Log24

Sunday, June 10, 2018

Pieces of April

Filed under: General — Tags: , — m759 @ 12:25 am

This journal on April 16, 2018 —

Happy birthday to Pope Emeritus Benedict XVI.

Related material from another weblog in a post also dated April 16, 2018 —

"As I write this, it’s April 5, midway through the eight-day
festival of Passover. During this holiday, we Jews air our
grievances against the ancient Pharaoh who enslaved
and oppressed us, and celebrate the feats of strength
with which the Almighty delivered us from bondage —
wait a minute, I think I’m mixing up Passover with Festivus."
. . . .

"Next month: Time and Tesseracts."

From that next post, dated May 16, 2018 —

"The tesseract entered popular culture through
Madeleine L’Engle’s 'A Wrinkle in Time' . . . ."

The post's author, James Propp, notes that

" L’Engle caused some of her readers confusion
when one of the characters … the prodigy
Charles Wallace Murray [sic ] , declared 'Well, the fifth
dimension’s a tesseract.' "

Propp is not unfamiliar with prodigies:

"When I was a kid living in the Long Island suburbs,
I sometimes got called a math genius. I didn’t think
the label was apt, but I didn’t mind it; being put in
the genius box came with some pretty good perks."

— "The Genius Box," a post dated March 16, 2018

To me, Propp seems less like Charles Wallace
and more like the Prime Coordinator —

For further details, see the following synchronicity checks:

Propp March 16     Log24 March 16

Propp April 16        Log24 April 16

Propp May 16        Log24 May 16 .

Saturday, April 19, 2008

Saturday April 19, 2008

Filed under: General,Geometry — Tags: , — m759 @ 5:01 am
A Midrash for Benedict

On April 16, the Pope’s birthday, the evening lottery number in Pennsylvania was 441. The Log24 entries of April 17 and April 18 supplied commentaries based on 441’s incarnation as a page number in an edition of Heidegger’s writings.  Here is a related commentary on a different incarnation of 441.  (For a context that includes both today’s commentary and those of April 17 and 18, see Gian-Carlo Rota– a Heidegger scholar as well as a mathematician– on mathematical Lichtung.)

From R. D. Carmichael, Introduction to the Theory of Groups of Finite Order (Boston, Ginn and Co., 1937)– an exercise from the final page, 441, of the final chapter, “Tactical Configurations”–

“23. Let G be a multiply transitive group of degree n whose degree of transitivity is k; and let G have the property that a set S of m elements exists in G such that when k of the elements S are changed by a permutation of G into k of these elements, then all these m elements are permuted among themselves; moreover, let G have the property P, namely, that the identity is the only element in G which leaves fixed the n – m elements not in S.  Then show that G permutes the m elements S into

n(n -1) … (n – k + 1)
____________________

m(m – 1) … (m – k + 1)

sets of m elements each, these sets forming a configuration having the property that any (whatever) set of k elements appears in one and just one of these sets of m elements each. Discuss necessary conditions on m, n, k in order that the foregoing conditions may be realized. Exhibit groups illustrating the theorem.”

This exercise concerns an important mathematical structure said to have been discovered independently by the American Carmichael and by the German Ernst Witt.

For some perhaps more comprehensible material from the preceding page in Carmichael– 440– see Diamond Theory in 1937.

Thursday, April 17, 2008

Thursday April 17, 2008

Filed under: General — Tags: , — m759 @ 8:28 am
Top Headlines

(at Google News):

  1. Obama, Clinton…

  2. Suicide bomber…

  3. Pope Benedict XVI…

In other words:

  1. The best lack all conviction
  2. while the worst
    Are full of passionate intensity.
  3. Surely some revelation is at hand….

    — William Butler Yeats

Revelation for  
April 16, 2008 —
day of the Pennsylvania
Clinton-Obama debate and
 of the Pope’s birthday —

The Pennsylvania Lottery:

PA Lottery April 16, 2008: Mid-day 413, Evening 441

Make of this revelation
what you will.

My own interpretations:
the Lichtung of 4/13 and
the Dickung of page 441
of Heidegger’s
Basic Writings, where
the terms Lichtung and
Dickung are described.

See also “The Shining of
May 29” (JFK’s birthday).

“By groping toward the light
we are made to realize
how deep the darkness is
around us.”

— Arthur Koestler,  
The Call Girls:
A Tragi-Comedy

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