"My words say split, but my words they lie" — Bruce Springsteen
See a search for "Split" in this journal.
Thursday, July 18, 2019
Thursday, January 26, 2017
Split
(Continued from Tuesday, Jan. 24, 2017)
"We have reached peak polarization."
— Olga Khazan in the online Atlantic today,
as quoted in the Muck Rack image below.
Perhaps not yet.
Consider the headline below,
"Why Trump Supporters Lie About the Inauguration Photo."
Consider also Olga's "Brain Bro" below in the context of
the film "Limitless" and of the book A Wrinkle in Time .
See also all posts now tagged "Split."
Comments Off on Split
Tuesday, January 24, 2017
Split
At left, just prior to the inauguration in 2009;
at right, during the inauguration in 2017.
Source of photos —
http://news.wgbh.org/2017/01/23/news/
photos-compare-crowd-trumps-inauguration-obamas.
For a more detailed image of the 2017 inauguration
from the new president's point of view, click here.
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Wednesday, December 23, 2015
Splitting Apart
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Saturday, April 21, 2012
Split
"So the sundering we sense between nature and culture
lies not like a canyon outside us, but splits our being
at its most intimate depths the way mind breaks off from body.
It is still another version of that bitter bifurcation
long ago decreed— our expulsion from Eden…."
— William H. Gass in Finding a Form ,
Cornell U. Press paperback, 1997, page 138
See also…
For another bitter bifurcation, see La Despedida .
Comments Off on Split
Tuesday, September 17, 2024
Friday, August 2, 2024
“Your campaign song, should you choose to accept it”
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Friday, June 14, 2024
Summer of ’42: Python’s Monty
From April 14, 2024, some culture notes that I prefer —
An example of pi.ai's clear and pleasant conversational style
(output format simplified for presentation here) —
Can you help with computer coding problems?
Absolutely, Steven! 💻 While I can't guarantee I'll have all the answers,
I'll certainly do my best to help you debug and find solutions to your
coding conundrums. Which coding language are you working with, and what's
giving you trouble?
I want to learn how Python can permute sections of a square array.
There are several ways to permute sections of a square array in Python,
depending on your specific needs. Here are a few examples:
Using NumPy's random.permutation() function:
python
import numpy as np
arr = np.array([[1, 2], [3, 4]])
permuted_arr = np.random.permutation(arr)
Using itertools.permutations():
python
import itertools
arr = [[1, 2], [3, 4]]
permutations = list(itertools.permutations(arr))
Using custom permutation algorithms:
python
def custom_permutation(arr):
# your custom permutation logic here
arr = [[1, 2], [3, 4]]
permuted_arr = custom_permutation(arr)
Each method has its own strengths and weaknesses, and which one
you choose will depend on the size of your array, the number of
permutations you need, and your performance requirements.
I would like to use python's custom permutation method to permute
the four quadrants of a 4×4 array.
Here's an example of how to define a custom permutation function
in Python to permute the four quadrants of a 4×4 array:
python
def custom_permutation(arr):
# Split array into 4 quadrants
q1 = arr[:2, :2]
q2 = arr[:2, 2:]
q3 = arr[2:, :2]
q4 = arr[2:, 2:]
# Permute quadrants
permuted_arr = np.block([
[q3, q1],
[q4, q2]
])
return permuted_arr
# Sample 4x4 array
arr = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
permuted_arr = custom_permutation(arr)
print(permuted_arr)
In this example, we've defined a function custom_permutation()
that takes a 4×4 NumPy array as input. The function splits the array
into four quadrants (q1, q2, q3, and q4), and then uses NumPy's block()
function to create a new array with the quadrants permuted. The
resulting permuted_arr array has its quadrants rearranged.
Of course, this is just one possible permutation of the array's quadrants.
You can modify the custom_permutation() function to implement other
permutations as needed.
I tried the code you gave me and got the error “np name not defined.”
Apologies for that! I missed an import statement in the previous example.
You need to import the NumPy library at the beginning of your script to
use the np alias and its functions. Here's the corrected code:
python
import numpy as np
def custom_permutation(arr):
# Split array into 4 quadrants
q1 = arr[:2, :2]
q2 = arr[:2, 2:]
q3 = arr[2:, :2]
q4 = arr[2:, 2:]
# Permute quadrants
permuted_arr = np.block([
[q3, q1],
[q4, q2]
])
return permuted_arr
# Sample 4x4 array
arr = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
permuted_arr = custom_permutation(arr)
print(permuted_arr)
This code should work now without any issues.
It did work. Thank you, Pi.
You're very welcome, Steven! I'm glad the code worked for you.
If you have any more questions or need help with anything else,
feel free to ask.
Comments Off on Summer of ’42: Python’s Monty
Sunday, April 14, 2024
Benchmarking Pi
An example of pi.ai's clear and pleasant conversational style
(output format simplified for presentation here) —
Can you help with computer coding problems?
Absolutely, Steven! 💻 While I can't guarantee I'll have all the answers,
I'll certainly do my best to help you debug and find solutions to your
coding conundrums. Which coding language are you working with, and what's
giving you trouble?
I want to learn how Python can permute sections of a square array.
There are several ways to permute sections of a square array in Python,
depending on your specific needs. Here are a few examples:
Using NumPy's random.permutation() function:
python
import numpy as np
arr = np.array([[1, 2], [3, 4]])
permuted_arr = np.random.permutation(arr)
Using itertools.permutations():
python
import itertools
arr = [[1, 2], [3, 4]]
permutations = list(itertools.permutations(arr))
Using custom permutation algorithms:
python
def custom_permutation(arr):
# your custom permutation logic here
arr = [[1, 2], [3, 4]]
permuted_arr = custom_permutation(arr)
Each method has its own strengths and weaknesses, and which one
you choose will depend on the size of your array, the number of
permutations you need, and your performance requirements.
I would like to use python's custom permutation method to permute
the four quadrants of a 4×4 array.
Here's an example of how to define a custom permutation function
in Python to permute the four quadrants of a 4×4 array:
python
def custom_permutation(arr):
# Split array into 4 quadrants
q1 = arr[:2, :2]
q2 = arr[:2, 2:]
q3 = arr[2:, :2]
q4 = arr[2:, 2:]
# Permute quadrants
permuted_arr = np.block([
[q3, q1],
[q4, q2]
])
return permuted_arr
# Sample 4x4 array
arr = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
permuted_arr = custom_permutation(arr)
print(permuted_arr)
In this example, we've defined a function custom_permutation()
that takes a 4×4 NumPy array as input. The function splits the array
into four quadrants (q1, q2, q3, and q4), and then uses NumPy's block()
function to create a new array with the quadrants permuted. The
resulting permuted_arr array has its quadrants rearranged.
Of course, this is just one possible permutation of the array's quadrants.
You can modify the custom_permutation() function to implement other
permutations as needed.
I tried the code you gave me and got the error “np name not defined.”
Apologies for that! I missed an import statement in the previous example.
You need to import the NumPy library at the beginning of your script to
use the np alias and its functions. Here's the corrected code:
python
import numpy as np
def custom_permutation(arr):
# Split array into 4 quadrants
q1 = arr[:2, :2]
q2 = arr[:2, 2:]
q3 = arr[2:, :2]
q4 = arr[2:, 2:]
# Permute quadrants
permuted_arr = np.block([
[q3, q1],
[q4, q2]
])
return permuted_arr
# Sample 4x4 array
arr = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
permuted_arr = custom_permutation(arr)
print(permuted_arr)
This code should work now without any issues.
It did work. Thank you, Pi.
You're very welcome, Steven! I'm glad the code worked for you.
If you have any more questions or need help with anything else,
feel free to ask.
Comments Off on Benchmarking Pi
Sunday, March 3, 2024
Deep Blue Research: A Report by You.com AI
|
Cullinane Diamond Theorem Research Report by https://you.com/?chatMode=research on March 3, 2024 Overview of the Cullinane Diamond Theorem The Cullinane Diamond Theorem is a mathematical concept developed by Steven H. Cullinane that explores the symmetrical properties of certain geometric patterns. It is particularly concerned with the structure of finite projective geometry as it relates to the 35 square patterns found in R. T. Curtis's Miracle Octad Generator (MOG). The theorem asserts that every G-image of a diamond figure D possesses some form of ordinary or color-interchange symmetry. Symmetry and Group Theory The theorem is deeply rooted in group theory, with G being isomorphic to the affine group A on the linear 4-space over the finite field GF(2). This group has a significant order of 322,560 and underlies the symmetry of both the diamond-theorem figures and the square patterns of the MOG . The 35 structures of the 840 G-images of D are isomorphic to the 35 lines in the 3-dimensional projective space over GF(2), which explains the symmetry of the line diagrams and the two-color patterns. The Diamond Theorem in Various Dimensions The diamond theorem can be applied to different cases, such as the 4×4, 2×2, and even 3-dimensional cubes like the 2x2x2 and 4x4x4 cubes. The generalized statement of the theorem involves inscribing a white diamond in a black square and dividing it into four quadrants, each with a diagonal split into black and white halves. Algebraic Implications The theorem has algebraic implications, such as the ability to express every 4-coloring as a sum of three 2-colorings. This algebraic formulation is useful for demonstrating that certain four-colored graphic images can form a ring under multiplication. There is also an infinite family of such 'diamond' rings, isomorphic to rings of matrices over GF(4). Philosophical and Cultural Context Steven H. Cullinane has also explored the philosophical implications of the diamond theorem, referring to it in the context of Plato's Meno dialogue and opposing it to the 'Story Theory of truth' as discussed by Richard J. Trudeau. The theorem is seen as a correct statement of the relation between geometry and the physical universe. Clarification on Cullinan Diamonds It is important to note that the Cullinane Diamond Theorem is unrelated to the Cullinan diamond, which is a famous large gemstone discovered in South Africa and now part of the British Crown Jewels. The Cullinan diamond has its own historical and cultural significance, with its various cut shapes and ownership history. In summary, the Cullinane Diamond Theorem is a mathematical concept that reveals the symmetrical properties of certain geometric patterns, with applications in group theory and algebra. It also has philosophical implications, drawing connections to classical ideas about truth and geometry. |
Instagram ad for You.com AI in research mode
"Show me ALL your sources, babe."
