T R U T O N
by Kalman Klim Brattman
"Give me matter, and I will construct a world out of it."
Immanuel Kant, Kant's Cosmology
("Universal Natural History and Theory Of Heavens ")
3. On the Absolute Fix Space and the Absolute Time Variable in Nature

 

The primeval Level of Organization Of Nature (the primeval LOON) has been portrayed as consisting of XB-blocks gliding in the limitless XV-space of Nature. The gliding motion is another name for the linear translatory motion of constant speed --a motion that represents the simplest, and thus the default motion in Nature.

A motion to be well-defined must be referenced to a particular frame of reference which in turn must exist into a well-defined space. A well-defined space in Nature is a space where both its mathematical and its physical structure are well-defined.
  • A mathematical structure of a space is defined through the definition of the distance between any two points in that respective space, i.e., through its metric. If the distance between any two points in a particular space is measured through a straight line, we say that the respective space has an Euclidean structure or that its metric is Euclidean. If, to the contrary, the metric of a space is not derived from a straight line, we say that respective space is a non-linear or non-Euclidean space. An example of a non-Euclidean space is the Riemannian space.
  • A physical structure or the background of a space is defined as the physical medium or the physical "arena of existence" of that geometric space.

Motions, from another viewpoint, could also be classified as relative or absolute. For the absolute motions (that are the motions that we deal with in the primeval LOON), we need to have defined an absolute fix frame of reference imbedded into a well-defined absolute immobile physical space. And that is provided below when we tackle the space concept employed in TRUTON. The material space cocept will further be detailed below.

Asides from space, another fundamental concept that cannot be separated from motion is the concept of time. That is because all motions take place at particular times and are characterized by a duration or a distance in time. So asides from a spatial distance, we can talk also about a distance in time. The time concept will also be expanded in here, below.

Last, but not least, the motion cannot be separated from the concept of energy. That is because something that moves is said to have "active" energy --the energy of motion known as the kinetic energy. We also can have "dormant" energy known as the potential energy that is a locked-up or stored active energy, i.e., an active energy that is not able to manifest its existence as a motion due to a constrain or constrains placed on it. Following this "classic" line in describing energy we cannot answer what energy is. To understand its foundational nature, we will begin --like all the beginnings in TRUTON-- from examining the primeval LOON. That study of the energy concept is done separately in a subsequent section.

The three concepts just noted --space, time, and energy associated with motion are said to be foundational concepts in the sense that they create the foundation or the background upon which all dynamics of Nature can be formulated with. They represent indeed the background (or the basic) concepts of Nature referred through the BACONs acronym.
To not offend our observant Jewish or Muslim readers for whom the 'bacon' is a forbidden food, we note that those three BACONs that represent the three foundational concepts of Nature transcend over all boundaries of Nature and as such, they are also called the transphysical concepts of Nature or in short the transphysicals.

The origin of the transphysicals spring from the observed physical entities of Nature that are being converted into conceptualizations, through our abstract rational thinking (ART), that evolved with the biological evolution of the human brain. However, with that evolution of the human brain, a potential mortal danger for ART began to emerge in the course of the human brain evolution.
The potential mortal danger threatening our abstract rational thinking (ART) tool in deciphering the secrets of Nature has been that ART was no longer the only player available to the human brain. Another two major lethal players become also available to the human mind for its abstract thinking: one, the Irrational Thinking; and the other, the Speculative Thinking. We could call those two capacities of the human brain as forming its abstract playground components.
When mingled together, the three capacities of the human thought --the rational with the irrational and the speculative thinkings, we can obtain truly catastrophic results that have very little or nothing in common with the reality of Nature --a reality that, of course, exists independent than our own existence. The scrupulous guarding of the Rational Thinking of not allowing it to be tainted by the mind's playground components is vital, if we hope to get to the bottom in understanding Nature with all its apparent intricacies. Preserving the absolute purity of Rational Thinking is indeed mandatory in science if we want to get to the real picture of Nature.

Mathematics is the only science that has employed consistently only the Rational Thinking in its purest form (and staying completely away from the playground components of the mind) in obtaining its results. On the other hand, Physics (the mother of all Natural Sciences) and Astronomy (the oldest of all Natural Sciences) have departed considerably --in the "modern" era-- from their past path introducing now in the mainstream science speculative and irrational thinking on a massive scale. All that departure is an embarrassment --at best, and a criminal act --at worst, in the mankind's pursuit in deciphering the secrets of Nature. It is indeed, the ultimate goal of TRUTON to stop that trend originated with the implantation by Albert Einstein of two preposterous theories purporting to describe Nature --that of his "Special" and "General" theories of Relativity.

