“Nay, by him that gave to our generation the tetractys, which contains the fount and root of eternal nature.” – Aetius, I, 3, 8 (Pythagorean oath)1
We return now to the three approaches to ultimate reality – scientific, philosophical, and theological. We have already examined in detail the scientific perspective which we found distilled down to an intersection of the very small – that is what makes up the substances of the universe – and the incomprehensibly large – that is the entirety of the cosmos including its structural, dynamic, and transcendental features. I ended on the following comment:
“If we assemble all of the pieces into a single understanding of ultimate reality we are left with not only awe of the physical, but a near mystical understanding of existence that has been “sensed” by the great thinkers and the great spiritualists in human history. Perhaps they were never far off the mark, only limited by vocabulary and knowledge needed to fully express it.”
Today we pick up that thread with the pre-Socratic Greek philosophers starting with Pythagoras. Of course we have no record written by the great Master himself, rather the extracts by later philosophers of the texts of his followers. Diogenes Laertius credits him as the originator of both the word philosophia and kosmos, but his concept of ultimate reality appears to be numbers and mathematics. Numbers are in fact things to Pythagoras endowed with mystical significance; for example, justice is identified with the number 4. Proclus tells us Pythagoras sought his “first principles in a higher realm of reality” when creating his geometrical philosophy.2
The Pythagoreans “saw simply the ultimate, single, nature (physis) of things in their mathematical structure.”3 One number of particular importance is 10, the very essence of number as it represents the sum of the tetrad – 1+2+3+4. In physical space 1 represents a point, 2 a line, 3 a triangle, and 4 a pyramid; thus encompassing the dimensions of space and the principles of all things.4
In the view of Pythagoras, the universe is endless (a-teles) in time providing for a Nietzsche-like ‘eternal recurrence’5 but limited (peras) in space while ordered by a mathematically-derived harmonia. As such there is a kinship and unity of life culminating in transmigration of eternal souls. Beauty is also inherent in mathematical order as seen in the numerical harmony of musical notes. As eternal, the universe is divine, and likewise, man is a fragment of the divine.6
Modern science confirms some of the teachings of Pythagoras. Mathematics is vital to physics, particularly for its more speculative assertions which often can be explained only in mathematical terms. While modern science states the universe had a beginning in the Big Bang, a multiverse might not, and in any case it remains unclear that the universe has an end. Pythagoras appears to have been correct that the universe is limited in size (even if we cannot be sure in the case of a multiverse). However, scientists would surely balk at the idea that numbers have a reality outside human construction, although there is room for debate here. In a sense Pythagoras remains the most modern of all the ancient philosophers, and no scholarship to date entirely confutes his beliefs.
1Allen, Reginald E., Greek Philosophy: Thales to Aristotle. The Free Press, New York, NY, 1966. Page 38.
2Ibid., page 37.
3Edwards, Paul (editor), The Encyclopedia of Philosophy. Macmillan Publishing Co., Inc. & The Free Press, 1972. Volume 7, page 38.
4Allen, Reginald E., Greek Philosophy: Thales to Aristotle. The Free Press, New York, NY, 1966. Page 39.
5Barnes, Jonathan, Early Greek Philosophy. Penguin Books, London, England, 2001. Page 35.
6Edwards, Paul (editor), The Encyclopedia of Philosophy. Macmillan Publishing Co., Inc. & The Free Press, 1972. Volume 7, page 37-39.