Log24

Tuesday, April 11, 2017

Partitioning the Crimson Abyss

Filed under: General — Tags: , — m759 @ 6:00 PM

For the title, see Crimson + Abyss in this journal.

"Ready when you are, C. B."

Hexagram 63, "After Completion"

Wednesday, March 29, 2017

The Crimson Abyss

Filed under: General,Geometry — Tags: , , — m759 @ 3:19 PM

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson , March 29

1984

IMAGE- 'Affine Groups on Small Binary Spaces,' illustration

2010

Logo design for Stack Exchange Math by Jin Yang
 

Recent posts now tagged Crimson Abyss suggest
the above logo be viewed in light of a certain page 29

"… as if into a crimson abyss …." —

Update of 9 PM ET March 29, 2017:

Prospero's Children  was first published by HarperCollins,
London, in 1999. A statement by the publisher provides
an instance of the famous "much-needed gap." —

"This is English fantasy at its finest. Prospero’s Children 
steps into the gap that exists between The Lion, the Witch
and the Wardrobe
  and Clive Barker’s Weaveworld , and
is destined to become a modern classic."

Related imagery —

See also "Hexagram 64 in Context" (Log24, March 16, 2017).

Design Abyss

Filed under: General — Tags: , , — m759 @ 1:00 PM


http://www.log24.com/images/IChing/hexagram29.gif  
Hexagram 29,
The Abyss (Water)

This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —

http://www.8164.org/☵☲/  .

In that post, the designer quotes the Wilhelm/Baynes I Ching  to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —

"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."

See also this  journal on Walpurgisnacht (April 30), 2010 —

http://www.log24.com/images/IChing/hexagram29.gif

Hexagram 29:
Water

http://www.log24.com/log/pix10A/100430-Commentary.jpg

http://www.log24.com/images/IChing/hexagram30.gif

Hexagram 30:
Fire

"Hates California,
it's cold and it's damp.
"

Image--'The Fire,' by Katherine Neville

A thought from another German-speaking philosopher

"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."

See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.

Monday, August 31, 2020

Hollywood Logic

Filed under: General — Tags: — m759 @ 8:19 PM

See as well a recent post in memory of “Chariots of Fire” actor Ben Cross.

From  a Chrome Browser announcement  today —

Compare and contrast  “The Ghost and the Darkness” (Constellation, 1996)
and the new film “Rogue” (Lionsgate, 2020).

“Elijah?… Elijah?!” — Megan Fox in “Rogue” (00:41:47)

Ars Gratia Artis — MGM.

How Deep the Darkness*

Filed under: General — Tags: — m759 @ 11:51 AM

http://www.log24.com/log/pix08/080413-Marabar.jpg

* See the title phrase in this journal.

Saturday, August 29, 2020

Shadowlands

Filed under: General — Tags: — m759 @ 1:46 PM

“What have they done to my song?”. . . C. S. Lewis might ask.

To Wakanda

Filed under: General — Tags: — m759 @ 4:30 AM

      Update of 5:01 PM ET the same day —

Thursday, August 27, 2020

Acid Snark

Filed under: General — Tags: — m759 @ 2:00 AM

Another historical quote: “Don’t take the Brown acid.”

Tuesday, August 25, 2020

Gail Sheehy and the Source

Filed under: General — Tags: — m759 @ 3:45 PM

Sheehy reportedly died on Monday, August 24, 2020.

YouTube has the Vermont speech:

From this  journal on that date

From 'The Politics of Experience,' by R.D. Laing

Summary:  “Turn on, tune in, drop dead.

Saturday, December 21, 2019

Last of the God Professors

Filed under: General — Tags: , — m759 @ 10:32 AM

From some autobiographical remarks by Simon During,
who was featured in the previous post

For more on the phrase "god professor," see

"The Ownership of Knowledge in Higher Education
in Australia 1939-1996
," Hannah Forsyth, Ph.D. thesis,
University of Sydney, 2012

Simon During at Utrecht earlier this year —

For the Church of Synchronology, other April 11, 2019, remarks —

See in particular the phrase "Eritis sicut dei " in the Log24 remarks.

Sunday, May 5, 2019

Transgressive Politics at Harvard

Filed under: General — Tags: , , — m759 @ 1:02 PM

Related material —

See also the previous post.