— Line adapted from Leonardo DiCaprio
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Saturday, September 30, 2023
The Algorithm and Mrs. Davis
On the recent Peacock series "Mrs. Davis" —
"The algorithm is known as Mrs. Davis … and is
the all-seeing, all-knowing, not-quite-all-merciful
manifestation of artificial intelligence to whom
humanity has plighted its troth in this eight-part
manifestation of real intelligence from creators
Tara Hernandez and Damon Lindelof."
— John Anderson in The Wall Street Journal ,
Tuesday, April 18, 2023
For The Algorithm , see last evening's Michaelmas post and . . .
For a different Mrs. Davis, see . . .
|
From Tom McCarthy's review yesterday of The Maniac , a novel about 1940s social life at Los Alamos — "The mathematician Martin Davis’s wife, Lydia, storms out of a Trinity dinner party, condemning the men’s failure to fully take on board the consequences of their atom splitting. Besides sharing her name with our own age’s great translator of Blanchot and Proust, this Lydia Davis is a textile artist — a hanging detail that points back toward the novel’s many looms and weavings. For the Greeks, the fates spinning the threads of human lives were female (as Conrad knew, recasting them as Belgian secretaries in 'Heart of Darkness'). So was Theseus’ wool-ball navigator, Ariadne. And so, too, was the Ithacan ur-weaver Penelope, whose perpetual making and unraveling of her tapestry beat Gödel to an incompleteness theory by thousands of years. 'Text,' by the way, means something woven, from which we get 'textile.' It might just be that Penelope was not only testing her own version of the ontological limit, but also embedding it — in absent form, a hole — within the weft and warp of what we would eventually call the novel." |
Martin Davis reportedly died this year on New Year's Day.
This journal on that date —
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Friday, September 29, 2023
Wednesday, January 25, 2023
Victor’s Spoils: Space, Space, Space
A check of the phrase "memory-alpha" in the above URL
reveals that it comes from a 1969 Star Trek episode
written by Shari Lewis and her husband Jeremy Tarcher.
Tarcher reportedly died on Sunday, Sept. 20, 2015.
From this journal on that date —
On the editor of the anthology Space, Space, Space :
"Sloane’s writing is drum-tight, but his approach
is looser; he pulls the reader in and then begins
turning up the heat. He understood that before
a pot can boil, it must simmer." — Stephen King
Of related literary interest to fans of the late Russell Banks,
whose novel title Cloudsplitter refers to Mt. Marcy, the
highest mountain in New York State —
Marcy was a New York State politician who is said to have
coined the above phrase
"to the victor go the spoils."
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Sunday, January 8, 2023
Oil City Snow
From AP News in The Derrick , Oil City, PA, today —
"Banks lived part of the year in Florida, and for a time
had a home in Jamaica, but he was essentially a man
of the North, with an old Puritan’s sense of consequences.
Snow fell often in his fiction . . . ." — Hillel Italie
Update of 3:33 PM ET —
From a link target in this journal on April 4, 2004 —
"Puzzle begun I write in the day's space . . . ."
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Monday, August 1, 2022
Interality Again: The Art of the Gefüge
"Schufreider shows that a network of linguistic relations
is set up between Gestalt, Ge-stell, and Gefüge, on the
one hand, and Streit, Riß, and Fuge, on the other . . . ."
— From p. 14 of French Interpretations of Heidegger ,
edited by David Pettigrew and François Raffoul.
State U. of New York Press, Albany, 2008. (Links added.)
One such "network of linguistic relations" might arise from
a non-mathematician's attempt to describe the diamond theorem.
(The phrase "network of linguistic relations" appears also in
Derrida's remarks on Husserl's Origin of Geometry .)
For more about "a system of slots," see interality in this journal.
The source of the above prefatory remarks by editors Pettigrew and Raffoul —
"If there is a specific network that is set up in 'The Origin of the Work of Art,'
a set of structural relations framed in linguistic terms, it is between
Gestalt, Ge-stell and Gefüge, on the one hand, and Streit, Riß and Fuge,
on the other; between (as we might try to translate it)
configuration, frame-work and structure (system), on the one hand, and
strife, split (slit) and slot, on the other. On our view, these two sets go
hand in hand; which means, to connect them to one another, we will
have to think of the configuration of the rift (Gestalt/Riß) as taking place
in a frame-work of strife (Ge-stell/Streit) that is composed through a system
of slots (Gefüge/Fuge) or structured openings."
— Quotation from page 197 of Schufreider, Gregory (2008):
"Sticking Heidegger with a Stela: Lacoue-Labarthe, art and politics."
Pp. 187-214 in David Pettigrew & François Raffoul (eds.),
French Interpretations of Heidegger: An Exceptional Reception.
State University of New York Press, 2008.
Update at 5:14 AM ET Wednesday, August 3, 2022 —
See also "six-set" in this journal.
"There is such a thing as a six-set."
— Saying adapted from a 1962 young-adult novel.
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Monday, July 18, 2022
“The Shape of Ideas”
Some may prefer other concepts of shape. For instance …
… and, from Log24 on the above Yalebooks date —
Related material:
|
From "Higman- Sims Graph," a webpage by A. E. Brouwer — "Similar to the 15+35 construction of the Hoffman-Singleton graph is the 30+70 construction of the Higman-Sims graph. In the former the starting point was that the lines of PG(3,2) can be labeled with the triples in a 7-set such that lines meet when the corresponding triples have 1 element in common. This time we label the lines of PG(3,2) with the 4+4 splits of an 8-set, where intersecting lines correspond to splits with common refinement 2+2+2+2. Clearly, both descriptions of the lines of PG(3,2) are isomorphic. Take as vertices of the Higman-Sims graph the 15 points and 15 planes of PG(3,2) together with the 70 4-subsets of an 8-set. Join two 4-sets when they have 1 element in common. A 4-set determines a 4+4 split and hence a line in PG(3,2), and is adjacent to the points and planes incident with that line. A plane is adjacent to the nonincident points. This yields the Higman-Sims graph." |
See also PG(3,2) in this journal.
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Monday, April 18, 2022
For the Church of Perfect Coordinates*
https://blacklistdeclassified.net/2022/04/15/
%f0%9f%94%b4-script-916-helen-maghi/ —
Red: If I may offer some counsel –
“Do not go where the path may lead.
Go instead where there is no path
and leave a trail.”
In the spirit of that, I bring an unusual case….
This post is in honor of Thandiwe Newton,
who left a Westworld trail —
Vide Bulk Apperception.
* Cf. a post from Day 3 of 2022.
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Saturday, February 5, 2022
Mathieu Cube Labeling
Shown below is an illustration from "The Puzzle Layout Problem" —
- September 2003
-
Lecture Notes in Computer Science 2912:500-501
DOI:10.1007/978-3-540-24595-7_50 - Source: DBLP
-
Conference: Graph Drawing, 11th International Symposium,
GD 2003, Perugia, Italy, September 21-24, 2003, Revised Papers - Authors: Kozo Sugiyama, Seok-Hee Hong, Atsuhiko Maeda
Exercise: Using the above numerals 1 through 24
(with 23 as 0 and 24 as ∞) to represent the points
∞, 0, 1, 2, 3 … 22 of the projective line over GF(23),
reposition the labels 1 through 24 in the above illustration
so that they appropriately* illustrate the cube-parts discussed
by Iain Aitchison in his March 2018 Hiroshima slides on
cube-part permutations by the Mathieu group M24.
A note for Northrop Frye —
Interpenetration in the eightfold cube — the three midplanes —
A deeper example of interpenetration:
Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.
* "Appropriately" — I.e. , so that the Aitchison cube octads correspond
exactly, via the projective-point labels, to the Curtis MOG octads.
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Saturday, September 11, 2021
Reality for Academia
The title of the previous post, "Ground Omega," suggests a related nightmare . . .
A writer of fiction in the previous post —
"When we say a thing is unreal, we mean it is too real…."
Old joke —
"What you mean 'we,' paleface?"
At Ground Omega in the above My Hero Academia site —
"The twenty-four students are split into six groups of four…."
I prefer the similar splittings of the Curtis Omega —
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Thursday, June 17, 2021
Easy E . . .
Continues.
Lyrics from Bruce Springsteen and
the Pointer Sisters —
Well, Romeo and Juliet, Samson and Delilah
Baby you can bet a love they couldn't deny
My words say split, but my words they lie
Cause when we kiss, ooh, fire
{Bridge}
Oh fire
Kisses like fire…
Burn me up with fire
I like what you're doin now, fire
Touchin' me, fire
Touchin' me, burnin me, fire
Take me home
Related remarks (suggested by Emma Stone's appearance
in the "Drop Me a Line" post of August 30, 2015) —
Comments Off on Easy E . . .
Thursday, May 20, 2021
Hope
From a story about the May 2017 un-cancellation ot "Timeless" —
"The nation’s only hope is an unexpected team. . . ."
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Friday, March 12, 2021
Grid
See Trinity Cube in this journal and . . .
McDonnell’s illustration is from 9 June 1983.
See as well a less official note from later that June.
