Donald in Mathmagic Land
Friday, May 22, 2015
Mathmagic Land
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Friday, July 25, 2014
Magic for Jews
(Continued from April 8, 2013.)
See Two Blocks Short of a Design (May 5, 2011).
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Magic in the Moonshine
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine.”
— Joseph Conrad in Heart of Darkness
“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,
Random House, 1973, page 118
“Spectral evidence is a form of evidence
based upon dreams and visions.” —Wikipedia
See also Moonshine (May 15, 2014) and, from the date of the above
New York Times item, two posts tagged Wunderkammer .
Related material: From the Spectrum program of the Mathematical
Association of America, some non-spectral evidence.
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Thursday, July 24, 2014
Death in Mathmagic Land
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Wednesday, May 14, 2014
Death in Mathmagic Land
"It was our old friend Pythagoras who discovered
that the pentagram was full of mathematics."
— Narrator, "Donald in Mathmagic Land," Disney, 1959
… and it was Peter J. Cameron who discovered that
mathematics was full of pentagrams.
From Log24 on May 3: Gray Space —
Robert J. Stewart (left) and a pentagram photo posted May 2
by Oslo artist Josefine Lyche. See also Lyche in this journal.
From Log24 on May 13: An Artist's Memorial —
The death mentioned in the above May 13 post occurred on
May 12, the date of a scheduled Black Mass at Harvard.
Related material:
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Monday, April 8, 2013
Magic for Jews
A commenter on Saturday's "Seize the Dia" has
suggested a look at the work of one Mark Collins.
Here is such a look (click to enlarge):
I find attempts to associate pure mathematics with the words
"magic" or "mystic" rather nauseating. (H. F. Baker's work
on Pascal's mystic hexagram is no exception; Baker was
stuck with Pascal's obnoxious adjective, but had no truck
with any mystic aspects of the hexagram.)
The remarks above by Clifford Pickover on Collins, Dürer, and
binary representations may interest some non-mathematicians,
who should not be encouraged to waste their time on this topic.
For the mathematics underlying the binary representation of
Dürer's square, see, for instance, my 1984 article "Binary
Coordinate Systems."
Those without the background to understand that article
may enjoy, instead of Pickover's abortive attempts above at
mathematical vulgarization, his impressively awful 2009 novel
Jews in Hyperspace .
Pickover's 2002 book on magic squares was, unfortunately,
published by the formerly reputable Princeton University Press.
Related material from today's Daily Princetonian :
See also Nash + Princeton in this journal.
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Thursday, May 5, 2011
On Art and Magic
Two Blocks Short of a Design:
A sequel to this morning's post on Douglas Hofstadter
Photo of Hofstadter by Mike McGrath taken May 13, 2006 |
Related material — See Lyche's "Theme and Variations" in this journal
and Hofstadter's "Variations on a Theme as the Essence of Imagination"
— Scientific American October 1982
A quotation from a 1985 book by Hofstadter—
"… we need to entice people with the beauties of clarity, simplicity, precision,
elegance, balance, symmetry, and so on.
Those artistic qualities… are the things that I have tried to explore and even
to celebrate in Metamagical Themas . (It is not for nothing that the word
'magic' appears inside the title!)"
The artistic qualities Hofstadter lists are best sought in mathematics, not in magic.
An example from Wikipedia —
|
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
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Monday, April 27, 2020
The Cracked Nut
“At that instant he saw, in one blaze of light, an image of unutterable
conviction, the reason why the artist works and lives and has his being –
the reward he seeks –the only reward he really cares about, without which
there is nothing. It is to snare the spirits of mankind in nets of magic,
to make his life prevail through his creation, to wreak the vision of his life,
the rude and painful substance of his own experience, into the congruence
of blazing and enchanted images that are themselves the core of life, the
essential pattern whence all other things proceed, the kernel of eternity.”
— Thomas Wolfe, Of Time and the River
“… the stabiliser of an octad preserves the affine space structure on its
complement, and (from the construction) induces AGL(4,2) on it.
(It induces A8 on the octad, the kernel of this action being the translation
group of the affine space.)”
— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside….”
— Joseph Conrad in Heart of Darkness
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Tuesday, December 17, 2019
A Singular Eye
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Wednesday, October 2, 2019
A Long Literary Tradition
"There's a long literary tradition associating
certain kinds of geometry with horror."
— American Mathematical Society yesterday:
See also yesterday's Log24 post "Transylvania Revisited."
