Log24

Monday, March 11, 2013

Ready When You Are, C. B.

Filed under: General — m759 @ 3:15 am

The late film director Micky Moore playing St. Mark as a child:

See also a clip introducing St. Mark from DeMille's 1927 "The King of Kings." 

Moore reportedly died at 98 at his Malibu home on March 4th.

Sunday, March 10, 2013

Galois Space

Filed under: General,Geometry — Tags: — m759 @ 5:30 pm

(Continued)

The 16-point affine Galois space:

Further properties of this space:

In Configurations and Squares, see the
discusssion of the Kummer 166 configuration.

Some closely related material:

  • Wolfgang Kühnel,
    "Minimal Triangulations of Kummer Varieties,"
    Abh. Math. Sem. Univ. Hamburg 57, 7-20 (1986).

    For the first two pages, click here.

  • Jonathan Spreer and Wolfgang Kühnel,
    "Combinatorial Properties of the 3 Surface:
    Simplicial Blowups and Slicings,"
    preprint, 26 pages. (2009/10) (pdf).
    (Published in Experimental Math. 20,
    issue 2, 201–216 (2011).)

Sunday School

Filed under: General — m759 @ 10:00 am

The previous post described briefly a  2002 
book on magic and religion, Golems of Gotham .

For a Sunday New York Times  review,  click here.

Friday, March 8, 2013

Pinter Play

Filed under: General — m759 @ 11:01 pm

A brief drama inspired by Peter J. Cameron's post today
on a March 4-8  combinatorics conference at
Florida Atlantic University (FAU) in Boca Raton:

Scene 1

Scene 2

Scene 3

Scene 4

Recommended Reading
for Hogwarts Students
on Devil’s Night (2005):

IMAGE- The Hellfire Club in 'The Shadow Guests'

Click on the above for details.

Thursday, March 7, 2013

Classroom from Hell

Filed under: General — m759 @ 10:10 pm

Click for some background music.

Proof Symbol

Filed under: General,Geometry — m759 @ 8:28 pm

Today's previous post recalled a post
from ten years before yesterday's  date.

The subject of that post was the
Galois tesseract.

Here is a post from ten years before
today's  date

The subject of that  post is the Halmos
tombstone:

"The symbol    is used throughout the entire book
in place of such phrases as 'Q.E.D.' or 'This
completes the proof of the theorem' to signal
the end of a proof."

Measure Theory  (1950)

For exact proportions, click on the tombstone.

For some classic mathematics related
to the proportions, see September 2003.

Ten Years After

Filed under: General,Geometry — m759 @ 8:00 am

Rock guitarist Alvin Lee, a founder of
the band Ten Years After , died
on March 6, 2013 (Michelangelo's
birthday). In his memory, a figure
from a post Ten Years Before —

Plato's reported motto for his Academy:
"Let no one ignorant of geometry enter."

For visual commentary by an artist ignorant
of geometry, see a work by Sol LeWitt.

For verbal commentary by an art critic  ignorant
of geometry, see a review of LeWitt by
Robert Hughes—

"A Beauty Really Bare" (TIME, Feb. 6, 2001).

See also Ten Years Group and Four Gods.

Wednesday, March 6, 2013

Final Club

Filed under: General — m759 @ 8:00 am

For Robert Langdon  (Angels & Demons )

See Final Club (Wikipedia) and Kiss Club (this journal).

The Red Pill

Filed under: General — m759 @ 1:20 am

On the late Hugo Chávez:

"A couple of years later, I asked him why,
so late in the day, he had decided to
adopt socialism. He acknowledged that he
had come to it late, long after most of
the world had abandoned it, but said that it
had clicked for him after he had read
Victor Hugo’s epic novel Les Misérables .
That, and listening to Fidel."

The New Yorker 's  Jon Lee Anderson

"As you can see, we've had our eye on you
for some time now, Mr. Anderson."

Midnight in Pynchon*

Filed under: General,Geometry — m759 @ 12:00 am

"It is almost as though Pynchon wishes to
repeat the grand gesture of Joyce’s Ulysses…."

Vladimir Tasic on Pynchon's Against the Day

Related material:

Tasic's Mathematics and the Roots of Postmodern Thought  
and Michael Harris's "'Why Mathematics?' You Might Ask"

*See also Occupy Galois Space and Midnight in Dostoevsky.

Tuesday, March 5, 2013

But Seriously…

Filed under: General — m759 @ 11:09 pm

(Continued)

"Now this is fairly serious stuff."

As is this.

Monday, March 4, 2013

Occupy Galois Space

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

Continued from February 27, the day Joseph Frank died

"Throughout the 1940s, he published essays
and criticism in literary journals, and one,
'Spatial Form in Modern Literature'—
a discussion of experimental treatments
of space and time by Eliot, Joyce, Proust,
Pound and others— published in
The Sewanee Review  in 1945, propelled him
to prominence as a theoretician."

— Bruce Weber in this morning's print copy
of The New York Times  (p. A15, NY edition)

That essay is reprinted in a 1991 collection
of Frank's work from Rutgers University Press:

See also Galois Space and Occupy Space in this journal.

Frank was best known as a biographer of Dostoevsky.
A very loosely related reference… in a recent Log24 post,
Freeman Dyson's praise of a book on the history of
mathematics and religion in Russia:

"The intellectual drama will attract readers
who are interested in mystical religion
and the foundations of mathematics.
The personal drama will attract readers
who are interested in a human tragedy
with characters who met their fates with
exceptional courage."

Frank is survived by, among others, his wife, a mathematician.

Saturday, March 2, 2013

Discourse

Filed under: General — Tags: — m759 @ 2:04 pm

(Continued)

"No puzzle has exercised more fascination
upon writers interested in the history of mathematics."

— Sir Thomas Little Heath, quoted by Mark Dominus in
his journal "The Universe of Discourse" on January 22, 2009.

If synchronicity is admitted to the universe of discourse,
a post in this  journal on that same date may be of interest.

Life of Pi

Filed under: General — Tags: — m759 @ 1:06 am

Earlier

Princeton Harvard Eating —

Harvard Math Department Pi Day event

"But the tigers come at night,
With their voices soft as thunder."

Les Miserables

Friday, March 1, 2013

Spinning in Infinity

Filed under: General — Tags: — m759 @ 11:09 pm

(Continued from Jan. 13 and Feb. 19.)

The founder of Graylock Press
died at 96 in Bethesda on Feb. 19:

For some background on the original Bethesda,
see a webpage on Angels in America.

For some background on noted Graylock authors, 
see Pavel Alexandrov.

For deeper background, see a book praised by Freeman Dyson:

"The intellectual drama will attract readers
who are interested in mystical religion
and the foundations of mathematics.
The personal drama will attract readers
who are interested in a human tragedy
with characters who met their fates with
exceptional courage."

Graduate

Filed under: General — m759 @ 2:24 pm

In memory of a 1961 graduate of
Beverly Hills High School who died today—

last night's Eiger post and a tall white mountain.

Thursday, February 28, 2013

Parts of a World

Filed under: General — m759 @ 10:31 pm

Bruce Reynolds, chief architect of
the Great Train Robbery, who reportedly
died today:

"We all have our benchmarks….
it’s the same madness, I suppose,
that drives people to bivouac on
the north face of the Eiger."

For the Eiger in this journal, see "Parts of a World."

Two-Part Invention

Filed under: General,Geometry — m759 @ 10:01 pm

Signet

 Ring

Paperweights

Filed under: General,Geometry — Tags: , — m759 @ 1:06 pm

A different dodecahedral space (Log24 on Oct. 3, 2011)—

R. T. Curtis, symmetric generation of M12 in a dodecahedron

Wednesday, February 27, 2013

Chanson

Filed under: General — m759 @ 11:02 pm

(A sequel to yesterday's post Publication )

IMAGE- A Death in Paris on February 26

Meanwhile, in this journal 

Les Miserables  at the Academy Awards

Midrash

Filed under: General — m759 @ 9:00 pm

News summary in today's previous post:

Van Cliburn Dies. Pope Bids Farewell.

Midrash:

Friday, July 11, 2008, 7:11 PM ET and Plato's Ghost.

