Log24

Friday, March 23, 2018

From the Personal to the Platonic

Filed under: General,Geometry — Tags: , , — m759 @ 11:01 am

On the Oslo artist Josefine Lyche —

"Josefine has taken me through beautiful stories,
ranging from the personal to the platonic
explaining the extensive use of geometry in her art.
I now know that she bursts into laughter when reading
Dostoyevsky, and that she has a weird connection
with a retired mathematician."

Ann Cathrin Andersen
    http://bryggmagasin.no/2017/behind-the-glitter/

Personal —

The Rushkoff Logo

— From a 2016 graphic novel by Douglas Rushkoff.

See also Rushkoff and Talisman in this journal.

Platonic —

The Diamond Cube.

Compare and contrast the shifting hexagon logo in the Rushkoff novel above 
with the hexagon-inside-a-cube in my "Diamonds and Whirls" note (1984).

Friday, January 5, 2018

Subway Art for Plato’s Ghost

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

Suggested by the previous post

See also the post Plato's Ghost of March 3, 2010.

Tuesday, September 17, 2024

Geometry for Jews:
“Kickin’ Down the Cobblestones…” — Song lyric

Filed under: General — Tags: — m759 @ 2:58 am

Kirkenes at newyorker.com

Some less stressful material . . .

"a medley cobbled together" —

Wednesday, July 31, 2024

My Links — Steven H. Cullinane

Filed under: — m759 @ 4:14 pm

Main webpage of record . . .

Encyclopedia of Mathematics  https://encyclopediaofmath.org/wiki/Cullinane_diamond_theorem

Supplementary PDF from Jan. 6, 2006  https://encyclopediaofmath.org/images/3/37/Dtheorem.pdf

Originally published in paper version . . .

Computer Graphics and Art, 1978  http://finitegeometry.org/sc/gen/Diamond_Theory_Article.pdf
AMS abstract, 1979: "Symmetry Invariance in a Diamond Ring"  https://www.cullinane.design/
American Mathematical Monthly, 1984 and 1985: "Triangles Are Square"  http://finitegeometry.org/sc/16/trisquare.html

Personal sites . . .

Primary —

Personal journal   http://m759.net/wordpress/
Mathematics website  http://finitegeometry.org/sc/
Mathematics Images Gallery  http://m759.net/piwigo/index.php?/category/2

Secondary —

Portfoliobox   https://cullinane.pb.design/
Substack   https://stevenhcullinane.substack.com/  
Symmetry Summary   https://shc759.wordpress.com
Diamond Theory Cover Structure  https://shc7596.wixsite.com/website

SOCIAL:

Pinterest   https://www.pinterest.com/stevenhcullinane/ (many mathematics notes)
Flickr  https://www.flickr.com/photos/m759/ (backup account for images of mathematics notes)
Instagram   https://www.instagram.com/stevencullinane
TikTok   https://www.tiktok.com/@stevenhcullinane
X.com   https://x.com/shc759

OTHER:

Replit viewer/download  https://replit.com/@m759/View-4x4x4?v=1
SourceForge download  https://sourceforge.net/projects/finitegeometry/
Academia.edu   https://stevenhcullinane.academia.edu/ GitHub    https://github.com/m759 (finite geometry site download)
Internet Archive: Notes on Groups and Geometry   https://archive.org/details/NotesOnGroupsAndGeometry1978-1986/mode/2up         

Cited at  . . .

The Diamond Theorem and Truchet Tiles   http://www.log24.com/log22/220429-Basque-DT-1.pdf 
April 2024 UNION article in Spanish featuring the diamond theorem  https://union.fespm.es/index.php/UNION/article/view/1608/1214
April 2024 UNION article in English  http://log24.com/notes/240923-Ibanez-Torres-on-diamond-theorem-Union-April-2024-in-English.pdf
Cullinane in a 2020 Royal Holloway Ph.D. thesis   https://pure.royalholloway.ac.uk/ws/portalfiles/portal/40176912/2020thomsonkphd.pdf         
Squares, Chevrons, Pinwheels, and Bach   https://www.yumpu.com/en/document/read/36444818/fugue-no-21-elements-of-finite-geometry      
Observables  programmed presentation of diamond theorem  https://observablehq.com/@radames/diamond-theory-symmetry-in-binary-spaces
Josefine Lyche — Plato's Diamond  https://web.archive.org/web/20240222064628/http://www.josefinelyche.com/index.php?/selected-exhibitions/platos-diamond/
Josefine Lyche — Diamond Theorem  https://web.archive.org/web/20230921122049/http://josefinelyche.com/index.php?/selected-exhibitions/uten-ramme-nye-rom/

Professional sites . . .

