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HoST Fall 2010 Tues/Thurs. starting at 4:00 in Babio 203 |
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This is 2010, not 2011...
This is 2010, not 2011...
This is 2010, not 2011...
Week of 9/14 and 9/16
Assignment 2
Greeks>Plato>Numbers
Updated: 8/31/11 4:20 PM
Plato holding
his book, Timaeus
[In Latin, Timeo]. Detail from Raphael's "School
of Athens"
Fresco ca.
1511, Vatican Collection. Plato's
face is supposedly based on Leonardo
(1452-1519).
Why do you
suppose he is pointing up?
While poking
around the internets, I found some crazies who think that Leonardo
made the shroud of Turin based on himself.
I posted a link
to this hypothesis as an example of horrible scholarship, easily found on the
web. Note the .com URL as well as
the total lack of direct supporting evidence beyond their picture with lines
connecting the facial hair of each image. By their logic and powers of
observation, anyone with a beard and moustache could be Jesus or could be
Leonardo. It's patently absurd....
but also oddly entertaining.
We start Lucretius next
week. Make sure you have a copy of
the book. See Assignment 0 for
details.
Read at least 1 and 2 for
Tuesday.
1-Read McClellan and Dorn, pp.
55-65. The Pre-Socratics and
Ionians et al. This reading
provides background and setting for the following readings. 10pp
2-Read the following sections listed
below from this PDF which has excerpts from Francis CornfordÕs translation of
PlatoÕs Republic.
They are all contained in this one PDF. Plato_RepublicExcerptsCornford-120min-5.7MB.pdf These readings are
excellent essay inspiration.
-WomenÕs
Issues: pp. 144-164.
This
stuff is pretty provocative and at times offensive. 20pp
-The
Cave: pp. 227-235.
This is
one of the most important philosophical stories ever. Read it closely. 8pp
3-Read Waterfield's
Introduction on pp. 23-31 and then choose a number and read 4 or 5 pages from that
section in IamblichusÕ Theology of Arithmetic.
I have included the chapters on the monad [1], the dyad [2], the triad
[3], the tetrad [4], the heptad [7], octad [8], ennead [9], and the decad [10].
Iamblichus_TheologyOfArithmetic100-4.1MB.pdf
The
style of arithmetic (arithmology) exemplified by this reading in IamblichusÕ Theology of
Arithmetic shows up throughout western history and variations of it
throughout the world. It is closely associated with Pythagoreanism and as such
shows up in most all philosophies that deal with numbers. Some remnants continue on to this day
– Lucky 7, Perfect 6,... etc.
ca.
12pp
4-Read this entire web
page. I put some good stuff below.
Citations
for the above readings:
Iamblichus
(Attributed to). The
Theology of Arithmetic: On the Mystical, Mathematical and Cosmological
Symbolism of the First Ten Numbers [Theologoumena Arithmeticae]. Translated
by Robin Waterfield with a foreword by Keith Critchlow. Grand Rapids, Mich.:
Phanes Press, 1988.
McClellan, James E.,
and Harold Dorn. Science
and Technology in World History : An Introduction. Baltimore, Md.: The
Johns Hopkins University Press, 1999.
Plato. The Republic of
Plato. Translation, notes, and commentary by Francis Macdonald Cornford.
Oxford: Clarendon Press, 1950.
Essay assignment for this week.
If you want to do an essay this week to fulfill one of the 4 due this term, here is the assignment. [Please tell me at the top of your essay if you are doing a short or a long essay.]: I also recommend doing this particular essay (long or short) because the Plato readings are particularly provocative.
Short Essay Option: Write an approx.
600 word, single-spaced essay (about 1 full page of single-spaced text) on some
aspect of this week's readings. Do
not write an essay generally describing the overall reading. I have already read it and do not need
your outline. Instead, latch onto
a particular issue and respond to it. Did something bother you in the
reading? Does anything in the
reading remind you of something?
Explore some aspect of the reading that caught your attention. [Remember to put your name, and the
assignment number on the top of your essay.]
Use illustrations or
even audio or video if it will help you present your ideas. If you use alternate
media, use your own judgment for how that will effect the length of the overall
essay. Only some pictures are worth a 1000 words. Only use alternate media if
you discuss it in some way.
Pictures are not decoration.
If you use a picture, talk about it. Cite everything including class
readings and lectures. I am
letting you follow your own noses here.
