On Five Ways of Thinking: Pythagoras

Philosofactory: Pythagoras
Philosophy On A Porch

(by pyrrho for publishing jointly at MLW and DocuDharma)

Pythagoras: A Mathematical Universe

zeno I will be using the print version of the Oxford “Dictionary of
Philosophy” to refresh myself for this series.

Links offered may or may not have been referenced to research this post. I
may or may not believe their assertions or have been exposed to them, but
they are given to ease your direct research further into Pythagoras. I try to
present them fairly and clearly. I am a skeptic myself, a relativist with
opinions on all these schools, and a tendency to eschew the doctrinaire side
of each of these schools, but as a skeptic, I’m equipped to give a philosophy
a fair shake. Myself, and tend to seek and emphasize the reusable tools each
school has to offer.

Most of you will know Pythagoras from the Pythagorean Theorum, but
Pythagoras was not just a mathematician and geometrician. His mathematics was
not separate from his life and his ideas were not limited to mathematics. As
with all these ancient philosophies I am covering in this series, Pythagoras’
is also has a whole system concerned with how to live… a worldview. This
worldview is what I am looking at in this series, because these philosophies
serve as archetypes for worldviews, archetypes I seem to encounter daily, and
which you do to. Archetypes not fundamental, but nevertheless ancient and
soaked into us. The epicurean is looking for a pleasurable life, to find the
small pleasures and live simply Simply, perhaps, but still nearby these
pleasures. The stoic is more hardened, does not expect pleasure as reward and
even scoffs at it as such, being as indifferent to pleasure as they have
chosen to be to pain. The pythagoreans then are those that have their head in
abstractions. One imagines the sort that has had no time for epicurean
pleasures like meals, having been preoccupied with a logical proof. To these
sort, the sublime superiority of a mathematical pattern was and remains as
obvious as the rising sun.

This series is presenting five ancient schools of philosophy as
archetypes. In the interest of honesty I must state my own philosophical
archetype is skepticism, but skepticism affords me the freedom to see the
strengths of these other archetypes. By no means are these five archetypes
meant to be limiting, according to a relative and skeptical approach any
number of archetypes can be constructed and used, but these do have the
particular quality of having been developed and infused into our “Western
Culture” over thousands of years, at least.

Their framings still exist, not merely as maxims come to mean other
things, linguistic ornaments merely, but at conceptual levels, such that one
can recognize a well worn conceptual tool with novel expressions in

The archetypes are so far as follow:

  • Epicurean: “Enjoy the simple pleasures, such as friendship, food and
    wine. Nature is filled with pleasure and suffering alike.”
  • Stoic: “Live with virtue and be indifferent to the harshness of life.
    Nature is indifferent but ordered.”
  • Pythagorean: “Truth and beauty lie in the abstractions of mathematics
    and geometry. Nature can be described with number.”
  • ???
  • ???

Indeed, the followers of Pythagoras were prone to taking Pythagoras himself
as a god become human to teach mankind these sublime truths. I do not find it
surprising that such a man led to a philosophy including vegetarianism and a
semi-divine presumption. If that sound dismissive, I share the pythagorean’s
sensibilities, if more humbly so, with an eye to the errors it introduces
with its beauties. As for the nearly religious awe I can feel before a
mathematical truth, take pi, a ratio that relates, among other things, the
length of the side of a circle to the length of the sides of a square, such
that, if you were to take the width of a square, and the radius of the circle
having the same circumference as the “circumference” of the square, then the
relation between the two involves a number whose digits never end, which
cannot be finitely represented. To me that’s stunning, but that turning
square into a circle requires a transcendental number is not stunning but
fitting. It is sublime, divine, and while expected, only ironically. And that
the ratio is well named as a “transcendental” number is no doubt a product of
our shared if inexplicable love for the beauty of math and geometry.