Friday, May 3, 2019

“As a Chinese jar” — T. S. Eliot

Filed under: General — Tags: , , , , — m759 @ 1:06 PM

 

Monday, April 15, 2019

In Related News…

Filed under: General — Tags: , — m759 @ 10:31 AM

Sacerdotal Jargon

Filed under: General — Tags: , — m759 @ 12:38 AM

The interested reader can easily find the source of the above prose.

Saturday, April 13, 2019

An Apt Pupil

Filed under: General — Tags: , — m759 @ 10:17 PM

A Case for Bosch

Filed under: General — Tags: , — m759 @ 3:14 AM

"The fifth season of Bosch is set to premiere
on April 19, 2019." — Wikipedia

Thursday, April 11, 2019

Misery Continues.

Filed under: General — Tags: , — m759 @ 2:40 AM

Part I: Sharp Objects

Part II: Out of Blue

Part III: Misery

Misery according to Simone Weil

Monday, August 20, 2018

A Wheel for Ellmann

Filed under: General — Tags: — m759 @ 12:12 PM

The title was suggested by Ellmann's roulette-wheel analogy
in the previous post, "The Perception of Coincidence."

I Ching hexagrams as a Singer 63-cycle, plus zero

The Perception of Coincidence

Filed under: General — Tags: — m759 @ 2:15 AM

Ellmann on Joyce and 'the perception of coincidence' —

"Samuel Beckett has remarked that to Joyce reality was a paradigm,
an illustration of a possibly unstatable rule. Yet perhaps the rule
can be surmised. It is not a perception of order or of love; more humble
than either of these, it is the perception of coincidence. According to
this rule, reality, no matter how much we try to manipulate it, can only
assume certain forms; the roulette wheel brings up the same numbers
again and again; everyone and everything shift about in continual
movement, yet movement limited in its possibilities."

— Richard Ellmann, James Joyce , rev. ed.. Oxford, 1982, p. 551

Sunday, August 19, 2018

Possible Permutations

Filed under: General,Geometry — Tags: — m759 @ 9:18 PM

John Calder, an independent British publisher who built a prestigious list
of authors like Samuel Beckett and Heinrich Böll and spiritedly defended
writers like Henry Miller against censorship, died on Aug. 13 in Edinburgh.
He was 91.

— Richard Sandomir in the online New York Times  this evening

On Beckett —

http://www.log24.com/log/pix18/180819-Joyce-Possible_Permutations-Cambridge_Companion-2004-p168.gif

Also on August 13th

http://www.log24.com/log/pix18/180813-Knight_Moves-080116-page-top.gif

Thursday, October 12, 2017

East Meets West

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 8:09 PM

Saturday, April 15, 2017

A Cinematographer Departs

Filed under: General — Tags: , — m759 @ 2:04 AM

In memory of cinematographer Michael Ballhaus, who reportedly
died at 81 in Berlin on Tuesday evening, April 11, the first full day 
of Passover, 2017.

From a New York Times  description of his work —

"The sinuous shot, which shows people parting  
like the Red Sea. . . ." — Margalit Fox tonight

From Log24 on the reported date of Ballhaus's death:

Wednesday, March 29, 2017

Art Space Illustrated

Filed under: General,Geometry — Tags: , , — m759 @ 10:45 AM

Another view of the previous post's art space  —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

More generally, see Solomon's Cube in Log24.

See also a remark from Stack Exchange in yesterday's post Backstory,
and the Stack Exchange math logo below, which recalls the above 
cube arrangement from "Affine groups on small binary spaces" (1984).

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Art Space, Continued

Filed under: General — Tags: , , — m759 @ 4:35 AM

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson  today

From Log24 posts tagged Art Space

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
The Universal Kummer Threefold,” by
Qingchun Ren, Steven V Sam, Gus Schrader, and
Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Thursday, April 14, 2016

Strange Awards

Filed under: General,Geometry — Tags: , — m759 @ 10:38 AM

From a review of a play by the late Anne Meara* —

"Meara, known primarily as an actress/comedian
(half of the team of Stiller & Meara, and mother of
Ben Stiller), is also an accomplished writer for the
stage; her After Play  was much acclaimed….
This new, more ambitious piece starts off with a sly
send-up of awards dinners as the late benefactor of
a wealthy foundation–the comically pixilated scientist
Herschel Strange (Jerry Stiller)–is seen on videotape.
This tape sets a light tone that is hilariously
heightened when John Shea, as Arthur Garden,
accepts the award given in Strange's name." 