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Saturday, January 30, 2021
Associative Logic
By Ema R. Schumer, Crimson Staff Writer
The co-ed Delphic-Bee Club will split into the all-male Delphic Club
and the all-female Bee Club three years after merging, according to
club affiliates.
See also the previous post, “Bee Season.“
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Kind of a Drag* . . .
* The title is from a post of last December —
Also on Linden Street —
Related news —
By Ema R. Schumer, Crimson Staff Writer
The co-ed Delphic-Bee Club will split into the all-male Delphic Club
and the all-female Bee Club three years after merging, according to club affiliates.
Comments Off on Kind of a Drag* . . .
Sunday, May 17, 2020
“The Ultimate Epistemological Fact”
"Let me say this about that." — Richard Nixon
Interpenetration in Weyl's epistemology —
Interpenetration in Mazzola's music theory —
Interpenetration in the eightfold cube — the three midplanes —
A deeper example of interpenetration:
Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.
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Saturday, May 2, 2020
Turyn’s Octad Theorem: The Next Level*
From the obituary of a game inventor who reportedly died
on Monday, February 25, 2013 —
” ‘He was hired because of the game,’ Richard Turyn,
a mathematician who worked at Sylvania, told
the Washington Post in a 2004 feature on Diplomacy.”
* For the theorem, see Wolfram Neutsch, Coordinates .
(Published by de Gruyter, 1996. See pp. 761-766.)
Having defined (pp. 751-752) the Miracle Octad Generator (MOG)
as a 4×6 array to be used with Conway’s “hexacode,” Neutsch says . . .
“Apart from the three constructions of the Golay codes
discussed at length in this book (lexicographic and via
the MOG or the projective line), there are literally
dozens of alternatives. For lack of space, we have to
restrict our attention to a single example. It has been
discovered by Turyn and can be connected in a very
beautiful way with the Miracle Octad Generator….
To this end, we consider the natural splitting of the MOG into
three disjoint octads L, M, R (‘left’, ‘middle’, and ‘right’ octad)….”
— From page 761
“The theorem of Turyn” is on page 764 —
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Thursday, April 23, 2020
Octads and Geometry
See the web pages octad.group and octad.us.
Related geometry (not the 759 octads, but closely related to them) —
#/media/File:150614-PG-3-2-schoolgirls-arrangement.png)
The 4×6 rectangle of R. T. Curtis
illustrates the geometry of octads —
Curtis splits the 4×6 rectangle into three 4×2 "bricks" —
.
"In fact the construction enables us to describe the octads
in a very revealing manner. It shows that each octad,
other than Λ1, Λ2, Λ3, intersects at least one of these ' bricks' —
the 'heavy brick' – in just four points." . . . .
— R. T. Curtis (1976). "A new combinatorial approach to M24,"
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42.
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Thursday, July 18, 2019
Apperception
From BUtterfield 8 (1960) —
From the 7/20/2017 post "Divided Attention" —
Another phrase for divided attention is "bulk apperception."
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Avatar for Inspector Tennison
Image from a post of November 13, 2006.
See as well Schoolgirl Tetrahedron.
Related lyrics from Bruce Springsteen and
the Pointer Sisters —
Well, Romeo and Juliet, Samson and Delilah
Baby you can bet a love they couldn't deny
My words say split, but my words they lie
Cause when we kiss, ooh, fire
{Bridge}
Oh fire
Kisses like fire…
Burn me up with fire
I like what you're doin now, fire
Touchin' me, fire
Touchin' me, burnin me, fire
Take me home
Comments Off on Avatar for Inspector Tennison
Friday, May 10, 2019
I Ching g6
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Tuesday, April 2, 2019
Plan
"If this weren't a public situation, I'd be tempted to get into this on a
psychiatric level." — Christopher Alexander to Peter Eisenman, 1982
Scene from the sequel to Unbreakable and Split —
Not to mention elevation .
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Sunday, July 22, 2018
Thursday, July 20, 2017
Divided Attention
The previous post alluded to the phrase "undivided attention."
An example of divided attention —
The "Orphan Black" scene (at right above) is from a post, "Art's Space,"
of Saturday, July 15, 2017. The themes of the Orphan Black series —
in the context of Silicon Valley, not of Orphan Black — were discussed
in the Los Angeles Review of Books on Monday, July 17, 2017. Other
Silicon Valley themes appear in the recent film "The Circle" (at left above).
Another phrase for divided attention is "bulk apperception."
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Sunday, April 9, 2017
Wednesday, February 8, 2017
Rhymes with Prize
On the triangle in the excerpt above —
"A golden triangle can be split into
a golden triangle and a golden gnomon.
The same is true for a golden gnomon.
A golden gnomon and a golden triangle
with their equal sides matching each other
in length are also referred to as the obtuse
and acute Robinson triangles.
These isosceles triangles can be used to
produce Penrose tilings."
— Adapted from Wikipedia (Wikipedia's word
"bisected" is replaced above by the word "split.")
The previous post dealt with women and lies.
Related material — Quilt Prize in this journal.
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Monday, January 23, 2017
The In Crowd
The New York Times online on Thursday, Jan. 19, 2017 —
" 'Split' is being released by Universal under the Blumhouse label,
a brand associated with unpretentious, clever, neo-traditionalist
scare-pictures like 'Insidious,' 'Paranormal Activity' and 'The Purge.'
That seems like the right company for Mr. Shyamalan . . . ."
A check of the Blumhouse label leads to a NY Times article
dated July 15, 2012 —
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Wednesday, August 26, 2015
“The Quality Without a Name”
The title phrase, paraphrased without quotes in
the previous post, is from Christopher Alexander's book
The Timeless Way of Building (Oxford University Press, 1979).
A quote from the publisher:
"Now, at last, there is a coherent theory
which describes in modern terms
an architecture as ancient as
human society itself."
Three paragraphs from the book (pp. xiii-xiv):
19. Within this process, every individual act
of building is a process in which space gets
differentiated. It is not a process of addition,
in which preformed parts are combined to
create a whole, but a process of unfolding,
like the evolution of an embryo, in which
the whole precedes the parts, and actualy
gives birth to then, by splitting.
20. The process of unfolding goes step by step,
one pattern at a time. Each step brings just one
pattern to life; and the intensity of the result
depends on the intensity of each one of these
individual steps.
21. From a sequence of these individual patterns,
whole buildings with the character of nature
will form themselves within your thoughts,
as easily as sentences.
Compare to, and contrast with, these illustrations of "Boolean space":
(See also similar illustrations from Berkeley and Purdue.)
Detail of the above image —
Note the "unfolding," as Christopher Alexander would have it.
These "Boolean" spaces of 1, 2, 4, 8, and 16 points
are also Galois spaces. See the diamond theorem —
Comments Off on “The Quality Without a Name”
Saturday, March 8, 2014
Conwell Heptads in Eastern Europe
“Charting the Real Four-Qubit Pauli Group
via Ovoids of a Hyperbolic Quadric of PG(7,2),”
by Metod Saniga, Péter Lévay and Petr Pracna,
arXiv:1202.2973v2 [math-ph] 26 Jun 2012 —
P. 4— “It was found that Q +(5,2) (the Klein quadric)
has, up to isomorphism, a unique one — also known,
after its discoverer, as a Conwell heptad [18].
The set of 28 points lying off Q +(5,2) comprises
eight such heptads, any two having exactly one
point in common.”
P. 11— “This split reminds us of a similar split of
63 points of PG(5,2) into 35/28 points lying on/off
a Klein quadric Q +(5,2).”
[18] G. M. Conwell, Ann. Math. 11 (1910) 60–76
A similar split occurs in yesterday’s Kummer Varieties post.
See the 63 = 28 + 35 vectors of R8 discussed there.
For more about Conwell heptads, see The Klein Correspondence,
Penrose Space-Time, and a Finite Model.
For my own remarks on the date of the above arXiv paper
by Saniga et. al., click on the image below —
Walter Gropius
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Monday, December 2, 2013
Finite-Geometry Notes
See my Google Sites page if you would like to
download a zipped copy (31 MB) of my
Finite-Geometry Notes site
(not zipped, at finitegeometry.org/sc/map.html).
Or you can of course use a website downloader.
(Suggested by a recent NY Times piece on
a company, Citia, that splits books into pieces
for easier electronic access. The large zipped
file referred to above is sort of a reverse of this
process.)
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Sunday, June 3, 2012
Child’s Play
“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”
– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art , Cornell U. Press, 1975
Related material—
Wednesday, April 6, 2011
Harvard Hicks
Austin Considine on a Tennessee tourist trap—
"It would be easy for a city slicker to assume this place misses its own punch lines."
It probably doesn't, but a certain academic tourist trap does .
A trio of Harvard hicks—
1. The chairman of the Harvard philosophy department, Sean D. Kelly—
"Football can literally bring meaning to life."
(See also Garry Wills on Kelly, Rite of Spring, and Heisman Trophy.)
2. A professor of English at Harvard, Marjorie Garber, in a deconstructive meditation—
Garber notes that the word "literature" has two meanings– the English department's meaning, and that of other departments' references to "the literature."
"Whenever there is a split like this, it is worth pausing to wonder why. High/low, privileged/popular, aesthetic/professional, keep/throw away. It seems as if the category of literature in what we might inelegantly call the literary sense of the word is being both protected and preserved in amber by the encroachment, on all sides, of the nonliterary literature that proliferates in professional-managerial culture. But literature has always been situated on the boundary between itself and its other."
— The Use and Abuse of Literature , published by Pantheon on March 29, 2011
3. The president of Harvard, Drew Faust—
A comment recently made to Faust—
“[A] tyrant wanted a crimson-tinged report that he was running a democracy, and for a price, a Harvard expert obliged…."
