From the journal of Steven H. Cullinane... 2005 April 16-30

Saturday, April 30, 2005  9:00 PM

City of God

Kevin Baker in 2001 on
E. L. Doctorow's City of God:

"...the nature of the cosmos
(Augustine's City of God?)"

David Van Biema in Time Magazine
(May 2, 2005, p. 43)

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on Augustine's City of God:

"A key concept in Augustine's great
The City of God is that the Christian church
is superior and essentially alien
to its earthly surroundings."

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  Click on the above for a rendition of
  Appalachian Spring.

This year's April - Mathematics Awareness Month -
theme is "Mathematics and the Cosmos."

For my own views on this theme as it applies
to education, see Wag the Dogma.

For some other views, see this year's
Mathematics Awareness Month site.

One of the authors at that site,
which is mostly propaganda
for the religion of Scientism,
elsewhere quotes
an ignorant pedagogue:

"'The discovery of non-Euclidean geometries
contradicted the "absolute truth" view
of the Platonists.'"

-- Sarah J. Greenwald,
   Associate Professor,
   Department of Mathematics
   Appalachian State University, Boone, NC

Damned nonsense.  See Math16.com.


Saturday, April 30, 2005  9:00 AM

Nine is a Vine,
continued

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Larry Gelbart on the film
Up Close and Personal:
"A Brenda Starr is Born.''

Related material:
O'Hara's Fingerpost,
Eight is a Gate,
Art Wars,
In the Details,
and the words
"White Christmas."


Friday, April 29, 2005  10:10 AM

Midrash Jazz Quartet

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Harvard's Barry Mazur likes to quote Aristotle's Metaphysics.  See 1, 2, 3.

Here, with an introductory remark by Martha Cooley, is more from the Metaphysics:

The central aim of Western religion --

"Each of us has something to offer the Creator...
the bridging of
masculine and feminine,
life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)
The central aim of Western philosophy --
 Dualities of Pythagoras
as reconstructed by Aristotle:
Limited Unlimited
Odd Even
Male Female
Light Dark
Straight Curved
... and so on ....

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is... the central aim of all Western philosophy."
-- Jamie James in The Music of the Spheres (1993)

"In the garden of Adding
live Even and Odd...
And the song of love's recision
is the music of the spheres."
-- The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000)

Harvard University, Department of English:

The Morris Gray Lecture, a reading by E.L. Doctorow.
Wednesday, April 27, 6:00 PM

Thompson Room, The Barker Center
CANCELED


Today's birthday: Jerry Seinfeld.
Related material:
Is Nothing Sacred? and Symmetries.


Thursday, April 28, 2005  4:00 PM

Black Moses

For an explanation of the title, see
the previous entry and
Robert P. Moses and The Algebra Project.

For another algebra project, see
Log24 entries of April 14-25 as well as
the following "X in a box" figure
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from March 10, 2005 and
April 5, 2005.

Those interested in artistic rather than mathematical figures may compare this diagram with that of Samuel Beckett in Quad (1981):

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Related quotations:


Barry Mazur on a seminal paper of algebraist Saunders Mac Lane:

The paper was rejected "because the editor thought that it was 'more devoid of content' than any other he had read.  'Saunders wrote back and said, "That’s the point,"' Mazur said.  'And in some ways that’s the genius of it. It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else.'"

J. Peter May, a professor of mathematics at the University of Chicago quoted in the Chicago Tribune:

"There are some ideas you simply could not think without a vocabulary to think them."

Amen.


Thursday, April 28, 2005  2:00 PM

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Tuesday, April 26, 2005  6:29 AM

The Ring of Falsehood

In memory of Philip Morrison, bombmaker,

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Morrison

Scientific American columnist,
  pioneer of the
Search for Extraterrestrial Intelligence (SETI)
and author of
The Ring of Truth

Morrison died
in Cambridge, Massachusetts,
on Friday, April 22, 2005.

From The Measure of a Life:
Does religion play a role in attitudes toward ETIs? Philip Morrison gave his considered opinion... “Well, it might, but I think that it’s just one of the permissive routes; it isn’t an essential factor. My parents were Jewish. Their beliefs were conventional but not very deep. They belonged to the Jewish community; they went to services infrequently, on special occasions—funerals and high holidays”....