Compare and contrast —

A circular I Ching

I of course prefer the Galois I Ching .

* See the May 25, 2015, post The Secret Life of the Public Mind.

Wednesday, April 13, 2016

Black List

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

A search for "Max Black" in this journal yields some images
from a post of August 30, 2006 . . .

A circular I Ching

The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified the seventh symbol."
— Stargate

The "Jackson" above is played by the young James Spader,
who in an older version currently stars in "The Blacklist."

"… the memorable models of science are 'speculative instruments,'
to borrow I. A. Richards' happy title. They, too, bring about a wedding
of disparate subjects, by a distinctive operation of transfer of the
implications  of relatively well-organized cognitive fields. And as with
other weddings, their outcomes are unpredictable."

Max Black in Models and Metaphors , Cornell U. Press, 1962

Friday, February 11, 2011

Brightness at Noon (continued)

Filed under: General — Tags: — m759 @ 12:00 PM

From The Seventh Symbol

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

"First of all, I'd like to thank the Academy…"

Monday, July 27, 2009

Monday July 27, 2009

Filed under: General,Geometry — Tags: — m759 @ 2:29 PM
Field Dance

The New York Times
on June 17, 2007:

 Design Meets Dance,
and Rules Are Broken

Yesterday's evening entry was
on the fictional sins of a fictional
mathematician and also (via a link
to St. Augustine's Day, 2006), on
the geometry of the I Ching* —

The eternal
combined with
the temporal:

Circular arrangement of I Ching hexagrams based on Singer 63-cycle in the Galois field GF(64)

The fictional mathematician's
name, noted here (with the Augustine-
I Ching link as a gloss) in yesterday's
evening entry, was Summerfield.

From the above Times article–
"Summerspace," a work by
 choreographer Merce Cunningham
and artist Robert Rauschenberg
that offers a competing
 vision of summer:

Summerspace — Set by Rauschenberg, choreography by Cunningham

Cunningham died last night.

John Cage, Merce Cunningham, Robert Rauschenberg in the 1960's

From left, composer John Cage,
choreographer Merce Cunningham,
and artist Robert Rauschenberg
in the 1960's

"When shall we three meet again?"

* Update of ca. 5:30 PM 7/27– today's online New York Times (with added links)– "The I Ching is the 'Book of Changes,' and Mr. Cunningham's choreography became an expression of the nature of change itself. He presented successive images without narrative sequence or psychological causation, and the audience was allowed to watch dance as one might watch successive events in a landscape or on a street corner."

Thursday, December 18, 2008

Thursday December 18, 2008

Filed under: General — Tags: — m759 @ 1:00 PM
Polar Opposites

Susan Sontag in
this week's New Yorker:
"The mind is a whore."

Embedded in the Sontag
article is the following:

The New Yorker on Santa's use of the word 'ho'

I Ching hexagrams as a Singer 63-cycle, plus zero

Act One

South Pole:

David Mamet's book 'A Whore's Profession'

Hexagram 21 in the King Wen sequence

Shi Ho

Act Two

North Pole:

Susan Sontag

Hexagram 2 in the King Wen sequence

Kun

"If baby I'm the bottom,
you're the top."
Cole Porter   

Happy birthday,
Steven Spielberg.

Tuesday, December 16, 2008

Tuesday December 16, 2008

Filed under: General,Geometry — Tags: , — m759 @ 8:00 PM
The Square Wheel
(continued)

From The n-Category Cafe today:

David Corfield at 2:33 PM UTC quoting a chapter from a projected second volume of a biography:

"Grothendieck’s spontaneous reaction to whatever appeared to be causing a difficulty… was to adopt and embrace the very phenomenon that was problematic, weaving it in as an integral feature of the structure he was studying, and thus transforming it from a difficulty into a clarifying feature of the situation."

John Baez at 7:14 PM UTC on research:

"I just don’t want to reinvent a wheel, or waste my time inventing a square one."

For the adoption and embracing of such a problematic phenomenon, see The Square Wheel (this journal, Sept. 14, 2004).

