Log24

Friday, January 25, 2019

Crucible Raiders Continues.

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

Fans of the New York Times  philosophy series "The Stone"
(named for the legendary philosophers' stone) may consult 
posts tagged "Crucible Raiders" in this journal.

Some context — the previous post, "Night at the Social Media."

Thursday, January 24, 2019

“The Stone” Contributor Dies

Filed under: General — Tags: — m759 @ 3:00 AM

"He was a regular contributor to the New York Times 
philosophical forum, The Stone." — South Bend Tribune

See also Gutting in this  journal.

Wednesday, October 24, 2018

Raiders of the Lost Crucible Continues

Filed under: General — Tags: , , — m759 @ 10:22 PM

Tuesday, October 2, 2018

Raiders of the Lost Crucible

Filed under: General — Tags: — m759 @ 11:22 AM

See other posts now tagged Crucible Raiders.

Related entertainment —

From YouTube:

From NBC:

For more from the above date,
Oct. 8, 2016, click "seriously" below.

But seriously

Saturday, September 2, 2017

A Touchstone

Filed under: General,Geometry — Tags: , — m759 @ 10:16 PM

From a paper by June Barrow-Green and Jeremy Gray on the history of geometry at Cambridge, 1863-1940

This post was suggested by the names* (if not the very abstruse
concepts ) in the Aug. 20, 2013, preprint "A Panoramic Overview
of Inter-universal Teichmuller Theory
," by S. Mochizuki.

* Specifically, Jacobi  and Kummer  (along with theta functions).
I do not know of any direct  connection between these names'
relevance to the writings of Mochizuki and their relevance
(via Hudson, 1905) to my own much more elementary studies of
the geometry of the 4×4 square.

Saturday, October 31, 2015

Raiders of the Lost Crucible

Filed under: General,Geometry — Tags: , — m759 @ 10:15 AM

Stanford Encyclopedia of Philosophy
on the date Friday, April 5, 2013 —

Paraconsistent Logic

“First published Tue Sep 24, 1996;
substantive revision Fri Apr 5, 2013”

This  journal on the date Friday, April 5, 2013 —

The object most closely resembling a “philosophers’ stone
that I know of is the eightfold cube .

For some related philosophical remarks that may appeal
to a general Internet audience, see (for instance) a website
by I Ching  enthusiast Andreas Schöter that displays a labeled
eightfold cube in the form of a lattice diagram —

Related material by Schöter —

A 20-page PDF, “Boolean Algebra and the Yi Jing.”
(First published in The Oracle: The Journal of Yijing Studies ,
Vol 2, No 7, Summer 1998, pp. 19–34.)

I differ with Schöter’s emphasis on Boolean algebra.
The appropriate mathematics for I Ching  studies is,
I maintain, not Boolean algebra  but rather Galois geometry.

See last Saturday’s post Two Views of Finite Space.
Unfortunately, that post is, unlike Schöter’s work, not
suitable for a general Internet audience.

Friday, July 27, 2012

Raiders of the Lost Ring

Filed under: General,Geometry — Tags: , , — m759 @ 11:30 AM

Wikipedia on a magical ring

IMAGE- Wikipedia article, 'Seal of Solomon'

Background—  The Ring and the Stone, a story linked to here Wednesday.

“By then he was familiar with the work of the Vienna Actionists….
He once said that he had his first taste of the movement
when he heard the screams of his mother’s dental patients
from her office next door to the family’s apartment.”

Obituary of a Viennese artist who reportedly died Wednesday

Is it safe?

Tuesday, May 3, 2011

Phantasmagorical Touchstone

Filed under: General — Tags: — m759 @ 10:31 PM

"Ira Cohen made phantasmagorical films that became cult classics….

In certain artistic and literary circles, Mr. Cohen was a touchstone"

— Douglas Martin in the online New York Times  on May 1, 2011

http://www.log24.com/log/pix11A/110503-BorrowedTimePoet.jpg

The rest  of the picture—

http://www.log24.com/log/pix11A/110503-DiamondHead-BorrowedTime.jpg

"Borrowed Time," a 1982 album by Diamond Head

It is said that the touchstone died at 76 on April 25 (Easter Monday).

