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



 Updated: 8/31/11 4:20 PM

:::::AV:Fine arts:Raphael fl. 1510:School of Athens:PlatowithTimeo.jpg

Plato holding his book, Timaeus [In Latin, Timeo].  Detail from Raphael's "Diclac gel 5 kaufen"

Fresco ca. 1511, Vatican Collection.  Plato's face is supposedly based on Buy flagyl ireland (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 Cornford’s translation of Plato’s Republic. They are all contained in this one PDF.  Plato_RepublicExcerptsCornford-120min-5.7MB.pdf    These readings are excellent essay inspiration. 


-Women’s 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 Iamblichus’ 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].



            The style of arithmetic (arithmology) exemplified by this reading in Iamblichus’ 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 don’t 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 more…

women’s 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, chaos… 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. 



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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 of…

                      Plato 427-348/7, teacher of…

                         Aristotle 384-322, teacher of Alexander the Great…


                 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) …’the Cynic.’


:::::Downloads:Diogenes the Cynic:Bastein-Lepage_Diogenes.jpg

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 LaĎrtius.] 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 Zeppelin’s 4th album.

The inner sleeve of this album (below left) shows Diogenes the Cynic holding a lantern looking for “an honest man.”  He apparently went around looking for one in broad daylight. He couldn’t find one. The image on the right is the Tarot card upon which this image was clearly based.  Whether Zeppelin realized that this “Hermit” was Diogenes is doubtful.  They probably just thought it looked cool.


1085_hermit   9-VIIII-IX-Hermite





You will notice that these symbols from Zeppelin’s 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 Socrates’ definition of a human being was simply a “featherless biped.” 

Diogenes, ever the pistol, presented a plucked chicken to Plato, calling it a fellow human.


:::::Downloads:Diogenes the Cynic:Diogenes_at_sculoa_di_atene.jpg

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.


Here are the three standard “means” 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 “equidistant between both extremes.” 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.

“…the dimension of a side [c] that generates a square of equal [area]” to that of a rectangle with sides measuring a and b. Example:

a : c : b = 4 : 6 : 9

Harmonic Mean

“The proportion between the shortest and the longest dimensions is the same [proportion] as that [quantity] between the shortest and the middle, and … that [quantity] between the middle one and the longest. The ratio between the outer numbers equals the ratio between the differences between the numbers. 


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.



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 observations….. (again, notice the patterns in the tetractys)






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




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


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Added 10/18/2010

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



-blind spot