For a connection of the square wheel with yesterday's entry for Julie Taymor's birthday, see a note from 2002:

Wolfram's Theory of Everything
and the Gameplayers of Zan
.

Related pictures–

From Wolfram:

http://www.log24.com/log/pix08A/081216-WolframWalsh.gif

A Square

From me:

http://www.log24.com/log/pix08A/081216-IChingWheel.gif

A Wheel

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General — Tags: , — m759 @ 8:28 AM
"Caught up 
    in circles…"

— Song lyric,  
Cyndi Lauper

http://www.log24.com/log/pix08/080525-Alethiometer.jpg

Alethiometer from
"The Golden Compass"

 

The 64 hexagrams of the I Ching in a circular arrangement suggested by a Singer 63-cycle

The I Ching
as Alethiometer

Update:

See also this morning's
later entry, illustrating
the next line of Cyndi
Lauper's classic lyric
"Time After Time" —

"… Confusion is    
  nothing new."

Friday, February 29, 2008

Friday February 29, 2008

Filed under: General — m759 @ 11:32 AM

I Have a
Dreamtime
 
http://www.log24.com/log/pix08/080229-Doonesbury3.jpg

Noting today that the time was 11:32 (AM ET),  a portentous number in Finnegans Wake, I decided to practice a bit of chronomancy (use of time for augury).  My weblog's server infomed me when I pressed "enter" that it thought the exact time was 11:32:39.  Consulting (as in Symmetry and Change in the Dreamtime) the I Ching for the meaning of (hexagram) 39, I found the following:

The hexagram pictures a dangerous abyss lying before us and a steep, inaccessible mountain rising behind us…. One must join forces with friends of like mind and put himself under the leadership of a man equal to the situation: then one will succeed in removing the obstacles.

For the abyss and the mountain, see the five log24 entries ending on July 5, 2005, with "The Edge of Eternity." As for "friends of like mind," see the previous entry's references to July 2005.  "The leadership of a man equal to the situation" is more difficult to interpret.  Perhaps it refers, as a politician recently noted, to "a king who took us to the mountain-top and pointed the way to the promised land." Or perhaps to a different king.

http://www.log24.com/log/pix08/080229-Obama.gif

Click on image for details.
Note the time: 11:32 (of 13:09).
The moment is that of the syllable
"mount" in the quotation above.

Saturday, February 23, 2008

Saturday February 23, 2008

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM
Jumpers

"An acute study of the links
between word and fact"
Nina daVinci Nichols

 
Thanks to a Virginia reader for a reminder:
 
Virginia /391062427/item.html? 2/22/2008 7:37 PM
 
The link is to a Log24 entry
that begins as follows…

An Exercise

of Power

Johnny Cash:
"And behold,
a white horse."

Springer logo - A chess knight
Chess Knight
(in German, Springer)

This, along with the "jumper" theme in the previous two entries, suggests a search on springer jumper.That search yields a German sports phrase, "Springer kommt!"  A search on that phrase yields the following:
"Liebe Frau vBayern,
mich würde interessieren wie man
mit diesem Hintergrund
(vonbayern.de/german/anna.html)
zu Springer kommt?"

Background of "Frau vBayern" from thePeerage.com:

Anna-Natascha Prinzessin zu Sayn-Wittgenstein-Berleburg 

F, #64640, b. 15 March 1978Last Edited=20 Oct 2005

     Anna-Natascha Prinzessin zu Sayn-Wittgenstein-Berleburg was born on 15 March 1978. She is the daughter of Ludwig Ferdinand Prinz zu Sayn-Wittgenstein-Berleburg and Countess Yvonne Wachtmeister af Johannishus. She married Manuel Maria Alexander Leopold Jerg Prinz von Bayern, son of Leopold Prinz von Bayern and Ursula Mohlenkamp, on 6 August 2005 at Nykøping, Södermanland, Sweden.

 

The date of the above "Liebe Frau vBayern" inquiry, Feb. 1, 2007, suggests the following:

From Log24 on
St. Bridget's Day, 2007:

The quotation
"Science is a Faustian bargain"
and the following figure–

Change

The 63 yang-containing hexagrams of the I Ching as a Singer 63-cycle

From a short story by
the above Princess:

"'I don't even think she would have wanted to change you. But she for sure did not want to change herself. And her values were simply a part of her.' It was true, too. I would even go so far as to say that they were her basis, if you think about her as a geometrical body. That's what they couldn't understand, because in this age of the full understanding for stretches of values in favor of self-realization of any kind, it was a completely foreign concept."

