Pythagorean Proof—Micro Essay by Christopher Bek—PM Micro 2019.1—Issue 9

Summary—This micro essay discusses monads, relativity, certain and infallible knowledge, the Pythagorean theorem and the proof by rearrangement. Pythagoras sits at the base of Western rational thought.

Quotation—The universe begins when God creates a primordial particle out of nothing. From it matter irradiates spherically in all directions in an inexpressibly great yet limited number of unimaginably yet not infinitely minute atoms. —Edgar Allan Poe

Pythagoras (570–500 BC) was a Greek philosopher and mathematician and the founder of Pythagoreanism. His political and religious teachings influenced Plato and Aristotle and the entirety of Western philosophy through them. Pythagoras travelled to Croton and founded a school whose initiates were sworn to secrecy and lived a communal, ascetic lifestyle that advocated moderate vegetarianism. His teachings identified with metempsychosis or the transmigration of the soul. It holds that every soul is immortal and upon death enters into a new body. He also devised the doctrine of musica universalis which holds that the planets move according to mathematical equations which resonate faithfully and reasonably in a universal symphony.

Monads. Pythagoras also developed the concept of monads that refer to indivisible entities or atoms that compose reality. Gottfried Leibniz’s (1646-1716) then turned monadology into a mature philosophy that is a system of great simplicity and beauty. He referred to monads as windowless, indivisible, elementary particles that follow a pre-established harmony. Leibniz argued that humans and animals have one overriding monad which orchestrates the lower monads in the body. The ontological levels of monads or electrons are matter, life consciousness and self-awareness or souls. Leibniz used monadology as the basis for his version of calculus.

Relativity. The Pythagorean theorem was the first realization of certain and infallible knowledge. In fact, relativity theory is nothing but an application of the theorem. It tells us that as we accelerate towards light speed we begin to shrink in the direction of motion. If we actually reach light speed, we literally exit spacetime—meaning light speed is a boundary of the universe. Inside the universal sphere is spacetime while outside is nothingness. The photon travels along the boundary while electrons sew the fabric of reality at the boundary. This innate reality is like a computer while perceived reality is like a computer screen. From this we can see that reality is a façade, which modern man would know if he sought certain and infallible knowledge.

Pythagorean Theorem. In mathematics the Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c whereby: a2 + b2 = c2 (eg. 32 + 42 = 52).

Pythagorean Proof. The theorem has possibly the most proofs of any mathematical theorem. They are very diverse, including both geometric and algebraic proofs some dating back thousands of years. The theorem can be generalized to include higher-dimensional spaces that are objects which are not Euclidean right triangles but n-dimensional solids. In fact, string theory, like everything else, flows naturally from Pythagoras.

Proof by Rearrangement. The Pythagorean theorem was known long before Pythagoras but he may well have been the first to prove it. In any event the proof attributed to him is very simple and is called proof by rearrangement. Imagine a box containing four identical right triangles. The triangles are first arranged in the corners of the box with the space in the middle representing c2. It is then a simple matter of rearranging the triangles to show the equivalence of the spaces proving that a2 + b2 = c2 thus yielding the Pythagorean theorem. QED.

Conclusion. Pythagoreanism is an early Pre-Socratic Greek school of philosophy based around the metaphysical beliefs of Pythagoras and his followers. Pythagoras leads to relativity which leads to universal boundedness which leads to one photon which leads to the illusion of reality. Pythagoras sits at the base of Western rational thought.


On a visit to Leningrad some years ago I consulted a map to find out where I was, but I could not make it out. From where I stood, I could see several enormous churches, yet there was no trace of them on my map. When finally an interpreter came to help me, he said—We don’t show churches on our maps. Contradicting him, I pointed to one that was very clearly marked. For which he responded—That is a museum and not a living church, which we don’t show. It then occurred to me that this was not the first time I had been given a map which failed to show many things I could see right in front of my eyes. All through school and university I had been given maps of life and knowledge on which there was hardly a trace of the things that I most cared about and that seemed to me to be of the greatest possible importance to the conduct of my life. I remembered that for many years my perplexity had been complete—and no interpreter had come along to help me. It remained complete until I ceased to suspect the sanity of my perceptions and began instead to suspect the soundness of the maps.

—EF Schumacher

Once in Sunday school while going over the Greek New Testament, I asked a question regarding the meaning of a parable. The headmaster’s answer was so utterly confused and convoluted that I actually experienced my first true moment of consciousness—that is, I suddenly became aware with excruciating clarity that he knew nothing at all. From that moment forward, I began to think for myself, or at least knew that I could. I remember clearly the classroom with its windows so high that we could not see out, the desks, the platform on which the headmaster sat, his thin scholarly face, his nervous habits of twitching his mouth and jerking his hands—and then suddenly this profound inner revelation that neither he nor anyone else knew about anything that mattered. It was this threshold moment that was to be the starting point of my liberation from the external world. I knew then for certain that true knowledge could only be arrived at by authentic inner perception—and that all my loathing of religion, as it was taught to me, was at last vindicated.

—Maurice Nicoll

I want to know God’s thoughts.

The rest are details.

—Albert Einstein