T R U T O N byKalman
Klim
Brattman Give
me the simplest form of
matter
and motion,
and I will construct, out of them, the world of
Nature.

"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 Transphysical Distances and Frames of Refernces
Concepts with
emphasis on
Space and Time Concepts VS. the Nonsensical
Spacetime Concept

The
study of motion, plays a pivotal role in
TRUTON --as motion indeed is an integral and
independent component of the formation of
Nature to be studied in the next
page.

The
study of motion cannot be separated from the
concept
of distance.
There are two, and only two, kind of distances
that the Mind can conceive to exist when
studying Nature:

one,
a distance in extent called
Space; and

the
other, a distance in duration called
Time.

Those
two concepts, Space and Time, were already
inherited and implanted into Mind's existence as
the nervous system of
alllocomotive
living
organisms (organisms that are able to
move),
without exception, were endowed with a
recognition of their surrounding environment
that was affected by a Time (e.g., day or night,
the beginning or ending of a season, etc.) and
by a Space (e.g., distance to a safer place, to
water, to a tree, to a warmer place, etc.). That
universal primeval recognition of a Space and a
Time common to all locomotive livings, while
quite different for each species, had one thing
in common: that it all developed from one
singular interest that was the interest of
survival. That survival interest was born
out of these two simple but basic concerns: WHEN
to move (e.g., day or night) or
WHERE to move (e.g., places that are
safer than other places, places near water,
etc.) in order to stay alive.

That
simple recognition of the survival interest
existing in all locomotive living creatures of
Nature is remarkable indeed, because it implies
that the nervous systems of all moving living
organisms, regardless how primitive they were,
all, by virtue of evolution, were able to
"communicate" with and recognize their
surrounding Nature via their own mechanism of
perceptions in identifying their surrounding
Space and Time. Biological body-clocks of all
livings are the result of their Time-perception
relationship with Nature, while the recognition
and the marking of their habitat is the result
of their Space-perception relationship with
Nature.

The
Space and Time concepts devised by the human
Mind evolved out of that survival interest of
the living and eventually become
unique
because of the Mind's unique ability to engage
in abstract
thinking.
And by UMCOT,
there is no limit in how far that ability can
develop and expand. The outer Space or the
Cosmic Space is one example of such an
expansion. Mathematics, through its ever
increase development, was able to create
--through its ever deeper logical abstract
inferences-- even deeper abstract mental objects
and concepts that led to a considerable
expansion of the Space and Time concepts coined
by the Mind.

With
respect to the Space concept, the development of
Mathematics was channeled into two major
directions that were able to generate new and
quite complex abstract spaces:

i)
one development was towards
mathematical structures giving
rise to a number of new type of
abstract spaces such as the
non-Euclidean spaces, group and field
spaces, topological spaces, etc.; ii) the other development was
related to the dimension of
mathematical spaces, generating new
concepts such as mathematical fields,
manifolds, n-spaces, etc.

The
concept of Time was also affected by the
advancement of Mathematics. The gradual
introduction and acceptance of negative numbers
(once called and regarded, in the 15th century
France, as "absurd numbers") was able to pave
the incorporation of the "negative time" into
the Time concept. Thus, with this new abstract
addition, we were able to associate past events
with corresponding to a negative time.

! DO
NOT
OVERPASS

.

It is important to stress that our formed Space
and Time concepts incorporated into the study of
Nature are creations of the Mind and, as such,
they reside only in our Mind, and nowhere else,
as they do not have a separate material
existence in Nature. They are just
mental
frames of reference
created
by the Mind and nothing else. To them we
cannot
associate, in a meaningful way, physical
characteristics such as temperature, density,
elasticity, etc., because
they
are not physical
entities.

In
TRUTON, an absolute demarcation is always made
between abstract mental objects --called
mentalons and the real physical objects
of Nature called realtons. Let us stress
again that mentalons, as oppose to realtons, do
not possess physical properties because they are
objects of the Mind and not of Nature. What
mentalons can possess is a close affinity to
Mathematics as outlined further
below.