See that date in this journal. See also Phantasmagoria.

http://www.log24.com/log/pix11A/110503-April25Diamond.jpg

The above-mentioned Easter post

http://www.log24.com/log/pix11A/110503-EasterDiamond.jpg

Friday, January 25, 2019

Design Theory

Filed under: General — Tags: — m759 @ 11:00 PM

Last night's post "Night at the Social Media" suggests . . .

A 404 for Katherine Neville (born on 4/04) —

Thursday, January 24, 2019

Night at the Social Media

Filed under: General — Tags: — m759 @ 11:40 PM

See also Katherine Neville,  Karl Pribram, and Cooper Hewitt in this journal.

Sunday, September 30, 2018

Advocate

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

Click the above for an example.

Iconology of the Eightfold Cube

Filed under: General,Geometry — Tags: — m759 @ 11:13 AM

Found today in an Internet image search, from the website of
an anonymous amateur mathematics enthusiast

Forming Gray codes in the eightfold cube with the eight
I Ching  trigrams (bagua ) —

Forming Gray codes in the eightfold cube with the eight I Ching trigrams (bagua)

This  journal on Nov. 7, 2016

A different sort of cube, from the makers of the recent
Netflix miniseries "Maniac" —

See also Rubik in this  journal.

Thursday, September 15, 2016

Metaphysics at Notre Dame

Filed under: General,Geometry — Tags: , — m759 @ 11:07 PM

Recommended reading —

"When Analogies Fail," by Alexander Stern,
a doctoral candidate in philosophy at Notre Dame, in
The Chronicle of Higher Education  online September 11, 2016.

Related material —

That same Alexander Stern in this  journal on April 17, 2016:

See also the eightfold cube in the previous post,
Metaphysics at Scientific American:

Saturday, October 24, 2015

Two Views of Finite Space

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

The following slides are from lectures on “Advanced Boolean Algebra” —

The small Boolean  spaces above correspond exactly to some small
Galois  spaces. These two names indicate approaches to the spaces
via Boolean algebra  and via Galois geometry .

A reading from Atiyah that seems relevant to this sort of algebra
and this sort of geometry —

” ‘All you need to do is give me your soul:  give up geometry
and you will have this marvellous machine.’ (Nowadays you
can think of it as a computer!) “

Related material — The article “Diamond Theory” in the journal
Computer Graphics and Art , Vol. 2 No. 1, February 1977.  That
article, despite the word “computer” in the journal’s title, was
much less about Boolean algebra  than about Galois geometry .

For later remarks on diamond theory, see finitegeometry.org/sc.

Tuesday, March 18, 2014

Oye Como Va

Filed under: General — m759 @ 12:00 AM

Steve Winwood Leads Carlos Santana Tribute
at Kennedy Center Honors —

Saturday, February 22, 2014

Grundlagenkrise*

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

The title was suggested by a 1921 article
by Hermann Weyl and by a review* of
a more recent publication —

The above Harvard Gazette  piece on Davos is
from St. Ursula’s Day, 2010. See also this  journal
on that date.

See as well a Log24 search for Davos.

A more interesting piece by Peter E. Gordon
(author of the above Davos book) is his review
of Charles Taylor’s A Secular Age .
The review is titled

The Place of the Sacred
in the Absence of God
.”

(The place of the sacred is not, perhaps, Davos,
but a more abstract location.)

* Grundlagenkrise  was a tag for a Jan. 13, 2011,
review in The New Republic  of Gordon’s
book on Cassirer and Heidegger at Davos.

Wednesday, January 22, 2014

A Riddle for Davos

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM

Hexagonale Unwesen

Einstein and Thomas Mann, Princeton, 1938


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


See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.

January 13 was also the dies natalis  of St. James Joyce.

Some related reflections —

"Praeterit figura huius mundi  " — I Corinthians 7:31 —

Conclusion of of "The Dead," by James Joyce—

The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live.

Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling.

A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.

Friday, April 5, 2013

The Crucible

Filed under: General — Tags: — m759 @ 6:12 AM

"Though we had many pieces, we did not have the whole.
It was thirty years before we deciphered the formula.
But we did it at last.