Her response—
"Faust replied that for her to say anything about this would make her 'scold in chief.'"
— University Diaries today. See the excellent commentary there.
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Saturday, August 7, 2010
Rift Designs
From the current index to obituaries at Telegraph.co.uk—
Teufel is also featured in today's New York Times—
"Mr. Teufel became a semicelebrity, helped in no small part by his last name, which means 'devil' in German."
From Group Analysis , June 1993, vol. 26 no. 2, 203-212—
by Ronald Sandison, Ledbury, Herefordshire HR8 2EY, UK
In my contribution to the Group Analysis Special Section: "Aspects of Religion in Group Analysis" (Sandison, 1993) I hinted that any consideration of a spiritual dimension to the group involves us in a discussion on whether we are dealing with good or evil spirits. But if we say that God is in the group, why is not the Devil there also? Can good and evil coexist in the same group matrix? Is the recognition of evil "nothing but" the ability to distinguish between good and bad? If not, then what is evil? Is it no more than the absence of good?
These and other questions were worked on at a joint Institute of Group Analysis and Group-Analytic Society (London) Workshop entitled "The Problem of Good and Evil." We considered the likelihood that good and evil coexist in all of us, as well as in the whole of the natural world, not only on earth, but in the cosmos and in God himself What we actually do with good and evil is to split them apart, thereby shelving the problem but at the same time creating irreconcilable opposites. This article examines this splitting and how we can work with it psychoanalytically.
This suggests a biblical remark—
"Now there was a day… when the sons of God
came to present themselves before the Lord,
and Satan came also among them."
— Job 1:6, quoted by Chesterton in The Man Who Was Thursday
Sandison died on June 18. See the Thursday, August 5, Log24 post "The Matrix."
Teufel died on July 6. See the Log24 posts for that day.
The title of this post, "rift designs," refers to a recurring theme in the July 6 posts. It is taken from Heidegger.
From a recent New Yorker review of Absence of Mind by Marilynne Robinson—
"Robinson is eloquent in her defense of the mind’s prerogatives, but her call for a renewed metaphysics might be better served by rereading Heidegger than by dusting off the Psalms."
Following this advice, we find—
"Propriation gathers the rift-design of the saying and unfolds it in such a way that it becomes the well-joined structure of a manifold showing."
— p. 415 of Heidegger's Basic Writings , edited by David Farrell Krell, HarperCollins paperback, 1993
"Das Ereignis versammelt den Aufriß der Sage und entfaltet ihn zum Gefüge des vielfältigen Zeigens."
— Heidegger, Weg zur Sprache
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Thursday, July 1, 2010
Plato’s Code
John Allen Paulos yesterday at Twitter—
"Plato's code cracked? http://bit.ly/ad6k1S
Fascinating if not a hoax or hype."
The story that Paulos linked to is about a British
academic who claims to have found some
symbolism hidden in Plato's writings by
splitting each into 12 parts and correlating
the 12 parts with semitones of a musical scale.
I prefer a different approach to Plato that is
related to the following hoax and hype—
HOAX:
From Dan Brown's novel Angels & Demons (2000)—
HYPE:
This four-elements diamond summarizes the classical
four elements and four qualities neatly, but some scholars
might call the figure "hype" since it deals with an academically
disreputable subject, alchemy, and since its origin is unclear.
For the four elements' role in some literature more respectable
than Dan Brown's, see Poetry's Bones.
Although an author like Brown might spin the remarks
below into a narrative— The Plato Code — they are
neither hoax nor hype.
NOT HOAX:
NOT HYPE:
For related non-hoax, non-hype remarks, see
The Rational Enterprise: Logos in Plato's Theaetetus,
by Rosemary Desjardins.
Those who prefer hoax and hype in their philosophy may consult
the writings of, say, Barbara Johnson, Rosalind Krauss, and—
in yesterday's NY Times's "The Stone" column— Nancy Bauer.
— The New York Times
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Thursday, February 5, 2009
Thursday February 5, 2009
Through the
Looking Glass:
A Sort of Eternity
From the new president’s inaugural address:
“… in the words of Scripture, the time has come to set aside childish things.”
The words of Scripture:
“through a glass”—
[di’ esoptrou].
By means of
a mirror [esoptron].
Childish things:
© 2005 The Institute for Figuring
Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)
Not-so-childish:
Three planes through
the center of a cube
that split it into
eight subcubes:
Through a glass, darkly:
A group of 8 transformations is
generated by affine reflections
in the above three planes.
Shown below is a pattern on
the faces of the 2x2x2 cube
that is symmetric under one of
these 8 transformations–
a 180-degree rotation:
(Click on image
for further details.)
But then face to face:
A larger group of 1344,
rather than 8, transformations
of the 2x2x2 cube
is generated by a different
sort of affine reflections– not
in the infinite Euclidean 3-space
over the field of real numbers,
but rather in the finite Galois
3-space over the 2-element field.
Galois age fifteen,
drawn by a classmate.
These transformations
in the Galois space with
finitely many points
produce a set of 168 patterns
like the one above.
For each such pattern,
at least one nontrivial
transformation in the group of 8
described above is a symmetry
in the Euclidean space with
infinitely many points.
For some generalizations,
see Galois Geometry.
Related material:
The central aim of Western religion–
"Each of us has something to offer the Creator... the bridging of masculine and feminine, life and death. It's redemption.... nothing else matters." -- Martha Cooley in The Archivist (1998) The central aim of Western philosophy– Dualities of Pythagoras as reconstructed by Aristotle: Limited Unlimited Odd Even Male Female Light Dark Straight Curved ... and so on .... “Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy.” — Jamie James in The Music of the Spheres (1993) “In the garden of Adding — The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000) A quotation today at art critic Carol Kino’s website, slightly expanded: “Art inherited from the old religion — Octavio Paz,”Seeing and Using: Art and Craftsmanship,” in Convergences: Essays on Art and Literature (New York: Harcourt Brace Jovanovich 1987), 52 From Brian O’Doherty’s 1976 Artforum essays– not on museums, but rather on gallery space: “We have now reached
“Space: what you — James Joyce, Ulysses |
Comments Off on Thursday February 5, 2009
Monday, July 30, 2007
Monday July 30, 2007
The Deathly Hallows Symbol
Some fear that the Harry Potter books introduce children to the occult; they are not entirely mistaken.
According to Wikipedia, the “Deathly Hallows” of the final Harry Potter novel are “three fictional magical objects that appear in the book.”
The vertical line, circle, and triangle in the symbol pictured above are said to refer to these three magical objects.
One fan relates the “Deathly Hallows” symbol above, taken from the spine of a British children’s edition of the book, to a symbol for “the divine (or sacred, or secret) fire” of alchemy. She relates this fire in turn to “serpent power” and the number seven:
Kristin Devoe at a Potter fan site:
“We know that seven is a powerful number in the novels. Tom Riddle calls it ‘the most powerfully magic number.‘ The ability to balance the seven chakras within oneself allows the person to harness the secret fire. This secret fire in alchemy is the same as the kundalini or coiled snake in yogic philosophy. It is also known as ‘serpent power’ or the ‘dragon’ depending on the tradition. The kundalini is polar in nature and this energy, this internal fire, is very powerful for those who are able to harness it and it purifies the aspirant allowing them the knowledge of the universe. This secret fire is the Serpent Power which transmutes the base metals into the Perfect Gold of the Sun.
It is interesting that the symbol of the caduceus in alchemy is thought to have been taken from the symbol of the kundalini. Perched on the top of the caduceus, or the staff of Hermes, the messenger of the gods and revealer of alchemy, is the golden snitch itself! Many fans have compared this to the scene in The Order of the Phoenix where Harry tells Dumbledore about the attack on Mr. Weasley and says, ‘I was the snake, I saw it from the snake’s point of view.‘
The chapter continues with Dumbledore consulting ‘one of the fragile silver instruments whose function Harry had never known,’ tapping it with his wand:
The instrument tinkled into life at once with rhythmic clinking noises. Tiny puffs of pale green smoke issued from the minuscule silver tube at the top. Dumbledore watched the smoke closely, his brow furrowed, and after a few seconds, the tiny puffs became a steady stream of smoke that thickened and coiled into he air… A serpent’s head grew out of the end of it, opening its mouth wide. Harry wondered whether the instrument was confirming his story; He looked eagerly at Dumbledore for a sign that he was right, but Dumbledore did not look up.
“Naturally, Naturally,” muttered Dumbledore apparently to himself, still observing the stream of smoke without the slightest sign of surprise. “But in essence divided?”
Harry could make neither head not tail of this question. The smoke serpent, however split instantly into two snakes, both coiling and undulating in the dark air. With a look of grim satisfaction Dumbledore gave the instrument another gentle tap with his wand; The clinking noise slowed and died, and the smoke serpents grew faint, became a formless haze, and vanished.
Could these coiling serpents of smoke be foreshadowing events to come in Deathly Hallows where Harry learns to ‘awaken the serpent’ within himself? Could the snake’s splitting in two symbolize the dual nature of the kundalini?”
Related material
and the following
famous illustration of
the double-helix
structure of DNA:
This is taken from
a figure accompanying
an obituary, in today’s
New York Times, of the
artist who drew the figure.
The double helix
is not a structure
from magic; it may,
however, as the Rowling
quote above shows, have
certain occult uses,
better suited to
Don Henley’s
Garden of Allah
than to the
Garden of Apollo.
Similarly, the three objects
above (Log24 on April 9)
are from pure mathematics–
the realm of Apollo, not
of those in Henley’s song.
The similarity of the
top object of the three —
the “Fano plane” — to
the “Deathly Hallows”
symbol is probably
entirely coincidental.