Mentalons
--the exclusive products of the Mind, could be
of different kinds. Some mentalons are
images created by the Mind of real or
imaginary objects and,

called
imagelons,when
representing imaginary objects of
fantasies and dreams,
and

called
imagetrons, when representing
real objects observed from Nature.

Mentalons that are not images, are
thoughts that

could
be vested in rational deductive
reasoning called
rationalities (with
Mathematics being a prime example of
being made entirely of
rationalities); or

could
be vested in fantasies, dreams, and
irrationalities (aka,
irrational thinking) forming the
Mind's Playground whose
constituents, collectively, are
called playlons.

Mentalons can be used to study the Mind itself
or to study the real material Nature. Mentalons
that are "transported" to study the Mind are
called transmentals, while when
"transported" to study Nature are called
transphysicals. The study of transmentals
is the object of Psychology that is the
academic study of mental functions and
behaviors, while the study of transphysicals is
done in Physics.

There
are seven (7) major types of
transmentals
capabilities and processes of the Mind:

•
one, with respect to the Mind's
rationalities --the
Logic
functionality;

•
other, with respect to the Mind's
capability to store information
--the Memory;

•
other, with respect to human Mind's
capability of self-reflection,
self-examination, and self-learning
from experience --the
Introspection;

•
other, with respect to human Mind's
capability of holding a particular
conjecture or premise to be true
outside experience or its sphere of
accumulated knowledge --the
Belief;

•
other, with respect Mind's
capability of directing and
committing to a particular course
action --the
Volition;

•
other, with respect to the Mind's
Playground vested in its playlons
--the Imagination;
and finally,

•
other, with respect to Mind's states
involving
perception, cognition, creativity,
motivation and emotion -- the
Mental
States.

Transphysicals,
on the other hand, are the
Reference
concepts of Space and Time that are
indispensable for the
study
of Motion
in Nature. In the remaining part of this
page, we take a closer look at the two
identified transpysicals, Space and Time,
through the lens of Mathematics.

Time
of Nature Through the Lens of
Mathematics

Before we "transport" our transphysicals into
the material world of Nature, it is useful to
discern their characteristics. For instance, we
recognize that the concept of time
evolved from the 'linear
distance'
in duration. But a linear distance in
Mathematics is represented through a line
(straight curve). Therefore, the 'time' concept
has incorporated all the mathematical properties
of the 'line' concept. We can see all this from
the comparative 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
timeepisode), 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
fis 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
entirepast-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, as we
have noted, are an essential element of life.
The 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.

Space
of Nature Through the Lens of
Mathematics
And On the Nonsensical Spacetime
Concept

The arena of existence in extent and the
arena of existence in duration in Nature
are expressed by two fundamental concepts,
respectively --that of space and that of
time. A location is represented or
expressed through the concept of a point in
space while an event in Nature is
represented or expressed through the concept of
a point in time.

Since
in Nature, the location of a point in space can
be identified exactly through three and only
three independent like-parameters, called
space parameters, noted say as
[x, y, z], we say that the
Space of Nature is a 3-dimensional
continuum. The mathematical "structure" of that
continuum is defined formally (in the language
of Mathematics) through a so-called metric,
called the metric of space.

Unlike
a point in space that can travel randomly in a
3-dimensional volume, a point in time can travel
only linearly in the unidimensional space of the
line called the timeline. Because of that
characteristic, a time point can be
identified completely through one, and only one,
single parameter, called the timeline
parameter and usually denoted
with t.

Thus,
for a particular point of Nature, its space
parameters are function of its sole timeline
parameter and, we can write this as x=x(t),
y=y(t), and z=z(t). So to reflect this
time-parameter, the space
[x, y, z] can now be written
as
[x(t), y(t), z(t)].

.

