Saturday, January 7, 2012

Past Tense

Filed under: General — Tags: — m759 @ 4:09 PM

From a post that was written for Twelfth Night

Bernhard Weiss on the philosophy of Michael Dummett—

" … debates about realism, that is, those debates that ask
whether or not one or another aspect of the world is independent
of the way we represent that aspect to ourselves. For example,
is there a realm of mathematical entities that exists fully formed
independently of our mathematical activity? Are there facts about
the past that our use of the past tense aims to capture?"

Yes and Yes.

See also The Whirligig of Time in this journal.

Saturday, March 8, 2008

Saturday March 8, 2008

Filed under: General,Geometry — m759 @ 1:00 PM
Tilting at

From a New York Times list

of literary “signature passages” —

Don Quixote -- 'wasteland and crossroad places'

An answer:

The whirligig of time
— Shakespeare, Twelfth Night


Log24, Twelfth Night, 2006:

Hamilton’s Whirligigs

Hamilton's Whirligigs: The 8-element quaternion group as a subgroup of the 48-element group GL(2,3)

Click image to enlarge.

Related material:

Rotation in the complex plane.

The plane was discovered
in the late 1700’s by Wessel:

Caspar Wessel

by J.J. O’Connor
 and E.F. Robertson:

“Wessel’s paper [in Danish] was not noticed by the mathematical community until 1895… A French translation… was published in 1897 but an English translation of this most remarkable work was not published until 1999 (exactly 200 years after it was first published)….

We have called Wessel’s work remarkable, and indeed although the credit has gone to Argand, many historians of mathematics feel that Wessel’s contribution was [1]:-

… superior to and more modern in spirit to Argand’s.

In the [1] article the approaches by Argand and Wessel are compared and contrasted. Of course Wessel was a surveyor and his paper was motivated by his surveying and cartography work:-

Wessel’s development proceeded rather directly from geometric problems, through geometric-intuitive reasoning, to an algebraic formula. Argand began with algebraic quantities and sought a geometric representation for them. … Wessel’s initial formulation was remarkably clear, direct, concise and modern. It is regrettable that it was not appreciated for nearly a century and hence did not have the influence it merited.

However more is claimed for Wessel’s single mathematical paper than the first geometric interpretation of complex numbers. In [3] Crowe credits Wessel with being the first person to add vectors. Again this shows the depth of Wessel’s thinking but again, as the paper was unnoticed it had no influence on mathematical development despite appearing in the Memoirs of the Royal Danish Academy which by any standard was a major source of publications….

1. … Biography in Dictionary of Scientific Biography (New York 1970-1990).

3. M.J. Crowe, A History of Vector Analysis (Notre Dame, 1967).”

Tuesday, June 5, 2007

Tuesday June 5, 2007

Filed under: General — m759 @ 11:08 AM
A Whirligig Tour

Symbol from a
website on
Creedal Standards”

The above symbol
appeared here
on 11/8/02.

Related material:

1. The remarks of
Bradley Whitford

at Princeton’s
Class Day yesterday:

The image “http://www.log24.com/log/pix07/070605-Whitford.jpg” cannot be displayed, because it contains errors.

2. An illustration from
Log 24 on 11/10/06:

Paul Robeson in
King Solomon’s


3. The Whirligig of Time

The image “http://www.log24.com/log/pix07/070605-Whirligig.jpg” cannot be displayed, because it contains errors.

4. Natalie Angier, priestess of Scientism
  (5/26/07), and her new book
The Canon: A Whirligig Tour of
the Beautiful Basics of Science
(available as a special from

Better Together Buy this book with
God Is Not Great:
How Religion Poisons Everything
by Christopher Hitchens today!