Comments Off on Monday July 30, 2007
Wednesday, November 22, 2006
Wednesday November 22, 2006
Rock of Ages
“Who knows where madness lies?”
— Rhetorical question
in “Man of La Mancha”
(See previous entry.)
Using madness to
seek out madness, let us
consult today’s numbers…
Pennsylvania Lottery
Nov. 22, 2006:
Mid-day 487
Evening 814
The number 487 leads us to
page 487 in the
May 1977 PMLA,
“The Form of Carnival
in Under the Volcano“:
“The printing presses’ flywheel
marks the whirl of time*
that will split La Despedida….”
From Dana Grove,
A Rhetorical Analysis of
Under the Volcano,
page 92:
“… In this way, mystical as well as psychological dimensions are established. Later on, the two pass by a printer’s shop window and curiously stop to inspect, amidst wedding portraits and well in front of the revolving flywheel of the printing machines, ‘a photographic enlargement purporting to show the disintegration of a glacial deposit in the Sierra Madre, of a great rock split by forest fires.’ Significantly the picture is called ‘La Despedida,’ the Parting. Yvonne cannot help but see the symbolic significance of the photograph and wishes with all of her might ‘to heal the cleft rock’ just as she wishes to heal the divorce….”
Some method in this madness
is revealed by the evening
lottery number, 814, which
leads to an entry of 8/14:
is revealed by the evening
lottery number, 814, which
leads to an entry of 8/14:
“… a point of common understanding
between the classic and romantic worlds.
Quality, the cleavage term between
hip and square, seemed to be it.”
— Robert M. Pirsig
Rebecca Goldstein
The 8/14 entry also deals with
Rebecca Goldstein, who
seems to understand
such cleavage
very well.
(See also today’s previous entry.)
* Cf. Shakespeare’s “whirligig of time“
linked to in the previous entry.)
Comments Off on Wednesday November 22, 2006
Saturday, October 14, 2006
Saturday October 14, 2006
The Line
Continued
from Aug. 15, 2004:
Continued
from Aug. 15, 2004:
Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Part III:
“The wave of crystallization rolled ahead. He was seeing two worlds, simultaneously. On the intellectual side, the square side, he saw now that Quality was a cleavage term. What every intellectual analyst looks for. You take your analytic knife, put the point directly on the term Quality and just tap, not hard, gently, and the whole world splits, cleaves, right in two…
hip and square, classic and romantic, technological and humanistic…and the split is clean. There’s no mess. No slop. No little items that could be one way or the other. Not just a skilled break but a very lucky break. Sometimes the best analysts, working with the most obvious lines of cleavage, can tap and get nothing but a pile of trash. And yet here was Quality; a tiny, almost unnoticeable fault line; a line of illogic in our concept of the universe; and you tapped it, and the whole universe came apart, so neatly it was almost unbelievable. He wished Kant were alive. Kant would have appreciated it. That master diamond cutter. He would see. Hold Quality undefined. That was the secret.”
See also the discussion of
subjective and objective
by Robert M. Pirsig in
Zen and the Art of
Motorcycle Maintenance,
Part III,
followed by this dialogue:
Are We There Yet?
Chris shouts, “When are we
going to get to the top?”
“Probably quite a way yet,”
I reply.
“Will we see a lot?”
“I think so. Look for blue sky
between the trees. As long as we
can’t see sky we know it’s a way yet.
The light will come through the trees
when we round the top.”
Related material:
The Boys from Uruguay,
Lichtung!,
The Shining of May 29,
A Guiding Philosophy,
Ticket Home.
The philosophy of Heidegger
discussed and illustrated
in the above entries may
be regarded as honoring
today’s 100th anniversary
of the birth of Heidegger’s
girlfriend, Hannah Arendt.
See also
Comments Off on Saturday October 14, 2006
Thursday, December 15, 2005
Thursday December 15, 2005
In honor of Freeman Dyson’s birthday:
“Mahlburg likens his approach to an analogous one for deciding whether a dance party has an even or odd number of attendees. Instead of counting all the participants, a quicker method is to see whether everyone has a partner—in effect making groups that are divisible by 2.
In Mahlburg’s work, the partition numbers play the role of the dance participants, and the crank splits them not into couples but into groups of a size divisible by the prime number in question. The total number of partitions is, therefore, also divisible by that prime.
Mahlburg’s work ‘has effectively written the final chapter on Ramanujan congruences,’ Ono says.
‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”
— Erica Klarreich in Science News Online, week of June 18, 2005
This would seem to meet the criteria set by Fritz Leiber for “a story that works.” (See previous entry.) Whether the muse of dance (played in “Xanadu” by a granddaughter of physicist Max Born– see recent entries) has a role in the Dyson story is debatable.
|
Born Dec. 11, 1882, Breslau, Germany. Died Jan. 5, 1970, Göttingen, |
 Max Born |
Those who prefer less abstract stories may enjoy a mythic tale by Robert Graves, Watch the North Wind Rise, or a Christian tale by George MacDonald, At the Back of the North Wind.
Related material:
“The valley spirit never dies. It’s named the mystic woman.”
For an image of a particular
incarnation of the mystic woman
(whether as muse, as goddess,
or as the White Witch of Narnia,
I do not know) see Julie Taymor.“Down in the valley,
valley so low,
hang your head over,
hear the wind blow.”“Which is the sound of the land
Full of the same wind
That is blowing in
the same bare placeFor the listener,
who listens in the snow,
And, nothing himself, beholds
Nothing that is not there
and the nothing that is.”
Comments Off on Thursday December 15, 2005
Thursday, December 8, 2005
Thursday December 8, 2005
Aion Flux
That Nature is a Heraclitean Fire…
— Poem title, Gerard Manley Hopkins
— Poem title, Gerard Manley Hopkins
From Jung's Map of the Soul, by Murray Stein:
"… Jung thinks of the self as undergoing continual transformation during the course of a lifetime…. At the end of his late work Aion, Jung presents a diagram to illustrate the dynamic movements of the self…."
"The formula presents a symbol of the self, for the self is not just a stable quantity or constant form, but is also a dynamic process. In the same way, the ancients saw the imago Dei in man not as a mere imprint, as a sort of lifeless, stereotyped impression, but as an active force…. The four transformations represent a process of restoration or rejuvenation taking place, as it were, inside the self…."
"The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness, which the alchemists expressed through the symbol of the uroboros, and finally the formula repeats the ancient alchemical tetrameria, which is implicit in the fourfold structure of unity.
What the formula can only hint at, however, is the higher plane that is reached through the process of transformation and integration. The 'sublimation' or progress or qualitative change consists in an unfolding of totality into four parts four times, which means nothing less than its becoming conscious. When psychic contents are split up into four aspects, it means that they have been subjected to discrimination by the four orienting functions of consciousness. Only the production of these four aspects makes a total description possible. The process depicted by our formula changes the originally unconscious totality into a conscious one."
— Jung, Collected Works,
Vol. 9, Part 2, Aion: Researches into the Phenomenology of the Self (1951)
Related material:
"Although 'wholeness' seems at first sight to be nothing but an abstract idea (like anima and animus), it is nevertheless empirical in so far as it is anticipated by the psyche in the form of spontaneous or autonomous symbols. These are the quaternity or mandala symbols, which occur not only in the dreams of modern people who have never heard of them, but are widely disseminated in the historical recods of many peoples and many epochs. Their significance as symbols of unity and totality is amply confirmed by history as well as by empirical psychology. What at first looks like an abstract idea stands in reality for something that exists and can be experienced, that demonstrates its a priori presence spontaneously. Wholeness is thus an objective factor that confronts the subject independently of him… Unity and totality stand at the highest point on the scale of objective values because their symbols can no longer be distinguished from the imago Dei. Hence all statements about the God-image apply also to the empirical symbols of totality."
— Jung, Aion, as quoted in
Carl Jung and Thomas Merton
Comments Off on Thursday December 8, 2005
Thursday, October 6, 2005
Thursday October 6, 2005
A Voice
In memory of Harold Leventhal,
folk-music concert producer,
who died on Tuesday
(Rosh Hashana, 2005)
folk-music concert producer,
who died on Tuesday
(Rosh Hashana, 2005)
Leventhal recently appeared in the American Masters Bob Dylan documentary on PBS. According to today’s NYT obituary, “Mr. Leventhal was… widely, if tacitly, acknowledged to have been the inspiration for Irving Steinbloom, the folk impresario whose memorial concert sets in motion the plot of the 2003 film comedy ‘A Mighty Wind.'”
From a Rosh Hashana sermon by Devra Felder Noily:
“Throughout these Holy Days we will chant Unetaneh Tokef, a liturgical poem more than a thousand years old. In it we find the words:
U-ve shofar gadol yi-ta-ka. V’ kol d’ma-ma da-kah yi-shama. The great shofar is sounded. And a still small voice is heard….
The prayer quotes from the book of Kings. There, the prophet Elijah has reached his breaking point, and God reaches out to him. The text tells us:
Then the Eternal passed by. There was a great and mighty wind, splitting mountains and shattering rocks by the power of God, but God was not in the wind. After the wind, an earthquake– but God was not in the earthquake. After the earthquake, fire– but God was not in the fire. And after the fire, a still small voice.”
Comments Off on Thursday October 6, 2005
Wednesday, May 4, 2005
Wednesday May 4, 2005
The Fano Plane
Revisualized:
Revisualized:
or, The Eightfold Cube
Here is the usual model of the seven points and seven lines (including the circle) of the smallest finite projective plane (the Fano plane):
Every permutation of the plane's points that preserves collinearity is a symmetry of the plane. The group of symmetries of the Fano plane is of order 168 and is isomorphic to the group PSL(2,7) = PSL(3,2) = GL(3,2). (See Cameron on linear groups (pdf).)