Claves

Filed under: General — Tags: — m759 @ 1:06 pm

The News Today:

Van Cliburn Dies

Pope Bids Farewell

Image search from 2011:

Claves  (2 MB)

Tuesday, February 26, 2013

Publication

Filed under: General,Geometry — Tags: — m759 @ 4:00 pm

"I’ve had the privilege recently of being a Harvard University
professor, and there I learned one of the greatest of Harvard
jokes. A group of rabbis are on the road to Golgotha and 
Jesus is coming by under the cross. The young rabbi bursts
into tears and says, 'Oh, God, the pity of it!' The old rabbi says,
'What is the pity of it?' The young rabbi says, 'Master, Master,
what a teacher he was.'

'Didn’t publish!'

That cold tenure- joke at Harvard contains a deep truth.
Indeed, Jesus and Socrates did not publish."

— George Steiner, 2002 talk at York University

Related material

See also Steiner on Galois.

Les Miserables  at the Academy Awards

Snow

Filed under: General — m759 @ 2:01 am

"Hans Castorp is a searcher after the Holy Grail.
You would never have thought it when you read
his story—if I did myself, it was both more and
less than thinking. Perhaps you will read the
book again from this point of view. And perhaps
you will find out what the Grail is: the knowledge
and the wisdom, the consecration, the highest
reward, for which not only the foolish hero but
the book itself is seeking. You will find it in the
chapter called 'Snow'…."

— Thomas Mann, "The Making of
     The Magic Mountain "

In related entertainment news…

Click image for some backstory.

Mann's tale is set in Davos, Switzerland.
See also Mayer  at Davos.

Monday, February 25, 2013

Off the Road

Filed under: General — Tags: — m759 @ 6:00 pm

Starring Snow White! 

IMAGE- Winter storm; stay off roads, authorities say.

IMAGE- Off the road in 'New in Town' (2009 romantic comedy).

See also Thomas Pynchon’s remark in the previous post.

Thursday, February 21, 2013

Galois Space

Filed under: General,Geometry — Tags: — m759 @ 6:00 pm

(Continued)

The previous post suggests two sayings:

"There is  such a thing as a Galois space."

— Adapted from Madeleine L'Engle

"For every kind of vampire, there is a kind of cross."

Thomas Pynchon

Illustrations—

(Click to enlarge.)

Tuesday, February 19, 2013

Configurations

Filed under: General,Geometry — Tags: , , — m759 @ 12:24 pm

Yesterday's post Permanence dealt with the cube
as a symmetric model of the finite projective plane
PG(2,3), which has 13 points and 13 lines. The points
and lines of the finite geometry occur in the cube as
the 13 axes of symmetry and the 13 planes through
the center perpendicular to those axes. If the three
axes lying in  a plane that cuts the cube in a hexagon
are supplemented by the axis perpendicular  to that
plane, each plane is associated with four axes and,
dually, each axis is associated with four planes.

My web page on this topic, Cubist Geometries, was
written on February 27, 2010, and first saved to the
Internet Archive on Oct. 4, 2010

For a more recent treatment of this topic that makes
exactly the same points as the 2010 page, see p. 218
of Configurations from a Graphical Viewpoint , by
Tomaž Pisanski and Brigitte Servatius, published by
Springer on Sept. 23, 2012 (date from both Google
Books
and Amazon.com):

For a similar 1998 treatment of the topic, see Burkard Polster's 
A Geometrical Picture Book  (Springer, 1998), pp. 103-104.

The Pisanski-Servatius book reinforces my argument of Jan. 13, 2013,
that the 13 planes through the cube's center that are perpendicular
to the 13 axes of symmetry of the cube should be called the cube's 
symmetry planes , contradicting the usual use of of that term.

That argument concerns the interplay  between Euclidean and
Galois geometry. Pisanski and Servatius (and, in 1998, Polster)
emphasize the Euclidean square and cube as guides* to
describing the structure of a Galois space. My Jan. 13 argument
uses Galois  structures as a guide to re-describing those of Euclid .
(For a similar strategy at a much more sophisticated level,
see a recent Harvard Math Table.)

Related material:  Remarks on configurations in this journal
during the month that saw publication of the Pisanski-Servatius book.

* Earlier guides: the diamond theorem (1978), similar theorems for
  2x2x2 (1984) and 4x4x4 cubes (1983), and Visualizing GL(2,p)
  (1985). See also Spaces as Hypercubes (2012).

Monday, February 18, 2013

Permanence

Filed under: General,Geometry — m759 @ 2:00 pm

Inscribed hexagon (1984)

The well-known fact that a regular hexagon
may be inscribed in a cube was the basis
in 1984 for two ways of coloring the faces
of a cube that serve to illustrate some graphic
aspects of embodied Galois geometry

Inscribed hexagon (2013)

A redefinition of the term "symmetry plane"
also uses the well-known inscription
of a regular hexagon in the cube—

IMAGE- Redefining the cube's symmetry planes: 13 planes, not 9.

Related material

"Here is another way to present the deep question 1984  raises…."

— "The Quest for Permanent Novelty," by Michael W. Clune,
     The Chronicle of Higher Education , Feb. 11, 2013

“What we do may be small, but it has a certain character of permanence.”

— G. H. Hardy, A Mathematician’s Apology

Sunday, February 17, 2013

FROM an Entertainer

Filed under: General — m759 @ 9:00 pm

IMAGE- 'Michael Chabon can write like a magical spider....'

IMAGE- Book cover with 'WONDER BOYS' typewriter key

See also Back Space and Shift Lock .

For an Entertainer

Filed under: General — m759 @ 1:06 pm

"Forget about your rainbow schemes,
Spin a little web of dreams."

Song lyric

Related material: 

Big Time and The Lost Tesseract.

Zero Theorem

Filed under: General — m759 @ 12:25 am

See "Mind of Winter" in this journal.

"And we may see the meadow in December…."

FROM Christoph Waltz

Filed under: General — m759 @ 12:12 am

"Currently in post-production": The Zero Theorem.

For Christoph Waltz

Filed under: General — m759 @ 12:00 am

Raiders of the Lost Tesseract  continues…

SOCRATES: Is he not better off in knowing his ignorance?
MENO: I think that he is.
SOCRATES: If we have made him doubt, and given him the 'torpedo's shock,' have we done him any harm?
MENO: I think not.

Torpedo… LOS!

Saturday, February 16, 2013

Second Life

Filed under: General — m759 @ 11:19 pm

Part I: The Midnight Ending Lincoln's Birthday, 2013

Part II: The Death of Barnaby Conrad on that day

Part III: The Second Life of John Wilkes Booth

Whether Conrad now enjoys a second life, I do not know.

Friday, February 15, 2013

Hollywood Valentine

Filed under: General — m759 @ 12:31 pm

Part I: Professor Marvin W. Meyer (this journal yesterday)

Part II: Producer/writer Richard Collins (Los Angeles Times  today)

Thursday, February 14, 2013

Chapman’s Homer

Filed under: General — Tags: , — m759 @ 12:00 pm

(Continued from August 23, 2012)

“Good is a noun. That was it.
That was what Phaedrus had been looking for.
That was the homer over the fence
that ended the ballgame.”

Robert M. Pirsig

But perhaps not a proper  noun.
See the link to Good's Singularity
at the end of today's previous post.

Annals of Quantum Hype

Filed under: General — Tags: , — m759 @ 11:00 am

Yesterday's link to Aaronson and Turing suggests a review
of events on August 16, 2012 in the light of Log24 on that date.

Exhibit A: New Institute for Quantum Studies at Chapman University—

Exhibit B: The Aug. 16, 2012, death of Chapman University's Indiana Jones—

Whether this Indiana Jones successfully transgressed
the boundaries of space and time, I do not know.

Exhibit C: Related quantum hype— 

Chapman Professor Lands Discover  Cover Story,
Chapman University Happenings, March 18, 2010

See also Good's Singularity.

Wednesday, February 13, 2013

Form:

Filed under: General,Geometry — Tags: , , , — m759 @ 9:29 pm

Story, Structure, and the Galois Tesseract

Recent Log24 posts have referred to the 
"Penrose diamond" and Minkowski space.