A related post —
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Friday, July 5, 2019
Wednesday, October 18, 2017
Dürer for St. Luke’s Day
Structure of the Dürer magic square
16 3 2 13
5 10 11 8 decreased by 1 is …
9 6 7 12
4 15 14 1
15 2 1 12
4 9 10 7
8 5 6 11
3 14 13 0 .
Base 4 —
33 02 01 30
10 21 22 13
20 11 12 23
03 32 31 00 .
Two-part decomposition of base-4 array
as two (non-Latin) orthogonal arrays —
3 0 0 3 3 2 1 0
1 2 2 1 0 1 2 3
2 1 1 2 0 1 2 3
0 3 3 0 3 2 1 0 .
Base 2 –
1111 0010 0001 1100
0100 1001 1010 0111
1000 0101 0110 1011
0011 1110 1101 0000 .
Four-part decomposition of base-2 array
as four affine hyperplanes over GF(2) —
1001 1001 1100 1010
0110 1001 0011 0101
1001 0110 0011 0101
0110 0110 1100 1010 .
— Steven H. Cullinane,
October 18, 2017
See also recent related analyses of
noted 3×3 and 5×5 magic squares.
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Tuesday, October 17, 2017
Plan 9 Continues
See also Holy Field in this journal.
Some related mathematics —
Analysis of the Lo Shu structure —
Structure of the 3×3 magic square:
4 9 2
3 5 7 decreased by 1 is …
8 1 6
3 8 1
2 4 6
7 0 5
In base 3 —
10 22 01
02 11 20
21 00 12
As orthogonal Latin squares
(a well-known construction) —
1 2 0 0 2 1
0 1 2 2 1 0
2 0 1 1 0 2 .
— Steven H. Cullinane,
October 17, 2017
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Monday, October 16, 2017
Highway 61 Revisited
"God said to Abraham …." — Bob Dylan, "Highway 61 Revisited"
Related material —
-
"Inner Truth" in this journal
-
"On Linguistic Creation," June 25, 1999
-
"Ultra Super Magic Squares of 5×5" at
http://mathsforeurope.digibel.be/magic.htm .
See as well Charles Small, Harvard '64,
"Magic Squares over Fields" —
— and Conway-Norton-Ryba in this journal.
Some remarks on an order-five magic square over GF(52):
on the numbers 0 to 24:
22 5 18 1 14
3 11 24 7 15
9 17 0 13 21
10 23 6 19 2
16 4 12 20 8
Base-5:
42 10 33 01 24
03 21 44 12 30
14 32 00 23 41
20 43 11 34 02
31 04 22 40 13
Regarding the above digits as representing
elements of the vector 2-space over GF(5)
(or the vector 1-space over GF(52)) …
All vector row sums = (0, 0) (or 0, over GF(52)).
All vector column sums = same.
Above array as two
orthogonal Latin squares:
4 1 3 0 2 2 0 3 1 4
0 2 4 1 3 3 1 4 2 0
1 3 0 2 4 4 2 0 3 1
2 4 1 3 0 0 3 1 4 2
3 0 2 4 1 1 4 2 0 3
— Steven H. Cullinane,
October 16, 2017
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Tuesday, April 5, 2016
Spring Play
The spring play this March at Princeton's McCarter Theatre Center
was Agatha Christie's "The Mousetrap."
In related news —
See as well, in this journal, a post from the date pictured above,
that of the Disneyland Diamond Celebration on May 22, 2015 —
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Monday, September 29, 2014
Michaelmas Mystery
Some related material in this journal: “Peter J. Cameron” + Magic.
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Tuesday, July 29, 2014
Radio Days
In memoriam :
“Margot Adler, an iconic NPR correspondent and Wiccan priestess,
died on Monday July 28 from endometrial cancer at the age of 68.”
— Huffington Post 07/28/2014 5:39 pm EDT
See also Log24 posts tagged NPR Magic.
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Sunday, July 13, 2014
Useful Princeton
See…
- An Apple for Devlin (July 2)
- Thanks for having me on (July 11)
- Useful Idiot (Wikipedia article)
-
Useful Fictions (a Princeton mathematics
department Spring 2014 course)
"Numbers themselves are fictions, abstractions humans invented
to gain more control over the world." — Keith Devlin
Related material:
-
From today's New York Times Sunday Review ,
The World According to Maxwell Smart, Part 1
- Madonna, "Get Stupid," a political video from 2008
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Friday, July 11, 2014
Thanks for having me on.
