Log24

Friday, August 4, 2017

Sangaku

Filed under: General — m759 @ 12:00 AM

Friday, September 28, 2012

Geometretos*

Filed under: General — m759 @ 12:00 PM

MEDEIS AGEOMETRETOS EISITO

— Inscription at entrance to
     Plato's Academy, according to
     an elementary introduction to
     philosophy by James L. Christian 

For Irving Adler, who reportedly
died on September 22, 2012—

 

Background: See Sangaku in this journal.

See also the following, from a different  
elementary introduction, by Adler—
Giant Golden Book of Mathematics,
illustrated by Lowell Hess

.

   (Detail of Flickr photo)


* See Liddell and Scott.

Tuesday, June 9, 2009

Tuesday June 9, 2009

Filed under: General — m759 @ 2:56 PM
Recessional

"I know what 
nothing means."
— Joan Didion, 
Play It As It Lays

President Faust at Harvard Baccalaureate, June 2, 2009

Faust

President Faust of Harvard on Joan Didion:

"She was referring to life as a kind of improvisation: that magical crossroads of rigor and ease, structure and freedom, reason and intuition. What she calls being prepared to 'go with the change.'"
 

Bippity Boppity Boo.


Didion's own words
:

"I think about swimming with him into the cave at Portuguese Bend, about the swell of clear water, the way it changed, the swiftness and power it gained as it narrowed through the rocks at the base of the point. The tide had to be just right. We had to be in the water at the very moment the tide was right. We could only have done this a half dozen times at most during the two years we lived there but it is what I remember. Each time we did it I was afraid of missing the swell, hanging back, timing it wrong. John never was. You had to feel the swell change. You had to go with the change. He told me that. No eye is on the sparrow but he did tell me that."

From the same book:

"The craziness is receding but no clarity is taking its place."

— Joan Didion, The Year of Magical Thinking

For a magical crossroads at another university, see the five Log24 entries ending on November 25, 2005:


The sign of the crossroads at Stanford

This holy icon
appeared at
N37°25.638'
W122°09.574'
on August 22, 2003,
at the Stanford campus.

Also from that date,
an example of clarity
  in another holy icon —

A visual proof of the Pythagorean theorem

— in honor of better days
 at Harvard and of a member
of the Radcliffe Class of 1964.
 

Friday, September 17, 2004

Friday September 17, 2004

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

God is in…
The Details

From an entry for Aug. 19, 2003 on
conciseness, simplicity, and objectivity:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest.

Another Harvard psychiatrist, Armand Nicholi, is in the news lately with his book The Question of God: C.S. Lewis and Sigmund Freud Debate God, Love, Sex, and the Meaning of Life.

Pope

Nicholi

Old
Testament
Logos

New
Testament
Logos

For the meaning of the Old-Testament logos above, see the remarks of Plato on the immortality of the soul at

Cut-the-Knot.org.

For the meaning of the New-Testament logos above, see the remarks of R. P. Langlands at

The Institute for Advanced Study.

On Harvard and psychiatry: see

The Crimson Passion:
A Drama at Mardi Gras

(February 24, 2004)

This is a reductio ad absurdum of the Harvard philosophy so eloquently described by Alston Chase in his study of Harvard and the making of the Unabomber, Ted Kaczynski.  Kaczynski's time at Harvard overlapped slightly with mine, so I may have seen him in Cambridge at some point.  Chase writes that at Harvard, the Unabomber "absorbed the message of positivism, which demanded value-neutral reasoning and preached that (as Kaczynski would later express it in his journal) 'there is no logical justification for morality.'" I was less impressed by Harvard positivism, although I did benefit from a course in symbolic logic from Quine.  At that time– the early 60's– little remained at Harvard of what Robert Stone has called "our secret culture," that of the founding Puritans– exemplified by Cotton and Increase Mather.

From Robert Stone, A Flag for Sunrise:

"Our secret culture is as frivolous as a willow on a tombstone.  It's a wonderful thing– or it was.  It was strong and dreadful, it was majestic and ruthless.  It was a stranger to pity.  And it's not for sale, ladies and gentlemen."

Some traces of that culture:

A web page
in Australia:

A contemporary
Boston author:

Click on pictures for details.

A more appealing view of faith was offered by PBS on Wednesday night, the beginning of this year's High Holy Days:

Armand Nicholi: But how can you believe something that you don't think is true, I mean, certainly, an intelligent person can't embrace something that they don't think is true — that there's something about us that would object to that.

Jeremy Fraiberg: Well, the answer is, they probably do believe it's true.

Armand Nicholi: But how do they get there? See, that's why both Freud and Lewis was very interested in that one basic question. Is there an intelligence beyond the universe? And how do we answer that question? And how do we arrive at the answer of that question?

Michael Shermer: Well, in a way this is an empirical question, right? Either there is or there isn't.

Armand Nicholi: Exactly.

Michael Shermer: And either we can figure it out or we can't, and therefore, you just take the leap of faith or you don't.

Armand Nicholi: Yeah, now how can we figure it out?

Winifred Gallagher: I think something that was perhaps not as common in their day as is common now — this idea that we're acting as if belief and unbelief were two really radically black and white different things, and I think for most people, there's a very — it's a very fuzzy line, so that —

Margaret Klenck: It's always a struggle.

Winifred Gallagher: Rather than — I think there's some days I believe, and some days I don't believe so much, or maybe some days I don't believe at all.

Doug Holladay: Some hours.

Winifred Gallagher: It's a, it's a process. And I think for me the big developmental step in my spiritual life was that — in some way that I can't understand or explain that God is right here right now all the time, everywhere.