The Penrose diamond has nothing whatever
to do with my 1976 monograph "Diamond Theory,"
except for the diamond shape and the connection
of the Penrose diamond to the Klein quadric—

IMAGE- The Penrose diamond and the Klein quadric

The Klein quadric occurs in the five-dimensional projective space
over a field. If the field is the two-element Galois field GF(2), the
quadric helps explain certain remarkable symmetry properties 
of the R. T. Curtis Miracle Octad Generator  (MOG), hence of
the large Mathieu group M24. These properties are also 
relevant to the 1976 "Diamond Theory" monograph.

For some background on the quadric, see (for instance)

IMAGE- Stroppel on the Klein quadric, 2008

See also The Klein Correspondence,
Penrose Space-Time, and a Finite Model
.

Related material:

"… one might crudely distinguish between philosophical
and mathematical motivation. In the first case one tries
to convince with a telling conceptual story; in the second
one relies more on the elegance of some emergent
mathematical structure. If there is a tradition in logic
it favours the former, but I have a sneaking affection for
the latter. Of course the distinction is not so clear cut.
Elegant mathematics will of itself tell a tale, and one with
the merit of simplicity. This may carry philosophical
weight. But that cannot be guaranteed: in the end one
cannot escape the need to form a judgement of significance."

– J. M. E. Hyland. "Proof Theory in the Abstract." (pdf)
Annals of Pure and Applied Logic 114, 2002, 43-78.

Those who prefer story to structure may consult 

  1. today's previous post on the Penrose diamond
  2. the remarks of Scott Aaronson on August 17, 2012
  3. the remarks in this journal on that same date
  4. the geometry of the 4×4 array in the context of M24.

Transgressing the Boundary

Filed under: General — Tags: , — m759 @ 12:00 pm

The title refers not to the 1996 Sokal hoax (which has
Boundaries , plural, in the title), but to the boundary
discussed in Monday's Penrose diamond post

"Science is a differential equation.
Religion is a boundary condition."

Alan Turing in the epigraph to the
first chapter of a book by Terence Tao

From the Tao book, page 170—

"Typically the transformed solution extends to the
boundary of the Penrose diamond and beyond…."

Transgressing the boundary between science
and religion is the topic of a 1991 paper available
at JSTOR for $29.

For the Pope on Ash Wednesday:

"Think you might have access 
to this content via your library?" —JSTOR

See also Durkheim at Harvard.

Midnight in the Garden

Filed under: General,Geometry — m759 @ 12:00 am

(Continued, to mark Tuesday's birthdays of Lincoln and Darwin.)

A British reporter who died at 97 on Tuesday is said to have
"covered the space race in its entirety." In his honor, here
in review are posts containing the phrase Space Race
and, more generally, the two words Galois + Space.

Monday, February 11, 2013

The Penrose Diamond

Filed under: General,Geometry — Tags: , — m759 @ 2:01 pm

IMAGE- The Penrose Diamond

Related material:

(Click to enlarge.)

See also remarks on Penrose linked to in Sacerdotal Jargon.

(For a connection of these remarks to
the Penrose diamond, see April 1, 2012.)

Pope To Resign

Filed under: General — m759 @ 12:00 pm

Logo

Filed under: General — m759 @ 3:09 am

In memory of Rabbi David Hartman, who died yesterday.

The architecture is by Lou Gelehrter.
I do not know the logo designer's name.

Please Mister Please

Filed under: General — m759 @ 12:25 am

IMAGE- Mumford & Sons wins Album of Year for 'Babel'

Related material:  Group Actions and B17.

Sunday, February 10, 2013

Semiotics for Kearney*

Filed under: General — Tags: — m759 @ 4:16 pm

Click image for some background.

Context:

and the following post from last October:

* Who is Kearney? See, for instance, this book.

Topics

Filed under: General — m759 @ 12:25 am

Suggested by a recent review of a
book by Richard Kearney:

The World,  the Flesh, and the Devil.

Talk amongst yourselves.

The Cleaning

Filed under: General,Geometry — m759 @ 12:00 am

Arthur Jaffe CV:

"In 2005 Arthur Jaffe succeeded Sir Michael Atiyah as
Chair of the Board of the Dublin Institute for Advanced Study,
School of Theoretical Physics."

Related material:

Biddies in this journal and

Detail:

An early version of quaternions.

Saturday, February 9, 2013

Snow Dance

Filed under: General,Geometry — m759 @ 2:09 pm

The Snow White dance from last Nov. 14
features an ad that was originally embedded
in an American Mathematical Society Notices
review describing three books of vulgarized
mathematics. These books all use "great
equations" as a framing device.

This literary strategy leads to a more abstract
snow dance. See the ballet blanc  in this journal
on Balanchine's birthday (old style) in 2003.
That dance involves equation (C) below.

Recall that in a unit ring ,
"0" denotes the additive identity,
"1" the multiplicative identity, and "-1" the
additive inverse of the multiplicative identity.

Three classic equations:

(A)  1 + 1 = 2    (Characteristic 0, ordinary arithmetic)

(B)  1 + 1 = 0   (Characteristic 2 arithmetic, in which 2 = 0)

(C)  1 + 1 = -1 (Characteristic 3 arithmetic, in which 2 = -1)

Cases (B) and (C), in which the characteristic is prime,
occur in Galois geometry.

For a more elaborate snow dance, see Master Class.

Friday, February 8, 2013

Dictum

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

A review of the life of physicist Arthur Wightman,
who died at 90 on January 13th, 2013. yields 
the following.

Wightman at Wikipedia:
"His graduate students include
 Arthur Jaffe,  Jerrold Marsden, and Alan Sokal."

"I think of Arthur as the spiritual leader
of mathematical physics and his death
really marks the end of an era."

— Arthur Jaffe in News at Princeton , Jan. 30

Marsden at Wikipedia
"He [Marsden] has laid much of the foundation for
symplectic topology." (Link redirects to symplectic geometry.)

A Wikipedia reference in the symplectic geometry article leads to

THE SYMPLECTIZATION OF SCIENCE:
Symplectic Geometry Lies at the Very
Foundations of Physics and Mathematics

Mark J. Gotay
Department of Mathematics
University of Hawai‘i

James A. Isenberg
Institute of Theoretical Science and Department of Mathematics
University of Oregon

February 18, 1992

Acknowledgments:

We would like to thank Jerry Marsden and Alan Weinstein
for their comments on previous drafts.

Published in: Gazette des Mathématiciens  54, 59-79 (1992).

Opening:

"Physics is geometry .  This dictum is one of the guiding
principles of modern physics. It largely originated with
Albert Einstein…."

A different account of the dictum:

The strange term Geometrodynamics 
is apparently due to Wheeler.

Physics may or may not be geometry, but
geometry is definitely not physics.

For some pure geometry that has no apparent 
connection to physics, see this journal
on the date of Wightman's death.

Thursday, February 7, 2013

Mathematics and Narrative, continued…

Filed under: General — Tags: — m759 @ 2:01 pm

Primes Are Forever

"If diamonds are a girl's best friend,
prime numbers are a mathematician's….

A Mersenne prime is of the form 2P-1,
where the variable P is itself a prime—
making the Mersenne an elite sort of prime,
a James Bond among spies."

— Anonymous author at
    Fox News, Feb. 5, 2013

The author notes that the smaller
Mersenne primes include 7.

Related Material

April 7, 2003:

April is Math Awareness Month.

This year's theme is "mathematics and art."

Mathematics and Art: Totentanz from Seventh Seal

Update of 2:56 PM Feb. 7:

See also Paul Bateman and, in this journal, the date of Bateman's death.

For mathematics rather than narrative, see (for instance)

.

Wednesday, February 6, 2013

A Bus Named Desire

Filed under: General — m759 @ 12:00 pm

For Kiefer Sutherland, Hasty Pudding Man of the Year, 2013

Act I:

Current Validity for Erlangen…?

… MathOverflow question dated March 28, 2011

Act II:

Erlangen

… Starring Elke Sommer, former Erlangen student

Act III:

The Sweet Smell of Avon

… See also Bus 318 and 3/18 in 2012.

