PYTHAGORAS
.pdf
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/359497726
PYTHAGORAS
Article · March 2022
CITATIONS |
READS |
0 |
834 |
1 author:
Herb Spencer
SPSI - Spencer-Pacific Scientific Institute
142 PUBLICATIONS 222 CITATIONS
SEE PROFILE
All content following this page was uploaded by Herb Spencer on 26 March 2022.
The user has requested enhancement of the downloaded file.
1
PYTHAGORAS– A Critical Review of the Most Influential Greek Mystic © H. J. Spencer [25Mar.2022] <04 pages; 2,000 words>
ABSTRACT
This is the third in series of brief, analytic biographies of the 'Top-Nine' thinkers, whose thoughts have powerfully influenced large numbers of people across extended time scales. They are all reviewed here in the order of their birth. Negative thinkers (e.g. Hitler, Stalin) are ignored, while 'Mythic' talkers (like Jesus) are also ignored as little direct written information is available. Pythagoras has the enviable reputation as the founder of Greek Philosophy (the attempt to produce a communicable description of reality using an agreed set of words and fixed-symbols or shapes;). He was the first to define philosophy as the pursuit of wisdom (intrinsic knowledge) for its own sake, not for it sits utilitarian uses, like today [or 'lover of wisdom']. He is acknowledged as influencing Plato and several major mathematicians and scientists, such as Copernicus, Kepler and Newton. He established a community of followers in Southern Italy based on sharing all their possessions in common ("All things shared between friends"); his reputation exploded so that many of his discoveries may have proposed by his followers or from earlier sources, like his eponymous theorem of right triangles that were long known in Egypt and his theory of musical harmony: ambiguity is the result of long times.
This essay allowed me to investigate directly one of the most influential thinkers that have played too strong a role in western thinking, especially the central significance of mathematics in descriptions of reality: a broad myth that is rarely challenged enough today [see Numbers essay]. The mythic nature of ancient fame is illustrated in the large Wiki article, where almost every statement about Pythagoras is immediately contradicted.
REVIEWER'S BIOGRAPHY
Herb Spencer (born in Glasgow, Scotland in 1943) is a writer, researcher and natural philosopher. He was trained as a theoretical physicist at Imperial College, London University before losing interest in its too mathematical style, after a short, successful post-doctoral period of publishing several papers in the leading physics journals, based on his two-year PhD thesis research. He fell into the new world of computing and quickly built an understanding that allowed him to pursue a career in management consulting about computer innovation in business. Eventually, he set up a new software company to offer fixed-price projects for several industries, finally writing a gigantic software system for the insurance industry. This provided him with sufficient capital to seek early retirement, where he could expand his own education and pursue his own research and writing. This research has resulted in posting 100 papers on the Academia web site that are freely available to all.
REVIEWER'S WEBSITE
All of the reviewer's prior essays and other reviews (referenced herein) may be found, freely available at: https://jamescook.academia.edu/HerbSpencer
1
1.0INTRODUCTION
1.1LIFE
1.1.1 EARLY LIFE
Pythagoras was born on the island of Samos (an island off the Ionian Coast) around 570 BC, his father was reputed to be a successful gem-engraver. When young, he is reputed to have travelled widely to acquaint himself with the wisdom of the ancients. This included a major spell of 22 years in Egypt studying with the priests as well as meeting with the Chaldeans. He is likely to have discussed their religious views as well as their mathematical discoveries. He briefly returned to Samos before deciding on going to the Greek colony near Croton by 530 BC in Southern Italy ('Magna Graecia'), where he established his own school, where the 300 initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This involved a number of dietary restrictions, perhaps avoiding eating animal flesh. After addressing the Croton locals, he was invited to participate in its government.
1.1.2 THE SCHOOL
Reputed to be a mystic as well as a thinker, the school he founded would nowadays be thought of as a religious cult or monastery. Key to his thinking was the metaphysical idea of the migration of souls (the commonest explanation for the mystery of life and death, based on the assumption that all souls are immortal, so that after death, a soul is transferred into a new body: this process - called metempsychosis was never elaborated upon). The "Constancy of Souls" is never commented on either, where do the new ones come from or even where are the excess of dead souls 'parked' while waiting for a new owner?
1.1.3 DEATH
Pythagoras's secrecy and arrogance may have contributed to his death, as local rivalries and jealousies were stirred up by local Crotons disagreeing on how the School should be run. The locals attacked the school one night, burning several buildings and killing many members with only the younger and more active managing to escape. There is much confusion here in the story but Pythagoras likely died in 497 BC; an alternative ending has Pythagoras escaping to Metapontum, where he committed suicide by starvation.