There at night in the darkness of Fourier’s laboratory,
the four of us stood and watched the philosophers’ stone
forming in the crucible."

The Eight , by Katherine Neville
     (2008 Ballantine Books mass market edition, p. 640)

A journal post from August 25, 2009:

Image from a different journal earlier that same day, August 25, 2009:

Thirty-year medallion from Alcoholics Anonymous —

 

See also, in this  journal, "The Eight" + Damnation.

Thursday, December 27, 2012

Object Lesson

Yesterday's post on the current Museum of Modern Art exhibition
"Inventing Abstraction: 1910-1925" suggests a renewed look at
abstraction and a fundamental building block: the cube.

From a recent Harvard University Press philosophical treatise on symmetry—

The treatise corrects Nozick's error of not crediting Weyl's 1952 remarks
on objectivity and symmetry, but repeats Weyl's error of not crediting
Cassirer's extensive 1910 (and later) remarks on this subject.

For greater depth see Cassirer's 1910 passage on Vorstellung :

IMAGE- Ernst Cassirer on 'representation' or 'Vorstellung' in 'Substance and Function' as 'the riddle of knowledge'

This of course echoes Schopenhauer, as do discussions of "Will and Idea" in this journal.

For the relationship of all this to MoMA and abstraction, see Cube Space and Inside the White Cube.

"The sacramental nature of the space becomes clear…." — Brian O'Doherty

Thursday, July 26, 2012

Solomon’s Seal

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

(Mathematics and Narrative, continued)

Narrative—

The Ring and The Stone from yesterday’s post, and…

“In Medieval Jewish, Christian and Islamic legends,
the Seal of Solomon was a magical signet ring
said to have been possessed by King Solomon….”

— Wikipedia article, Seal of Solomon

Mathematics—

IMAGE- Eric Temple Bell on the mathematics of 'Solomon's Seal' (in his 'Development of Mathematics')

A fact related to the mathematical
“Solomon’s seal” described above by Bell:

IMAGE- J.W.P. Hirschfeld on the mathematics of 'Solomon's Seal', with reference to Edge on the same topic

The reference to Edge is as follows—

[3] Edge, W. L., Quadrics over GF(2) and
their relevance for the cubic surface group
,
Canadian J. Maths. 11 (1959) ….

(This reference relates Hirschfeld’s remarks
quoted above to the 64-point affine space
illustrated below (via the associated
63-point projective  space PG (5, 2)).

As for the narrative’s Stone… 

See Solomon’s Cube.

IMAGE- 'Solomon's Cube'

Wednesday, July 25, 2012

Tale

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

The Ring and the Stone

Saturday, September 24, 2011

Kernels of Being

Filed under: General,Geometry — Tags: — m759 @ 10:29 PM

For the Pope in Germany

"We wish to see Jesus. For somehow we know, we suspect, we intuit, that if we see Jesus we will see what Meister Eckhart might call “The Divine Kernel of Being”— that Divine Spark of God’s essence, God’s imago Dei, the image in which we are created. We seem to know that in seeing Jesus we just might find something essential about ourselves."

—The Reverend Kirk Alan Kubicek, St. Peter’s at Ellicott Mills, Maryland, weblog post of Saturday, March 28, 2009, on a sermon for Sunday, March 29, 2009

See also this journal in March 2009.

Related non-theology—

Weyl on coordinate systems, Cassirer on the kernel of being, and A Study in Art Education.

Wednesday, September 21, 2011

Symmetric Generation

Filed under: General,Geometry — Tags: , , , , — m759 @ 2:00 PM

Suggested by yesterday's Relativity Problem Revisited and by Cassirer on Objectivity

From Symmetric Generation of Groups , by R.T. Curtis (Cambridge U. Press, 2007)—

"… we are saying much more than that G M 24 is generated by
some set of seven involutions, which would be a very weak
requirement. We are asserting that M 24 is generated by a set
of seven involutions which possesses all the symmetries of L3(2)
acting on the points of the 7-point projective plane…."
Symmetric Generation , p. 41

"It turns out that this approach is particularly revealing and that
many simple groups, both sporadic and classical, have surprisingly
simple definitions of this type."
Symmetric Generation , p. 42

See also (click to enlarge)—

http://www.log24.com/log/pix11B/110921-CassirerOnObjectivity-400w.jpg

Cassirer's remarks connect the concept of objectivity  with that of object .