Act IV:

Desire

… Log24 post dated March 28, 2011

Tuesday, February 5, 2013

Serious Error

Filed under: General — m759 @ 6:00 pm

IMAGE- News item: 'Prime numbers... have little mathematical importance.'

Related material:  G. H. Hardy on seriousness.

Review

Filed under: General — m759 @ 5:10 pm

John Berryman in The New York Review of Books :

FEBRUARY 1, 1963 • VOLUME 1, NUMBER 1

"Now he has become, abrupt, an industry.
Professional-Friends-Of-Robert-Frost all over
open their mouths
while the quirky medium of so many truths
is quiet. Let’s all be quiet. Let’s listen:
while he begins to talk with Horace."

Grail

Filed under: General — Tags: — m759 @ 3:33 pm

Today's online Telegraph  has an obituary of The Troggs' 
lead singer Reg Presley, who died yesterday at 71.

The unusually brilliant style  of of the unsigned obituary
suggests a review of the life of a fellow Briton— 
F. L. Lucas (1894-1967), author of Style .

According to Wikipedia, Virginia Woolf described Lucas as
"pure Cambridge: clean as a breadknife, and as sharp."

Lucas's acerbic 1923 review of The Waste Land  suggests,
in the context of Woolf's remark and of the Blade and Chalice
link at the end of today's previous post, a search for a grail.

Voilà.

Arsenal

The previous post discussed some fundamentals of logic.

The name “Boole” in that post naturally suggests the
concept of Boolean algebra . This is not  the algebra
needed for Galois geometry . See below.

IMAGE- Logic related to 'the arsenal of algebraic analysis tools for fields'

Some, like Dan Brown, prefer to interpret symbols using
religion, not logic. They may consult Diamond Mandorla,
as well as Blade and Chalice, in this journal.

See also yesterday’s Universe of Discourse.

Entities

Filed under: General — Tags: — m759 @ 12:24 pm

From January 26, 2013

IMAGE- Yahoo CEO Marissa Mayer at Davos and the ontology of entities

Related material: "universe of discourse"

Monday, February 4, 2013

The Universe of Discourse

Filed under: General — Tags: — m759 @ 10:00 pm

A Raven's Remark—

Related material:

Fish Story, Object Lesson, The Universe of Discourse,
Archimedes's Approximation of Pi, and

Sunday, February 3, 2013

Trophy

Filed under: General — Tags: , — m759 @ 11:30 pm

From the 1984 New Orleans film Tightrope

http://www.log24.com/log/pix11A/110615-EastwoodFootball400w.jpg

Related material: Walking the Tightrope and Transgressing.

Sermon

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

Blake on the Bus

Note the contemptible adolescent misinformation
about Jim Morrison, The Doors, and Blake.

The Doors may have been named after neither
Blake's original version of the phrase "the doors
of perception" nor  Aldous Huxley's 1954
drug-related book by that title.

See also The Perception of Doors in this journal.

The Gospel According to Cartier

Filed under: General — Tags: , , , — m759 @ 10:30 am

Yesterday's 11 AM post Mad Day concluded
with a link to a 2001 American Mathematical Society
article by Pierre Cartier that sums up the religion and
politics of many mathematicians

"Here ends the infancy narrative of the gospel…."

"… while Simone Weil's Catholicism was violently
anti-Semitic (in 1942!), Grothendieck's Buddhism
bears a strong resemblance to the practices of
his Hasidic ancestors."

See also Simone Weil in this journal.

Note esp. a post of April 6, 2004 that provides
a different way of viewing Derrida's notion of
inscription .

Saturday, February 2, 2013

Catholic Schools Week

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

"The theme for the National Catholic Schools Week 2013
is 'Catholic Schools Raise the Standards.' The annual
observance starts the last Sunday in January and runs
all week, which in 2013 is January 27 to February 2." 

"After all, tomorrow is another day." —Scarlett O'Hara,
quoted here in a post of May 9, 2005.

"Dr.  Tomorrow is another guy ." —A comment on that post.

The Dr. Tomorrow link leads to a page promoting something
called the Institute of Noetic Sciences. This in turn leads to
the 2009 Dan Brown novel The Lost Symbol .

For related material in this journal, see
Raiders of the Lost Dingbat.

As for raising the standards, see the conclusion of
Adolf Holl's The Left Hand of God 

Mad Day

Filed under: General — Tags: , , , — m759 @ 11:00 am

A perceptive review of Missing Out: In Praise of the Unlived Life

IMAGE- The perception of doors

"Page 185: 'Whatever else we are, we are also mad.' "

Related material— last night's Outside the Box and, from Oct. 22 last year

"Some designs work subtly.
Others are successful through sheer force."

Par exemple—

IMAGE- The Cartier diamond ring from 'Inside Man'

See also Cartier in this journal.

The Cartier link leads to, among other things

A Mad Day’s Work: From Grothendieck to Connes and Kontsevich.
The Evolution of Concepts of Space and Symmetry
,”
by Pierre Cartier, Bulletin of the American Mathematical Society ,
Vol. 38 (2001) No. 4, pages 389-408

Outside the Box

Filed under: General — m759 @ 1:00 am

In memory of the late Ed Koch
a poem and a link:

Poem — "The Shoebox," by Sheila Gogol

Link  Sheila in this journal

Friday, February 1, 2013

Get Quotes

Filed under: General — Tags: , — m759 @ 4:01 pm

For Tony Kushner fans:

For logic fans:

IMAGE- NY Times market quotes, American Express Gold Card ad, Kevin Spacey in 'House of Cards' ad

John Searle on Derrida:

On necessity, possibility, and 'necessary possibility'

In the box-diamond notation, the axiom Searle quotes is

.

"The euclidean property guarantees the truth of this." — Wikipedia

Linking to Euclid

Clicking on "euclidean" above yields another Wikipedia article

"In mathematics, Euclidean relations are a class of binary relations that satisfy a weakened form of transitivity that formalizes Euclid's 'Common Notion 1' in The Elements : things which equal the same thing also equal one another."

Verification: See, for instance, slides on modal logic at Carnegie Mellon University and modal logic at plato.stanford.edu.

Thursday, January 31, 2013

Necessary Possibility

Filed under: General — Tags: — m759 @ 9:05 pm

The inscription  link in the previous post suggests
a review of the rather paradoxical concept of 
"necessary possibility."

See a deconstructionist view , a scholarly view,
and a graphic view.

Scholarship in 1961…

Filed under: General,Geometry — m759 @ 12:00 pm

Before Derrida's writings on Plato and on inscription

A remark by the late William Harris:

"Scholarship has many dark ages, and they do not all fall
in the safe confines of remote antiquity."

For more about Harris, see the previous post.

Discussing an approach to solving a geometrical problem 
from section 86e of the Meno , Harris wrote that

"… this is a very important element of method and purpose,
one which must be taken with great seriousness and respect.
In fact it is as good an example of the master describing for us
his method as Plato ever gives us. Tricked by the appearance
of brevity and unwilling to follow through Plato's thought on
the road to Euclid, we have garbled or passed over a unique
piece of philosophical information."

Harris, though not a geometer, was an admirable man.
His remark on the Meno  method is itself worthy of respect.

In memory of Harris, Plato, and pre-Derrida scholarship, here
are some pages from 1961 on the problem Harris discussed.

A pair of figures from the 1961 pages indicates how one view of the
section 86e problem (at right below) resembles the better-known 
demonstration earlier in the Meno  of how to construct
a square of area 2 —

Wednesday, January 30, 2013

The Problem Problem

Filed under: General,Geometry — m759 @ 11:01 pm

Continued from Jan. 22, 2013:

IMAGE- Triangle, circle, square

Given these choices for a solution ,
what is a suitable problem ?

The problem sketched on Jan. 22 was a joke.

A more serious triangle-circle-square problem:  

Introductory commentary from the same source—

See also a description of this problem by the late William Harris,
Harvard '48, Professsor Emeritus of Classics at Middlebury College,
who died on February 22, 2009*—

"… this is a very important element of method and purpose,
one which must be taken with great seriousness and respect.
In fact it is as good an example of the master describing for us
his method as Plato ever gives us. Tricked by the appearance
of brevity and unwilling to follow through Plato's thought on
the road to Euclid, we have garbled or passed over a unique
piece of philosophical information."