The Canon: A Whirligig Tour of the Beautiful Basics of Science God Is Not Great: How Religion Poisons Everything

Buy Together Today: $31.19

Customers who bought this item
also bought

God Is Not Great:
How Religion Poisons Everything
by Christopher Hitchens

Wednesday, January 5, 2005

Wednesday January 5, 2005

Filed under: General — Tags: — m759 @ 7:11 AM

Death and the Spirit

A meditation for Twelfth Night
on "the whirligig of time"

Today's New York Times obituaries feature two notable graphic artists: 
  • Frank Kelly Freas, who created, among other works, 400 portraits of saints for the Franciscans and the covers of Mad Magazine from 1958 through 1962. "I found it difficult to shift my artistic gears from the sublime to the ridiculous and back again," he said of his departure from Mad.
  • Will Eisner, "an innovative comic-book artist who created the Spirit, a hero without superpowers, and the first modern graphic novel."

Yesterday's entry provided an approach to The Dark Lady, Kali, that was, in Freas's apt word, "ridiculous."  The illustration below, "Mate," is an attempt to balance yesterday's entry with an approach that is, if not sublime, at least more serious.  It is based on a similar illustration from Jan. 31, 2003, with actress Judy Davis playing The Dark Lady.  Today it seems appropriate to replace Davis with another actress (anonymous here, though some may recognize her).  I once knew her (unlike Davis) personally.  One of my fondest memories of high school is reading Mad Magazine with her in the school lunch room.  Our lives diverged after high school, but I could happily have spent my life in her company.


– S. H. Cullinane, Twelfth Night, 2005

The image “http://log24.com/log/pix05/050105-Mate.jpg” cannot be displayed, because it contains errors.

A diamond and its dual "whirl" figure—
or a "jewel-box and its mate"

For details, see the five Log24 entries
ending on Feb. 1, 2003, and the
perceptive remarks of Ryan Benedetti
on Sam Spade and Brigid O'Shaughnessy.

As for Eisner and "The Spirit,"
which has been called
"the quintessential noir detective series,"
those preferring non-graphic stories
may picture Spade or his creator,
Dashiell Hammett, in the title role.

Then, of course, there are Eisner's later
  story, "A Contract With God,"
  John 4:24, and 1916 4/24.

Monday, January 5, 2004

Monday January 5, 2004

Filed under: General — m759 @ 12:25 AM


Thus the whirligig of time
     brings in his revenges.”
Twelfth Night. Act v. Sc. 1.

Twelfth night is the night of January 5-6.

Tonight is twelfth night in Australia;
12:25 AM Jan. 5 in New York City is
4:25 PM Jan. 5 in Melbourne.

Sunday, January 5, 2003

Sunday January 5, 2003

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


Thus the whirligig of time brings in his revenges.
Twelfth Night. Act v. Sc. 1.

Twelfth night is the night of January 5-6.

Tonight is twelfth night in Australia; 4 AM Jan. 5
in New York City is 8 PM Jan. 5 in Sydney.

An October 6 entry:

Twenty-first Century Fox

On Sunday, October 6, 1889, the Moulin Rouge music hall opened in Paris, an event that to some extent foreshadowed the opening of Fox Studios Australia in Sydney on November 7, 1999.  The Fox ceremonies included, notably, Kylie Minogue singing "Diamonds are a Girl's Best Friend." 


Red Windmill

Kylie Minogue

For the mathematical properties of the red windmill (moulin rouge) figure at left, see Diamond Theory.

An October 5 entry:

The Message from Vega

"Mercilessly tasteful"
 — Andrew Mueller,
review of Suzanne Vega's
"Songs in Red and Gray"

In accordance with the twelfth-night
"whirligig of time" theme,
here are two enigmatic quilt blocks:

Devil's Claws, or
Hourglass Var. 3

Yankee Puzzle, or
Hourglass Var. 5

One can approach these symbols in either a literary or a mathematical fashion. For a purely mathematical discussion of the differences in the two symbols' structure, see Diamond Theory. Those who prefer literary discussions may make up their own stories.
"Plato is wary of all forms of rapture other than reason's. He is most deeply leery of, because himself so susceptible to, the literary imagination. He speaks of it as a kind of holy madness or intoxication and goes on to link it to Eros, another derangement that joins us, but very dangerously, with the gods."
Rebecca Goldstein in The New York Times,
    December 16, 2002 
"It's all in Plato, all in Plato; bless me,
what do they teach them at these schools?"
— C. S. Lewis in the Narnia Chronicles 

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