Armand Nicholi: How do you experience that?

Winifred Gallagher: I experience it through a glass darkly, I experience it in little bursts. I think my understanding of it is that it's, it's always true, and sometimes I can see it and sometimes I can't. Or sometimes I remember that it's true, and then everything is in Technicolor. And then most of the time it's not, and I have to go on faith until the next time I can perhaps see it again. I think of a divine reality, an ultimate reality, uh, would be my definition of God.

Winifred
Gallagher

Sangaku

Gallagher seemed to be the only participant in the PBS discussion that came close to the Montessori ideals of conciseness, simplicity, and objectivity.  Dr. Montessori intended these as ideals for teachers, but they seem also to be excellent religious values.  Just as the willow-tombstone seems suited to Geoffrey Hill's style, the Pythagorean sangaku pictured above seems appropriate to the admirable Gallagher.

Tuesday, September 9, 2003

Tuesday September 9, 2003

Filed under: General — m759 @ 9:37 PM

Olympic Style

For Dr. Mary McClintock Dusenbury,
Radcliffe College Class of 1964,
who shares an August 22 birthday with
the late Leni Riefenstahl —

Three occurrences of the same
sangaku (temple tablet):

August 19, 2003,

August 22, 2003,

September 6, 2003.

Sunday, September 7, 2003

Sunday September 7, 2003

Filed under: General — Tags: — m759 @ 11:11 PM

Horse Sense

Mathematicians are familiar with the emblem of Springer Verlag, the principal publisher of higher mathematics.

Ferdinand Springer, son of Julius Springer, founder of Springer Verlag, "was a passionate chess player and published a number of books on the subject. In 1881 this personal hobby and the name Springer led the company to adopt the knight in chess (in German, Springer) as its colophon."

Hermann Hesse on a certain sort of serenity:

"I would like to say something more to you about cheerful serenity, the serenity of the stars and of the mind…. neither frivolity nor complacency; it is supreme insight and love, affirmation of all reality, alertness on the brink of all depths and abysses; it is a virtue of saints and of knights; it is indestructible and only increases with age and nearness to death. It is the secret of beauty and the real substance of all art."

— From The Glass Bead Game

A saint and a knight, Jeanne d'Arc, was memorably portrayed by Milla Jovovich in The Messenger.

(Jovovich seems fated to play more-than-human characters in religious epics; see The Fifth Element.)

Another Springer, related to horses and to the accusation of witchcraft faced by Jeanne d'Arc, is Nancy Springer, the author of

The Hex Witch of Seldom.

Springer has written a number of books about horses, as well as other topics.

All of the above…. especially the parts having to do with mathematics and horses… was prompted by my redrawing today of a horse-shape within mathematics.  See my entry The Eight of April 4, 2003, and the horse-figure redrawn at right below.

 



Springer
Verlag



The
 Messenger



A
7-Cycle

Believers in the story theory of truth may wish to relate the gifts of Jeanne d'Arc and of the girl in The Hex Witch of Seldom to the legend of Pegasus.  See, for instance,

Plato, Pegasus, and the Evening Star.

For another connection between mathematics and horses, see Sangaku.
 

Saturday, September 6, 2003

Saturday September 6, 2003

Filed under: General — m759 @ 2:56 PM

Pictures for Kurosawa

Five years ago on this day, director Akira Kurosawa died.

The above pictures are offered as a remembrance of Kurosawa and also of Charlotte Selver, who died on August 22, 2003.

The picture at right is from an entry of August 22.  As one obituary of Selver says, “She was very sharp and very precise.”

The picture at left is the cover of Alan Watts’s book The Spirit of Zen (a religion that is also very sharp and very precise).

From
A New Seeing,
by Mary Alice Roche

The connection with Alan Watts was a fateful one. As Charlotte recalls it, “My aunt wrote me from San Francisco, ‘last night I heard a man lecture about what you do.’ And she sent me Alan Watts’s first little book, The Spirit of Zen. I had never heard of Zen, was amazed and fascinated, and decided to visit the author.” She did so in August of 1953, and that was the beginning of a long relationship with Zen Buddhism – and also the beginning of a long series of joint seminars with Alan Watts, first in New York, and later, on Watts’s ferryboat in Sausalito, California. Some of the titles of their seminars were “Moving Stillness,” “The Unity of Opposites,” “Our Instantaneous Life,” “The Mystery of Perception,” “The Tao in Rest and Motion.” (Watts always said that Charlotte Selver taught a Western equivalent of Taoism.)

The picture at right above is intended as a sangaku, or Japanese temple tablet.

The picture at left above on the cover of Watts’s book may be regarded as illustrating the following:

“As these flowing rivers that go towards the ocean, when they have reached the ocean, sink into it, their name and form are broken, and people speak of the ocean only, exactly thus these sixteen parts of the spectator that go towards the person (purusha), when they have reached the person, sink into him, their name and form are broken, and people speak of the person only, and he becomes without parts and immortal. On this there is this verse:

‘That person who is to be known, he in whom these parts rest, like spokes in the nave of a wheel, you know him, lest death should hurt you.’ “

Prasna Upanishad

Friday, August 22, 2003

Friday August 22, 2003

Filed under: General,Geometry — m759 @ 12:12 AM

Birthday Tablet

“Of the world’s countless customs and traditions, perhaps none is as elegant, nor as beautiful, as the tradition of sangaku, Japanese temple geometry.”

Tony Rothman

Sangaku means “mathematical tablet.”

Here is a sangaku for
Dr. Mary McClintock Dusenbury
on her birthday.

For an explanation,
click here.

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