The above model indicates with great clarity six symmetries of the plane– those it shares with the equilateral triangle. It does not, however, indicate where the other 162 symmetries come from.
Shown below is a new model of this same projective plane, using partitions of cubes to represent points:
The cubes' partitioning planes are added in binary (1+1=0) fashion. Three partitioned cubes are collinear if and only if their partitioning planes' binary sum equals zero.
The second model is useful because it lets us generate naturally all 168 symmetries of the Fano plane by splitting a cube into a set of four parallel 1x1x2 slices in the three ways possible, then arbitrarily permuting the slices in each of the three sets of four. See examples below.
For a proof that such permutations generate the 168 symmetries, see Binary Coordinate Systems.
(Note that this procedure, if regarded as acting on the set of eight individual subcubes of each cube in the diagram, actually generates a group of 168*8 = 1,344 permutations. But the group's action on the diagram's seven partitions of the subcubes yields only 168 distinct results. This illustrates the difference between affine and projective spaces over the binary field GF(2). In a related 2x2x2 cubic model of the affine 3-space over GF(2) whose "points" are individual subcubes, the group of eight translations is generated by interchanges of parallel 2x2x1 cube-slices. This is clearly a subgroup of the group generated by permuting 1x1x2 cube-slices. Such translations in the affine 3-space have no effect on the projective plane, since they leave each of the plane model's seven partitions– the "points" of the plane– invariant.)
To view the cubes model in a wider context, see Galois Geometry, Block Designs, and Finite-Geometry Models.
For another application of the points-as-partitions technique, see Latin-Square Geometry: Orthogonal Latin Squares as Skew Lines.
For more on the plane's symmetry group in another guise, see John Baez on Klein's Quartic Curve and the online book The Eightfold Way. For more on the mathematics of cubic models, see Solomon's Cube.
For a large downloadable folder with many other related web pages, see Notes on Finite Geometry.
Comments Off on Wednesday May 4, 2005
Thursday, December 16, 2004
Thursday December 16, 2004
Nothing Nothings
(Again)
Background: recent Log24 entries (beginning with Chorus from the Rock on Dec. 5, 2004) and Is Nothing Sacred? (quotations compiled on March 9, 2000).
From an obituary of Paul Edwards, a writer on philosophy, in this morning's New York Times:
"Heidegger's Confusions, a collection of Professor Edwards's scholarly articles, was published last month by Prometheus."
Edwards, born in Vienna in 1923 to Jewish parents, died on December 9.
Some sites I visited earlier this evening, before reading of Edwards's death:
-
" 'Nothingness itself nothings' — with these words, uttered by Martin Heidegger in the early 1930s, the incipient (and now-familiar) split between analytic and continental philosophy began tearing open. For Rudolf Carnap, a leader of the Vienna Circle [Wiener Kreis] of logical empiricists and a strident advocate of a new, scientific approach to philosophy, this Heideggerian proposition exemplified 'a metaphysical pseudo-sentence,' meaningless and unable to withstand any logical analysis. Heidegger countered that Carnap’s misplaced obsession with logic missed the point entirely."
— Review of A Parting of the Ways: Carnap, Cassirer, and Heidegger
- Carnap's Criticism of Heidegger, by Abraham D. Stone (dated, for what it's worth, June 16, 2004… the 100th anniversary of Bloomsday.)
- "Death and Metaphysics," by Peter Kraus, pp. 98-111 in Death and Philosophy, ed. by Jeff Malpas and Robert Solomon. Heidegger's famous phrase (misquoted by Quine in Gray Particular in Hartford) "Das Nichts selbst nichtet" is discussed on page 102.
Comments Off on Thursday December 16, 2004
Sunday, December 12, 2004
Sunday December 12, 2004
Ideas, Stories, Values:
Literati in Deep Confusion
“We tell ourselves stories in order to live….
We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas‘ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.
Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling.”
Interview with Joseph Epstein:
“You can do in stories things that are above those in essays,” says Epstein. “In essays and piecework, you are trying to make a point, whereas in stories you are not quite sure what the point is. T.S. Eliot once said of Henry James, ‘He had a mind so fine no idea could violate it,’ which, I think, is the ultimate compliment for an author. Stories are above ideas.”
Harvard President Lawrence H. Summers, Sept. 12, 2004:
“You are entering a remarkable community, the Harvard community. It is a community built on the idea of searching for truth… on the idea of respect for others….
… we practice the values we venerate. The values of seeking truth, the values of respecting others….”
“… Hegel discusses ‘culture’ as the ‘world of self-alienated spirit.’ The idea seems to be that humans in society not only interact, but that they collectively create relatively enduring cultural products (stories, dramas, and so forth) within which they can recognise their own patterns of life reflected.”
The “phantasmagoria” of Didion seems related to the “phenomenology” of Hegel…
From Michael N. Forster, Hegel’s Idea of a Phenomenology of Spirit:
“This whole system is conceived, on one level at least, as a defense or rational reworking of the Christian conception of God. In particular, its three parts are an attempt to make sense of the Christian idea of a God who is three in one — the Logic depicting God as he is in himself, the Philosophy of Nature God the Son, and the Philosophy of Spirit God the Holy Spirit.”
and, indeed, to the phenomenology of narrative itself….
From Patrick Vert,
The Narrative of Acceleration:
“There are plenty of anecdotes to highlight the personal, phenomenological experience of railway passage…
… a unique study on phantasmagoria and the history of imagination. The word originates [in] light-projection, the so-called ghost-shows of the early 19th century….
… thought becomes a phantasmagorical process, a spectral, representative location for the personal imagination that had been marginalized by scientific rationalism….
Truly, ‘immediate experience is [or becomes] the phantasmagoria of the idler’ [Walter Benjamin, The Arcades Project. Cambridge: Harvard University Press, 1999. Page 801.]….
Thought as phantasm is a consequence of the Cartesian split, and… a further consequence to this is the broad take-over of perceptual faculty…. What better example than that of the American railway? As a case-study it offers explanation to the ‘phantasmagoria of the idler’….
This phantasmagoria became more mediated over time…. Perception became increasingly visually oriented…. As this occurred, a narrative formed to encapsulate the phenomenology of it all….”
For such a narrative, see
the Log24.net entries of
November 5, 2002, 2:56 AM,
November 5, 2002, 6:29 AM,
January 3, 2003, 11:59 PM,
August 17, 2004, 7:29 PM,
August 18, 2004, 2:18 AM,
August 18, 2004, 3:00 AM, and
November 24, 2004, 10:00 AM.
Sunday, September 5, 2004
Sunday September 5, 2004
Symmetry and Change
in the Dreamtime
Notes from the Journal
of Steven H. Cullinane
Summary:
| Aug 31 2004 07:31:01 PM |
Early Evening, Shining Star |
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| Sep 01 2004 09:00:35 AM |
Words and Images |
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| Sep 01 2004 12:07:28 PM |
Whale Rider |
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| Sep 02 2004 11:11:42 AM |
Heaven and Earth |
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| Sep 02 2004 07:00:23 PM |
Whale Road |
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| Cinderella’s Slipper |
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| Sep 03 2004 10:01:56 AM |
Another September Morn |
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| Noon |
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| De Nada |  |
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| Ite, Missa Est |  |
Symmetry and Change, Part 1…
Early Evening,
Shining Star
Hexagram 01
The Creative:
The Image
Heaven
Heaven
The movement of heaven
is full of power.
Click on picture
for details.
The Clare Lawler Prize
for Literature goes to…
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For the thoughts on time |
Symmetry and Change, Part 2…
Words and Images
Hexagram 35
Progress:
The Image
Fire
Earth
The sun rises over the earth.
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“Oh, my Lolita. I have only words “This is the best toy train set “As the quotes above by Nabokov and Welles suggest, we need to be able to account for the specific functions available to narrative in each medium, for the specific elements that empirical creators will ‘play with’ in crafting their narratives.” |
For
James Whale
and
William French Anderson —
Words
In the Spirit of
Dave Barry’s Book of Bad Songs:
Stay for just a while…
Stay, and let me look at you.
It’s been so long, I hardly knew you.
Standing in the door…
Stay with me a while.
I only want to talk to you.
We’ve traveled halfway ’round the world
To find ourselves again.
September morn…
We danced until the night
became a brand new day,
Two lovers playing scenes
from some romantic play.
September morning still can
make me feel this way.
Look at what you’ve done…
Why, you’ve become a grown-up girl…
— Neil Diamond
Images
In the Spirit of
September Morn:
The Last Day of Summer:
Photographs by Jock Sturges
“In 1990, the FBI entered Sturges’s studio and seized his work, claiming violation of child pornography laws.”
Related material:
and
Log24 entries of
Aug. 15, 2004.
Those interested in the political implications of Diamond’s songs may enjoy Neil Performs at Kerry Fundraiser.
I personally enjoyed this site’s description of Billy Crystal’s remarks, which included “a joke about former President Clinton’s forthcoming children’s
“Puff, puff, woo, woo, off we go!”
Symmetry and Change, Part 3…
Hexagram 28
Preponderance of
the Great:
The Image
Lake
Wind
The lake rises
above the trees.
“Congratulations to Clare Lawler, who participated very successfully in the recently held Secondary Schools Judo Championships in Wellington.”
For an explanation of this entry’s title, see the previous two entries and
Oxford Word
(Log24, July 10, 2004)
Symmetry and Change, Part 4…
Heaven and Earth
Hexagram 42
Increase:
The Image
Wind
Thunder
Wind and thunder:
the image of Increase.
“This time resembles that of
the marriage of heaven and earth”
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you gotta ride it like you find it.
