Log24

Thursday, March 2, 2017

Ageometretos*

Filed under: General — Tags: — m759 @ 1:40 PM

Or:  "A Hologram for the King" Meets "Big"

* A reference to an alleged motto of Plato's Academy

Saturday, April 25, 2015

Ageometretos Medeis Eisito

Filed under: General — m759 @ 10:30 AM

Wednesday, May 23, 2012

Ageometretos Medeis Eisito

Filed under: General — m759 @ 8:00 PM

See Bagombo Snuff Box and
"Will this be on the test?"

IMAGE- Dr. Hannibal Lecter

Friday, March 4, 2011

Ageometretos Medeis Eisito*

Filed under: General,Geometry — Tags: — m759 @ 7:11 PM

Your mission, should you choose to accept it…

IMAGE- Future Bead Game Master Joseph Knecht's mission to a Benedictine monastery

See also “Mapping Music” from Harvard Magazine , Jan.-Feb. 2007—

“Life inside an orbifold is a non-Euclidean world”

— as well as the cover story “The Shape of Music” from Princeton Alumni Weekly ,
Feb. 9, 2011, and “Bead Game” + music in this  journal (click, then scroll down).
Those impressed by the phrase “non-Euclidean” may also enjoy
Non-Euclidean Blocks and Pilate Goes to Kindergarten.

The “Bead Game” + music search above includes, notably, a passage describing a
sort of non-Euclidean abacus in the classic 1943 story “Mimsy Were the Borogoves.”
For a visually related experience, see the video “Chord Geometries Demo: Chopin
on a Mobius Strip” at a music.princeton.edu web page.

* Motto of the American Mathematical Society, said to be also the motto of Plato’s Academy.

Wednesday, February 13, 2019

April 18, 2003 (Good Friday), Continued

Filed under: General,Geometry — Tags: , — m759 @ 11:03 AM

"The purpose of mathematics cannot be derived from an activity 
inferior to it but from a higher sphere of human activity, namely,
religion."

Igor Shafarevitch, 1973 remark published as above in 1982.

"Perhaps."

— Steven H. Cullinane, February 13, 2019

From Log24 on Good Friday, April 18, 2003

. . . What, indeed, is truth?  I doubt that the best answer can be learned from either the Communist sympathizers of MIT or the “Red Mass” leftists of Georgetown.  For a better starting point than either of these institutions, see my note of April 6, 2001, Wag the Dogma.

See, too, In Principio Erat Verbum , which notes that “numbers go to heaven who know no more of God on earth than, as it were, of sun in forest gloom.”

Since today is the anniversary of the death of MIT mathematics professor Gian-Carlo Rota, an example of “sun in forest gloom” seems the best answer to Pilate’s question on this holy day.  See

The Shining of May 29.

“Examples are the stained glass windows
of knowledge.” — Vladimir Nabokov

AGEOMETRETOS MEDEIS EISITO

Motto of Plato’s Academy


 The Exorcist, 1973

Detail from an image linked to in the above footnote —

"And the darkness comprehended it not."

Id est :

A Good Friday, 2003, article by 
a student of Shafarevitch

" there are 25 planes in W . . . . Of course,
replacing {a,b,c} by the complementary set
does not change the plane. . . ."

Of course.

See. however, Six-Set Geometry in this  journal.

Wednesday, January 10, 2018

Logos

Filed under: General — m759 @ 8:35 PM

(Continued)

New logo of the American Mathematical Society, Jan. 10, 2018

Updates of 9:40 PM ET Jan. 10
to 5:45 AM ET the next day:

See a letter from the AMS on their new logo.

      Recent revision (pre-2018) of the former AMS logo

The Society's letter describes perceptions of the pre-2018 logo —

"… market research on our current logo revealed that
the connection between a Greek temple and
a mathematical society has become increasingly tenuous
among non-members and younger mathematicians, who
associate the Greek temple with a financial institution."

The omission of the alleged motto of Plato's Academy,
AGEOMETRETOS ME EISITO, in the recent (pre-2018)
revision of the logo was part of the Society's ongoing
process of politically correct dumbing-down. That omission
may have influenced the perception of the logo as picturing
a Greek temple rather than the Academy.

Some related remarks from 2005 —

Thursday, July 13, 2017

Conspiracy Meets Confederacy

Filed under: General — m759 @ 12:00 AM

Sure you don't.