The problem itself, from the Perseus site:

[87a] whether a certain area is capable of being inscribed as a triangular space in a given circle: they reply—“I cannot yet tell whether it has that capability; but I think, if I may put it so, that I have a certain helpful hypothesis for the problem, and it is as follows: If this area is such that when you apply it to the given line of the circle you find it falls short by a space similar to that which you have just applied, then I take it you have one consequence, and if it is impossible for it to fall so, then some other. Accordingly I wish to put a hypothesis, before I state our conclusion as regards inscribing this figure [87b] in the circle by saying whether it is impossible or not.” In the same way with regard to our question about virtue, since we do not know either what it is or what kind of thing it may be, we had best make use of a hypothesis in considering whether it can be taught or not, as thus: what kind of thing must virtue be in the class of mental properties, so as to be teachable or not? In the first place, if it is something dissimilar or similar to knowledge, is it taught or not—or, as we were saying just now, remembered? Let us have no disputing about the choice of a name: [87c] is it taught? Or is not this fact plain to everyone—that the one and only thing taught to men is knowledge?

Meno
I agree to that.

Socrates
Then if virtue is a kind of knowledge, clearly it must be taught?

Meno
Certainly.

Socrates
So you see we have made short work of this question—if virtue belongs to one class of things it is teachable, and if to another, it is not.

Meno
To be sure.

For further details, consult (for instance) a 1955 paper at JSTOR.

* See a post from that date in this journal.
   See also a remark by Harris:

  "Scholarship has many dark ages, and they do not all fall
    in the safe confines of remote antiquity."

Abstract Possibility

Filed under: General — m759 @ 1:01 pm

Today's NY Times  "Stone Links" to philosophy include
a link to a review of a collection of Hilary Putnam's papers.

Related material, from Putnam's "What is Mathematical
Truth?
" (Historia Mathematica  2 (1975): 529-543)—

"In this paper I argue that mathematics should be interpreted realistically – that is, that mathematics makes assertions that are objectively true or false, independently of the human mind, and that something answers to such mathematical notions as ‘set’ and ‘function’. This is not to say that reality is somehow bifurcated – that there is one reality of material things, and then, over and above it, a second reality of ‘mathematical things’. A set of objects, for example, depends for its existence on those objects: if they are destroyed, then there is no longer such a set. (Of course, we may say that the set exists ‘tenselessly’, but we may also say the objects exist ‘tenselessly’: this is just to say that in pure mathematics we can sometimes ignore the important difference between ‘exists now’ and ‘did exist, exists now, or will exist’.) Not only are the ‘objects’ of pure mathematics conditional upon material objects; they are, in a sense, merely abstract possibilities. Studying how mathematical objects behave might better be described as studying what structures are abstractly possible and what structures are not abstractly possible."

See also Wittgenstein's Diamond and Plato's Diamond.

Tuesday, January 29, 2013

Clash of the Caped Crusaders

Filed under: General — Tags: , — m759 @ 2:29 pm

The New Yorker , quoted here yesterday, on a meeting in 1638 of Galileo and Milton—

"… it’s like those comic-book specials in which Superman meets Batman…."

Related news yesterday from The Hollywood Reporter

IMAGE- Producer Lloyd Phillips dies at 63

      Phillips's upcoming Superman film stars Amy Adams.

      Other entertainment:

      Log24 posts from the day of Phillips's death—

Binder

Filed under: General — Tags: , — m759 @ 12:00 pm

A sequel to last midnight's post

IMAGE- Inauguration 2013: Schumer, Binder, Beyoncé

See also Midnight Politics and On the Cusp.

Midnight in the Garden

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

(Continued)

     For a related essay, click on the image below.

    

Monday, January 28, 2013

Serpents’ Eyes Only

Filed under: General — m759 @ 9:48 pm

    "The serpent's eyes shine as he wraps around the vine" — Don Henley

Encounter

Filed under: General — Tags: , , — m759 @ 9:00 pm

"Sometime in 1638, John Milton visited Galileo Galilei in Florence. The great astronomer was old and blind and under house arrest, confined by order of the Inquisition, which had forced him to recant his belief that the earth revolves around the sun, as formulated in his 'Dialogue Concerning the Two Chief World Systems.' Milton was thirty years old—his own blindness, his own arrest, and his own cosmological epic, 'Paradise Lost,' all lay before him….

Beyond the sheer pleasure of picturing the encounter— it’s like those comic-book specials in which Superman meets Batman— there’s something strange about imagining these two figures inhabiting the same age. Though Milton was the much younger man, in some ways his world system seems curiously older than the astronomer’s empirical universe."

Jonathan Rosen, The New Yorker , June 2, 2008, "Return to Paradise"

More in the spirit of Superman and Batman:

    "Huh. You know what? Galileo didn't even write this."
    "What!"
    "The poem is signed John Milton."
    "John Milton ?" The influential English poet who wrote
Paradise Lost  was a contemporary of Galileo's and a
savant who conspiracy buffs put at the top of their list
of Illuminati suspects. Milton's alleged affiliation with
Galileo's Illuminati was one legend Langdon
suspected was true. Not only had Milton made a
well documented 1638 pilgrimage to Rome to
"commune with enlightened men," but he had held
meetings with Galileo during the scientist's house
arrest, meetings portrayed in many Renaissance
paintings….
    "Milton knew Galileo, didn't he?" Vittoria said, finally
pushing the folio over to Langdon. "Maybe he wrote
the poem as a favor?"

Angels & Demons  , by Dan Brown
     (first published in 2000)

See also this journal on August 16, 2009.

Addendum for Aaron Swartz (see today's previous post)—

"The Vatican, it seemed, took their archives
a bit more seriously than most." — Dan Brown

PEP Talk

Filed under: General — Tags: — m759 @ 1:00 pm

Review: A page linked to here on Jan. 25
psychoanalyst Heinz Kohut on the "nuclear self"—

IMAGE- Kohut, 'Restoration of the Self,' p. 182

The Psychoanalytic Electronic Publishing (PEP) website has a 
paper on Kohut's concept— "Nuclear Conflict and the Nuclear Self"—
to which access is restricted:

IMAGE- Psychoanalytic Electronic Publishing (PEP) access statement

Perhaps the late Aaron Swartz (below) now has freer access
to this and other restricted reading.

Sunday, January 27, 2013

Patrick’s Days

Filed under: General — m759 @ 7:00 pm

Continued from previous post 

For what it's worth

A birth and a death, each on the Feast of St. Patrick

"Donald Frederick Hornig was born on March 17, 1920, in Milwaukee
and attended Harvard, earning his undergraduate degree there
in 1940 and his Ph.D. in 1943, both in chemistry. His dissertation
was titled 'An Investigation of the Shock Wave Produced by an Explosion'…."

— "Donald Hornig, Last to See First A-Bomb, Dies at 92,"
New York Times  print version today (p. A20, New York edition)

A death elsewhere in Wisconsin 92 years later, on March 17, 2012—

IMAGE- Paul S. Boyer, 78, Historian; Studied A-Bomb and Witches

more »

Citation Needed

Filed under: General — m759 @ 11:09 am

IMAGE- Wikipedia: Citation needed for Aiken as source of 'Swiftly Tilting Planet' title

IMAGE- Aiken citation on copyright page of 'Swiftly Tilting Planet'

The Square Fish logo was designed by Filomena Tuosto.

Sunday School

Filed under: General — Tags: — m759 @ 9:48 am

"The newspaper Diario de Santa Maria  reported
that the fire started at around 2 a.m. at the Kiss club
in the city at the southern tip of Brazil, near the borders
with Argentina and Uruguay."  more »

Ay Que Bonito

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

Meditations for 2 AM —

Shining Forth

Filed under: General — m759 @ 12:09 am

See noon yesterday 

IMAGE- Yahoo's Marissa Mayer on the ontology of entities

and the date of Donald Hornig’s death:

Saturday, January 26, 2013

Nine Years

Filed under: General — m759 @ 12:00 pm

IMAGE- Yahoo CEO Marissa Mayer and the ontology of entities

Excerpt from an essay cached nine years ago:

"The current dominant conceptual framework
which pictures the self as an inner entity
is slowly breaking up. And I am convinced that
some, if not all, of the approaches to the self
sketched here will form the basis for a new
conceptual framework…."