Get your ticket at the station
of the Rock Island Line.
in Rock Island, Illinois
“What it all boiled down to really was everybody giving everybody else a hard time for no good reason whatever… You just couldn’t march to your own music. Nowadays, you couldn’t even hear it… It was lost, the music which each person had inside himself, and which put him in step with things as they should be.”
— The Grifters, Ch. 10, 1963, by
James Myers Thompson
“The Old Man’s still an artist
with a Thompson.”
— Terry in “Miller’s Crossing”
For some of “the music which
each person had inside,”
click on the picture
with the Thompson.
It may be that Kylie is,
in her own way, an artist…
with a 357:
(Hits counter at
The Quality of Diamond
as of 11:05 AM Sept. 2, 2004)
For more on
“the marriage of heaven and earth,”
see
Plato, Pegasus, and the Evening Star.
Symmetry and Change, Part 5…
Whale Road
Hexagram 23
Splitting Apart:
The Image
Mountain
Earth
The mountain rests
on the earth.
“… the plot is different but the monsters, names, and manner of speaking will ring a bell.”
— Frank Pinto, Jr., review of Seamus Heaney’s translation of Beowulf
Other recommended reading, found during a search for the implications of today’s previous entry, “Hexagram 42”:
This excellent meditation
on symmetry and change
comes from a site whose
home page
has the following image:
Symmetry and Change, Part 6…
Cinderella’s Slipper
Hexagram 54
The Marrying Maiden:
The Image
Thunder
Lake
See
“… a Thoreau-like retreat
by a nearby lake….
Both men have
a ‘touch of the poet’….
The symmetry is perfect.”
by a nearby lake….
Both men have
a ‘touch of the poet’….
The symmetry is perfect.”
Symmetry and Change, Part 7…
Another September Morn
Hexagram 56:
The Wanderer
The Image
Fire
Mountain
Fire on the mountain,
Run boys run…
Devil’s in the House of
The Rising Sun!
Friday, September 3, 2004
Symmetry and Change, Part 8…
Hexagram 25
Innocence:
The Image
Heaven
Thunder
Friday, September 3, 2004
Symmetry and Change, Part 9…
Hexagram 49
Revolution:
The Image
the image of Revolution.
“I sit now in a little room off the bar at four-thirty in the morning drinking ochas and then mescal and writing this on some Bella Vista notepaper I filched the other night…. But this is worst of all, to feel your soul dying. I wonder if it is because to-night my soul has really died that I feel at the moment something like peace. Or is it because right through hell there is a path, as Blake well knew, and though I may not take it, sometimes lately in dreams I have been able to see it? …And this is how I sometimes think of myself, as a great explorer who has discovered some extraordinary land from which he can never return to give his knowledge to the world: but the name of this land is hell. It is not Mexico of course but in the heart.”
— Malcolm Lowry, Under the Volcano
Friday, September 3, 2004
Symmetry and Change, conclusion…
Ite, Missa Est
Hexagram 13
Fellowship With Men:
The Image
Heaven
Fire
“A pretty girl —
is like a melody —- !”
For details, see
A Mass for Lucero.
Comments Off on Sunday September 5, 2004
Thursday, September 2, 2004
Thursday September 2, 2004
Symmetry and Change, Part 5…
Whale Road
Hexagram 23
Splitting Apart:
The Image
Mountain
Earth
The mountain rests
on the earth.
“… the plot is different but the monsters, names, and manner of speaking will ring a bell.”
— Frank Pinto, Jr., review of Seamus Heaney’s translation of Beowulf
Other recommended reading, found during a search for the implications of today’s previous entry, “Hexagram 42”:
This excellent meditation
on symmetry and change
comes from a site whose
home page
has the following image:
Comments Off on Thursday September 2, 2004
Sunday, August 15, 2004
Sunday August 15, 2004
The Line
Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Ch. 6 (italics are mine):
“A classical understanding sees the world primarily as underlying form itself. A romantic understanding sees it primarily in terms of immediate appearance.”
STRANGER – We are far from having exhausted the more exact thinkers who treat of being and not-being. But let us be content to leave them, and proceed to view those who speak less precisely; and we shall find as the result of all, that the nature of being is quite as difficult to comprehend as that of not-being.
THEAETETUS – Then now we will go to the others.
STRANGER – There appears to be a sort of war of Giants and Gods going on amongst them; they are fighting with one another about the nature of essence.
THEAETETUS – How is that?
STRANGER – Some of them are dragging down all things from heaven and from the unseen to earth, and they literally grasp in their hands rocks and oaks; of these they lay hold, and obstinately maintain, that the things only which can be touched or handled have being or essence, because they define being and body as one, and if any one else says that what is not a body exists they altogether despise him, and will hear of nothing but body.
THEAETETUS – I have often met with such men, and terrible fellows they are.
STRANGER – And that is the reason why their opponents cautiously defend themselves from above, out of an unseen world, mightily contending that true essence consists of certain intelligible and incorporeal ideas; the bodies of the materialists, which by them are maintained to be the very truth, they break up into little bits by their arguments, and affirm them to be, not essence, but generation and motion. Between the two armies, Theaetetus, there is always an endless conflict raging concerning these matters.
THEAETETUS – True.
— Translated by Benjamin Jowett
Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Ch. 18:
“The wave of crystallization rolled ahead. He was seeing two worlds, simultaneously. On the intellectual side, the square side, he saw now that Quality was a cleavage term. What every intellectual analyst looks for. You take your analytic knife, put the point directly on the term Quality and just tap, not hard, gently, and the whole world splits, cleaves, right in two…
hip and square, classic and romantic, technological and humanistic…and the split is clean. There’s no mess. No slop. No little items that could be one way or the other. Not just a skilled break but a very lucky break. Sometimes the best analysts, working with the most obvious lines of cleavage, can tap and get nothing but a pile of trash. And yet here was Quality; a tiny, almost unnoticeable fault line; a line of illogic in our concept of the universe; and you tapped it, and the whole universe came apart, so neatly it was almost unbelievable. He wished Kant were alive. Kant would have appreciated it. That master diamond cutter. He would see. Hold Quality undefined. That was the secret.”
What Pirsig means by “quality” is close to what Yagoda means, in the previous entry, by “style.”
Comments Off on Sunday August 15, 2004
Thursday, July 8, 2004
Thursday July 8, 2004
Bandito
12:25 PM July 8:
|
"Willst Du lieber
— Martin Cruz Smith, |
Personally, I prefer
a blue-green star:
Follow-up of
2 PM July 9, 2004 —
"Texas Bandito, how much money
did you put in your pocket today?"
John Mellencamp crooned
in a country ballad.
In a two-and-a-half hour gala
that raised $7.5 million,
a record for a single event,
Chevy Chase poked fun at
the president's pronunciation
of "nuclear"…
The concert brought 6,200 people,
paying $250 to $25,000 each…
beating the $6.8 million haul
from a parallel gala last month
in Los Angeles featuring
Barbra Streisand,
Willie Nelson,
and Billy Crystal.
The take will be split….
Here, Chevy, is another
way to pronounce "nuclear"–
The Source:
Click on picture for details.
Wednesday, March 10, 2004
Wednesday March 10, 2004
Split
The first idea was not our own. Adam
in Eden was the father of Descartes.— Wallace Stevens,
Notes Toward a Supreme FictionA very interesting web site at
Middle Tennessee State University
relates the Stevens quote
to two others:“The sundering we sense, between nature and culture, lies not like a canyon outside us but splits our being at its most intimate depths the way mind breaks off from body. It is still another version of that bitter bifurcation long ago decreed: our expulsion from Eden. It differs from the apparently similar Cartesian crease across things in the fact that the two halves of us once were one; that we did not always stand askance like molasses and madness–logically at odds–but grew apart over the years like those husbands and wives who draw themselves into different corners of contemplation.”
— William Gass,
“The Polemical Philosopher”“The experiment [to make rationality primary] reached the reductio ad absurdum following the attempt by Descartes to solve problems of human knowledge by giving ontological status to the dichotomy of thinking substance and extended substance, that is subject and object. Not only were God and man, sacred and secular, being and becoming, play and seriousness severed, but now also the subject which wished to unite these fragmented dichotomies was itself severed from that which it would attempt to reconcile.”
— David Miller, God and Games
“Which is it then? For Gass, the Cartesian schism is a post- lapsarian divorce-in progress, only apparently similar to the expulsion from paradise. For Stevens the fault is primordial and Descartes only its latter-day avatar. For Miller, Descartes is the historical culprit, the patriarch of the split.”
Comments Off on Wednesday March 10, 2004
Tuesday, March 2, 2004
Tuesday March 2, 2004
Passion
From the previous entry:
1.
Oscar:
military phonetic
for the letter
‘O’
From an entry of Dec. 21, 2002, some background in literary theory:
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“I know what ‘nothing’ means….” “How do you solve a problem like Maria?” “…problems can be solved by manipulating just two symbols, 1 and 0….” “The female and the male continue this charming dance, populating the world with all living beings.” “According to Showalter’s essay*, ‘In Elizabethan slang, ‘nothing’ was a term for the female genitalia . . . what lies between maids’ legs, for, in the male visual system of representation and desire…. Ophelia’s story becomes
the Story of O — the zero, the empty circle or mystery of feminine difference, the cipher of female sexuality to be deciphered by feminist interpretation.’ (222)* Ophelia is a highly sexual being…” — Leigh DiAngelo, *Showalter, Elaine. “Representing Ophelia: Women, Madness, and the Responsibilities of Feminist Criticism.” Hamlet. Ed. Susanne L. Wofford. Boston: Bedford Books of St.Martin’s Press, 1994. 220-238. |
At the Oscars Sunday night, a thought attributed by Billy Crystal to Sean Connery:
“Pussy Galore! I just got it! That’s vulgar.”