See also Ageometretos  and
tonight's previous post.

Monday, May 30, 2016

Perfect Number

Filed under: General,Geometry — Tags: — m759 @ 10:00 AM

"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—

For the birthday of Marissa Mayer, who turns 41 today —

VOGUE Magazine,
AUGUST 16, 2013 12:01 AM
by JACOB WEISBERG —

"As she works to reverse the fortunes of a failing Silicon Valley
giant, Yahoo’s Marissa Mayer has fueled a national debate
about the office life, motherhood, and what it takes to be the
CEO of the moment.

'I really like even numbers, and
I like heavily divisible numbers.
Twelve is my lucky number—
I just love how divisible it is.
I don’t like odd numbers, and
I really don’t like primes.
When I turned 37,
I put on a strong face, but
I was not looking forward to 37.
But 37 turned out to be a pretty amazing year.
Especially considering that
36 is divisible by twelve!'

A few things may strike you while listening to Marissa Mayer
deliver this riff . . . . "

Yes, they may.

A smaller number for Marissa's meditations:

Six has been known since antiquity as the first "perfect" number.
Why it was so called is of little interest to anyone but historians
of number theory  (a discipline that is not, as Wikipedia notes, 
to be confused with numerology .)

What part geometry , on the other hand, played in Marissa's education,
I do not know.

Here, for what it's worth, is a figure from a review of posts in this journal
on the key role played by the number six in geometry —

Wednesday, April 22, 2015

Purely Aesthetic

Filed under: General,Geometry — Tags: , — m759 @ 11:00 AM

G. H. Hardy in A Mathematician's Apology —

What ‘purely aesthetic’ qualities can we distinguish in such theorems as Euclid’s or Pythagoras’s?

I will not risk more than a few disjointed remarks. In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions. There are no complications of detail—one line of attack is enough in each case; and this is true too of the proofs of many much more difficult theorems, the full appreciation of which demands quite a high degree of technical proficiency. We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way. 

Related material:

Sunday, April 19, 2015

Preoccupied

Filed under: General — m759 @ 12:00 PM

http://www.log24.com/log/pix12/120108-CardinalPreoccupied.jpg

"The Cardinal seemed a little preoccupied today."

See also a post found via a search in
this journal for "April 19 ".

Ageometretos medeis eisito .

Sunday, September 21, 2014

Saturday-Morning Concept

Filed under: General,Geometry — m759 @ 7:59 PM

Why Is Our Sci-Fi So Glum About A.I.?,”
by Jayson Greene, NY Times Sunday Magazine  today —

“You come to pity these advanced beings, bumping against
the dunderheaded constraints that their less-advanced
creators have placed on them. Johansson’s Lucy grows so
powerful as her cerebral capacity multiplies that she is able
to manipulate her cellular structure. And yet, when pursued
by an entire planet’s worth of law enforcement, she settles
on a disguise straight out of Saturday-morning cartoons —
really big sunglasses and a hairdo change.”

See also this  journal on Saturday morning for a definition, and
Geometry of the I Ching for examples, of

changeable, instantiable entities, i.e., concrete universals.

Above the entrance to Plato's Academy: AGEOMETRETOS MEDEIS EISITO

Monday, November 19, 2012

Poetry and Truth

Filed under: General,Geometry — Tags: , , , , — m759 @ 7:59 PM

From today's noon post

"In all his poems with all their enchantments
for the poet himself, there is the final enchantment
that they are true. The significance of the poetic act
then is that it is evidence. It is instance and illustration.
It is an illumination of a surface,
the movement of a self in the rock.
Above all it is a new engagement with life.
It is that miracle to which the true faith of the poet
attaches itself."

— Wallace Stevens at Bard College, March 30, 1951

Stevens also said at Bard that

"When Joan of Arc said: 

Have no fear: what I do, I do by command.
My brothers of Paradise tell me what I have to do.

these words were the words of an hallucination.
No matter what her brothers of Paradise drove her to do,
what she did was never a poetic act of faith in reality
because it could not be."

There are those who would dispute this.

Some related material:

"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—

A poetic approach to geometry—

"A surface" and "the rock," from All Saints' Day, 2012

Spaces as Hypercubes

— and from 1981—

http://www.log24.com/log/pix09/090217-SolidSymmetry.jpg

Some mathematical background for poets in Purgatory—

"… the Klein correspondence underlies Conwell's discussion 
of eight heptads. These play an important role in another
correspondence, illustrated in the Miracle Octad Generator
of R. T. Curtis, that may be used to picture actions
of the large Mathieu group M24."

