Static and Dynamic Chaos
Order and Chaos
Of ferman: Fernando Mancebo Rodr�guez ----- Personal page And Version espa�ola

Se puede ver resumenes de mis principales trabajos en las siguientes p�ginas:

Model of Cosmos ||| Atomic model||| Speed of Forces ||| Magnet : N-S Magnetic Polarity ||| Chaos
Radial coordinates||| Theory on the physical and mathematical sets | Algebraic product of sets.||| Planar angles: Trimetry |||
Properties of division
Spherical Molecules ||| Metaphysics (Spanish) ||| In Genetic Heredity ||| Brain and Consciousness
Rotary Engine ||| Andalusian Roof Tile
The Garbage Triangle : Quantum mechanics, Relativity and Standard Theory ||| Nuclei of galaxies
||| Formation of water, hydrocarbons and life principles on the Earth. |||Cosmos' Formula : (metaphysics) ||| Chaos fecundity. Symbiosis: from chaos to Evolution

Static and Dynamic Chaos
Order and Chaos

Let�s remember firstly the definition of Chaos in Structural Cosmology:

"Chaos is the interaction among autonomous elements or subsets when they stay and move in the same vital space".

(So at first, all interaction or interrelation among elements can be considered initially as a chaotic state, although later on could be necessary to analyze its chaotic degree.
In this sense and in my set theory, three integration degrees of symbiosis of the set elements are given, which go from the scrappily set (where no symbiotic relation seems to exist) to the fusion set where a total integration or symbiosis exists, and the elements already form a much defined physical body.)

That is to say, for creating a chaotic state firstly we need the existence of elements with autonomy and own characteristics, and second that these elements can have interaction among them.
Of this previous explanation we also take out diverse queries that later will try of clarifying.
The most important would be respect to if chaos is a human appreciation only, or if chaos really has physical consistency.

The observable Chaos

A first consideration to keep in mind is that chaos besides being a physical reality that takes place when all the elements of a group are disconnected some from other and they don't keep any type of structural relationship among them, but also chaos in some way is a subjective consideration of the people that observe these set.
Now then, the study of the physical reality would be very difficult and not very useful for us because we would never arrive to observe the physical reality in all their points.
For it, we study the subjective chaos that includes to the real physical chaos and also to the subjective chaos observable for us.

Therefore we should accept ahead of time that our measures are relative or observables measures due to the used units are not completely physical, but conceptual units that are adapted to our understanding.

This way in the static chaos we will see that one ( 1 ) chaotic degree represents the total chaos of the elements of the group and one ( 1 ) order degree represents the total order of the elements of the group.

Classes of Chaos

We will consider two types or characteristic of Chaos that will be the Static Chaos and the Dynamic Chaos.

As their names tell us, the Static Chaos will be given when the elements of the group to consider don't have motion.
You can also consider as static chaos to an instantaneous picture "photo" from a dynamic chaos that is taken for its study and consideration as static chaos.

On the other hand the Dynamic Chaos takes place when the elements of a group move inside the same one, and this way, another type of chaos take place that is the Fluctuation Chaos.
Here the important thing it is not the form and structure that the elements keep among them, but the change of mobility or fluctuation that each one of these elements can have regarding to the other ones.
This way if two elements coming closer one to other and they collide or they are simply rejected themselves changing of direction or speed, we say that what it happened is a double fluctuation due two element have changed of direction or speed.

Static Chaos

The static chaos has an important subjective component, say, that we can consider that a set of elements has chaotic consistency ( or not ) for the simple reason that its elements form figures, lines, etc. always from our point observation, although they could not represent any real physical ordination or coordination.
If for example in any paper we see several separate letters ( u s h e o ) we can say that they form a chaotic set.
But if we unite the letters and we form the orderly word ( h o u s e ) then we say that this set of letters forms an orderly set and no chaotic.
On the other hand if the word is in Chinese, for us the word could follow been quite chaotic. But this is a subjective idea of us, because from the physical point of view both states of the set should have the same consideration.

Now then, although they are subjective forms of observation, for us it is necessary to find methods of measure of these chaotic concepts.

And for it, I expose the following formula:


Previously we have seen two antagonistic concepts, Order and Chaos.
Order represents to the total integration and ordination of elements of the group and Chaos represents the total disintegration and disorder of the same one.
This parallel study is important since when we change the structure of the set, we can realize that what one of the concepts win is lost by the other one: When chaos diminishes � order increases, and vice verse.
Because well, here we have put some very simple formulas that I believe they fit inside the subjective concept that we are giving to this study of Chaos and Order.

In this case the Order is represented by the formula 1/n where n is the number of resultant elements after the integration and ordination of the set.

And Chaos is represented by the formula n-1 / N where n continues being the number of integrated elements and N the total number of initial elements.

In the case that we put previously (house), firstly we would have a set with five disordered elements (( u s h e o )) and after the integration of the letters with obtain a single element (( h o u s e )).
In this case the application of the order formula would be:

Before the integration: (( u s h e o )) 5 elements.

1 / 5 = 0,2 Od ordination degrees

And after the integration: (( h o u s e )) 1 integrated element.

1 / 1 = 1 Od.

--------------------- And as for the Chaos we would have that:

Before the integration: (( u s h e o )) 5 elements.

5-1 / 5 = 0,8 Chd chaotic degrees

And after the integration: (( h o u s e )) 1 integrate element.

1-1 / 5 = 0 Chd.

On the other hand in the static chaos we don't consider to space and time as parameter that intervene in the same one.
In the previous example it doesn't care if the letters are small or giant, or if the set formed during one minute or one year.

Dynamic Chaos

As we have said, the Dynamic Chaos has different characteristics than the Static Chaos since here what interests us it is the changes of motion of the elements that it will produce us that idea of Chaos of the motion.
Now then, in the dynamic chaos as in the static one a subjective great component exists, since perception of motion depend on our observation capacity.
Therefore here we say that the dynamic chaos is the one taken place by the motion changes or fluctuations that can be OBSERVABLE for us.
If the change is so small that we don't appreciate them clearly, this change won't produce us any chaos sensation, and therefore we don't consider it as chaos. Now then, if we can observe it by means of instruments or devices, or we simply want to make it to theoretical title, then yes, we can use any fluctuation for small that is.

To explain and to measure the dynamic chaos I have put the following formula:


As we see this formula it is also extremely simple. Where F is the fluctuation coefficient or number of fluctuations for cubic meter and second.
F is the number of fluctuations measured in a set; V is the volume where the measure is taken; and T is the time during which the measure is made.
The dynamic chaos is relative and dependent of space and time, in fact because the motion is carried out inside the space and during certain time.

In the dynamic chaos the purpose is to measure and consider the movement changes, and therefore, to these changes we call them fluctuations.
And it is in fact the measure of the fluctuations taken place in a set what we try to measure with the formula.
So the formula represents to the coefficient of fluctuation of the elements of a set, say, the number of fluctuations inside a set that are considered by unit of volume and time.
To the unit, which we will call Flu, it will be when a fluctuation takes place per second in a volume of a cubic meter.
Nevertheless, the fluctuations can also be measured in surfaces o areas, in this case by square meter. Flus = Fluct/m2/s.