading to the invention of the theory of limits, infinitesimal calculus, integral, differential, algebraic equations, infinite series, complex number, hypercomplex, etc. Math begins a transformation into a very specialized subject that necessitated many years of study and research and specialization.

The sad thing is that the questions of what is an electric charge or what is matter remain to be satisfactorily answered not by math but by new physical insight.

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