Mysticism has gone hand in hand with mathematics since the beginning of time, that is, if time can be said to have a beginning. The greatest mathematicians have always had profound mystical beliefs. Their numbers include Pythagoras, Leibniz, Fourier, Laplace, Pascal, Kepler, Ptolemy, Euclid, Plato, and Gödel. Virtually everywhere, mysticism is thought of as the mysterious occult or the word conjures imagery of witchcraft. Mysticism can be experienced as the existence of realities beyond perceptual apprehension, realities that are directly accessible by subjective experience.
Essentially, mystical tradition does not adhere to any philosophy; rather, it is the direct apprehension of one’s personal identity with God. The central teaching of mysticism is that reality is one. According to mystics throughout time, the road to enlightenment can only be walked along the path of meditation. Through this type of practice one can associate oneself with the cosmic mind which is in fact everywhere, contrary to the popular belief that the mind is localized to the brain.
The 20th century mathematician Kurt Gödel offers this method on how best to experience the cosmic mind directly. He asserts that the first thing that needs to be done is for the senses to be closed off by lying or sitting in a quiet place. He emphasizes that it is a mistake to allow everyday reality to condition possibility, and only to imagine the combinations and permutations of physical objects the mind is truly capable of directly experiencing. Only by closing off one’s senses can one leave the finite behind and proceed towards the infinite. Gödel claims that the ultimate goal of all philosophy is perception of the absolute.
Through such practice, it is possible for one to detach oneself from physical reality and to enter into the realm of God, where space and time cease to exist altogether, and everything is one. This reality can only be grasped through intuition rather than through logical reasoning methods. Bertrand Russell asserts there are four main characteristics of mysticism.
(i) Intuition is a direct way of knowing. David Suzuki calls this way of knowing the world prajna. This type of way of knowing can neither be taught nor dissertated; rather, it is communicated through a mystical grasping of the world in its unity.
(ii) A belief in the unity of all things. In other words, it is the refusal to admit opposition or division anywhere. Mystics throughout history have asserted that all of reality is in fact a cosmic dance. In Hinduism, the dance is called maya, it is the illusion of the separateness of all things; to pierce the veil of maya is to see through the illusion and directly perceive the infinite.
(iii) All evil is mere appearance. It is an illusion produced by the divisions and oppositions of the analytic mind. When unified with the cosmic mind, there is no such thing as evil, and it is our sense of separation that allows for the illusion of evil to exist. Mysticism does not maintain that such things as cruelty are good, rather it denies that they are real, they belong to the lower world of phantoms from which we are to be liberated by the insight of vision. The mystic lives in full light of this vision: what others dimly seek, he knows with a knowledge beside which all other knowledge is ignorance.
(iv) The denial of the reality of time. The importance of time is theoretical, existing only in relation to our desires, rather than to knowledge of truth. Even though time can seem real, to realize, in both thought and feeling, the unimportance of time is the gateway to wisdom. In fact, this thought, which has been known to mystics throughout the centuries, was truly proven when Albert Einstein published his Relativity Theory.
Relativity Theory asserts that as an object approaches the speed of light time slows down. Virtually all physicists now agree that if an astronaut were to travel to a distant star and return, moving at a velocity close to that of light, he could, in theory, travel thousands of years into the Earth’s future. If one were to travel at the speed of light itself, then time would completely stop, and one would be, as they say, “stuck in a moment”.
The conjecture now is that tachyons, particles moving faster than light, actually exist. Relativity theory leaves no escape from the fact that anything moving at a velocity faster than the speed of light – or “several multiples of c” as Kevin Spacey’s character says in K-Pax – would move backwards in time. The implications of the existence of such tachyons are endless, and could pave the way for a real life Delorien to exist in the future, or even the past for that matter. This type of creative development would be the ultimate merger of mysticism and mathematics.
Many of the great names of history have merged their wisdom of mathematics and mysticism. Among them, none ranks higher than Pythagoras. He was at once a wizard and a mathematical icon, and the founder of the Pythagorean School, a mystical sect who dealt with mathematics and philosophy, and it is their work that is frequently credited with bringing about the birth of modern mathematical physics.
While they made advanced leaps and bounds in mathematics, they were best known for the tenet of metempsychosis, another term for reincarnation. Pythagoras is said to have been able to remember many of his past lives as well as having many other “supernatural” powers. They believed that there is one cosmic mind or soul, and that you are alive because a small piece of this soul is imprisoned in your body, and that bit of soul that animates you will animate many other bodies before returning to unity with the one cosmic soul.
The Pythagoreans adhered to a great number of rules and taboos in an effort to bring themselves into closer harmony with the cosmos. Among them were strict vegetarianism and not accepting pay for their teachings. It was hoped that if you could bring yourself into close enough harmony with the one cosmic soul when your body died, the soul that vivified it might return to the source instead of incarnating again.
The Pythagorean School was also where a young Plato learned mathematics after the death of his teacher Socrates. Like Pythagoras, Plato sought the key to the universe in arithmetic and geometry. When asked about the occupation of God, Plato answered that “He geometrizes continually”. In fact, Plato believed that the good of geometry is set aside and destroyed when reduced to the world of sense instead of being elevated with the ethereal images of thought, as employed by God for which reason he is always God. He also believed that the study of geometry is a necessary preparation for the study of philosophy. He observed that geometry trained the mind for correct and vigorous thinking. He placed this inscription over his porch “Let no man who is unacquainted with geometry enter here.”
Mathematicians in the last 500 years have faced stricter opposition for holding mystical beliefs. Modern sceptics of mysticism are abundant throughout the mathematical world. Twentieth century giants such as Gödel and Einstein come to mind as examples of modern mystics; their mathematical achievements are crowned without their denying the existence of a supreme reality. Despite the scepticism of the scientific community, the fact remains that mathematics and mysticism exist concurrently as necessary requisites for anyone who wishes to adequately comprehend the universe.
Russell, Bertrand. Mysticism and Logic and Other Essays. London: G, Allen & Unwin, 1917. Print.
“Maya: Illusion.”The Heart of Hinduism. ISKCON
Communications, 2004. Web. 9 May. 2011.
K-Pax. Dir. Iain Softley. Perf. Kevin Spacey, Jeff Bridges, and Mary McCormack. Universal Pictures, 2001. DVD.
http://www.thalesians.com/finance/index.php/Quotes
Mackey, G. Albert, and Haywood, L. Harry. Encyclopedia of Freemasonry. Chicago: The Masonic History Company, 1946. Print.
Riedweg, Christoph. Pythagoras. Trans. and Ed. Steven
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Rendall. New York: Cornell University Press, 2005. Print
Math Stories For You 