Throughout the entire mankind's existence, the properties of Nature, without exception, were discovered through observations and experiments which were catalogued and classified in accordance with certain patterns that were noted to exist. To each such pattern discovered, hypotheses were associated which were further refined and tested to determine whether a logical link could be established among such hypotheses and whether they could be reduced to an underlying common denominator. Physical theories of Nature were born out of such intellectual processes. Isaac Newton in a letter written in 1672 to Henry Oldenberg, the Secretary of the Royal Society articulated this process of discovering 'things' in Nature as follows:

"For the best and safest method of philosophizing seems to be, first diligently to investigate the properties of things and establish them by experiment, and then to seek hypotheses to explain them. For hypotheses ought to be fitted merely to explain the properties of things and not attempt to predetermine them except in so far as they can be an aid to experiments. If any one offers conjectures about the truth of things from the mere possibility of hypotheses, I do not see how anything certain can be determined in any science; for it is always possible to contrive hypotheses, one after another, which are found rich in new tribulations. Wherefore I judged that one should abstain from considering hypotheses as from a fallacious argument, and that the force of their opposition must be removed, that one may arrive at a maturer and more general explanation."

The experimental and observational method employed in Physics, reached an insurmountable impasse when it arrived at studying the atomic and subatomic worlds. It was Werner Heisenberg who recognized first, in a brilliant fashion, this inherent limitation posed by Classical Physics in studying the atom and its structure. The problem, as Heisenberg noted, was that when we perform experiments at the atomic and subatomic level, regardless how careful we are, we will create and introduce large and uncontrollable perturbations, making therefore the results and the data obtained highly unreliable. According to this realization, our very presence will generate uncontrollable large perturbations which will distort so much the data obtained that it will make meaningless the entire result obtained from any given experiment. This realization and recognition of the inherent "interaction between observer and object" which later evolved into Heisenberg's famous uncertainty (or indeterminacy) principle was articulated by him as follows in his now classic book "The Physical Principles of the Quantum Theory" (Dover Publications, 1949, p. 3):

"... in classical physical theories it has always been assumed either that this interaction is negligibly small, or else that its effect can be eliminated from the result by calculations based on 'control' experiments. This assumption is not permissible in atomic physics; the interaction between observer and object causes uncontrollable and large changes in the system being observed.
... The immediate consequence of this circumstance is that in general every experiment performed to determine some numerical quantity renders the knowledge of others illusory, since the uncontrollable perturbation of the observed system alters the values of previously determined quantities." [Emphasis supplied.]

This profound realization and dilemma recognized by Heisenberg that an observer, through the observer's very existence, will create at the atomic and subatomic level large and uncontrollable perturbations, regardless how careful the experiment is set, would lead a rational person to the unavoidable conclusion that experiments at the atomic and subatomic levels are useless since their results and data obtained are highly corrupted by being uncontrollably distorted. But if this is so, then what our method of discovering 'things' at the atomic and subatomic level ought to be?

Well, looking 'around' for inspiration, we are immediately struck by the elegance and the reliability of the method employed by Mathematics in discovering 'things' and thus, it become irresistible not to take a closer look at the general method upon which Mathematics derives its results and see how could we emulate the method of discovering results in Mathematics for Physics. We begin with this analysis in our next section so, if you are ready, let us proceed.

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