Log24

As G. M. Conwell pointed out in a 1910 paper, the group of all
40,320 permutations of an 8-element set is the same, in an
abstract sense, as the group of all collineations and dualities
of PG(3,2), the projective 3-space over the 2-element field.

This suggests we study the geometry related to the above group's
actions on the 105 partitions of an 8-set into four separate 2-sets.

Note that 105 equals 15×7 and also 35×3.

In such a study, the 15 points of PG(3,2) might correspond (somehow)
to 15 pairwise-disjoint seven-element subsets of the set of 105 partitions,
and the 35 lines of PG(3,2) might correspond (somehow) to 35 pairwise-
disjoint three-element subsets of the set of 105 partitions.

Exercise:  Is this a mere pipe dream?

A search for such a study yields some useful background . . .

.

Taylor's Index of Names  includes neither Conwell nor the
more recent, highly relevant, names Curtis  and Conway .

"Show all your work."

"No problema."

"Does the name 'Coulter' mean anything to you?"

See as well this  journal on 07/19/2021, the Lotus-page date above. 

Cube Bricks 1984 —

Related material —

Note the three quadruplets of parallel edges  in the 1984 figure above.

Further Reading —

The above Gates article appeared earlier, in the June 2010 issue of
Physics World , with bigger illustrations. For instance —

Exercise: Describe, without seeing the rest of the article,
the rule used for connecting the balls above.

Wikipedia offers a much clearer picture of a (non-adinkra) tesseract —

      And then, more simply, there is the Galois tesseract —

For parts of my own  world in June 2010, see this journal for that month.

The above Galois tesseract appears there as follows:

See also the Klein correspondence in a paper from 1968
in yesterday's 2:54 PM ET post. 

Exercise — Translate "cardinal interplay."

Related material — Language animal in this journal.

Click to enlarge.

Related material:  Folk Etymology  (Dec. 10, 2016).

See Exercise in this journal.
Happy birthday to Pope Francis.

On film director Stanley Kubrick:

On physics writer Peter Woit:

Illustration from a post of
Schicksalstag  2009

For illustrations based on the above equations, see
Coxeter and the Relativity Problem  and Singer 7-Cycles .

Mathematics vulgarizer Keith Devlin on July 1
posted an essay on Common Core math education.

His essay was based on a New York Times story from June 29,
“Math Under Common Core Has Even Parents Stumbling.”

An image from that story:

The Times  gave no source, other than the photographer’s name,
for the above image.  Devlin said,

“… the image of a Common Core math worksheet
the Times  chose to illustrate its story showed
a very sensible, and deep use of dot diagrams,
to understand structure in arithmetic.”  

Devlin seems ignorant of the fact that there is
no such thing as a “Common Core math worksheet.”
The Core is a set of standards without  worksheets
(one of its failings).

Neither the Times  nor whoever filled out the worksheet
nor Devlin seemed to grasp that the image the Times  used
shows some multiplication word problems that are more
advanced than the topic that Devlin called the
“deep use of dot diagrams to understand structure in arithmetic.”

This Core topic is as follows:

For some worksheets that are  (purportedly) relevant, see,
for instance…

http://search.theeducationcenter.com/search/
_Common_Core_Label-2.OA.C.4–keywords-math_worksheets,
in particular the worksheet
http://www.theeducationcenter.com/editorial_content/multipli-city:

Some other exercises said to be related to standard 2.OA.C.4:

The Common Core of course fails to provide materials for parents
that are easily findable on the Web and that give relevant background
for the above second-grade topic.  It leaves this crucial task up to
individual states and school districts, as well as to private enterprise.
This, and not the parents’ ignorance described in  Devlin’s snide remarks,
accounts for the frustration that the Times  story describes.

Harvard Gazette , March 4th, 2013:

"Winfrey will speak on May 30 during Commencement day’s
Afternoon Exercises, which serve as the annual meeting of
the Harvard Alumni Association. The exercises will take place
in the Tercentenary Theatre of Harvard Yard,
between Memorial Church and Widener Library."

On the 1977 Octavia Butler novel Mind of My Mind :

"The first chapter in a history that Butler has already taken up
at a much later stage in Patternmaster  (1976).
Mind of My Mind  begins with Doro, a ruthless mutant
as old as the pyramids who has spent the last 4,000 years
trying to breed a race in his own image. The culminating
experiment is his daughter Mary. But, to Doro's astonishment,
Mary's first instinct on attaining her full powers is to begin
building a mental community— a Pattern— out of the
wretched thousands of Doro's half-telepathic failures
and partial successes. Despite some ragged moments,
Butler is clearly on to a promising vein— something like
Zenna Henderson's 'People' stories without their
saccharine silliness. There's a lot of intrinsic energy in the
Pattern idea, and one wants to see where this erratic, gifted
storyteller will pick it up next."