The above quotations perhaps indicate how the Mathieu group M 24 may be viewed as an object.

"This is the moment which I call epiphany. First we recognise that the object is one  integral thing, then we recognise that it is an organised composite structure, a thing  in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that  thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany."

— James Joyce, Stephen Hero

For a simpler object "which possesses all the symmetries of L3(2) acting on the points of the 7-point projective plane…." see The Eightfold Cube.

For symmetric generation of L3(2) on that cube, see A Simple Reflection Group of Order 168.

Monday, June 7, 2010

Inspirational Combinatorics

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM

According to the Mathematical Association of America this morning, one purpose of the upcoming June/July issue of the Notices of the American Mathematical Society  is

"…to stress the inspirational role of combinatorics…."

Here is another contribution along those lines—

Eidetic Variation

from page 244 of
From Combinatorics to Philosophy: The Legacy of  G.-C. Rota,
hardcover, published by Springer on August 4, 2009

(Edited by Ernesto Damiani, Ottavio D'Antona, Vincenzo Marra, and Fabrizio Palombi)

"Rota's Philosophical Insights," by Massimo Mugnai—

"… In other words, 'objectivism' is the attitude [that tries] to render a particular aspect absolute and dominant over the others; it is a kind of narrow-mindedness attempting to reduce to only one the multiple layers which constitute what we call 'reality.' According to Rota, this narrow-mindedness limits in an essential way even of [sic ] the most basic facts of our cognitive activity, as, for example, the understanding of a simple declarative sentence: 'So objectivism is the error we [make when we] persist in believing that we can understand what a declarative sentence means without a possible thematization of this declarative sentence in one of [an] endless variety of possible contexts' (Rota, 1991*, p. 155). Rota here implicitly refers to what, amongst phenomenologists is known as eidetic variation, i.e. the change of perspective, imposed by experience or performed voluntarily, from which to look at things, facts or sentences of the world. A typical example, proposed by Heidegger, in Sein und Zeit  (1927) and repeated many times by Rota, is that of the hammer."

* Rota, G.-C. (1991), The End of Objectivity: The Legacy of Phenomenology. Lectures at MIT, Cambridge, MA, MIT Mathematics Department

The example of the hammer appears also on yesterday's online New York Times  front page—

http://www.log24.com/log/pix10A/100606-Touchstones.jpg

Related material:

From The Blackwell Dictionary of Western Philosophy

Eidetic variation — an alternative expression for eidetic reduction

Eidetic reduction

Husserl's term for an intuitive act toward an essence or universal, in contrast to an empirical intuition or perception. He also called this act an essential intuition, eidetic intuition, or eidetic variation. In Greek, eideo  means “to see” and what is seen is an eidos  (Platonic Form), that is, the common characteristic of a number of entities or regularities in experience. For Plato, eidos  means what is seen by the eye of the soul and is identical with essence. Husserl also called this act “ideation,” for ideo  is synonymous with eideo  and also means “to see” in Greek. Correspondingly, idea  is identical to eidos.

An example of eidos— Plato's diamond (from the Meno )—

http://www.log24.com/log/pix10A/100607-PlatoDiamond.gif

For examples of variation of this eidos, see the diamond theorem.
See also Blockheads (8/22/08).

Related poetic remarks— The Trials of Device.

Saturday, March 7, 2009

Saturday March 7, 2009

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

One or Two Ideas
 
Today's birthday: Piet Mondrian
 
From James Joyce's A Portrait of the Artist as a Young Man:

he hearth and began to stroke his chin.

–When may we expect to have something from you on the esthetic question? he asked.

–From me! said Stephen in astonishment. I stumble on an idea once a fortnight if I am lucky.

–These questions are very profound, Mr Dedalus, said the dean. It is like looking down from the cliffs of Moher into the depths. Many go down into the depths and never come up. Only the trained diver can go down into those depths and explore them and come to the surface again.