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Monday, May 12, 2014
Mass Appeal
For those disappointed by the cancellation
of this evening’s Black Mass at Harvard,
here is a somewhat less exciting substitute.
See also Peter J. Cameron + Magic.
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Sunday, May 11, 2014
For the Perplexed
From a New York Times obituary by Bruce Weber tonight—
Charles Marowitz, Director and Playwright, Dies at 82
“There are two kinds of bafflement in the theater: the kind that fascinates as it perplexes, and the kind that just perplexes,” he wrote in The Times in 1969 in an essay about Mr. Shepard’s play “La Turista,” which had recently opened in London. “If a play doesn’t make quick sense, but enters into some kind of dialogue with our subconscious, we tend to admit it to that lounge where we entertain interesting-albeit-unfamiliar strangers.
“If it only baffles, there are several courses open to us: we can assume it is ‘above our heads’ or directed ‘to some other kind of person,’ or regretfully conclude that it confuses us because it is itself confused. However, the fear of being proved wrong is so great today that almost every new work which isn’t patently drivel gets the benefit of the doubt.”
Another play by Sam Shepard mentioned in the obituary suggests a review of…
- “From the Witch Ball,” a post from May 2,
the reported date of Marowitz’s death - “Two Satanic Majesties Request All-Devouring Fame,”
a NY Times review from October 9, 2006 - This journal on that date— October 9, 2006—
“Art Wars: To Apollo.”
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Saturday, May 3, 2014
Gray Space
Or: Three Shades of Gray
(Continued from previous Gray Space posts.)
Click the above image for some related mathematics.
Those who prefer “magic” approaches to mathematics*
may consult the works of Robert J. Stewart and his
mentor William G. Gray.
Robert J. Stewart (left) and a pentagram photo posted yesterday evening
by Oslo artist Josefine Lyche. See also Lyche in this journal.
* See the April 2014 banners displayed at the websites
of the American Mathematical Society and of the
Mathematical Association of America, as well as
a mathematician’s remarks linked to here last evening.
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Friday, May 2, 2014
From the Witch Ball
See also, in this journal, Arcade Fire and Witch Ball.
This post was suggested by remarks today of mathematician
Peter J. Cameron, who seems to enjoy playing the role of
Lord Summerisle (from The Wicker Man , a 1973 horror classic).
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Friday, April 25, 2014
Bingo
For John Milton at the Cervecería XX —
- Bingo in this journal, as well as
- Black Mass and
- “The Platonic Heritage in Under the Volcano“
(Studies in Canadian Literature, v. 3, no. 1, 1978)
Related material: Peter J. Cameron on Bertrand Russell
in A Midnight Exorcism.
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Sunday, January 26, 2014
A Midnight Exorcism
The summoning of the spirit of Bertrand Russell
yesterday by Peter J. Cameron at his weblog
suggests a review of this weblog’s posts of
Christmas Eve, December 24-25, 2013.
(Recall that Robert D. Carmichael, who, in a book
linked to at midnight last Christmas Eve discusses
some “magic” mathematical structures,
reportedly was trained as a Presbyterian minister.
See also The Presbyterian Exorcist.)
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Tuesday, June 24, 2008
Tuesday June 24, 2008
Random Walk with
X's and O's
X's and O's
Part I: Random Walk
Part II: X's
3/22:
"Shakespeare, Rilke, Joyce,
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
are of central importance,
for whom chiasmus is a
generator of meaning,
tool of discovery and
philosophical template."
for whom chiasmus is a
generator of meaning,
tool of discovery and
philosophical template."
— Chiasmus in the
Drama of Life
Drama of Life
Part III: O's —
A Cartoon Graveyard
in honor of the late
Gene Persson †
Today's Garfield —
See also
Midsummer Eve's Dream:
"The meeting is closed
with the lord's‡ prayer
and refreshments are served."
† Producer of plays and musicals
including Album and
The Ruling Class
‡ Lower case in honor of
Peter O'Toole, star of
the film version of
The Ruling Class.
(This film, together with
O'Toole's My Favorite Year,
may be regarded as epitomizing
Hollywood's Jesus for Jews.)
Those who prefer
less randomness
in their religion
may consult O'Toole's
more famous film work
involving Islam,
as well as
the following structure
discussed here on
the date of Persson's death:
"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah."
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Wednesday, June 8, 2005
Wednesday June 8, 2005
Kernel of Eternity
Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”
“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”
— Thomas Wolfe, Of Time and the River
“… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)”
— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)
“… donc Dieu existe, réponse!”
— attributed, some say falsely, to Leonhard Euler
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