It
is important to note, right here and
right now, that unlike the parameters
x, y, and z that are of
the
same
nature
being therefore able to be interchanged
one with another, the timeline
parameter t is of an entirely
different
nature.
As such, it is meaningless indeed to
unite the timeline parameter with any
other kind of parameters as such a
union cannot be combined in a
meaningful matter. In a meaningful
combination all of parameters forming a
space must be of the same kind or
nature. Thus, the timeline parameter
t can never ever --in a
meaningful way-- be added as a forth
spatial dimension to represent a space
much less the Space of Nature. The
Space of Nature can be
represented only as
[x(t), y(t), z(t)]
but never ever, in a meaningful way, as
[x, y, z, t].
Nevertheless, such an absurdly,
introduced first by Albert Einstein,
continue to this day, to be employed
without any notable
reservation.

The
Space
of
Nature
cannot have a
physical
structure
because it is a mental object --a
mentalon
in the sense envisioned by Immanuel
Kant in his seminal work
"Critique of Pure Reason"
where both 'space' and 'time' are being
viewed as mental frameworks that humans
have created to study
Nature.

Physical
structures can be associated only with
matter, but not with Space or
Time that are mentalons. Space and Time
and nothing else but
mental
receptacles
that, by their very nature, cannot be
associated with having any physical
properties. "Bending" of Space or the
"dilation" or "contraction" of Time are
nonsensical concepts as they confuse
mentalons with realtons.

Thus,
the Space of Nature is the Space of
Immanuel Kant and Isaac Newton, being a
mental container devoid of any
implanted distorsions, and being thus,
par excellence, the Euclidean
Space. Because the Space of Nature
is governed by the Euclidean Geometry,
and only by Euclidean Geometry, we can
see from the diagram below how any
point source (S) of Nature will spread
its influence equally, in all
directions, obeying the
Inverse-Square Law Of Nature
(ISLON): that the intensity of the
influence at any given radius
r
is the source strength divided by the
area of the sphere. Being strictly of
geometric origin whose Space is
Euclidean, the
ISLON
applies to all unperturbed source
phenomena of propagation. Point sources
of gravitational force
(Newton's
Law of Universal
Gravitation),
electrostatic force (Coulomb's
Law),
light source, sound, or radiation
sources --are all obeying
ISLON.

ISLON

Let
us stress again:
ISLON,
by being a geometrical and not
a physical property, exists in
Nature only because the
structure of the Space of
Nature is Euclidean.
ISLON
will not exist in a Space of a
different mathematical
structure. And that
recognition is most important
indeed as, through it, we are
able to recognize at once the
validity of the Euclidean
Geometry as the geometrical
structure of the Space of
Nature.

As
already stated, the current
adopted Space structure of
Nature, of the so-called
spacetime continuum
structure introduced by
Einstein's Theory of
Relativity, combining Space
and Time into one single
substratum is an utterly
absurd concept because such an
union can never ever generate
a continuum in the
mathematical sense nor in any
other coherent sense. That is
because, as noted, the
parameter 'time" can never
ever combine, in a meaningful
way, with a parameter that is
of a different nature. To have
combination of parameters
forming a continuum, all
parameters must be of the same
nature.

That
truly absurd
spacetime
continuum
concept that forms the
backbone of Einstein's
General Theory of
Relativity (GTR)
purporting to represent the
reality of Nature's Space,
"explains" gravity not as
being a force [sic!!],
but as being a derivative
springing from the Space's
purported
curvature!

Finally, we note here
that because the motion of an object in Nature
can be referenced only through Space and Time,
those two concepts --Space and Time-- are also
called the base anchoring concepts of Nature
(BACON). Motion is the underlying concept of
BACON creating therefore the bridge of
communication (BOC) between the Space and
Time concepts. Motion therefore is an
indispensable primary given
characteristic of Nature that need to be
incorporated right from the beginning of our
study. All these ideas will considerably be
magnified as we advance with TRUTON. The general
blueprint that we have sketched herein will
further be expanded, magnified, and enhanced as
we go along. So, without further ado, let's
begin with our journey that we have set to
travel.