For further background, see
Passing the Crown (Aug. 24, 2003) and
The Agony and the Ya-Ya (Oct. 4, 2002).
Comments Off on Tuesday March 2, 2004
Wednesday, February 18, 2004
Wednesday February 18, 2004
Hard Core, Part II:
Star of Africa
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In memory of St. Katharine Hepburn,
who died on St. Peter’s Day, 2003:
“Although the greater saints
are more acceptable to God
than the lesser,
it is sometimes profitable
to pray to the lesser.”
— St. Thomas Aquinas
From The Times, UK, Feb. 18, 2004:
Straw denies
a big-three takeover
at EU summit
Britain’s Foreign Secretary “said that there were no plans to set up a small body within the EU to take control of its affairs.
However, he told a news conference at the Foreign Office that it made sense for the three biggest economies to work ‘collaboratively’ on matters of common interest….
At tonight’s summit Mr Blair, Gerhard Schröder, the German Chancellor, and President Chirac of France will discuss initiatives to co-ordinate and strengthen the EU’s industrial policy….
German commentators regard the summit as a sea-change in British policy towards Europe — a signal that London’s main aim is no longer to split Paris and Berlin.”
Wednesday, September 10, 2003
Wednesday September 10, 2003
4:04:08
The title refers to my entry of last April 4,
and to the time of this entry.
From D. H. Lawrence and the Dialogical Principle:
“Plato’s Dialogues…are queer little novels….[I]t was the greatest pity in the world, when philosophy and fiction got split. They used to be one, right from the days of myth. Then they went and parted, like a nagging married couple, with Aristotle and Thomas Aquinas and that beastly Kant. So the novel went sloppy, and philosophy went abstract-dry. The two should come together again, in the novel.”
— pp. 154-5 in D. H. Lawrence, “The Future of the Novel,” in Study of Thomas Hardy and Other Essays. Ed. Bruce Steele. Cambridge: Cambridge University Press,1983. 149-55.
“The wild, brilliant, alert head of St. Mawr seemed to look at her out of another world… the large, brilliant eyes of that horse looked at her with demonish question…. ‘Meet him half way,’ Lewis [the groom] said. But halfway across from our human world to that terrific equine twilight was not a small step.”
— pp. 30, 35 in D. H. Lawrence, “St. Mawr.” 1925. St. Mawr and Other Stories. Ed. Brian Finney. Cambridge: Cambridge University Press, 1983.
See also
Plato, Pegasus, and the Evening Star.
Katherine Neville’s novel The Eight, referred to in my note of April 4, is an excellent example of how not to combine philosophy with fiction. Lest this be thought too harsh, let me say that the New Testament offers a similarly ludicrous mixture.
On the other hand, there do exist successful combinations of philosophy with fiction… For example, The Glass Bead Game, Zen and The Art of Motorcycle Maintenance, Under the Volcano, the novels of Charles Williams, and the C. S. Lewis classic That Hideous Strength.
This entry was prompted by the appearance of the god Pan in my entry on this date last year, by Hugh Grant’s comedic encounters with Pan in “Sirens,” by Lawrence’s remarks on Pan in “St. Mawr,” and by the classic film “Picnic at Hanging Rock.”
Tuesday, January 21, 2003
Tuesday January 21, 2003
Diablo Ballet
Thanks to Meghan for the following:
not going, not coming,
rooted, deep and still
not reaching out, not reaching in
just resting, at the center
a single jewel, the flawless crystal drop
in the blaze of its brilliance
the way beyond.
— Shih Te (c. 730)
It turns out that Shih Te ("Foundling") was the sidekick of Han Shan ("Cold Mountain"). Here are some relevant links:
Thoughts of Robert Frost (see past two days' entries) lead to "Two Tramps in Mud Time," which in turn leads to Jack Kerouac and Gary Snyder splitting wood in The Dharma Bums.
This in turn leads, via a search on "Kerouac" and "axe," to the sentence
"There's the grace of an axe handle
as good as an Eglevsky ballet,"
in Big Sur.
Kerouac taught me when I was 16 and he is still teaching me now that I am 60.
Searching for "Eglevsky ballet" leads to this site on André Eglevsky, his work, his life, and his children. A further search leads to his daughter Marina Eglevsky, who stages dance for the Diablo Ballet.
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Marina Eglevsky and |
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Those who feel the above is too "arty" for them may nevertheless appreciate the movie by the same name: "Born to Dance" (1936), starring Eleanor Powell and James Stewart.
In the larger metaphorical sense, of course, Powell and Eglevsky are both part of the same dance… at the "still point" described so well by Shih Te.
"just resting, at the center
a single jewel…"
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"At the still point, |
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From Marshall's Jewelers, Tucson — The ideal cut is a mathematical formula for cutting diamonds to precise angles and proportions to maximize the reflection and refraction of light. In addition to these ideal proportions, the polish and symmetry of the diamond is done to the highest standards also. Only then does it qualify to receive the American Gem Society (AGS) "triple zero" rating. A "zero" rating is the most perfect rating that the AGS gives evaluating the cut, polish, and symmetry of the diamond. When a diamond receives the "zero" rating for each of these areas, (cut, polish, and symmetry), it gets three "zeros," hence the "triple zero" rating. Because of this attention to detail, it takes up to four times longer to cut a diamond to these standards than an "average" diamond. You may choose to compromise on color or clarity but to ensure the most brilliant diamond you should not compromise on cut…. The "triple zero" ideal cut guarantees you a magnificent balance of brilliance, sparkle, and fire. |
Postscript of 1/25/03:
See also the obituary of Irene Diamond, ballet patron, for whom the New York City Ballet's "Diamond Project" is named. Diamond died on January 21, 2003, the date of the above weblog entry.
Friday, December 6, 2002
Friday December 6, 2002
Great Simplicity
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is the day that Daisetsu Suzuki attained satori,
according to the Zen Calendar. “Daisetsu” is
said to mean “Great Simplicity.”
For those who prefer Harry Potter and
Diagon Alley, here is another calendar:
To Have and Have Not
Those who prefer traditional Western religions may like a site on the Trinity that contains this:
“Zen metaphysics is perhaps most succinctly set forth in the words ‘not-two.” But even when he uses this expression, Suzuki is quick to assert that it implies no monism. Not-two, it is claimed, is not the same as one.* But when Suzuki discusses the relationship of Zen with Western mysticism, it is more difficult to escape the obvious monistic implications of his thinking. Consider the following:
We are possessed of the habit of looking at Reality by dividing it into two… It is all due to the human habit of splitting one solid Reality into two, and the result is that my ‘have’ is no ‘have’ and my ‘have not’ is no ‘have not.’ While we are actually passing, we insist that the gap is impassable.**”
*See: Daisetz T. Suzuki, ‘Basic Thoughts Underlying Eastern Ethical and Social Practice’ in Philosophy and Culture — East and West: East-West Philosophy in Practical Perspective, ed. Charles A. Moore (Honolulu: University of Hawaii Press, 1968), p. 429
** Daisetsu Teitaro Suzuki, Mysticism Christian and Buddhist (London: George Allen & Unwin, 1957, Unwin paperback, 1979), p. 57.
Personally, I am reminded by Suzuki’s satori on this date that today is the eve of the anniversary of Pearl Harbor. I am also reminded by the rather intolerant tract on the Trinity quoted above that the first atomic bomb was exploded in the New Mexico desert at a test site named Trinity. Of course, sometimes intolerance is justified.
Concluding unscientific postscript:
On the same day in 1896 that D. T. Suzuki attained satori,
lyricist Ira Gershwin was born.
Dies irae, dies illa.
Comments Off on Friday December 6, 2002
Monday, November 25, 2002
Monday November 25, 2002
ART WARS
Driving the Point Home
From
SUSAN WEIL
From Finnegans Wake,
by James Joyce, p. 293:
The Vesica Piscis,
also known as
The Ya-Ya:
See also the
Geometries of Creation
art exhibit at the University of Waterloo.
Sunday, September 15, 2002
Sunday September 15, 2002
Evariste Galois and
The Rock That Changed Things
An article in the current New York Review of Books (dated Sept. 26) on Ursula K. Le Guin prompted me to search the Web this evening for information on a short story of hers I remembered liking. I found the following in the journal of mathematician Peter Berman:
- A Fisherman of the Inland Sea, Ursula K. Le Guin, 1994:
A book of short stories. Good, entertaining. I especially liked “The Rock That Changed Things.” This story is set in a highly stratified society, one split between elite and enslaved populations. In this community, the most important art form is a type of mosaic made from rocks, whose patterns are read and interpreted by scholars from the elite group. The main character is a slave woman who discovers new patterns in the mosaics. The story is slightly over-the-top but elegant all the same.
I agree that the story is elegant (from a mathematician, a high compliment), so searched Berman’s pages further, finding this:
between The French Mathematician (a novel about Galois) and Harry Potter and the Sorcerer’s Stone.
My own version of the Philosopher’s Stone (the phrase used instead of “Sorcerer’s Stone” in the British editions of Harry Potter) appears in my profile picture at top left; see also the picture of Plato’s diamond figure in my main math website. The mathematics of finite (or “Galois”) fields plays a role in the underlying theory of this figure’s hidden symmetries. Since the perception of color plays a large role in the Le Guin story and since my version of Plato’s diamond is obtained by coloring Plato’s version, this particular “rock that changes things” might, I hope, inspire Berman to extend his table to include Le Guin’s tale as well.
Even the mosaic theme is appropriate, this being the holiest of the Mosaic holy days.
Dr. Berman, G’mar Chatimah Tova.