Temporal Numbers (expected in April, 2021)
For the first time in history, imaginary numbers have a genuine meaning that unites between physics and mathematics!
https://www.amazon.com/dp/B086SFZ58F
The relation between “numbers” and
“time” is extremely profound and fundamental, since “counting” necessarily
implies some recurrence or repetition of the same primary “unit”, which is
normally denoted as “one”, that then adds and multiplies in various ways to
produce other quantities. For this reason, numbers are ideally represented as
contiguous points on a straight line that has a starting point and direction,
just like time. For this reason, also, when numbers whose square is negative
were encountered in solving the quadratic equations, they were termed
“imaginary”, as opposed to the “reals” that normally occupy the x axis,
since it subsequently turned out that these numbers have a geometrical meaning
that implies simultaneous counting in the x and y directions,
which is not possible with our normal notion and perception of time - as a
linear and one-directional flow, normally referred to as “the arrow of time”.
Henceforth, the combination of imaginary and real numbers is denoted as
“complex”, which were later extended to quaternions, octonions, sedenions and
other hyper-complex systems.
Counting is the process of
determining the number of elements of a set of objects in a group. The final
count itself is expressed as one number, that can be thought of as a whole new
unit. But, since it is composed of smaller units, it is not possible to
determine its value without going through these sub-units, and hence counting
them, which is essentially related to time.
This fundamental relation
between time and numbers is usually neglected in mathematics, and that was the
primary reason that made Euclidean geometry feasible. Mathematics, which is
primarily based on the five axioms established by Euclid about two thousand
years ago, worked out successfully and efficiently for all practical purposes
and most abstract problems. However, after the advent of the Theory of
Relativity in the early 19th century, many other
non-Euclidean geometries were introduced. The main motivation was the newly
discovered relation between space and time, together termed as “space-time”,
which implied that physical space itself is not uniform anymore, as it was
treated in Euclidean geometry which turned out to be an approximation that works
only in normal conditions of relatively short distances and weak gravitational
fields.
In normal Euclidean geometry,
“space” is considered an abstract background that had to be absolutely uniform
and infinitely extending in all (three) dimensions, and also idle throughout the
flow of time. Accordingly, all mathematical operations, whether algebraic,
arithmetic, and even infinitesimal calculus and other types of analysis, are
efficiently performed in Euclidean space for all practical purposes in all
fields of applied mathematics, including thermal (and statistical) physics and
classical (Newtonian) mechanics. Non-Euclidean geometry is required only in some
modern physics theories that deal with extreme conditions, such very large or
exceedingly small dimensions as well as extremely high gravitational fields, all
because “space” becomes fundamentally related to “time” and not uniform anymore.
However, the Theory of
Relativity, whether in its Special or General versions, and in its classical or
modern formulations; although it showed that space and time are connected, via
the speed of light, it did not explain the nature of this connection and how
exactly does it affect the ultimate structure of geometry. The reason for this
essential deficit, as it turned out to be, is the lack of any apprehension of
the ontological role of the speed of light c in the relation between
space and time, apart from its cardinal presence in the equations. In fact, so
far in modern physics, the constancy and invariance of the speed of light is
considered an axiom, which has been experimentally verified but without any
theoretical or philosophical explanation or interpretation.
As this book will clearly show,
revealing the ontological reason behind this distinct and illogical behavior of
light will have enormous consequences on the foundations of physics and
mathematics, because it delineates the very structure of geometry, and it will
be the gate for a new era in the history of science and philosophy.
According to the “Duality of
Time Theory”, which is based on the “Single Monad Model”, the whole cosmos,
including space and what it contains of matter particles, is being re-created
internally in the inner “real” levels of time, before it kinetically evolves
throughout the outer “imaginary” time that we normally encounter. Therefore, the
points of this “complex-time geometry” are perpetually and sequentially
fluctuating between existence and non-existence.
This chronological coming into
being, one point at a time, by the only one real and unique single monad, makes
the geometry intrinsically granular and self-contained, even without the need to
any minimum time or length scales or quanta, because the unit of quantization is
the frequency of re-creation, or the re-fresh rate, which is the ratio between
the inner and outer levels of times. This ratio is nothing but the speed of
light itself whose normalized value also corresponds to the fractal dimensions
of geometry, which then becomes “genuinely hyper-complex”, since both its real
and imaginary parts have the same nature (of time).