Association for Computing Machinery   https://member.acm.org/~scullinane
bio.site/cullinane … maintenance at https://biosites.com
ORCID bio page   https://orcid.org/0000-0003-1135-419X
Google Scholar   https://scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=NcjmFwQAAAAJ&sortby=pubdate

Academic repositories:

Harvard Dataverse   https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/KHMMVH
Harvard DASH article on PG(3,2)   https://dash.harvard.edu/handle/1/37373777 

Zenodo website download  https://zenodo.org/records/1038121
Zenodo research notes  https://zenodo.org/search?q=metadata.creators.person_or_org.name%3A%22Cullinane%2C%20Steven%20H.%22&l=list&p=1&s=10&sort=bestmatch

Figurate Geometry at Open Science Framework (OSF)   https://osf.io/47fkd/

arXiv: "The Diamond Theorem"  https://arxiv.org/abs/1308.1075

Monday, October 3, 2022

The Abstract and the Concrete

Filed under: General — Tags: — m759 @ 9:42 am

Counting symmetries with the orbit-stabilizer theorem

The above art by Steven H. Cullinane is not unrelated to
art by Josefine Lyche. Her work includes sculpted replicas
of the above abstract  Platonic solids, as well as replicas of
my own work related to properties of the 4×6 rectangle above.
Symmetries of both the solids and the rectangle may be
viewed as permutations of  parts — In the Platonic solids,
the parts are permuted by continuous  rotations of space itself.
In the rectangle, the parts are permuted by non-continuous 
transformations, as in the I Ching . . . i.e., by concrete  illustrations
of change.

Friday, January 11, 2019

Permutations at Oslo

Filed under: General — Tags: , , — m759 @ 8:45 pm

Webpage at Oslo of Josefine Lyche, 'Plato's Diamond'

See also yesterday’s  Archimedes at Hiroshima  and the
above 24 graphic permutations on  All Souls’ Day 2010.

For some backstory, see Narrative Line (November 10, 2014).

Monday, June 11, 2018

Glitter

Filed under: General,Geometry — Tags: — m759 @ 8:32 pm

A Scientific American  headline today —

Glittering Diamond Dust in Space
Might Solve a 20-Year-Old Mystery

Related art —

"Never underestimate the power of glitter."

Glitter by Josefine Lyche, as of diamond dust

Background:  "Diamond Dust" + Glitter in this journal.

Friday, April 29, 2016

Blackboard Jungle…

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

Continues .

An older and wiser James Spader —

"Never underestimate the power of glitter."

Glitter by Josefine Lyche, as of diamond dust

Tuesday, April 26, 2016

Interacting

Filed under: General,Geometry — Tags: — m759 @ 8:31 pm

"… I would drop the keystone into my arch …."

— Charles Sanders Peirce, "On Phenomenology"

" 'But which is the stone that supports the bridge?' Kublai Khan asks."

— Italo Calvino, Invisible Cities, as quoted by B. Elan Dresher.

(B. Elan Dresher. Nordlyd  41.2 (2014): 165-181,
special issue on Features edited by Martin Krämer,
Sandra Ronai and Peter Svenonius. University of Tromsø –
The Arctic University of Norway.
http://septentrio.uit.no/index.php/nordlyd)

Peter Svenonius and Martin Krämer, introduction to the
Nordlyd  double issue on Features —

"Interacting with these questions about the 'geometric' 
relations among features is the algebraic structure
of the features."

For another such interaction, see the previous post.

This  post may be viewed as a commentary on a remark in Wikipedia

"All of these ideas speak to the crux of Plato's Problem…."

See also The Diamond Theorem at Tromsø and Mere Geometry.