With this said, it is the scope of the remaining part of this section to magnify the transphysical concepts of space, and time. As noted, we leave the energy concept to be studied later, separately.

We start with examining the space concept. We begin this examination by noting that all living organisms have developed mechanisms in recognizing the existence, and thus the characteristics of their environment and thus of their 'space.' That recognition developed considerably with the evolution and development of the brain in the kingdom of the living whose apex arguably was reached with the appearance of the human species.

Indeed, we human began recognizing that the physical space far exceeded our immediate surrounding environment. New terms such as the cosmic space became part to that recognition. The exploration of that physical cosmic space became in earnest the frontier of the first science --the Astronomy.

The expansion of the space concept was done through the advancement of the abstract thinking whose seat has been in the Logic functionality of the brain --the place where rational deductive inferences are being produced. Thus, the space concept is par excellence a transphysical concept. Mathematics and Philosophy have been at the forefront in studying the nature of space through rigorous abstract thinking.
      In Mathematics, the 3-dimensional Euclidean space (that was the representation of the perceived physical space of Nature) was no longer the only space in use. New mathematical abstract spaces of any dimension were making their debuts together with mathematical spaces that were no longer Euclidean. As a result of that, a new renaissance in Mathematics began placing the abstract rational thinking on new heights and plateaus.
      In Philosophy, the abstract thinking led philosophers (such as the brilliant and unequalled Immanuel Kant with his seminal work "Critique of Pure Reason") to begin examining cosmological concepts in terms of how the human brain itself, through its logic functionality, treats those concepts. In his famous "Antinomies of Pure Reason" vested in his four thesis-antithesis propositions, Kant is both probing and battering the logic functionality of the human brain to unprecedented levels of scrutiny.

 We now are ready to introduce the absolute limitless Space of Nature, called HoloSpace (HOS) entity, that in TRUTON represents Nature's "arena of existence" and, represented by the (mathematical) open set containing the Nature's limitless vacuum-type continuum called xenovoid (XV). So the limitless XV-extent of Nature is embedded in the HOS. Thus, the "fabric" of HOS is XV. That implies that all xenovoid (XV) points are intrinsic fixed points of Nature. When an object moves in HOS, the object moves through XV rather than pushing away XV. That distiction and recognition leads us to

The First Fundamental Principle Of Nature (1st FUPON):  

All objects of Nature are being permeated by xenovoid that is the only absolute immobile fixture of Nature.

.Remark 1: The 1th FUPON has part of its roots in the absolute permeability (APER) property of XV to be discussed in the next section.
. Remark 2: The HoloSpace (HOS) of Nature is the identical space visualized and employed by Sir Isaac Newton and his followers.

Since all XV-points are absolute fixtures in Nature, it follows that we can talk about a fixed absolute frame of reference (AFOR) in Nature that the XV-fabric is providing it. Unless otherwise specified, all absolute motions in Nature are considered to be with respect to AFOR that is grounded in that immobile XV-background of Nature. Finally, we note that the mathematical structure of HOS is, as expected, the 3-dimensional Euclidean Geometrical Space --a space conforming with our given Common Sense.

A far more complex concept is the transphysical concept of time that evolved from the linear 'distance in duration' reality of Nature such as the 'distance' between day and night, between various phases of the Moon, between seasons, etc. Therefore the time concept incorporates all the characteristics of the distance concept --a concept that was considerable formalized in Mathematics. In particular, we note that the distance between any two points can be represented through a line (straight curve) joining those two points. Hence, the 'time' concept has assimilated all the (mathematical) properties of the 'line' concept. Thus, the properties of the 'line' are being carried into to the property of 'time.' We can see all this from the table below.

Formalization of 'line'
from Mathematics
Borrowed formalization
of the 'time' concept

1. A line has no beginning nor end. Between any two distinct points there is one, and only one, line that passes through them both. Because of this,

.

 

It is meaningless to talk about a "condensed" or a "stretched" mathematical line. A Mathematical line is of one, and only one, kind.

1'. Between any two distinct events, called EventPoints or TimePoints, there is one, and only one, straight line that passes through both of them called the EventLine or TimeLine of Nature (TILON) with no beginning and no end. Because of this,

.

 

It is nonsensical to talk about a condensed or stretched TimeLine/EventLine.

2. Between any two points in a line, there is a point between them.

2'. Between any two EventPoints/TimePoints of the EventLine/TimeLine, we always can have another EventPoint/TimePoint.

3. To a line L, we can associate a one-to-one function f=f(x) such that for any two points P and Q on L we have |PQ|=|f(P)-f(Q)| that is called the distance between P and Q. The number |PQ| is called the length of the line segment PQ and the points P and Q are called endpoints.