Actually, as we have shown in
the first three volumes of the Single Monad Model series, this genuine
complex-time geometry provided elegant solutions to many persisting problems in
physics and cosmology, including causality, non-locality, homogeneity, the arrow
of time, the mass-gap, the cosmological constant, super-symmetry and
matter-antimatter asymmetry, in addition to reconciling the inherent
contradictions between General Relativity and Quantum Mechanics, by providing
the smooth link between “discreteness” and “continuity”.
Therefore, the profound
implications of the Duality of Time propagate into Mathematics and Number
Theory, because it delineates the original edifice of Geometry. In fact, this
innovative theory removes all boundaries between Physics and Mathematics, not
only because it explains all the fundamental interactions, and not only gravity,
based on the new complex-time geometry, but even pure mathematics is now
fundamentally relativistic, since its very abstract geometrical points are being
dynamically created at the speed of light. Therefore, all kinds of objects in
creation are nothing but “temporal (hyper-complex, or time-time) numbers”, and
no truthful calculus can be performed without taking into account their
relativistic nature!
Hence, the Duality of Time
Theory made a substantial breakthrough in mathematics, physics, and cosmology,
as well as natural philosophy, because it exposes a deeper level of time and
original theory of creation that will cause a paradigm shift in our knowledge of
the fundamental nature of the cosmos, with its corporeal and incorporeal
structures.
For the first time in history,
and many centuries after their victorious introduction and successful
applications on various physical systems, imaginary numbers have a genuine and
fundamental meaning that unites between physics and mathematics! Because numbers
are fundamentally connected with it, discovering the inner levels of time
allowed simultaneous counting in various intersecting dimensions.
Plainly-stated, the Duality of Time Theory explains how the dimensions of
geometry are being structured in time, which is the ontological process that is
creating both the abstract space-time and its material contents.
In fact, with the new innovative
concept of the duality of time, (the hyperbolic) complex numbers (H) are
more realistic than the “reals”, because they can objectively and efficiently
describe all physical systems, while the reals are approached and justified only
in the extreme and non-realistic conditions which implies motion at the speed of
light; thus they can be adequately termed “imaginary”. However, this is also
true for all Euclidean and Hilbert spaces, which can be expressed by normal
complex numbers C, using the various extensions of hyper-complex systems
such as quaternions, octonions and sedenions.
In fact, as we shall see in this
book, the Euclidean geometry can efficiently describe existence in
(three-dimensional) space at any instance of time, but without motion or change,
i.e. without time! To describe the dynamic geometry, hyperbolic space is
required. The reason why Euclidean or Hilbert spaces, even with Riemannian
geometry, are not sufficient to the describe the real world is because it is
being re-created or perpetually fluctuating between existence and non-existence,
or vacuum and void. In other words, the Euclidean space is the geometry of
existence at every instance of time, which makes the vacuum that is space
without time. Because it is being re-created, (everything in) the world becomes
void in time, i.e. between any two consecutive instances of time. The world is
therefore constantly fluctuating between vacuum and void, which is the same
ancient atomistic philosophy, reinterpreted out of the most original theological
and philosophical conceptions, combined together with the principles and
conclusions of modern physics and cosmology.
However, in this perpetual
process of creation and re-creation, the state of vacuum, which is the spatial
existence that can be expressed by normal complex numbers C, is splitting
into two temporal and super-symmetrical hyperbolic spaces H that
correspond to the corporeal and incorporeal worlds, which then instantly
annihilate back into vacuum. The reason why this creation and annihilation
process is not causing any devastation or destruction, as we would normally
expect from such extremely energetic fissile reaction, even when it happens on
the slightest atomic scales, is because it is happening sequentially in the
inner levels of time before the physical mass is generated. Rather, this process
itself is the fundamental origin of the instantaneous generation of matter
particles and antiparticles, which then simultaneously repair and vanish into
the past, just to be re-created again, perpetually. As we described in the
“Ultimate Symmetry”, this perpetual and sequential dynamic formation causes the
illusion of motion and continuity of spatial dimensions, while in fact all this
multiplicity is being created from one metaphysical point, which is the Single
Monad that is the only entity described by real continuous existence.
Moreover, this splitting of the
three-dimensional Euclidean geometry into two hyperbolic planes on two arrows of
time, which then describe the entangled corporeal and incorporeal worlds, means
that the psychical entities have exactly the same structure as the physical
objects, with the same kinds of elementary particles, atoms, crystals, and even
rocks and mountains; but they are denoted as incorporeal because they exist in
an orthogonal dimension of time. Therefore, the fermions in our physical world
behave as bosons in the psychical world, and vice versa.