Context for the essay: 

A journal issue titled "The Opening of Narrative Space" (pdf, 475 KB)

For one sort of narrative space, see Giordano Bruno in this journal.

See also Nine Years.

Friday, January 25, 2013

Where Credit Is Due

Filed under: General — m759 @ 1:00 pm

Harvard's President Faust:

IMAGE- Harvard President Faust at Boston College, a Jesuit institution, on Oct. 10, 2012

Last evening's post Moondance was suggested by a check
in this journal of the date October 10, 2012. That date was
in turn suggested by the date of the above remarks.

Wer immer strebend sich bemüht,
Den können wir erlösen.

Who always striving efforts makes,
For him there is salvation
.

Faust Part 2, Act V, Scene 7: Mountain Gorges.

Matchmaker, Matchmaker

Filed under: General — m759 @ 12:31 pm

A Google search for images matching
Amy Adams's door in the 2005 film
"Standing Still" yields a surprising result.

Related material: Adams in "Doubt" (2008).

See also A Touch of Glass.

Public/Private

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

"I decided that there was a public Elise
and a private Elise, and they're not necessarily
the same person." — Amy Adams interview
on the 2005 film "Standing Still"

A division between public and private, from
"Standing Still"—

IMAGE- The perception of doors in 'Standing Still'

User review at IMDb:

"This movie reminded me of The Big Chill
(which I also loved)…."

See, too, a different door and a different Elise
in a post from Tuesday, Jan. 22, 2013

Also from that post—

"By recalling the past and freezing the present
he could open the gates of time…."

— Mark Helprin, In Sunlight and in Shadow

Thursday, January 24, 2013

Moondance

Filed under: General,Geometry — Tags: — m759 @ 9:01 pm

The title was suggested by an ad for a film that opens
at 10 PM EST today: "Hansel & Gretel: Witch Hunters."

Related material: Grimm Day 2012, as well as
Amy Adams in Raiders of the Lost Tesseract
and in a Film School Rejects page today.

See also some Norwegian art in
Trish Mayo's Photostream today and in
Omega Point (Log24, Oct. 15, 2012)—

Monday, October 15, 2012

Omega Point

m759 @ 2:00 PM 

For Sergeant-Major America—

IMAGE- Art exhibition with 'Omega Point' and geometric figures related to tesseract, along with movie 'Captain America' figure

The image is from posts of Feb. 20, 2011,
and Jan. 27, 2012.

This instance of the omega point is for 
a sergeant major who died at 92 on Wednesday,
October 10, 2012.

See also posts on that date in this journal—

Midnight,  Ambiguation,  Subtitle for Odin's Day,
 and Melancholia, Depression, Ambiguity.

Object Lesson

Filed under: General — Tags: , — m759 @ 7:59 pm

Suggested by yesterday's Garden Path

Commentary by Trish Mayo on a photo at Flickr:

Gazing Globe

These beautiful garden ornaments have a long history, beginning in the 13th century when they were made in Venice, Italy of hand-blown glass. They have been called by many names: Gazing Globe, Garden Globe, Witch Ball, Butler Globe and Globe of Happiness.

Legends formed about the mysterious powers of the globes. They were said to bring happiness, good luck and prosperity to those who owned it, known to ward off evil spirits, misfortune, illness and witches!

Some say the ball should be placed near the entrance to a house so that if a witch came by she would not be able to get past her reflection as she cannot tear herself away from her own image. Other accounts say a witch cannot bear to see her own reflection so she will not come near a "witch’s ball". A witch cannot sneak up on a person gazing into a globe as he can see if a witch approaches from behind. The smaller ball made of colored glass as opposed to the reflective kind was believed to attract and trap evil spirits.

Spiritually speaking, as one peers into the globe he can experience "oneness" with the universe.

The gazing globes practical purposes included being strategically placed on a path near the front entrance so that you could see when someone was coming for a visit. In Victorian times, the "Butler Ball" served as a mirror for servants to see when guests were needing assistance without staring at them throughout the meal. Another practical use was in the foyer of the home. Parents could keep a close eye on their daughter and her date as he bid her goodnight.

Today the globe is used ornamentally, allowing the whole garden, including the sky, to be viewed with one glance.

Under Covers

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

For Amy Adams and Trudie Styler:

http://www.log24.com/log/pix10B/101027-LangerSymbolicLogic.jpg

Click each cover for some background. See also

Cube Space

Filed under: General — Tags: , , — m759 @ 12:24 pm

For the late Cardinal Glemp of Poland,
who died yesterday, some links:

Wednesday, January 23, 2013

DNA and a Galois Field

Filed under: General,Geometry — m759 @ 9:29 pm

From Ewan Birney's weblog today:

WEDNESDAY, 23 JANUARY 2013

Using DNA as a digital archive media

Today sees the publication in Nature  of “Toward practical high-capacity low-maintenance storage of digital information in synthesised DNA,” a paper spearheaded by my colleague Nick Goldman and in which I played a major part, in particular in the germination of the idea.

Birney appeared in Log24 on Dec. 30, 2012, quoted as follows:

"It is not often anyone will hear the phrase 'Galois field' and 'DNA' together…."

— Birney's weblog on July 3, 2012, "Galois and Sequencing."

Birney's widespread appearance in news articles today about the above Nature  publication suggests a review of the "Galois-field"-"DNA" connection.

See, for instance, the following papers:

  • Gail Rosen and Jeff Moore. "Investigation of Coding Structure in DNA," IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Hong Kong, April 2003. [pdf]
  • Gail Rosen. "Finding Near-Periodic DNA Regions using a Finite-Field Framework," 2nd IEEE Genomic Signal Processing Workshop (GENSIPS), Baltimore, MD, May 2004. [pdf]
  • Gail Rosen. "Examining Coding Structure and Redundancy in DNA," IEEE Engineering in Medicine and Biology Magazine, Volume 25, Issue 1, January/February 2006. [pdf]

A  Log24 post of Sept. 17, 2012, also mentions the phrases "Galois field" and "DNA" together.

Garden Path

Filed under: General — m759 @ 12:00 pm

(Continued from Epiphany 2012)

Yesterday's link to the post Special Topics suggests
a review of the garden of forking paths.

An example of such paths, given in the Special Topics
post, came from a paper describing the modular group:

Modular group tree

Here is another view of the modular group's
forking paths:

"Tree for modular group" from the
Algebra page of the University of Glasgow

Tuesday, January 22, 2013

Für Elise

Filed under: General — Tags: — m759 @ 9:00 pm

Elise in "The Adjustment Bureau" (release date: March 4, 2011)—

IMAGE- The perception of doors in 'The Adjustment Bureau'

A quote for this unlikely pair:

"Harry decides his chief peacetime duty is to use his
gift for gab to further his 'overriding purpose,' namely:
'By recalling the past and freezing the present he could
open the gates of time and through them see all
allegedly sequential things as a single masterwork
with neither boundaries nor divisions.' Once he opens
these gates, Harry will flood his audience with his
redemptive epiphanic impression that 'the world was
saturated with love.' "

Liesl Schillinger, review of Mark Helprin's novel
In Sunlight and in Shadow  in The New York Times ,
Oct. 5, 2012

A more realistic pair: Chuck Schumer and Iris Weinshall.

See also Adjustment Team (Wikipedia) and Gnostic Dick (Log24).

For some more-serious material, see another review by Schillnger
in a Log24 post of August 17, 2006— Special Topics

But Seriously…

Filed under: General — m759 @ 1:14 pm

Introductory Aramaic

See also a theater review in yesterday's print NY Times
and a video in today's online Times:

The Problem Problem

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

For connoisseurs of psychological tests, 
here is an inverse puzzle:

IMAGE- Triangle, circle, square

Given these choices for a solution ,
what is a suitable problem

There is, of course, no single right answer.