3'. A segment of the EventLine or TimeLine, called an EventSegment/TimeSegment (or a time episode), is a part or a portion of the EventLine/TimeLine that is bounded by two EventPoints/TimePoints, say P and Q, called end-EventPoints/TimePoints and contains every EventPoint/TimePoint on the EventSegment/TimeSegment between its end-EventPoints/TimePoints.
The duration of a PQ EventSegment/TimeSegment or a PQ episode is the number |PQ|=|f(P)-f(Q)| where f is called the time function, f=f(t), that is a one-to-one function associated with the EventLine/TimeLine. The variable t is called the time variable or simply 'time.'

.

 

Remark 1:
Any two endpoints whose distance between them is 0 (zero) are said to be one and the same.

.

 

Remark 1':
Any two EventPoints/TimePoints that have a zero EventSegment/TimeSegment between them are said to be simultaneous.

.

 

Remark 2:
The variable x of function f(x) is not a discrete but a continuous variable on L. The continuous variable x is said to be mapping the line L, and it goes without saying that x
  • is a non-stretchable and a non-compressional entity;
    and that x
  • has no beginning nor end.

.

 

Remark 2':
The continuous time variable t (or time) of the time function f=f(t) is said to be mapping the TimeLine of Nature (TILON). Since TILON has no beginning or end, it follows that
  • that 'time' cannot be "compressed" or "stretched."; nor
  • that time (the time variable t) has an absolute beginning or an absolute end.

4. The coordinatization of the line:
The mapping f---->f(x) represents the coordinatization of the line. That is, it defines a coordinate system on the line. There is a point that corresponds to 0 (zero) and, there are points that correspond to the positive real numbers and points that correspond to the negative real numbers.

4'. The arrangement of the EventLine/TimeLine:
.There is an EventPoint/TimePoint called zero-EventPoint/TimePoint or the BirthTime that corresponds to the birth of a particular formation. The time referenced to the formation is called the relative time or the intrinsic time of that formation.
.There is an EventPoint/TimePoint called the now-EventPoint/TimePoint or the present-EventPoint/TimePoint that corresponds to a given number called present.
.There are EventPoints/TimePoints called bygone-EventPoints/TimePoints or past-EventPoints/TimePoints preceding the present-EventPoint/TimePoint that are corresponding to negative real numbers. We say that those points represent points of the past.
.There are EventPoints/TimePoints called EventPoints/TimePoints-to-be or future-EventPoints/TimePoints that are corresponding to positive real numbers. We say that those points represent points from an imaginary or virtual future.

5. A half-line or a ray-line is defined trough the concept of "order" of points of a line. When we have coordinatization, we say that the line is directed.
A half-line is part of a line which is finite in one direction, but infinite in the other.

It can be defined by two points, the initial point, A, and one other, B. The half-line is all the points in the line segment between A and B together with all points, C, on the line through A and B such that the points appear on the line in the order A, B, C.

If A is a point on a line such that the set of points C satisfy the relation f(A)f(C), then the set of points C are said to form a ray with A as its origin. If the set of points C satisfy the relation f(A)f(C), then the set of points C are said to form the opposite ray.

5'. The EventLine/TimeLine has two halves. A half-EventLine/TimeLine is defined through the concept of "order" of its EventPoints/TimePoints. When the EventPoints/TimePoints are arranged in the order of their successive occurrence, we say that the EventLine/TimeLine is directed. A half-EventLine/TimeLine is a part of the EventLine/TimeLine that is finite in one direction, but infinite in the other.
.We call the bygone-EventLine/TimeLine or past-EventLine/TimeLine, the half-EventLine/TimeLine whose origin is the present-EventPoint/TimePoint and whose all subsequent EventPoints/TimePoints are the bygone-EventPoints/TimePoints. We call that half-EventLine/TimeLine the entire past-line of Nature (EPLON).
.We call the EventLine/TimeLine-to-be, the half-EventLine/TimeLine whose origin is the present-EventPoint/TimePoint and whose all subsequent EventPoints/TimePoints are the future-EventPoints/TimePoints. We call that half-EventLine/TimeLine a virtual futuristic-line.

.

Internal biological mechanisms for measuring the duration of a time episode (as defined in point 3' hereinabove) have existed and perfected from the beginning of life. Natural time-markers are, as we have noted, an essential element of life. The evolutionary evolved human species added a new dimension of keeping track of time not through its existing biological clocks but through external clocks creating timekeeping devices called timepieces capable of functioning outside the body of human species. The evolution of those timekeeping devises from sundials and water clocks to pendulum clocks and culminating with quarts and atomic clocks has been indeed a most remarkable journey.