To make this excellent metaphor mathematically correct,
change "geometrical body" to "space"… as in

"For Princeton's Class of 2007"

Review of a 2004 production of a 1972 Tom Stoppard play, "Jumpers"–

John Lahr on Tom Stoppard's play Jumpers

Related material:

Knight Moves (Log24, Jan. 16),
Kindergarten Theology (St. Bridget's Day, 2008),
and

The image “My space -(the affine space of six dimensions over the two-element field
(Click on image for details.)

Thursday, February 1, 2007

Thursday February 1, 2007

Filed under: General — Tags: — m759 @ 7:59 AM
Change

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

The above is from
Feb. 15, 2006.

"I don't believe in an afterlife, so I think this is it, and I'm trying to spend my time as best I can, and I'm trying to spend my time so I'm proud of what I've done, and I try not to do any things that I'm not proud of."

Jim Gray, 2002 interview (pdf)
 

Commencement Address (doc)
to Computer Science Division,
College of Letters and Science,
University of California, Berkeley,
by Jim Gray,
May 25, 2003:

"I was part of Berkeley's class of 1965. Things have changed a lot since then….

So, what's that got to do with you? Well, there is going to be MORE change…. Indeed, change is accelerating– Vernor Vinge suggests we are approaching singularities when social, scientific and economic change are so rapid that we cannot imagine what will happen next.  These futurists predict humanity will become post-human. Now, THAT! is change– a lot more than I have seen.

If it happens, the singularity will happen in your lifetime– and indeed, you are likely to make it happen."

 

I Ching, Hexagram 39

For other singular
sci-fi tales, click on
the above hexagram.


More from Gray's speech:

"I am an optimist. Science is a Faustian bargain– and I am betting on mankind muddling through. I grew up under the threat of atomic war; we've avoided that so far. Information Technology is a Faustian bargain. I am optimistic that we can have the good parts and protect ourselves from the worst part– but I am counting on your help in that."


"Not fare well,
But fare forward, voyagers."

— T. S. Eliot,
"The Dry Salvages"

Wednesday, August 30, 2006

Wednesday August 30, 2006

Filed under: General,Geometry — Tags: — m759 @ 10:07 AM
The Seventh Symbol:

A Multicultural Farewell

to a winner of the
Nobel Prize for Literature,
the Egyptian author of
The Seventh Heaven:
Supernatural Stories
 —

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified
the seventh symbol."
Stargate

Other versions of
the seventh symbol —

Chinese version:

The image “http://www.log24.com/log/pix06A/060830-hexagram20.gif” cannot be displayed, because it contains errors.

pictorial version:

The image “http://www.log24.com/log/pix06A/060830-Box.jpg” cannot be displayed, because it contains errors.

algebraic version:

The image “http://www.log24.com/log/pix06A/060830-Algebra.jpg” cannot be displayed, because it contains errors.

"… Max Black, the Cornell philosopher, and others have pointed out how 'perhaps every science must start with metaphor and end with algebra, and perhaps without the metaphor there would never have been any algebra' …."

— Max Black, Models and Metaphors, Cornell U. Press, 1962, page 242, as quoted in Dramas, Fields, and Metaphors, by Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25

Monday, August 28, 2006

Monday August 28, 2006

Filed under: General,Geometry — Tags: — m759 @ 1:00 AM
Today's Sinner:

Augustine of Hippo, who is said to
have died on this date in 430 A.D.

"He is, after all, not merely taking over a Neoplatonic ontology, but he is attempting to combine it with a scriptural tradition of a rather different sort, one wherein the divine attributes most prized in the Greek tradition (e.g. necessity, immutability, and atemporal eternity) must somehow be combined with the personal attributes (e.g. will, justice, and historical purpose) of the God of Abraham, Isaac, and Jacob."

Stanford Encyclopedia of Philosophy on Augustine

Here is a rather different attempt
to combine the eternal with the temporal:

 

The Eternal

Symbol of necessity,
immutability, and
atemporal eternity:

The image “http://www.log24.com/log/pix06A/060828-Cube.jpg” cannot be displayed, because it contains errors.