Tuesday, October 1, 2013

Frame Tale

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

From an academic's website:

IMAGE- Remarks by Paul Hertz, alias Ignotus the Mage

For Josefine Lyche and Ignotus the Mage,
as well as Rose the Hat and other Zingari shoolerim —

Sabbatha hanti, lodsam hanti, cahanna risone hanti :
words that had been old when the True Knot moved
across Europe in wagons, selling peat turves and trinkets.
They had probably been old when Babylon was young.
The girl was powerful, but the True was all-powerful,
and Rose anticipated no real problem.

— King, Stephen (2013-09-24).
     Doctor Sleep: A Novel
     (pp. 278-279). Scribner. Kindle Edition. 

From a post of November 10, 2008:

Twenty-four Variations on a Theme of Plato

Twenty-four Variations on a Theme of Plato,
a version by Barry Sharples based on the earlier
kaleidoscope puzzle  version of Steven H. Cullinane

The King and the Corpse  —

"The king asked, in compensation for his toils
during this strangest of all the nights he had
ever known, that the twenty-four riddle tales
told him by the specter, together with the story
of the night itself, should be made known
over the whole earth and remain eternally
famous among men."

Frame Tale: 

Finnegans Wake  —

"The quad gospellers may own the targum
but any of the Zingari shoolerim may pick a peck
of kindlings yet from the sack of auld hensyne."

Monday, September 30, 2013

A Line for Frank

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

(Continued from High White Noon
Finishing Up at Noon, and A New York Jew.)

http://www.log24.com/log/pix10B/101008-StartingOut.jpg

Above: Frank Langella in "Starting Out in the Evening"

Below: Frank Langella and Johnny Depp in "The Ninth Gate"

"Not by the hair on your chinny-chin-chin."

IMAGE- Author's shirt with a Dharma Logo from 'Lost'

Above: Detail from a Wikipedia photo.

For the logo, see Lostpedia.

For some backstory, see Noether.

Those seeking an escape from the eightfold nightmare
represented by the Dharma logo above may consult
the remarks of Heisenberg (the real one, not the
Breaking Bad  version) to the Bavarian Academy
of Fine Arts.

Those who prefer Plato's cave to his geometry are
free to continue their Morphean adventures.

Monday, September 9, 2013

Viking Book

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

For the late Billy Wilder, director of Ace in the Hole  (1951)

IMAGE- Book by Halvor Bodin on the art of Josefine Lyche and others. See halvorbodin.com.

Click image for a larger version.

See, too, this morning's quarter-to-three post, and The Vikings  (1958)—

The art by Josefine Lyche in the Bodin book shown 
above is, as the artist notes, based on my own work.

Tuesday, July 9, 2013

Vril Chick

Filed under: General,Geometry — Tags: , , — m759 @ 4:30 am

Profile picture of "Jo Lyxe" (Josefine Lyche) at Vimeo

Profile picture for "Jo Lyxe" (Josefine Lyche) at Vimeo

Compare to an image of Vril muse Maria Orsitsch.

From the catalog of a current art exhibition
(25 May – 31 August, 2013) in Norway,
I DE LANGE NÆTTER —

Josefine Lyche
Born in 1973 in Bergen, Norway.
Lives and works in Oslo and Berlin.

Keywords (to help place my artwork in the
proper context): Aliens, affine geometry, affine
planes, affine spaces, automorphisms, binary
codes, block designs, classical groups, codes,
coding theory, collineations, combinatorial,
combinatorics, conjugacy classes, the Conwell
correspondence, correlations, Cullinane,
R. T. Curtis, design theory, the diamond theorem,
diamond theory, duads, duality, error correcting
codes, esoteric, exceptional groups,
extraterrestrials, finite fields, finite geometry, finite
groups, finite rings, Galois fields, generalized
quadrangles, generators, geometry, GF(2),
GF(4), the (24,12) Golay code, group actions,
group theory, Hadamard matrices, hypercube,
hyperplanes, hyperspace, incidence structures,
invariance, Karnaugh maps, Kirkman’s schoolgirls
problem, Latin squares, Leech lattice, linear
groups, linear spaces, linear transformations,
Magick, Mathieu groups, matrix theory, Meno,
Miracle Octad Generator, MOG, multiply transitive
groups, occultism, octahedron, the octahedral
group, Orsic, orthogonal arrays, outer automorphisms,
parallelisms, partial geometries,
permutation groups, PG(3,2), Plato, Platonic
solids, polarities, Polya-Burnside theorem, projective
geometry, projective planes, projective
spaces, projectivities, Pythagoras, reincarnation,
Reed-Muller codes, the relativity problem,
reverse engineering, sacred geometry, Singer
cycle, skew lines, Socrates, sporadic simple
groups, Steiner systems, Sylvester, symmetric,
symmetry, symplectic, synthemes, synthematic,
Theosophical Society tesseract, Tessla, transvections,
Venn diagrams, Vril society, Walsh
functions, Witt designs.