One path to an answer might involve
a British webpage and the recent film Branded.

Max von Sydow in Branded  (2012)

(See, too, related remarks on The Queen's Privy Council.)

Raven Light

Filed under: General — Tags: , , — m759 @ 11:40 am

"…a fundamental cognitive ability known as 'fluid' intelligence: the capacity to solve novel problems, to learn, to reason, to see connections and to get to the bottom of things. …

…matrices are considered the gold standard of fluid-intelligence tests. Anyone who has taken an intelligence test has seen matrices like those used in the Raven’s: three rows, with three graphic items in each row, made up of squares, circles, dots or the like. Do the squares get larger as they move from left to right? Do the circles inside the squares fill in, changing from white to gray to black, as they go downward? One of the nine items is missing from the matrix, and the challenge is to find the underlying patterns— up, down and across— from six possible choices. Initially the solutions are readily apparent to most people, but they get progressively harder to discern. By the end of the test, most test takers are baffled."

— Dan Hurley, "Can You Make Yourself Smarter?," NY Times , April 18, 2012

See also "Raven Steals the Light" in this  journal.

Related material:

Plan 9 from MIT and, perhaps exemplifying crystallized  rather than fluid  intelligence, Black Diamond.

Monday, January 21, 2013

Winner

Filed under: General — m759 @ 7:45 pm

"Well, I got there!"

— D. H. Lawrence,
"The Rocking-Horse Winner"

Shining Forth

Filed under: General,Geometry — m759 @ 11:40 am

(Continued from March 15, 2001)

IMAGE- On Quine, ontology, and regimentation

For one sort of regimentation, see Elements  of Geometry.

Sunday, January 20, 2013

On the Road

Filed under: General — Tags: — m759 @ 9:00 pm

(For Your Consideration  continued)

Today's New York Times  story on Jacobin  magazine
suggests the following sequel to a Jan. 10 post on
Spielberg's Lincoln .

The magazine has, the Times  says,

"earned [its creator] Mr. Sunkara, now a ripe 23,
extravagant praise from members of a (slightly) older
guard who see his success as heartening sign that
the socialist 'brand'— to use a word he throws around
with un-self-conscious ease— hasn’t been totally
killed off by Tea Party invective." —Jennifer Schuessler

Jacobin  magazine, summer 2012 double issue—

A related trinity of the Left:

Playwright Tom Stoppard, his son actor Ed Stoppard
(shown below in the 2012 film Branded ), and the late
activist Aaron Swartz

Inaugural Poem

Filed under: General — m759 @ 12:48 pm

"I, the Rock, I, the River, I, the Tree
I am yours—your passages have been paid."

Maya Angelou, January 20, 1993

     See also Rock,  River,  Tree.

In the Details

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

Part I:  Synthesis

Part II:  Iconic Symbols

IMAGE- Blackboard from 'Blackboard Jungle'

Blackboard Jungle , 1955

Part III:  Euclid vs. Galois

Field of Dreams

Filed under: General — m759 @ 12:48 am

The Presidential Medal of Freedom, the highest honor
that can be bestowed on a civilian, was presented to
Stan Musial at the White House on Feb 15, 2011.

Meanwhile…

Saturday, January 19, 2013

Executioner’s Song

Filed under: General — m759 @ 12:24 pm

For Terry Gilliam

IMAGE- Ace of Spades in Disney's version of 'Aquarela do Brasil,' uploaded Aug. 13, 2011

See also, from the the above uploading date, Taylor Made,
with its linked-to passage from a book by Charles Taylor.

For some more recent background, see

Tears in the Rain

Filed under: General — m759 @ 2:12 am

Top of the front page, tonight's online New York Times

Click the above image for the story of a rather different cyclist.

See also some images from Guy Fawkes Day, 2003

Related material:

Blade Runner in this journal and posts tagged "Fawkes"—

"Remember, remember the fifth of November."

Friday, January 18, 2013

Solomon’s Rep-tiles

Filed under: General,Geometry — Tags: — m759 @ 1:04 pm

"Rep-tiles Revisited," by Viorel Nitica, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics ,  American Mathematical Society, 2003—

"The goal of this note is to take a new look at some of the most amazing objects discovered in recreational mathematics. These objects, having the curious property of making larger copies of themselves, were introduced in 1962 by Solomon W. Golomb [2], and soon afterwards were popularized by Martin Gardner [3] in Scientific American…."

2.  S. W. Golomb: "Replicating Figures in the Plane," Mathematical Gazette  48, 1964, 403-412

3.  M. Gardner: "On 'Rep-tiles,' Polygons That Can Make Larger and Smaller Copies of Themselves," Scientific American  208, 1963, 154-157

Two such "amazing objects"—

Triangle

Square

For a different approach to the replicating properties of these objects, see the square-triangle theorem.

For related earlier material citing Golomb, see Not Quite Obvious (July 8, 2012; scroll down to see the update of July 15.).

Golomb's 1964 Gazette  article may now be purchased at JSTOR for $14.

Thursday, January 17, 2013

Brazil Revisited

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

Yesterday's post Treasure Hunt, on a Brazilian weblog,
suggests a review of Brazil  in this journal.  The post
most relevant to yesterday's remarks is from
August 15, 2003, with a link, now broken, to the work
of Brazilian artist Nicole Sigaud* that also uses the
four half-square tiles used in 1704 by Sebastien Truchet 
and somewhat later by myself in Diamond Theory 
(see a 1977 version).

A more recent link that works:

http://vismath9.tripod.com/sigaud/e-index.html

ANACOM PROJECT

 

APPLICATIONS
HISTORY
THE FONT
ALGORITHMS
FAMILY I
FAMILY 2
EXAMPLES
EXAMPLES II
DOWNLOADS
INTERACTIVE PROGRAM (JAVASCRIPT)
 
VisMathHOME

 

© 1997 – 2002 Nicole Sigaud

* Sigaud shares the interests of her fellow Brazilian
   whose weblog was the subject of yesterday's
   Treasure Hunt.—

   "For many years I have dedicated myself to the study
    of medieval magic, demonology, Kabbalah, Astrology,
    Alchemy, Tarot and divination in general."

     — Nicole Sigaud (translated by Google) in a self-profile: 
     http://www.recantodasletras.com.br/autor.php?id=78359.

    I do not share the interest of these authors in such matters,
    except as they are reflected in the works of authors like
    Charles Williams and Umberto Eco.

Wednesday, January 16, 2013

Treasure Hunt

Filed under: General,Geometry — Tags: — m759 @ 3:17 pm

The Mathematical Association of America (MAA)
newsmagazine Focus  for December 2012/January 2013: 

The Babylonian tablet on the cover illustrates the
"Mathematical Treasures" article.

A search for related material yields a Babylonian tablet
reproduced in a Brazilian weblog on July 4, 2012:

In that weblog on the same day, July 4, 2012,
another post quotes at length my Diamond Theory page,
starting with the following image from that page—

IMAGE- Plato's Diamond

That Brazilian post recommends use of geometry together
with Tarot and astrology. I do not concur with this 
recommendation, but still appreciate the mention.

Hamming It Up

Filed under: General — m759 @ 1:00 pm

Or:  Dr. Arroway Flies Again

Today's math news mentioning the Hamming Medal
suggests

Richard Hamming (d. 1998) as a real-life counterpart to
the techno-wizard S. R. Hadden in the 1997 film Contact .
Hamming devised a famous error-correcting code.

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

Review of a more recent Jodie Foster film, Flightplan :

"Is she crazy, or is she the victim of a conspiracy
that would have to be fragile, if not tortured, in its logic?"

Medals

Filed under: General,Geometry — m759 @ 11:00 am

National

IMAGE- Golomb and Mazur awarded National Medals of Science

International

IMAGE- The Leibniz medal

Click medal for some background. The medal may be regarded
as illustrating the 16-point Galois space. (See previous post.)

Related material: Jews in Hyperspace.

Space Race

Filed under: General,Geometry — m759 @ 3:33 am


 Japanese character
 for "field"

This morning's leading
New York Times  obituaries—

For other remarks on space, see
Galois + Space in this  journal.