Do the readings far enough in advance so that you can savor them and
then write on them. Rushing
through a reading is a total waste of time. Moving your eyes across a page is not reading. You donÕt get anything from it.
Here are a bunch of
free-associations to help you get started. These are just suggestions, not
demands, and they may be more confusing than helpful. There are hundreds moreÉ
womenÕs rights,
tetractys, gender differences, nudism, gymnastics, education, mathematics,
dating, dog breeding, eugenics, luck, the lottery, biological determinism,
lambda, marriage ages, ethics, cooking and weaving, harmony, reality vs.
perception, painting, imitative art, number, intellect, pattern, rationality,
number, arithmetic, music, geometry, astronomy, world of forms, world of
shadows, prisoner, slave, government, astronomy, reality, world-soul, the One,
the good, god, soul, body, one to many, elements of matter, chaosÉ etc.
The Long Essay
option is essentially the same as the short essay but should be about
1200 words long (about 2 full pages of single-spaced text) and must incorporate
one or more of the following additional materials:
- From the Plato reading above
(in reading #2), read -The Quadrivium of Mathematical Sciences: pp. 235-250.
- Pp. 33-50 from Navon, Robert. The Pythagorean
Writings: Hellenistic Texts from the 1st Cent. B.C.-3d Cent. A.D. On Life,
Morality, and the World : Comprising a Selection of the Neo-Pythagorean
Fragments, Texts, and Testimonia of the Hellenistic Period, Including Those of
Philolaus and Archytas. Great Works of Philosophy Series; Vol. 3. Kew
Gardens, N.Y.: Selene Books, 1986.
Navon-PythagoreanWritingsExcerpts-1.9MB.pdf
- Burch, George Bosworth.
"The Counter-Earth." Osiris 11 (1954): 267-294. Burch-The_Counter-Earth.pdf
[653KB]
-Pythagorean cosmological
theory. It's almost a heliocentric
theory, but really weird. If you
read this, I'd appreciate a diagram showing how it this cosmological model is
structured. This article doesn't
have one. How stupid is that?
- Bragg, Melvyn. Pythagoras.
Audio. London: BBC, 2009. Here is
a link to the web page for this episode [IOT-Pythagoras] on the BBC
site, but it doesn't always stream the show, however it does give you
information about the show and who the guests are... etc. Because the BBC site is unreliable for
streaming audio, here is a link to the MP3 file of this episode that you can
download and listen to on your computer or other device if you don't want to
bother with streaming. IOT_ Pythagoras.mp3
[19.2MB]
-
The Pythagoreans were an odd bunch.
If you use this, and want to cite it, be sure to identify the speaker
(as best as you can) and identify where in the recording the quote or idea can
be found along with other bibliographical information. This means that you should take notes
as you listen and jot down times as you do so.
Example of citing this source:
[This may not be totally correct in form, but it's the right idea.]
Bragg, Melvyn. "Pythagoras" from In Our Time. Audio. Broadcast on Dec. 10, 2010. London: BBC, 2009: quotation by Ian Stewart found at 15:48 in the audio file.
Here are some stray notes and things that may be of some help.
Thales of Miletus
c.630-c.550
Pythagoras of Samos c.570-490
Democritus of Abdera c.460-370
Epicurus (of Samos) 341-270
Aristarchus
of Samos ca. 310-230
Socrates 469-399, teacher
ofÉ
Plato 427-348/7, teacher ofÉ
Aristotle 384-322, teacher of Alexander the GreatÉ
Athenian
Democracy begins in the middle of the 5th c. BC and ends 370
B.C. How long is that?
Here is a lesser known interesting figure whose story was totally
ruined by prudish 19th c. scholars:
Diogenes of Sinope (412/399?-323 BC) ÉÕthe Cynic.Õ
Painting by Jules Bastien-Lepage, 1873
Here we see Diogenes with a small lantern, naked and living like a dog.
[Not to be confused with Diogenes La‘rtius.] Diogenes is said to
have eaten (and masturbated) in the agora (marketplace) of Athens, urinated on
the man who insulted him, defecated in the amphitheatre, and pointed at people
with his middle finger.
Stray and totally absurd story: When asked how to avoid lust of
the flesh, Diogenes began to masturbate. When rebuked for doing so, he
replied, "If only I could
soothe my hunger by rubbing my belly."
He supposedly lived in a tub or a huge ceramic jar and ate only
onions.