–If you mean speculation, sir, said Stephen, I also am sure that there is no such thing as free thinking inasmuch as all thinking must be bound by its own laws.

–Ha!

–For my purpose I can work on at present by the light of one or two ideas of Aristotle and Aquinas.

–I see. I quite see your point.

Besides being Mondrian's birthday, today is also the dies natalis (in the birth-into-heaven sense) of St. Thomas Aquinas and, for those who believe worthy pre-Christians also enter heaven, possibly of Aristotle.

Pope Benedict XVI explained the dies natalis concept on Dec. 26, 2006:

"For believers the day of death, and even more the day of martyrdom, is not the end of all; rather, it is the 'transit' towards immortal life. It is the day of definitive birth, in Latin, dies natalis."

The Pope's remarks on that date
were in St. Peter's Square.
 
From this journal on that date,
a different square —
 
The Seventh Symbol:
 

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

The square may be regarded as
symbolizing art itself.
(See Nov.30 – Dec.1, 2008.)

In honor of
Aristotle and Aquinas,
here is a new web site,
illuminati-diamond.com,
with versions of the diamond shape
made famous by Mondrian

Cover of  Mondrian: The Diamond Compositions

— a shape symbolizing
possibility within modal logic
 as well as the potentiality of
 Aristotle's prima materia.

Friday, March 6, 2009

Friday March 6, 2009

Filed under: General,Geometry — Tags: — m759 @ 7:30 PM
The Illuminati Stone

TV listing for this evening —
Family Channel, 7:30 PM:

"Harry Potter and
  the Sorcerer's Stone"

In other entertainment news —
Scheduled to open May 15:

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"
(Faust, Part Two)

Carl Gustav Jung  

Related material:

"For just about half a century, E.J. Holmyard's concisely-titled Alchemy has served as a literate, well-informed, and charming introduction to the history and literature of Western alchemy." —Ian Myles Slater

From 'Alchemy,' by Holmyard, the diamond of Aristotle's 4 elements and 4 qualities

For more about this
"prime matter" (prima materia)
see The Diamond Archetype

The Diamond Cross

and Holy the Firm.

 

Background:

Holmyard —

'Alchemy,' by Holmyard, back cover of Dover edition

— and Aristotle's
On Generation and Corruption.

Saturday, June 23, 2007

Saturday June 23, 2007

Filed under: General — m759 @ 6:00 PM
Raiders of
the Lost Stone

 
continued from March 10, 2006

The Roman Imperial Eagle
and, according to
C. B. DeMille in 1932 —

Opening of The Sign of the Cross (1932)

The above photo is courtesy of
the Cecil B. DeMille Collection
at DVD Beaver.

Sharon Stone in the pulpit of Harvard's Memorial Church
HARVARD CRIMSON/ ALEX R. LEVIN

Sharon Stone lectures at
Harvard’s Memorial Church

on March 14, 2005…

Ready when you are, C. B.

Related material —
Log24, Oct. 26, 2002 —

Midnight in the Garden,
starring

Nina Simone and eight-point star

Nina Simone

Friday, March 10, 2006

Friday March 10, 2006

Filed under: General — m759 @ 7:59 PM

Women’s History Month continues…

Raiders of the Lost

Stone

The image “http://www.log24.com/log/pix06/060310-Stone.jpg” cannot be displayed, because it contains errors.

In honor of the upcoming program
on Women and Mathematics
at the Institute for Advanced Study
and of Sharon Stone’s 2005 lecture
at Harvard’s Memorial Church,

here are links to reviews of
two Sharon Stone classics:


“King Solomon’s Mines” (1985),
said to be inspired by the
1981 box-office success
of
Raiders of the Lost Ark,” and

“Diabolique” (1996), starring
Stone as
a teacher of mathematics
at St. Anselm’s School for Boys.

For related material on St. Anselm
and mathematics at Princeton, see
Modal Theology and the
April 2006 AMS Notices
on Kurt Gödel.

See also yesterday’s entry
and
Log24, Jan. 1-15, 2006.

Today’s birthdays:
Sharon Stone and
Gregory La Cava.

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