HoST Fall 08

Assignment 2

Week of 9/10/2008



As usual, read this page in its entirity.  I generally suggest that you have most if not all of the readings done for Wednesday.

Read: McClellan and Dorn, pp. 55-65.  The Pre-Socratics and Ionians et al. 10pp.

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 one PDF.


 (Make sure you download this particular PDF from the eLibrary.  There may be other “Plato…” files in there.)


-Women’s Issues: pp. 144-164. 20pp


-The Cave: pp. 227-235. 8pp


-The Quadrivium of Mathematical Sciences: pp. 235-250. 15pp


Read 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].




            The style of arithmetic exemplified by this reading in Iamblichus’ Theology of Arithmetic shows up throughout western history and variations of it throughout the history of 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.  ca. 20pp


The following writing assignment is one of the assignments that counts towards the 5 total.  I you have no idea what this means, reread the class policies page linked on the Syllabus.  Assuming you did last week’s assignment (the comic bookish thing based on the Enuma elish) you have 4 left to do.  You may choose to do this one or you may choose to skip it and wait for one another one.

Write a 1 to 2-page single-spaced essay on some aspect of this reading.  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.  Relate some issue you have chosen to other issues from these Pythagorean/Platonic readings or from the Enuma elish or the Bible or some other external source.  Try to get at Pythago-Iamblichus-Plato’s larger worldview by making the readings bounce off one another.  Feel free to delve into the ethical and ontological and epistemological issues and evaluate Iamblichus/Plato from your own perspective.  As I like to promote, if illustrations will improve your essay, put some in.  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 words 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, tetraktys, gender differences, nudism, gymnastics, education, mathematics, dating, dog breeding, eugenics, luck, 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.

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) …’the Cynic.’


[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 abusrd 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.






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.



"Cynic" derived from Greek word for dog (kynikos).

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 were takes from L. B. Alberti, On the Art of Building [De re aedificatura], IX.6, p. 306-309, from the mid 15th c.)



2     3

4     6     9

8     12    18    27

Examples of means:  Notice the patterns these series make in the above pyramid, the tetraktys.


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 tetraktys)






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


Here are the citations for the above works:  Feel free to cut and paste them for your citations… but add the page numbers and other details as you see fit.


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 foreward 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.


Movie Clip on Free Will

John Barnes and David Leung from my Scientific Revolution class both recommended that I watch this.  It is a clip from a movie called “Waking Life.”  In this clip a man, who starts with nostrils but ends without them, talks about free will in relation to modern science and a smidgen of old natural philosophy.  He also appears to have a very tiny dog.  It’s only 3 minutes long, but it outlines the issue nicely.



Back to Syllabus [HoST Fall 2008]




Review Material: Posted 10/5/08

(These are my own notes or edited Power Points and may not be entirely coherent.)



 Interesting Science News


Carey- For the Brain, Remembering Is Like Reliving



Special Notice: CERN (the Large Hadron Collider) is starting up on Wednesday. 

Assuming everything goes as hoped we will still have class Wednesday evening. 

If not, we probably won’t know the difference anyway.



–If you run across an interesting story, let me know–