— Kirkus Reviews , Vol. XLV, No. 8 (1977), p. 453.

See this journal on Butler's dies natalis , the feast of St. Matthias, 2006.

Those who prefer Eastern approaches to religion may consult
Robert Thurman and his daughter Uma.

"Oprah, Uma. Uma, Oprah." — David Letterman

"He gazed out of the window hoping that somehow everything could make sense to him."

— "Passing in Silence," by Oliver Humpage

"You gotta be true to your code." —Sinatra

Exercise: Trace a path from the June 27 NY Lottery numbers
to the above two quotations.  Hint: See Cuernavaca and
Pilgrim's Progress  in TIME Magazine, May 3, 1948.

For some further background, click on the CBS quote above.
I still prefer, as I did in 1948, less  up-to-the-minute developments.

* The title refers to the phrase "the artist's signature."

This morning's exercise in lottery hermeneutics is unusually difficult.

Yesterday was Bloomsday (the date described in
James Joyce's Ulysses ) and the New York Lottery numbers were…

Midday  numbers:  3-digit 181, 4-digit 9219.

Evening numbers: 3-digit 478, 4-digit 6449.

For 181 and 9219, see the following—

"With respect to every event, we must ask
 which element has been subjected directly to change."
— Ferdinand de Saussure, Course in General Linguistics
   (New York, The Philosophical Library, Inc., 1959), page 181

That Saussure page number was referenced in the following thesis
on James Joyce's other major novel, Finnegans Wake—

The thesis is from the University of Vienna (Universität Wien ).

The word Wien , in the derived form denoting an inhabitant of that city,
figured prominently in yesterday's news.

As for the evening numbers—

478 perhaps signifies the year 478 BC,
cited in Lawrence Durrell's Sicilian Carousel  as the year
the ruler Gelon died.

For the evening 6449, note that the poem by Wallace Stevens quoted
here on June 15 in A for Anastasios deals with "the river of rivers"…
perhaps signifying time.

Interpreting 6449 chronologically yields 6/4/49.

The film artist  John Huston, discussed in an essay from that date,
might appreciate the representation of the ancient Sicilian
river god Gelas as a man-headed bull on a coin from
around the year 478 BC.

For some perceptive remarks about Durrell, see the
article by Nigel Dennis in LIFE magazine's Nov. 21, 1960
issue (with cover noting Kennedy's victory in that year's
presidential election).

All of the above may be viewed as an approach to the aesthetic
problem posed by Dennis in yesterday's Bloomsday post—

"The problem that arises with this sort of writing is
one of form, i.e. , how to make one strong parcel
out of so many differently shaped commodities,
how to impose method on what would otherwise
be madness."

"The world has gone mad today…." — Cole Porter

For some related remarks, see page 161 of
Joyce's Catholic Comedy of Language *
by Beryl Schlossman (U. of Wisconsin Press, 1985)
and James Joyce in the final pages of The Left Hand of God
by Adolf Holl.

* Update of July 6, 2011—
This title is a correction from the previous title
given here, Moral Language  by Mary Gore Forrester.
Google Books had Schlossman's content previewed
under Forrester's title.

From Harvard's 2010 Phi Beta Kappa ceremony—

Think of all the history you’ve read. It started somewhere.
It started at absolute zero, is what you thought.
Just because you couldn’t know what came before.
But imagine: something did.

"To help the graduates find rightness, two addresses are at the heart of the exercises ceremony.
 One is by a poet, who reads a work written for the occasion.
 The other is by an 'orator,' a guest invited to offer timely discourse."

From this morning's New York Times—

Related material—

Immediately following Inspector Pine in this morning's Times  obituary list
is Virginia B. Smith, a former president of Vassar College. Smith died at 87 on August 27.

From her obituary—

Ms. Smith is survived by her partner of 57 years, Florence Oaks.

From “Music and Lyrics” (2007)

Yesterday, Valentine’s Day, Hollywood released a romantic comedy, “Music and Lyrics,” based on a fictional reality-TV show called “Battle of the 80’s Has-Beens.”

This, along with the Feb. 13 Log24 entry touching on both pop science and pop music, and the fact that today is the anniversary of the 1988 death of physicist Richard Feynman, suggests the following exercise:

Compare and contrast the lives and works of Feynman (May 11, 1918 – Feb. 15, 1988) and the late Carl Sagan (Nov. 9, 1934 – Dec. 20, 1996).

(Being dead, both are, in a sense, has-beens, and both were popular in the 1980’s.)

I personally regard Feynman as one of science’s saints, and Sagan as, shall we say, a non-saint.  For some related reflections on pop science and pop music, see the five Log24 entries ending on Michaelmas 2002.  And then there is popcorn–

Click on picture for details.