Log24

Part I — Unity and Multiplicity
              (Continued from The Talented and Galois Cube)

Part II — "A feeling, an angel, the moon, and Italy"—

Click for details

Nietzsche in Switzerland —

“In August 1884, he wrote to Resa von Schirnhofer:
‘Here one can live well, in this strong, bright atmosphere,
here where nature is amazingly mild and solemn
and mysterious all at once— in fact, there is no place
that I like better than Sils-Maria.'”

For more about Resa,  see another weblog’s post
of April 30, 2013.

A remark on Nietzsche from the epigraph of that weblog:

“His life’s work was devoted to finding one’s ‘style’
within the chaos of existence. The trick, obviously,
is not to lose your mind in the process.”

A remark from this  weblog on the above date —
Walpurgisnacht 2013 —

(Continued from Walpurgisnacht 2012)

Wikipedia article on functional decomposition—

"Outside of purely mathematical considerations,
perhaps the greatest value of functional decomposition
is the insight it provides into the structure of the world."

Certainly this is true for the sort of decomposition
known as harmonic analysis .

It is not, however, true of my own decomposition theorem,
which deals only with structures made up of at most four
different sorts of elementary parts.

But my own approach has at least some poetic value.

See the four elements of the Greeks in (for instance)
Eliot's Four Quartets  and in Auden's For the Time Being .

A search tonight for material related to the four-color
decomposition theorem yielded the Wikipedia article
Functional decomposition.

The article, of more philosophical than mathematical
interest, is largely due to one David Fass at Rutgers.

(See the article's revision history for mid-August 2007.)

Fass's interest in function decomposition may or may not
be related to the above-mentioned theorem, which 
originated in the investigation of functions into the
four-element Galois field from a 4×4 square domain.

Some related material involving Fass and 4×4 squares—

A 2003 paper he wrote with Jacob Feldman—

(Click to enlarge.)

"Design is how it works." — Steve Jobs

An assignment for Jobs in the afterlife—

Discuss the Fass-Feldman approach to "categorization under
complexity" in the context of the Wikipedia article's
philosophical remarks on "reductionist tradition."

The Fass-Feldman paper was assigned in an MIT course
for a class on Walpurgisnacht 2003.

From today's NY Times—

Obituaries for mystery authors
Ralph McInerny and Dick Francis

From the date (Jan. 29) of McInerny's death–

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.'"

– Harvard University Press on Persons and Things (Walpurgisnacht, 2008), by Barbara Johnson

From the date (Feb. 14) of Francis's death–

The EIghtfold Cube

The "something missing" in the above figure is an eighth cube, hidden behind the others pictured.

This eighth cube is not, as Johnson would have it, a void and "vanishing point," but is instead the "still point" of T.S. Eliot. (See the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron. See also related material in this journal.) The automorphism group here is of course the order-168 simple group of Felix Christian Klein.

For a connection to horses, see
a March 31, 2004, post
commemorating the birth of Descartes
  and the death of Coxeter–

Putting Descartes Before Dehors

For a more Protestant meditation,
see The Cross of Descartes—

"I've been the front end of a horse
and the rear end. The front end is better."
— Old vaudeville joke

For further details, click on
the image below–

Notre Dame Philosophical Reviews