(See also the original catalog page.)

Clearly most of this (the non-highlighted parts) was taken
from my webpage Diamond Theory. I suppose I should be
flattered, but I am not thrilled to be associated with the
(apparently fictional) Vril Society.

For some background, see (for instance) 
Conspiracy Theories and Secret Societies for Dummies .

Friday, June 22, 2012

Bowling in Diagon Alley

Filed under: General,Geometry — Tags: , — m759 @ 8:28 am

IMAGE- Josefine Lyche bowling, from her Facebook page

Josefine Lyche bowling (Facebook, June 12, 2012)

"Where Does Math Come From?"

A professor of philosophy in 1984 on Socrates's geometric proof in Plato's Meno  dialogue—

"These recondite issues matter because theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling…."

— Ian Hacking in The New York Review of Books , Feb. 16, 1984

The same professor introducing a new edition of Kuhn's Structure of Scientific Revolutions

"Paradigms Regained" (Los Angeles Review of Books , April 18, 2012)—

"That is the structure of scientific revolutions: normal science with a paradigm and a dedication to solving puzzles; followed by serious anomalies, which lead to a crisis; and finally resolution of the crisis by a new paradigm. Another famous word does not occur in the section titles: incommensurability. This is the idea that, in the course of a revolution and paradigm shift, the new ideas and assertions cannot be strictly compared to the old ones."

The Meno  proof involves inscribing diagonals  in squares. It is therefore related, albeit indirectly, to the classic Greek discovery that the diagonals of a square are incommensurable  with its sides. Hence the following discussion of incommensurability seems relevant.

IMAGE- Von Fritz in 1945 on incommensurability and the tetractys (10 as a triangular number)

See also von Fritz and incommensurability in The New York Times  (March 8, 2011).

For mathematical remarks related to the 10-dot triangular array of von Fritz, diagonals, and bowling, see this  journal on Nov. 8, 2011— "Stoned."

Monday, May 21, 2012

Child’s Play (continued*)

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

You and I …

we are just like a couple of tots…

Sinatra

JOSEFINE LYCHE

Born 1973 in Bergen. Lives and works in Oslo.

Education

2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen

University of Bergen—

 It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’:

What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d).

The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary.

It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.

— Cameron McEwen, "The Digital Wittgenstein,"
    The Wittgenstein Archives at the University of Bergen

* See that phrase in this journal.

Thursday, August 4, 2011

Midnight in Oslo

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

For Norway's Niels Henrik Abel (1802-1829)
on his birthday, August Fifth

(6 PM Aug. 4, Eastern Time, is 12 AM Aug. 5 in Oslo.)

http://www.log24.com/log/pix11B/110804-Pesic-PlatosDiamond.jpg

Plato's Diamond

The above version by Peter Pesic is from Chapter I of his book Abel's Proof , titled "The Scandal of the Irrational." Plato's diamond also occurs in a much later mathematical story that might be called "The Scandal of the Noncontinuous." The story—

Paradigms

"These passages suggest that the Form is a character or set of characters common to a number of things, i.e. the feature in reality which corresponds to a general word. But Plato also uses language which suggests not only that the forms exist separately (χωριστά ) from all the particulars, but also that each form is a peculiarly accurate or good particular of its own kind, i.e. the standard particular of the kind in question or the model (παράδειγμα ) [i.e. paradigm ] to which other particulars approximate….

… Both in the Republic  and in the Sophist  there is a strong suggestion that correct thinking is following out the connexions between Forms. The model is mathematical thinking, e.g. the proof given in the Meno  that the square on the diagonal is double the original square in area."

