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HoST Fall 2011 Week of 9/13–9/15 |
Back to HoST Fall 2011 Syllabus Email me: host@mifami.org |
Assignment 2
Greeks >Plato & Numbers
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
REFRESH
ME
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 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.
-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
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 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: [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 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 . 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
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 [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 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.
Plato once told Diogenes that SocratesÕ definition of a human
being was simply a Òfeatherless biped.Ó
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.
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.
We will talk about 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 |
Interesting
Sciencey News
–If you run across an
interesting story, let me know–
Review Materials - 2-PreSocratics-Pythag-Plato-etc.pdf
[1.2 MB]
Again... these are a
bit of a mess.