HoST Fall 2011

Week of 9/13–9/15

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Assignment 2

Greeks >Plato & Numbers

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

Plato holding his book, Timaeus [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?


Updated: 10/13/11 4:54 PM


We start Lucretius next week.  Make sure you have a copy of the book.


For Tuesday and Wednesday:


1-Read McClellan and Dorn, pp. 55-65.  The Pre-Socratics and Ionians et al.  This reading provides background and setting for the rest of this week's readings.  10pp


2-Listen to this podcast: - Bragg, Melvyn. Pythagoras. Audio. London: BBC, 2009.  Here is a link to the web page for this episode on the BBC site, but it doesn't always stream the show, but it does give you information about the show and who the guests are... etc., IOT-Pythagoras.  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.  You should take notes as you listen so that we can discuss it in class.


3-Read this entire web page.  There is more below.



For Thursday (but I suggest you start reading this earlier.)


1. 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. 


-Family Issues: pp. 156-164 (stop about 1/2 way down p. 164).

This stuff is pretty provocative. 8pp


-The Cave: pp. 227-235.

This is one of the most important philosophical stories ever. Read it closely.  8pp



2. Watch: Matrix Philosophy - the Cave.  Optional: You may also watch this much longer video on the philosophy of the Matrix if you so choose.  Philosophy of the Matrix

:::::CAL Article:Conference files:PowerPoint image


3-Homework- Due Thursday: Mitchell (in our class) directed me to this interesting article on super-intelligent dogs in the Fortean Times. clever_canines.html.  Look it over.  You don't have to read the whole thing.  I'd like you all to create a citation to this article (see Class Policies for the general template).  It's not as easy as it looks.  Then write a paragraph discussing the credibility of this article. Here are a few questions that you might consider when discussing this article.  How is this source credible?  How is it not credible?  What is the Fortean Times? Who wrote it?  Could I use this source in a dissertation on dog intelligence?  Could I use this as a source in a dissertation on 19th-century animal psychology?  Could I use this as a source for a dissertation on Nazi science? 


Citations for the above readings and audio:


Bragg, Melvyn. "Pythagoras" from In Our Time. Audio. Broadcast on Dec. 10, 2009. London: BBC, 2009.  [If you use this as a source in an essay, try to give an approximate time within the episode where the specific information appears.]


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. [Remember, doing this is up to you, but you need to do 4 over the course of the term.]


If you want to do an essay this week to fulfill one of the 4 essays 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 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 or expand it or think about how it may be found in modern society or modern thought. 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, and if you send it as an attachment, to name it with your name and the assignment.  E.g., Newsome-ShortEssayPlato.docx.]


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: [You may suggest other readings to me if you have something in mind, but they must be credible sources.]


- From the Plato PDF for the regular class readings, read "The Quadrivium of Mathematical Sciences" on pp. 235-250.


- From the Plato PDF for the regular class readings, read "The Equality of Women" on pp. 144-155.


- Add in something on the cave....


- 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? 


      - In this PDF read Waterfield's Introduction on pp. 23-31 and then choose a number and read 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].  Iamblichus_TheologyOfArithmetic100-4.1MB.pdf   .  Here is the citation to this source.  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.


Everybody should read over the following.... It's part of the assignment.

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 [a bad thing to do back then].


Stray and totally absurd story about Diogenes: 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.


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.  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.


Plato once told Diogenes that Socrates’ definition of a human being was simply a “featherless biped.” 

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




Plato later added "with broad fingernails" to his definition in order to exclude plucked chickens.


:::::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.

We will talk about 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


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