How Things Work: A Brief History of Reality
Book II – The Power of Three (#42 "The Rational West")
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Tuesday August 2, 2022
“Mathematics, is, I believe, the chief source of belief in eternal and exact truth.”
– Bertrand Russell
CONSIDERATION #42 – The Rational West
PREFACE
Welcome Everybody!
This week, we are considering the nature of the Rational West. Whereas the East focused on the mystery of dualism within nature, the West found analytical enlightenment from exploring the power and possibility in utilizing our rational mind to overcome nature. In “Tiger-Dragon: The Essential and Fundamental Physics & Metaphysics of Martial Arts Training,” I focus on how both Eastern and Western philosophy have shaped the development of the martial arts. In my most recent book, “The Cosmic Symphony – Overtones of String Theory,” I focus on the development of sound as developed through Western thought eventually leading to modern String Theory. What both books have in common is a fundamental foundation of mathematical abstraction based on the principles and teachings of one unique Greek philosopher: Pythagoras.
Pythagoras – Mathematical Abstraction
In his time, Pythagoras was not what we would consider today a “math professor” in any sense. He was instead a high priest for the “mystery school” teaching the language of God – Mathematics. Geometry, in particular. His insights regarding the abstract nature of numbers was the foundation of Western thought and philosophy.
For Pythagoras, although numbers were not “real” in the world, their metaphysical abstraction became the only way to truly understand and control the “real” world. Pythagoras would essentially argue that abstract thought is more real than sense perception. Abstract thoughts exist outside of time and space, and are therefore eternal and non-changing. According to Russel: “Such eternal objects can be conceived as God’s thoughts.”
The key significance of Pythagoras is that for the first time, abstract reasoning and logic began to have substantial, practical influence in the real world. This solidified a legitimate connection between using abstract concepts, ideas, and logic to influence authentic outcomes in the real world. Perfection, such as a perfect geometrical circle, was an abstract principle that could not exist naturally in the real world. However, by understanding and acknowledging its perfect abstraction and metaphysical underpinnings, new advanced architecture could be created and successfully implemented there. Thus, abstraction became a new form of spiritual and intellectual discovery, leading Bertrand Russell to conclude:
“It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction… I do not know of any other man who has been as influential as he [Pythagoras] was in the sphere of thought.”
Frank Elkins – Tiger Dragon
One of the clearest examples of this kind of abstract metaphysical thinking is geometry. Based on a set of three completely hypothetical abstractions, an entire system of mathematical deduction was developed allowing abstractions of the mind to become physically manifested and implemented into the real physical world of the senses. Metaphysical points, lines, and planes became translated into roads, bridges, and aqueducts. Eventually, it allowed us to travel to the moon.
The Metaphysics of Geometry - Abstraction Becomes Reality
The foundation of geometry rests on three metaphysical abstractions: the point, the line, and the plane. The true essential revelation from these fundamentals is not one of mathematics, but of reality. These three self-evident axioms must be accepted without proof to begin the journey of geometry. However, once they are accepted as truth, you can understand and create anything in three-dimensional space such as bridges, aqueducts, skyscrapers, virtually any machine, and even go into space. Therefore, the underlying conclusion: Reality is built on Abstraction.
The first and primary metaphysical abstraction is the “point.” Although represented by a dot in geometry, a true metaphysical point is really just an abstract representation of a possible location in time and space. A metaphysical point has no length, no width, and no height. It has no measurable mass or density. In short, a point is something that doesn’t exist in the real world and can never exist in the real world. Like the perfect circle, you can look everywhere in the universe and never find one because they don’t actually exist in nature. It is only an idea, a concept, a possibility.
From the first abstraction comes the second, a line. A line, like a point, cannot exist in the real world, because it is predicated on the first abstraction itself, the point. A line is defined as a set of connected points extending infinitely in two opposite directions forever. It has infinite length, but no width or height. Notice the use of additional abstract terms such as “infinite,” “infinitely,” and “forever”.
The third and final component for our metaphysical foundation is the plane. A plane is a set of connected points extending infinitely far in all directions forever. It has infinite length, infinite width, and zero height or thickness. Establishment of the plane also establishes three-dimensional reality. A plane becomes the first abstraction that can be more easily replicated in the physical world. Typical planes built and utilized for our general use include floors, table-tops, parking lots, ice skating rinks, etc. Although not “perfect” metaphysical planes, we begin to clearly recognize the transition from abstraction to physical manifestation for the first time. From here, all three-dimensional manifestations are possible. Welcome to the real world.
Frank Elkins – Tiger Dragon
CONSIDERATION #42
The Rational West
A point is that which has no part.
A line is a breadthless length.