– William and Martha Kneale, The Development of Logic , Oxford University Press paperback, 1985

Plato's paradigm in the Meno

http://www.log24.com/log/pix11/110217-MenoFigure16bmp.bmp

Changed paradigm in the diamond theorem (2×2 case) —

http://www.log24.com/log/pix11/110217-MenoFigureColored16bmp.bmp

Aspects of the paradigm change—

Monochrome figures to
   colored figures

Areas to
   transformations

Continuous transformations to
   non-continuous transformations

Euclidean geometry to
   finite geometry

Euclidean quantities to
   finite fields

The 24 patterns resulting from the paradigm change—

http://www.log24.com/log/pix11B/110805-The24.jpg

Each pattern has some ordinary or color-interchange symmetry.

This is the 2×2 case of a more general result. The patterns become more interesting in the 4×4 case. For their relationship to finite geometry and finite fields, see the diamond theorem.

Related material: Plato's Diamond by Oslo artist Josefine Lyche.

Plato’s Ghost  evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost….”

— Princeton University Press on Plato’s Ghost: The Modernist Transformation of Mathematics  (by Jeremy Gray, September 2008)

"Remember me to her."

— Closing words of the Algis Budrys novel Rogue Moon .

Background— Some posts in this journal related to Abel or to random thoughts from his birthday.

Friday, March 11, 2011

Now Lens

Filed under: General — m759 @ 10:00 am

A Story in Pictures

Errol Morris in The New York Times  on March 9

"If everything is incommensurable, then everything is seen through the lens of the present, the lens of now ."

"Borges concluded by quoting Chesterton, 'there is nothing more frightening than a labyrinth that has no center.' [72]"

Now Lens

http://www.log24.com/log/pix11/110311-NowLens.jpg

Uncertified Copy

http://www.log24.com/log/pix11/110311-UncertifiedCopy.jpg

Del Toro

http://www.log24.com/log/pix11/110311-delToro.jpg

Plato's Diamond

http://www.log24.com/log/pix11/110311-LychePlatosDiamond256w.jpg

Portrait of an Artist

http://www.log24.com/log/pix11/110311-JosefineLyche.jpg

Meanwhile, back at the Times

http://www.log24.com/log/pix11/110311-CertifiedCopy.jpg

Thursday, July 15, 2010

Brightness at Noon, continued

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

"What exactly was Point Omega?"

This is Robert Wright in Nonzero: The Logic of Human Destiny.

Wright is discussing not the novel Point Omega  by Don DeLillo,
but rather a (related) concept of  the Jesuit philosopher Pierre Teilhard de Chardin.

My own idiosyncratic version of a personal "point omega"—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

For some other sorts of points, see the drawings
on the wall and Geometry Simplified

Image-- The trivial two-point affine space and the trivial one-point projective space, visualized

The two points of the trivial affine space are represented by squares,
and the one point of the trivial projective space is represented by
a line segment separating the affine-space squares.

For related darkness  at noon, see Derrida on différance
as a version of Plato's khôra

(Click to enlarge.)

Image-- Fordham University Press on Derrida, differance, and khora

The above excerpts are from a work on and by Derrida
published in 1997 by Fordham University,
a Jesuit institutionDeconstruction in a Nutshell

Image-- A Catholic view of Derrida

For an alternative to the Villanova view of Derrida,
see Angels in the Architecture.

Saturday, May 22, 2010

Art Space

Filed under: General,Geometry — Tags: , — m759 @ 2:02 am

From an interview with artist Josefine Lyche (see previous post) dated March 11, 2009—

Can you name a writer or book, fiction or theory that has inspired your works?
– Right now I am reading David Foster Wallace, which is great and inspiring. Others would be Aleister Crowley, Terence McKenna, James Joyce, J.L Borges, J.D Ballard, Stanislaw Lem, C. S. Lewis and Plato to mention some. Books, both fiction and theory are a great part of my life and work.

This journal on the date of the interview had a post about a NY Times  story, Paris | A Show About Nothing."

Related images—

 

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Space: what you damn well have to see.
– James Joyce, Ulysses

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