Although Sagan did not believe in God, he nevertheless said this about SETI’s importance... “It touches deeply into myth, folklore, religion, mythology; and every human culture in some way or another has wondered about that type of question. It’s one of the most basic questions there is.” In fact, in Sagan’s novel/film Contact, described by Keay Davidson as “one of the most religious science-fiction tales ever written”... Ellie discovers that pi—the ratio of the circumference of a circle to its diameter—is numerically encoded in the cosmos and this is proof that a super-intelligence designed the universe...

The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle—another circle, drawn kilometers downstream of the decimal point. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe.



Nell

See also yesterday's entry Mathematical Style.

Extra credit:
Discuss the difference betweeen physical constants and mathematical constants. Use the results of your discussion to show that the above discussion of pi is nonsense.


Monday, April 25, 2005  10:31 AM

Mathematical Style:
Mac Lane Memorial, Part Trois

(See also Part I and Part II.)

"We have seen that there are many diverse styles that lead to success in mathematics. Choose one mathematician... from the ones we studied whose 'mathematical style' you find most rewarding for you.... Identify the mathematician and describe his or her mathematical style."



Nell

-- Sarah J. Greenwald,
take-home exam from
Introduction to Mathematics
at Appalachian State U.,
Boone, North Carolina
From today's Harvard Crimson:

Ex-Math Prof Mac Lane, 95, Dies

[Saunders] Mac Lane was most famous for the ground-breaking paper he co-wrote with Samuel Eilenberg of Columbia in 1945 which introduced category theory, a framework to show how mathematical structures relate to each other. This branch of algebra has since influenced most mathematical fields and also has functions in philosophy and linguistics, but was first dismissed by many practical mathematicians as too abstract to be useful.

Gade University Professor of Mathematics Barry Mazur, a friend of the late Mac Lane, recalled that the paper had at first been rejected from a lower-caliber mathematical journal because the editor thought that it was "more devoid of content" than any other he had read.

"Saunders wrote back and said, 'That’s the point,'" Mazur said. "And in some ways that’s the genius of it. It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else."

He likened it to a sparse grammar of nouns and verbs and a limited vocabulary that is presented "in such a deft way that it will help you understand any language you wish to understand and any language will fit into it."

Beckett-like vocabulary
from April 24:

.

Also from Appalachian State University

(with illustration by Ingmar Bergman):
Get the Gospel Feeling
on April 24

"In my hour of weakness,
that old enemy
tries to steal my soul.
But when he comes
like a flood to surround me
My God will step in
and a standard he'll raise."

-- Jesus Be a Fence
Related material:
The Crimson Passion
 

Sunday, April 24, 2005  10:23 AM

April 24

Today's sermon:

.


Friday, April 22, 2005  9:00 AM

Mac Lane Memorial

In memory of Saunders Mac Lane, mathematician, who died Thursday, April 14, 2005:

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From MacTutor --

"It was during these years [the late 1930's] that he wrote his famous text A Survey of Modern Algebra with G. Birkhoff which was published in 1941. Kaplansky writes in [*] about this text:-

A Survey of Modern Algebra opened to American undergraduates what had until then been largely reserved for mathematicians in van der Waerden's Moderne Algebra, published a decade earlier. The impact of Birkhoff and Mac Lane on the content and teaching of algebra in colleges and universities was immediate and long sustained. What we recognise in undergraduate courses in algebra today took much of its start with the abstract algebra which they made both accessible and attractive.

[*] I. Kaplansky, "The early work of Saunders Mac Lane on valuations and fields," in I Kaplansky (ed.), Saunders Mac Lane: Selected Papers (New York - Heidelberg, 1979), 519-524."

Mac Lane is noted for introducing, with Eilenberg, category theory.

For some remarks on the place of category theory in the history of mathematics, see Log24  entries of Dec. 3, 2002.

Saturday, April 16, 2005  9:00 AM

Seal

The Log24 entry for yesterday, the date of Prince Rainier's funeral, discussed a figure sometimes called "Solomon's seal."  Here are some further reflections.

"Time and chance
happeneth to them all."
-- Solomon, Ecclesiastes 9:11

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Mid-day lottery number,
State of Grace,
April 15, 2005

5/28, 2003:

"The Eightfold Way
and Solomon's Seal
"