Therefore, in addition to
solving all the previous puzzles, reconciling between the two contradictory
theories of relativity and quantum mechanics, and uniting between physics and
mathematics, the Single Monad Model and Duality of Time Theory also explains how
the physical and psychical creations are developing on two orthogonal arrows of
time, thus bringing the incorporeal worlds under the same umbrella of the laws
that govern the physical cosmos.
These are only some glimpses of
the many doors opened as a result of understanding the connection between the
constancy and invariance of the speed of light and the fractal dimensions of
geometry, made possible by the Duality of Time Theory. We have discussed some of
these advances in the previous three volumes of the Single Monad Model series.
In this book we will explore the consequences of this innovative view on various
fields on the foundations of mathematics and its intersection with physics,
including geometry, infinitesimal calculus and number theory. Many fundamental
issues will be discussed, including the structures of number sets and their
inter-relations, in addition to various fundamental problems such as the
Yang-Mills conjecture and the Riemann hypothesis.
The Duality of Time Theory, that results from the Single Monad Model, explains how multiplicity is dynamically emerging from absolute Oneness, and vice versa, at every instance of time! This theory leads to the Ultimate Symmetry of Space and its instantaneous breaking into the physical and psychical creations, with two hyperbolically orthogonal arrows of time.
... time! This theory leads to the Ultimate Symmetry of Space and its instantaneous breaking into the physical and psychical creations, with two hyperbolically orthogonal arrows of time. ...
... by the Duality of Time Theory. We have discussed some of these advances in the previous three volumes of the Single Monad Model series. In this book we will explore the consequences of this INNOVATIVE VIEW on various fields on the foundations of mathematics and its intersection with physic ...
... ly expect from such extremely energetic fissile reaction, even when it happens on the slightest atomic scales, is because it is happening sequentially in the inner levels of time before the PHYSICAL MASS is generated. Rather, this process itself is the fundamental origin of the instantaneo ...
... ations of mathematics and its intersection with physics, including geometry, infinitesimal calculus and number theory. Many fundamental issues will be discussed, including the structures of NUMBER SETS and their inter-relations, in addition to various fundamental problems such as the Yang- ...
... a substantial breakthrough in mathematics, physics, and cosmology, as well as natural philosophy, because it exposes a deeper level of time and original theory of creation that will cause a PARADIGM SHIFT in our knowledge of the fundamental nature of the cosmos, with its corporeal and inco ...
... hing in) the world becomes void in time, i.e. between any two consecutive instances of time. The world is therefore constantly fluctuating between vacuum and void, which is the same ancient ATOMISTIC PHILOSOPHY , reinterpreted out of the most original theological and philosophical conceptio ...
... cs, physics, and cosmology, as well as natural philosophy, because it exposes a deeper level of time and original theory of creation that will cause a paradigm shift in our knowledge of the FUNDAMENTAL NATURE of the cosmos, with its corporeal and incorporeal structures. For the first time ...
... rations, whether algebraic, arithmetic, and even infinitesimal calculus and other types of analysis, are efficiently performed in Euclidean space for all practical purposes in all fields of APPLIED MATHEMATICS , including thermal (and statistical) physics and classical (Newtonian) mechanics ...
... implied that physical space itself is not uniform anymore, as it was treated in Euclidean geometry which turned out to be an approximation that works only in normal conditions of relatively SHORT DISTANCE s and weak gravitational fields. In normal Euclidean geometry, “space” is consider ...
... e have shown in the first three volumes of the Single Monad Model series, this genuine complex-time geometry provided elegant solutions to many persisting problems in physics and cosmology, INCLUDING CAUSAL ity, non-locality, homogeneity, the arrow of time, the mass-gap, the cosmological co ...
... troduction and successful applications on various physical systems, imaginary numbers have a genuine and fundamental meaning that unites between physics and mathematics! Because numbers are FUNDAMENTALLY CONNECTED with it, discovering the inner levels of time allowed simultaneous counting ...
... applied mathematics, including thermal (and statistical) physics and classical (Newtonian) mechanics. Non-Euclidean geometry is required only in some modern physics theories that deal with EXTREME CONDITIONS , such very large or exceedingly small dimensions as well as extremely high gravit ...
The science of Time is a noble science, that reveals the secret of Eternity. Only the Elites of Sages may ever come to know this secret. It is called the First Age, or the Age of ages, from which time is emerging.
