Physics goes deeper and sophisticates the field concept. The effort of eminent physicists at the end of XIX and beginnings of XX centuries created the so called Field Theory.
 
Among those scientists Faraday and Einstein conceived the possibility of expressing the whole underlying reality of the Universe by means of a field. But while Faraday saw the world as a field of forces, Einstein saw it as a field of "curved" spaces. According to Einstein forces were a tangible but illusory by-product, of an ultimate reality which was, for him, the space curvature.

Naturally Berkson did not know that when he wrote it and he did not know, either, in later Spanish editions, the field of associated angular factors, as these were established in practice at the beginning of the 90’s, as an attempt to make concrete the philosophy of Chaos Theory applied to Financial Markets.

Before, attempts had been made to create the field of associated angular factors applied fundamentally on the space of related connections (Weyl 1917), other attempts were applied on a variety of those space of related connections in which angles but not distances were kept constant (London 1967) and there were also more modern and of great theoretically brilliant attempts by Wheeler, but without practical results.

Hamilton’s principle, also called the principle of minimal action, it is the most general formulation of the general law of movement which postulates that a whole system which occupies determined positions in a certain moment, moves within these positions in a way that the resulting integral of this movement (the action) takes the minimum possible value.

According to Max Plank, this principle is more general than the "principle of conservation of energy" although the latter is much better known. Plank goes on by saying that "conservation of energy" comes from Hamilton’s principle but not the other way around.

In Newtonian physics, action is contrary to reaction. "Action" is the force exerted by a body to another one, which in turn exerts to the former a force of equal intensity and of contrary sense which is called "reaction".

Continuing in colloquial jargon, a system tends to occupy those contiguous positions in the field, where it has more available space or where space contraction is smaller.

On the contrary, if a system occupies other position with more contracted or with less available space, it can only be caused by dominant tendencies which oblige the system to be there. Yet, when these tendencies disappear, the system will go back to its habitual behaviour ruled by " the law of minimum effort".

3.2.- APPLICATION OF FIELDS OF ANGULAR FACTORS.

The importance of the "fields of associated angular factors" lays, principally, in its practical applications on phenomena ruled by complex oscillatory pattern, represented by means of a curve in a variable scale: equity and corporate charts which reflect the time series of the evolution of a key parameter: monthly cash flow, revenues, margins of products, costs, etc. which allow to extract consequences easily and swiftly, impossible to be detected, in many cases, by conventional methods.

It will be announced, within a short period of time the availability of its practical application to the corporate world, as strategic guide for decision making..

The construction of a "field of associated angular factors" sets off a more profound and general concept than the Cartesian coordinates, because it pretends the geometry of its spaces freely detaches from its own mathematics, without previous restrictive configurations, as it occurs if it sets off from Cartesian axis.

For this:

A / Instead of considering as unitary elements of a length, the aligned elementary lengths 1 and -1, it considers as unitary element the equivalent expression:

Being:

Of the two expressions before, the first uses the radian notation in the exponent to express the turning degrees, and the second uses the sexagesimal expression.

The implicit geometry in the unitary element expression "i power turning degrees divided by ninety", is of the angular browse from any initial position, to the opposite position, or what is the same, the implicit geometry is "a bundle of oriented axis" which opens as a fan, with its origin in the point where the aligned elementary lengths 1 and –1 of the Cartesian conception change sign, that is, the zero point.

In this survey only the Euclidian spaces are considered as underlying, but the generalization of conclusions to the other types of space is immediate, only by considering the following transformation:

Being:

• T = 180  for Euclidean plane spaces.
• T > 180 for Riemann’s closed spaces.
• T < 180 for Lobachevsky’s open spaces.

This would be the general expression of the UNIDIMENSIONAL ANGULAR SPACE, being T/2 , or 90º in Euclidean plane spaces, the angular openness of the bundle of oriented axis from which the negative stretches begins.
Moreover, the separation between both stretches in the real plane delimited by 1, starting position and –1 final position after the T/2º turn, is precisely the zero point of separation between both.

This tells us that the geometry of the implicit plane in the expression : "i power turning degrees, divided by 45" is a square divided in two parts by a dividing diagonal. Remember that if in the unidimensional expression 90 appeared, it was because the 0 point of separation was at 90º of the imaginary turn of the real axis 1 and –1.

Here, in the bidimensional expression, the appearance of 45 indicates that at 45º of the enclosing real axis the zero line of separation of two planes, positive and negative, will be found. In this case, the figure being a square they will be two surfaces in a triangle shape.