Tuesday, January 15, 2013

Speeds

Filed under: General — m759 @ 1:09 pm

The Speed of Thought

"I love  Quicksilver. I've been using it since nearly the beginning,
and I cannot live without it…. I just type, and things happen,
pretty much at the speed of thought."

Mac user, April 22, 2011

See also Speed of Thought in this journal and
Madeleine L'Engle on kything .

The Speed of Inference

See this journal on the above date— April 22, 2011:
Romancing the Hyperspace —and, more generally,
all April 2011 references to romancing .

See also a contributor to Edge.org:

"Sciences can move at the speed of inference
when individuals only need to consider logic and evidence.
Yet sciences move glacially (Planck's 'funeral by funeral')
when the typical scientist, dependent for employment
on a dense ingroup network, has to get the majority of her
guild to acknowledge fundamental, embarrassing
disciplinary errors." 

Wrap Party

Filed under: General — m759 @ 12:30 am

"The serpent's eyes shine
As he wraps around the vine"
— Don Henley, lyric from
    1995 Greatest Hits  album

"…the film proceeds with implacable logic…."
— Roger Ebert, 2005 review of the
    Jodie Foster film Flightplan

Monday, January 14, 2013

Quicksilver vs. Bat-Crazed and Moony

Filed under: General — Tags: — m759 @ 7:00 pm

The Acceptance Speech Award

"A humble master with a quicksilver imagination"

— Daniel Day-Lewis on Steven Spielberg, acceptance speech
at Sunday night's Golden Globe Awards

"Robert [Downey Jr.], I want to thank you for everything, for your
bat-crazed, rapid-fire brain, the sweet intro."

— Jodie Foster accepting the Cecil B. DeMille award Sunday night

And the acceptance speech award goes to

IMAGE- Robert Downey Jr. and Jodie Foster exit the stage at the 2012 Golden Globe Awards

Presenter Robert Downey Jr. and Accepter Jodie Foster

Related material—

Also from Jodie Foster's DeMille Award speech:

"I can’t help but get moony, you know. This feels like the end
of one era and the beginning of something else. Scary and
exciting, and now what?"

A tweet from Aaron Swartz on Dec. 9, 2012:

See as well three posts from this  journal on that same date.

Best Music

Filed under: General — m759 @ 11:01 am

Happy Birthday to Lawrence Kasdan.

Moses Supposes

Filed under: General — m759 @ 9:13 am

See also

Spelling Bee:
Manifesto I vs. Manifesto II—

I   The Commonist Manifesto
II  The Anti-Commonist Manifesto

Google's Choice:

IMAGE- 'Manifestos'- Google's preferred spelling

The People's Choice:

IMAGE- 'Manifestoes'- The People's Spelling Choice, according to search results

Sunday, January 13, 2013

Spinning in Infinity

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

A note for day 13 of 2013

How the cube's 13 symmetry planes* 
are related to the finite projective plane
of order 3, with 13 points and 13 lines—

IMAGE- How the cube's symmetry planes are related to the finite projective plane of order 3, with 13 points and 13 lines

For some background, see Cubist Geometries.

* This is not the standard terminology. Most sources count
   only the 9 planes fixed pointwise under reflections  as
   "symmetry planes." This of course obscures the connection
   with finite geometry.

Puzzles

Filed under: General — Tags: — m759 @ 2:01 am

The late Aaron Swartz on a 1978 psychological study

"But the puzzles kept coming—
and they kept getting harder. 'This isn’t fun anymore,'
the kids cried. But still, there were more puzzles."

Related material from Log24's Mathcamp —

"…Heaven and Hell relays. your team starts in hell,
when you get one right, one person can go to heaven
and work on heaven questions, but first they have to
pass through purgatory. aka this means entertain
the people running purgatory." 

Imaginary Thoughts and Irrational Ideas weblog

See also Swartz on philosophy:

"I’ve just been finding little bits and pieces
in all sorts of strange places: psychology experiments,
business books, philosophy, self-help, math, and
my friends. But since there’s no community around it,
it’s hard to discuss it with anyone…."

From the date of  these weblog posts by Swartz,
a post from this  journal—

Crown Heights Story

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

See yesterday's post "There Will Be Aaron"
(about a death in Crown Heights, Brooklyn)
and earlier posts now tagged "Sorkin."

Related material— Delphic.

Saturday, January 12, 2013

There Will Be Aaron

Filed under: General — Tags: , — m759 @ 3:48 pm

I learned this afternoon of a significant death:

See a NY Times  obit and "RIP, Aaron Swartz."

The latter quotes Swartz himself:

"Obviously shades of Sinclair here…"

Related material: 

Not so related:

  • This journal on the date— Feb. 23, 2010— of
    Shellie Branco's post, linked to above, on Bakersfield,
    Upton Sinclair, Taft CA, and "Blood"

     

    A post titled Fish Story 
    on secular vocabulary and San Diego.

(Content last updated 4:16 EST Jan. 12, 2013.)

Abstract*

Filed under: General — m759 @ 7:59 am
 

Saturday January 12, 2013,
8:00 a.m.-10:50 a.m. Pacific Standard Time

MAA Invited Paper Session on
Writing, Talking, and Sharing Mathematics

Room 2, Upper Level, San Diego
Convention Center

9:30 a.m.
Mathematics, Meaning, and Misunderstanding.
Gerald B. Folland, University of Washington
(1086-AH-1058)

Abstract:

Mathematicians develop habits of thought and employ
ways of expressing their ideas that are not always
shared by others who wish to learn mathematics or
use mathematics in their own disciplines. We shall
comment on various aspects of this phenomenon
and the (often amusing) pitfalls it creates for e ffective
communication. (Received September 18, 2012)

Remarks for a dead mathematician—

Click on the above image for the original post. 

Then click on the Harmonic Analysis  link for
some exposition by Folland.

* As opposed to concrete —
     See yesterday morning's Grapevine Hill and

SFGate 1/12/13 

Californians bring out gloves, hats
for cold spell


http://www.sfgate.com/news/us/article/
Zookeepers-growers-prepare-for-
California-freeze-4185448.php

A 40-mile stretch of a major highway north of
Los Angeles reopened some 17 hours after snow
shut the route and forced hundreds of truckers 
to spend the cold night in their rigs.

The California Highway Patrol shut the Grapevine
segment of Interstate 5 on Thursday afternoon,
severing a key link between the Central Valley 
and Los Angeles.

"There must have been 1,000 Mack trucks lined up,"
said traveler Heidi Blood, 40.

Friday, January 11, 2013

Grapevine Hill

Filed under: General — Tags: — m759 @ 5:55 am

IMAGE- 'The Ninth Wave,' first page of Ch. 3, 'Across the Grapevine'

See also the song at the end of yesterday morning's
"For Your Consideration."

The setting for that song, "Hot Rod Lincoln," is—
according to Wikipedia— the road described in Ch. 3
of Eugene Burdick's classic 1956 novel
The Ninth Wave . (See above.)

IMAGE- Map showing Grapevine Hill road, southeast of Taft, California

See also A Dante for Our Times.
 

Thursday, January 10, 2013

For Your Consideration

Filed under: General — Tags: — m759 @ 11:30 am

From the World Socialist Web Site:

(Click to enlarge.)

Note the bend sinister in the address bar:

Related remarks:

Related music: "Pulled out of San Pedro late one night…"

Wednesday, January 9, 2013

Bad Idea

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

For the 2013 Joint Mathematics Meetings in San Diego,
which start today, a cartoon by Andrew Spann—

(Click for larger image.) 

'Snakes on a Plane' cartoon

Related remarks:

This journal on the Feast of Epiphany, 2013

"The Tesseract is where it belongs: out of our reach."

The Avengers'  Nick Fury, played by Samuel L. Jackson

Today's New York Times —

"You never know what could happen.
If you have Sam, you’re going to be cool."

— The late David R. Ellis, film director

If anyone in San Diego cares about the relationship
of Spann's plane to Fury's Tesseract, he or she may
consult Finite Geometry of the Square and Cube.

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