2.0 NUMBER
Pythagoras obviously had a talent for mathematics as he and his followers were able to discover several new properties about them. The most obvious property is that stones (or pebbles) can be used to manipulate them. This led to arranging patterns of them in two or three dimensions. The 'tetracyts' of ten was seen as magical as it led directly to the number ten (fingers) the basis of western arithmetic 1+2+3+4 = 10. Two patterns led to the idea of the 'square' of a number that was vital to agrarian management and was needed to produce the proof of Pythagoras' best known theorem, using the squares of N2: 1, 4, 9, 16, ... This extended the Counting-View of numbers (quantitative) to the Spatial (or geometric view). A metaphysical view of the concept of Number was central to his whole philosophy becoming the root of his views on psychology, ethics and politics. For the Pythagoreans, Number is a living, qualitative reality that must be investigated experientially. Number was not something to be used (although he did introduce the first standard weights and measures in Greece) for Number is a principle or aspect of nature (like electricity). It also has a divine aspect as well; it represented Unity from which everything arose, Two then represented Duality (the beginning of multiplicity and strife) and Logos (the possibility of Relations).
3
2.1 IDEAS
2.1.1 MATHEMATICAL INNOVATIONS
The very narrow speciality of mathematics has long been a fruitful area to seek out innovation. Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field personally. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous triangular (and eponymous) theorem: ("in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the two other sides"). This theorem was known and used by the Babylonians and Indian mathematicians centuries before Pythagoras but he may have the first to introduce it to the Greeks on his return from his earlier travels.
The Pythagorean school were the first to investigate symmetry in solid shapes, they uncovered all FIVE regular solids. Their other undisputed claim is for the discovery of the Theory of Proportions between two sets of numbers that are related by a common proportionality factor.
2.1.2 ASTRONOMY
In ancient times, Pythagoras and his contemporary Parmenides of Elea were both credited with having been the first to teach that the Earth was spherical, the first to divide the globe into five climatic zones, and the first to identify the Morning Star and the Evening Star as the same celestial object (now known as the planet Venus).
3.0 HARMONY
It was the investigation of the single, stretched string with a moveable Bridge (or 'Monochord') where Pythagoras launched his basic physics. Plucking the stretched string: it first vibrates as a unit, then in two parts, then in three parts, four, and so on. As the string vibrates in smaller parts, higher tones are produced, becoming the harmonic series, reflecting the reciprocal length and the harmonic frequency. This device offered a rich, experiential investigation of the 'sweet' sounds in music. This confirmed Pythagoras' views on the centrality of arithmetic that eventually led him to a Universe of Sound or Cosmic Harmonies.
3.1 PHILOSOPHY
3.1.1 THE REPUBLIC
Plato's Republic may be partially based on the "tightly organized community of like-minded thinkers" established by Pythagoras at Croton.
3.1.2 THE ABSTRACT FORMS
Bertrand Russell, in his History of Western Philosophy, contends that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time. He concludes that "I do not know of any other man who has been as influential as he was in the school of thought."
3.1.3 IMPACT ON CHRISTIANITY
Many early Christians had a deep respect for Pythagoras. Eusebius (260-340 AD), bishop of Caesarea, praises Pythagoras in his Against Hierokles for his rule of silence, his frugality, his "extraordinary" morality, and his wise teachings. In another work, Eusebius compared Pythagoras to Moses. In one of his letters, the Church Father Jerome (c. 347 – 420 AD) praises Pythagoras for his wisdom and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him.
3
4
3.1.4 LATER INFLUENCE
During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts (in the university curriculum). He appears in numerous medieval depictions, in many illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres. The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe.
3.1.5 MODERN SCIENCE
Nicholas Copernicus cites various Pythagoreans in 1543 as the most important influences on the creation of his sun-centered model of the solar system. Johannes Kepler believed in the Pythagorean doctrine of musica universalis and it was his search for the mathematical equations behind this doctrine that led to his discovery of the elliptic Laws of Planetary Motion. Kepler titled his book on the subject: Harmonics of the World, after the Pythagorean teaching that had inspired him. He also called Pythagoras the "grandfather" of all Copernicans.
3.2 INFLUENCE ON WORLD
All schools are based on memory; students must remember what they have been told (and can later be checked). It also implies a bias towards the past (what has happened) rather than the future, which needs a powerful imagination.
4.0 PYTHAGOREANISM TODAY
Most professional mathematicians today would privately admit to being secret believers in Pythagoras but would probably deny this in public still being in thrall to a long-dead philosopher.
4.1ETHICS
4.2MERITOCRACY
The Greeks were huge egotists and competed to be the first or best; hence the many conflicting claims for precedence linked with Pythagoras. Most claims were verbal and could not be objectified (e.g. in stone). This psychic failure still corrupts Science today (e.g. Nobel Prizes) and aggressive competition
4.3 ROMANTICISM
Although Pythagoras developed a rare reputation for treating women well and was married with several children, he still persisted in the ancient Greek preference for masculinity (no female school-members) and has no quotations extent, in praise of Romantic Love.
5.0 SUMMARY & CONCLUSIONS
Pythagoras was obviously a smart, charismatic individual with a powerful grasp of the power of words to get people to follow him. His ongoing reputation is as a much a testimony to the creation of public institutions, like schools, that persist beyond the life of any its members.
His emphasis on the novelty of mathematics, which its reputation for unchanging truth, helped propel this narrow speciality into its civilizational control of human evolution. Today, the reputation of all mathematics means that almost everyone who gets the benefit of ongoing adult education must have shown a minimal competence in this esoterica (even nurses who skill set is practical), while the minority that have a built-in talent for mathematics, position themselves as the "smartest guys in the university".
4
View publication stats