Concomitant to this, however, is removal of the self from the material
world into the world of abstraction and the illusion that abstractions are
not even of this world. The pythagorean spirit, as archetype, might not even
concern itself with math or geometry, but some other family of abstractions.
But abstraction are made from material facts, from astronomy, from counting,
from imperfectly drawn lines in the sand, and from deducing concepts that can
explain the facts abstracted all at once. This has proved a practical and
rewarding endeavor, but it is a part of the loss of reason to consider an
abstraction so fine it’s not a part of this world. But now I have begun to
describe Plato… Pythagoras himself might in fact object, thinking the world
of mathematics imbued the world around us all the material reality it had for
us to perceive. If I may accept this archetype in such a light, it remains a
tactile abstractionism, we feel the mathematical world about us always. We
are not imperfect beings separated from this glory, but are abstract beauties
ourselves, actually made of it.

It is easy to forget that Pythagoras was not a mathematician, because, in
fact, geometry and mathematics were to him really the most important things,
things which justified the world, and study of which made for a good life. As
for the specifics of worldly life style of pythagoreans, they were on the
very self disciplined side of living, following traditions of silence and
observance of various taboos, such as prohibition on eating flesh and beans.
For those that mistake a love of mathematics and the belief that mathematics
underpinned the universe for a modern scientific perspective, please consider
that Pythagoras was much more of a mystical and spiritual teacher than that.
For example, it was said Pythagoras was able to remember each former
existence, being as they believed in reincarnation. Further, the form of
reincarnation they believed in was transmigratory, the spirit may come to
exist, or have existed, in plant or animal form in addition to humans. That’s
a view of reincarnation I personally endorse very strongly in the “if you are
going to believe it, you should also believe…”. To study the world of
mathematics, or, metaphorically, abstractions, had a spiritual value
according to Pythagoras, it could free the soul from this cycle of
incarnation and let it rejoin the cosmos as one. This is what combined his
worldview with his philosophy of mathematics and geometry.

Pythagoras and the pythagoreans were prone to numerology, and by extension
metaphorically any modern pythagorean-types are be prone to mysticism about
abstractions themselves. Often attributed to him is the view that all things
are numbers. This is undoubtedly a simplification of his views, but stop and
consider the success of that theory. Viewing things quantitatively, which is
to reduce them to numbers, has been very successful in engineering, science,
and I think especially, computer science. This love for abstraction is
overboard in pythagoras, I suspect, but it is also somewhat warming and nice
for one to be so driven to seek this kind of beauty, for it is that which
seeks the patterns of the universe… and finds some.

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  1. has a place of honor in the hearts here in this most musical household.  his ‘mathmetization’ of music (summarized here) is inspires us still

  2. numbers will play an important role today.  The Republicans were on the ropes as demonstrated by their unprecedented signage.  The vote for Town Supervisor will be an interesting one.  A local farmer, new to the area, is running against both the dems and the repubs.  He just might pull it off too.  He is personable, good at networking, and completely independent.

    Of course he most likely will split the Democrats more than the Republicans but we’ll see.

    I think I’d have to be described as Epicurean but don’t label me bro. 🙂

  3. as a Cynic.

    I always loved the story attributed to Diogenes, the most famous of the cynics, upon meeting Alexander the Great. 

    Having heard of Diogenes’ great reputation, Alexander sought out Diogenes as he was sitting in his bathtub outside one day. Alexander was so thrilled to meet Diogenes that he said he would grant any request that he made.

    Diogenes responded to Alexander as he stood next to the tub, “Stop blocking the sunlight.”

    • feline on November 6, 2007 at 9:12 pm

    Is that one of the ??? or bonus choices?

  4. but I live in the music, so go figure.  I am a skeptic, loving the idea of social justice and the virtues as an archetype.  I tolerate ambiguity, but I don’t like it.  I love the order found in nature, in human-made music and architecture, but I also don’t “get” most visual art. I love the abstract human but dislike most all of you/us in the flesh. I am agnostic and spiritual.  I believe in science and reason as far as their limits can take me.

    I think quantum and theoretical physics may be where the next layer of answers arise.

    And I believe that humans are in rapid decline, where technology and the ability to act trumps the rationale and thoughtfulness to determine the risk/benefits of acting, and thus guides the actions. In other words, just because you can doesn’t mean you should.

    My name could be Eeyore.

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