Friday, September 28, 2012

Geometretos*

Filed under: General — m759 @ 12:00 PM

MEDEIS AGEOMETRETOS EISITO

— Inscription at entrance to
     Plato's Academy, according to
     an elementary introduction to
     philosophy by James L. Christian 

For Irving Adler, who reportedly
died on September 22, 2012—

 

Background: See Sangaku in this journal.

See also the following, from a different  
elementary introduction, by Adler—
Giant Golden Book of Mathematics,
illustrated by Lowell Hess

.

   (Detail of Flickr photo)


* See Liddell and Scott.

Thursday, June 11, 2009

Thursday June 11, 2009

Filed under: General — Tags: — m759 @ 2:28 AM

Epigraph

Above the entrance to Plato's Academy: AGEOMETRETOS MEDEIS EISITO

Holocaust Memorial Museum in Washington, DC

(http://www.scrapbookpages.com/USHMM/Exterior.html)

Friday, July 13, 2007

Friday July 13, 2007

Filed under: General,Geometry — m759 @ 7:00 AM
Today’s birthday:
Harrison Ford is 65.

The image “http://www.log24.com/log/pix07/070713-Ford2.jpg” cannot be displayed, because it contains errors.

“Three times the concentred
     self takes hold, three times
The thrice concentred self,
     having possessed
The object, grips it
     in savage scrutiny,
Once to make captive,
     once to subjugate
Or yield to subjugation,
     once to proclaim
The meaning of the capture,
     this hard prize,
Fully made, fully apparent,
     fully found.”

— “Credences of Summer,” VII,
    by Wallace Stevens, from
    Transport to Summer (1947)

“It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….


Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real.”

   — Rebecca Goldstein, Mathematics and the Character of Tragedy

Related material:

Previous entry,
entries of July 1, 2007,
and A Little Story
(9/30/06)

Friday, March 31, 2006

Friday March 31, 2006

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

Women's History Month continues…
 
Ontology Alignment

"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally.  To understand who Michael Laski is you must have a feeling for that kind of compulsion."

— Joan Didion in the
Saturday Evening Post,
Nov. 18, 1967 (reprinted in
Slouching Towards Bethlehem)

"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.

— Joan Didion in
The Last Thing He Wanted,
Knopf, 1996

"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….

Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real."

— Rebecca Goldstein,
Mathematics and
the Character of Tragedy

Friday, April 18, 2003

Friday April 18, 2003

Filed under: General,Geometry — m759 @ 1:17 PM

To the Society of Jesus (also known as the Jesuits):

Have a Good Friday, Traitors

Prompted by Pilate’s question “What is truth?” and by my March 24 attack on Noam Chomsky, I decided this afternoon to further investigate what various people have written about Chomsky’s posing of what he calls “Plato’s problem” and “Orwell’s problem.”  The former concerns linguistics, the latter, politics.  As my March 24 entry indicates, I have nothing but contempt for both Chomsky’s linguistics and Chomsky’s politics.  What I discovered this afternoon is that Georgetown University, a Jesuit institution, in 2001 appointed a Chomskyite, David W. Lightfoot, as Dean of the Graduate School of Arts and Sciences.

“Why do we know so much more than we have evidence for in certain areas, and so much less in others? In tackling these questions — Plato’s and Orwell’s problem — Chomsky again demonstrates his unequalled capacity to integrate vast amounts of material.” — David W. Lightfoot, review of Chomsky’s Knowledge of Language

What, indeed, is truth?  I doubt that the best answer can be learned from either the Communist sympathizers of MIT or the “Red Mass” leftists of Georgetown.  For a better starting point than either of these institutions, see my note of April 6, 2001, Wag the Dogma.

See, too, In Principio Erat Verbum, which notes that “numbers go to heaven who know no more of God on earth than, as it were, of sun in forest gloom.”

Since today is the anniversary of the death of MIT mathematics professor Gian-Carlo Rota, an example of “sun in forest gloom” seems the best answer to Pilate’s question on this holy day.  See

The Shining of May 29.

“Examples are the stained glass windows of knowledge.” — Vladimir Nabokov

AGEOMETRETOS MEDEIS EISITO

Motto of Plato’s Academy


The Exorcist, 1973

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