[Given this diet, it is perhaps best that he pleasured only
himself and did not try to pleasure another.]
Plato is said to have commented that Diogenes the Cynic, was
Socrates gone mad. The stories of
Diogenes remind me stylistically of contemporary satire like Stephen Colbert or
The Office. His ridiculous
behavior points out how silly we are.
Famous images of
Diogenes: He is supposedly the person "searching for an honest man"
on ZOSO, Led ZeppelinÕs 4th album.
The inner sleeve of
this album (below left) shows Diogenes the Cynic holding a lantern looking for
Òan honest man.Ó He apparently
went around looking for one in broad daylight. He couldnÕt find one. The image
on the right is the Tarot card upon which this image was clearly based. Whether Zeppelin realized that this
ÒHermitÓ was Diogenes is doubtful.
They probably just thought it looked cool.
You will notice that these symbols from ZeppelinÕs album (above)
are somewhat similar to some of the symbols in the Iamblichus reading.
Geometry and arithmetic and symbolism have a long and
interconnected history.
In a moment of bonding, Plato once told Diogenes that SocratesÕ
definition of a human being was simply a Òfeatherless biped.Ó
Diogenes, ever the pistol, presented a plucked chicken to Plato,
calling it a fellow human.
Diogenes
looking all buff and clean. Harldy
dog-like, more like god-like.
Detail from Raphael's "School
of Athens"
Fresco
ca. 1511, Vatican Collection.
"Cynic" derived from Greek word for dog (kynikos).
Here is a link to a short video on Diogenes. It's not great, but it's not terrible
either.
http://www.youtube.com/watch?v=u5fNCyqo7NI
Here are the three standard
ÒmeansÓ which are discussed in most all arithmetical and harmonic/music
theoretical treatises starting in the 5th or 6th century
BC and very likely going back much further.
|
Arithmetic
mean |
c is linearly
equidistant from both a and b. |
The arithmetic mean is Òequidistant between both
extremes.Ó Example: a : c : b = 4 : 6 : 8 The common average. |
|
Geometric
mean |
a x b is a
rectangle, c is the
square that has the same
area. |
ÒÉthe dimension of a side [c] that
generates a square of equal [area]Ó to that of a rectangle with sides
measuring a and b. Example: a
: c : b = 4 : 6 : 9 |
|
Harmonic
Mean |
|
ÒThe proportion between the shortest and the
longest dimensions is the same [proportion] as that [quantity] between the
shortest and the middle, and É that [quantity] between the middle one and the
longest. The ratio between the outer numbers equals the ratio between the
differences between the numbers.
Example: a : c : b = 3 : 4 : 6 |
(The above
quotations about means were takes from L. B. Alberti, On the Art of Building [De re aedificatura],
IX.6, p. 306-309, from the mid 15th c.)
The following arrangement of numbers most famously described in Plato's Timaeus is often called the tetractys.
It is based on arithmetic and is a basis of harmonic theory.
I'll be demonstrating this in class next week.
1
2 3
4 6 9
8 12 18 27
Examples of means: Notice the patterns these series make
in the above pyramid, the tetractys.
Arithmetic: the earthy means:
2, 3, 4
4, 6, 8
6, 9, 12
Geometric means: the heavenly
means
4, 6, 9
1, 3, 9, 27
1, 2,4, 8
Harmonic means: the psychic
means: the intermediary between heaven and earth
3, 4, 6
6, 8, 12
9, 12, 18
36 and 55 observationsÉ..
(again, notice the patterns in the tetractys)
1+8+27=36
6+12+18=36
62=36
36= 2*18 = 3*12 = 4*9 = 6*6
36= 2*2*3*3 = 22(32)
55= 1+2+4+8+1+3+9+27 (the
external legs added together)
55= 1+2+3+4+6+9+12+18 (the
factors of 36)
2 3
4 6 9
8 12 18 27
20=30
21 31
22 21*31 32
23 22*31 21*32 33
sum of exponents equals 0
sum of
exponents equals 1
sum of
exponents
equals 2
sum of exponents equals 3
Back to HoST Fall 2010 Syllabus
Email me: host@mifami.org
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Exam notes:
-Pre-Socratic theories of nature
-Theories of Number
-Role of women
-Ideal society
-Allegory of the Cave and its
relevance later in history, both philosophical and in popular culture
-Diogenes the Cynic
-eugenics
-tetractys
-blind spot
-perception
-etc.