A plane surface is a surface which lies evenly
with the straight lines on itself.
Euclid’s original definitions – 300 BCE
The only conception of physical space for over 2,000 years, it [Euclidean geometry] remains the most compelling and useful way of modeling the world as it is experienced.
Jain Parul – Encyclopedia Britannica
Although Euclid’s original definitions for Plane Geometry sound very much like an illogical Taoist koan, they actually embrace the essential truths of Western rationalism. The key principles of Western civilization revolve around three fundamental abstractions: Reason, Mathematics, and Logic. The combination of these three abstract abilities would enable Western civilization to eventually alter and dominate the world in terms of science, medicine, and technology. There is perhaps no clearer example of these principles than Euclidean geometry.
“Within the metaphysical concepts of a point, line, and plane lie the blueprint for constructing roads, bridges, and buildings in the ‘real’ world.”
The Greeks’ entire understanding of what it was to be a human being was intrinsically connected to their ability to reason, develop abstract possibilities, and use logic to pose and solve abstract questions. Geometry is based on a set of abstractions (undefined or self-defined terms) leading to other abstractions that lead directly to the creation of physical objects in the world. Within the metaphysical concepts of a point, line, and plane lie the blueprint for constructing roads, bridges, and buildings in the “real” world. In terms of Western thought, the tangible is made possible by the intangible.
A point is an abstract theoretical concept used to hypothetically consider a specific location in space that has no length, width, or height; meaning it has no size, dimension, or mass. Therefore, there is no such thing as a point, they don’t really exist. From this "self-defined" point, we move to the next step of using it to define another abstract hypothetical concept called a line. Two points, and all points in between or passing through them, extending endlessly in two directions, constitute a line. Like the point, the line is not “real.” A line is just an abstract extension of a point, containing no size, shape, or mass, only an infinite extension in space. However, if we accept the truth of these two abstractions, we can move into the third and final abstraction called a plane.
“Once the third point is established and a plane is created, we have access and control over virtually all three-dimensional reality.”
A plane represents an infinite number of points extending forever in all directions with no height or other physical characteristics such as mass, dimension, or size. Think of a flat surface extending forever that is invisible! Once we have three points, establishing a plane, we can build an entire system of abstractions, known as geometry, that allows us to construct real physical buildings, bridges, and roads in the physical world that we then use and take for granted every day without thinking. Once the third point is established and a plane is created, we have access and control over virtually all three-dimensional reality. We can then use those abstractions to directly affect our own three-dimensional physical world.
We know this three-dimensionality as “space.” The abstraction of space consists of all points, lines, and planes possible, which manifest what we would consider physical reality. Consider the similarity to Eastern thought: the Tao begot one (the point), one begot two (two points equals a line), two begot three (the third point allows all three points to connect into a plane), Three begot the ten thousand things; from this abstract two-dimensional plane we can create unlimited real three-dimensional forms and objects in the physical world of “space.” This is the same kind of abstract thinking that would transform our reality from one of sensory perception, to one of using reason to intuit abstractions defining the nature of our existence.
“The philosophical inquiry regarding what constituted ‘matter,’ or physical ‘stuff,’ gave birth to a new abstraction of three: the atom.”
If geometry represented the underlying foundation of physicality, what were the underlying secrets of “matter” itself? This is a very Western question, because it follows a reasonable chain of logic leading to the next question. Without the physical properties of matter, the abstractions of geometry could not become manifested in the physical world at all. Therefore, the question, as to what matter is, becomes critical. The philosophical inquiry regarding what constituted “matter,” or physical “stuff,” gave birth to a new abstraction of three: the atom. This new model of physicality would alter our conception and perception of reality and usher in a new “atomic age” of science, medicine, and technology.
POSTSCRIPT
“The roots of Western thought and philosophy lie in mathematics, logic, reason and analysis. It is practical and pragmatic. The fruit of this tree is a Cartesian model of reality as mechanistic, a large complex system composed of many individual parts, and the key to understanding the system is through understanding its parts. This led to the advancement of modern science, industry, and Western medicine. It has also led to Quantum Physics, which ironically argues that there may in fact be no parts – only packets of potential energy managed into actuality through the direction of consciousness.”
Frank Elkins, Tiger Dragon – Lesson #13
Here we begin to see how the power of three influence science. Based on a triad of Reason, Mathematics, and Logic, other triadic systems, such as geometry, come into actuality. Later, the triad shows up as an atom consisting of a Proton, Neutron, and Electron as well as Einstein’s three-dimensional space. This same triadic balance of three would also become the dominate metaphysical symbol for Christianity: The Holy Trinity.
Next week we will consider this Spiritual metaphysical connection.
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