The complex concept of time evolved, as we have seen, from the recognition of the existence of a 'distance of duration.' Another type of distance that has been recognized by all living organisms has been the 'distance in length' or 'spatial distance.' That 'spatial distance' will lead us to the 'metric' of the Euclidean Space noted above.

.NOTE:
As we have seen, through our logic functionality, we were able in a coherent way to arrive at the transphysical concepts of space and time and that indeed is a remarkable achievement of our logic functionality. However, as we have noted above, logic functionality however was not the only "player" that human brain was equiped with. Irrationality was another functionality bestowed upon the human brain. And trough that platform of the Irrational, the abstract thinking could also be launched and it entered mainstream in 1905 with Albert Einstein's introduction of his Special Theory of Relativity (STR) and continuing by him 10 years later with the introduction of his General Theory of Relativity (GTR). Once the gate towards Irrational was opened, it was not long before the apparition of the Quantum Mechanics --a theory par excellence of the Absurd purporting to represent and explain the atomic and subatomic worlds of Nature. One of its founders, P. A. M. Dirac in the 1930 Preface of his classical work "The Principles of Quantum Mechanics" pleads with the reader to allow him to introduce elements of the irrational which he called them "irrelevancies," as well as, to allow him to use indiscriminately Mathematics as "it is the tool specially suited for dealing with abstract concepts of any kind as there is no limit to its power ..." A more recent physics professor while at Harvard University (now at University of Texas at Austin and a Nobel Laureate in Physics), in justifying for the necessity of introducing elements of the irrational in Quantum Mechanics blamed the human brain for its biological limitations arguing that as dogs could not be taught Calculus, similarly we, humans, could not expect to be able to grasp the atomic and subatomic world in a rational fashion. [sic!]. Well, hopefully the foundation of TRUTON will be able to change all that and bring down all that nonsense.

Out of that nonsensical, irrational, thinking it is worth mentioning one result that stands out --the nonsensical 4-dimensional space, called spacetime continuum, combining the 3-dimensional space (x, y, z) with the 1-dimensional time-line (t) resulting into the ridiculous nonsensical "(x, y, z, t)-space." Of course, if time t is a variable, we write the 3-dimensional space as [x(t), y(t), z(t)] but never ever introduce an 'unsustainable' spacetime continuum (x, y, z, t). It is 'unsustainable' because a space to be 'sustainable' must have all its coordonates be of the same kind --'spatial' kind. That is to say that the coordinates of a point in a given space must be of the same nature and thus be interchangeable if the respective space would have any meaning. If in other situation, for instance, we have a problem where the density d is a variable, we cannot create a nilly-willy nonsensical spacedensity continuum (x, y, z, d), but we use the same 3-dimensional physical space with d as the variable [x(d), y(d), z(d)].

Also, the concept of a space "curvature" attributed, nilly-willy, to the spacetime nonsensical continuum is an exercise into the absurd as it has no physics nor anything else in support thereof. From here somehow the origin of gravity is being "explained" being part of Albert Einstein's insane theory of Nature --his so-called General Theory of Relativity.
Albert Einstein
.Albert Einstein

    

(That Albert Einstein harbored a clinically insane mind has been well kept a most guarded secret by the Einstein estate. Einstein, in fact, was born with a mental disorder, was not able to speak until was 3, developed Schizophrenia that he passed to his children, was a mediocre student all his life, and professionally benefited greatly from his first wife that supplied for him most of the employed mathematics. In addition, he stole practically all of the 'relativistic' results from published materials of Henri Poincaré and Hendrik Lorentz including the famous 1904 Poincaré equation E=mc2 attributed to Einstein.)

If the nowadays "modern" Physics is marred by the massive amount of irrationalities that were implanted and continue to flourish, the nowadays "modern" Astronomy is being marred by its massive speculative concepts such as,
  • by its preposterous Big-Bang cosmological concept that considers that our existing Universe has somehow emerged out of the explosion of a nilly-willy point of infinite mass density;
  • by the existence of speculative "dark" energy and mass;
  • by the existence of the speculative "antimatter";
  • by the existence of some mysterious "black holes" with unseen imaginary physical properties;

and so on, and so on ...

What a terrible sad state the "modern" Physics and Astronomy have evolved into. Heartbreaking indeed.
.God, if there is one, is having a field day is seeing how far off we have strayed from deciphering the secrets of Nature and its modus operandi.
.

The last foundational concept connect to motion --the energy concept will be studied separately in a following section, as noted. Until then, we will turn our attention in identifying the primary ingredients of Nature --the subject of the next section.

.

      

Kalman Klim Brattman