For details, see
finite geometry of
the square and cube
.

The Temporal

Symbol of the
God of Abraham,
Isaac, and Jacob:

The image “http://www.log24.com/log/pix06A/060828-Cloud.jpg” cannot be displayed, because it contains errors.

For details, see
Under God
(Aug. 11, 2006)

The eternal
combined with
the temporal:

 

Singer 63-cycle in the Galois field GF(64) used to order the I Ching hexagrams

Related material:

Hitler's Still Point and
the previous entry.
 

Tuesday, July 18, 2006

Tuesday July 18, 2006

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

Sacred Order

In memory of Philip Rieff, who died on July 1, 2006:

The image “http://www.log24.com/log/pix06A/060604-Roots.jpg” cannot be displayed, because it contains errors.

Related material:

The image ?http://www.log24.com/theory/images/GF64-63cycleA495.gif? cannot be displayed, because it contains errors.

and

The image ?http://www.log24.com/theory/images/MySpace.jpg? cannot be displayed, because it contains errors.

For details, see the
five Log24 entries ending
on the morning of
Midsummer Day, 2006.

Thanks to University Diaries for pointing out the essay on Rieff.
 
That essay says Rieff had "a dense, knotty, ironic style designed to warn off impatient readers. You had to unpack his aphorisms carefully. And this took a while. As a result, his thinking had a time-release effect." Good for him.  For a related essay (time-release effect unknown), see Hitler's Still Point: A Hate Speech for Harvard.

Friday, June 23, 2006

Friday June 23, 2006

Filed under: General — Tags: — m759 @ 9:00 PM
Go with the Flow
continued

Review of a
Feb. 15, 2006, entry:

The image ?http://www.log24.com/theory/images/GF64-63cycleA495.gif? cannot be displayed, because it contains errors.

The image ?http://www.log24.com/images/IChing/WilhelmHellmut.gif? cannot be displayed, because it contains errors.

Wednesday, February 15, 2006

Wednesday February 15, 2006

Filed under: General,Geometry — Tags: — m759 @ 11:07 AM
Anthony Hopkins
Writes Screenplay
About God, Life & Death

These topics may be illuminated
by a study of the Chinese classics.

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

The image “http://www.log24.com/images/IChing/WilhelmHellmut.gif” cannot be displayed, because it contains errors.

If we replace the Chinese word "I"
(change, transformation) with the
word "permutation," the relevance
of Western mathematics (which
some might call "the Logos") to
the I Ching ("Changes Classic")
beomes apparent.

Related material:

Hitler's Still Point,
Jung's Imago,
Solomon's Cube,
Geometry of the I Ching,
and Globe Award.

Yesterday's Valentine
may also have some relevance.

Tuesday, September 14, 2004

Tuesday September 14, 2004

Filed under: General,Geometry — Tags: , — m759 @ 3:00 PM

The Square Wheel

Harmonic analysis may be based either on the circular (i.e., trigonometric) functions or on the square (i. e., Walsh) functions.  George Mackey's masterly historical survey showed that the discovery of Fourier analysis, based on the circle, was of comparable importance (within mathematics) to the discovery (within general human history) of the wheel.  Harmonic analysis based on square functions– the "square wheel," as it were– is also not without its importance.

For some observations of Stephen Wolfram on square-wheel analysis, see pp. 573 ff. in Wolfram's magnum opus, A New Kind of Science (Wolfram Media, May 14, 2002).  Wolfram's illustration of this topic is closely related, as it happens, to a note on the symmetry of finite-geometry hyperplanes that I wrote in 1986.  A web page pointing out this same symmetry in Walsh functions was archived on Oct. 30, 2001.

That web page is significant (as later versions point out) partly because it shows that just as the phrase "the circular functions" is applied to the trigonometric functions, the phrase "the square functions" might well be applied to Walsh functions– which have, in fact, properties very like those of the trig functions.  For details, see Symmetry of Walsh Functions, updated today.

"While the reader may draw many a moral from our tale, I hope that the story is of interest for its own sake.  Moreover, I hope that it may inspire others, participants or observers, to preserve the true and complete record of our mathematical times."

From Error-Correcting Codes
Through Sphere Packings
To Simple Groups
,
by Thomas M. Thompson,
Mathematical Association of America, 1983

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