“Diamond Theorem” Harvard « Search Results

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

Comments Off

Saturday, March 2, 2024

Wonder Box

Filed under: General — Tags: Delving, Frame Tale, Hillbilly Geometry — m759 @ 12:42 am

"Wundermärchen – the original German word for fairytale –
literally translates to ‘wonder tale’."

— Abigail Tulenko. a PhD student in philosophy at Harvard University,
at Aeon on Feb. 26, 2024.

Another example of abstract art . . .

"The discovery of the Cullinane Diamond Theorem is a testament
to the power of mathematical abstraction and its ability to reveal
deep connections and symmetries in seemingly simple structures."

— Bing Chat with GPT-4 on November 16, 2023.

Comments Off

Thursday, March 25, 2021

A Day at the Museum

Filed under: General — Tags: A Night at the Museum — m759 @ 1:51 pm

Context for the Cullinane diamond theorem in
the Smithsonian’s NASA Astrophysics Data System:

Comments Off

Friday, April 7, 2017

Personal Identity

Filed under: General,Geometry — Tags: Four Dots, Is and As — m759 @ 2:40 pm

From "The Most Notorious Section Phrases," by Sophie G. Garrett
in The Harvard Crimson on April 5, 2017 —

This passage reminds me of (insert impressive philosophy
that was not in the reading).

This student is just being a show off. We get that they are smart
and well read. Congrats, but please don’t make the rest of the us
look bad in comparison. It should be enough to do the assigned
reading without making connections to Hume’s theory of the self.

Hume on personal identity (the "self") —

For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception. When my perceptions are removed for any time, as by sound sleep, so long am I insensible of myself, and may truly be said not to exist. And were all my perceptions removed by death, and could I neither think, nor feel, nor see, nor love, nor hate, after the dissolution of my body, I should be entirely annihilated, nor do I conceive what is further requisite to make me a perfect nonentity.
^{. . . .}

I may venture to affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. Our eyes cannot turn in their sockets without varying our perceptions. Our thought is still more variable than our sight; and all our other senses and faculties contribute to this change: nor is there any single power of the soul, which remains unalterably the same, perhaps for one moment. The mind is a kind of theatre, where several perceptions successively make their appearance; pass, repass, glide away, and mingle in an infinite variety of postures and situations. There is properly no simplicity in it at one time, nor identity in different, whatever natural propension we may have to imagine that simplicity and identity. The comparison of the theatre must not mislead us. They are the successive perceptions only, that constitute the mind; nor have we the most distant notion of the place where these scenes are represented, or of the materials of which it is composed.

Related material —
Imago Dei in this journal.

Backstory —
The previous post
and The Crimson Abyss.

Comments Off

Thursday, March 2, 2017

Raiders of the Lost Crucible Continues

Filed under: General — m759 @ 9:59 pm

Mariner Books paperback, 2005

See, too, this evening's A Common Space
and earlier posts on Raiders of the Lost Crucible.

Also not without relevance —

The death of the photographer who took
the above cover photo
A Hate Speech for Harvard
A recent University of Bradford thesis —

Comments Off

Tuesday, September 9, 2014

Smoke and Mirrors

Filed under: General,Geometry — Tags: Class of 64, Elegantly Packaged, on140909, Rosenhain and Göpel — m759 @ 11:00 am

This post is continued from a March 12, 2013, post titled
"Smoke and Mirrors" on art in Tromsø, Norway, and from
a June 22, 2014, post on the nineteenth-century
mathematicians Rosenhain and Göpel.

The latter day was the day of death for
mathematician Loren D. Olson, Harvard '64.

For some background on that June 22 post, see the tag
Rosenhain and Göpel in this journal.

Some background on Olson, who taught at the
University of Tromsø, from the American Mathematical
Society yesterday:

Olson died not long after attending the 50th reunion of the
Harvard Class of 1964.

For another connection between that class (also my own)
and Tromsø, see posts tagged "Elegantly Packaged."
This phrase was taken from today's (print)
New York Times review of a new play titled "Smoke."
The phrase refers here to the following "package" for
some mathematical objects that were named after
Rosenhain and Göpel — a 4×4 array —

For the way these objects were packaged within the array
in 1905 by British mathematician R. W. H. T. Hudson, see
a page at finitegometry.org/sc. For the connection to the art
in Tromsø mentioned above, see the diamond theorem.

Comments Off

Saturday, March 15, 2014

Language Game

Filed under: General — Tags: Red to Green — m759 @ 3:00 pm

Cullinane = Cullinan + e

Greene = Green + e

Comments Off

Tuesday, June 25, 2013

Lexicon (continued)

Filed under: General,Geometry — m759 @ 7:20 pm

Online biography of author Cormac McCarthy—

"… he left America on the liner Sylvania, intending to visit
the home of his Irish ancestors (a King Cormac McCarthy
built Blarney Castle)."

Two Years Ago:

Blarney in The Harvard Crimson—

Melissa C. Wong, illustration for "Atlas to the Text,"
by Nicholas T. Rinehart:

Thirty Years Ago:

Non-Blarney from a rural outpost—

Illustration for the generalized diamond theorem,
by Steven H. Cullinane:

See also Barry's Lexicon .

Comments Off

Tuesday, February 19, 2013

Configurations

Filed under: General,Geometry — Tags: Fields, Spinning in Infinity, Springer — m759 @ 12:24 pm

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

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

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

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

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

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

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

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

Comments Off

Friday, March 4, 2011

Oh, When the Saints…

Filed under: General — Tags: Columns — m759 @ 7:59 am

In memory of John Miner —

March First —

Saturday, January 30, 2010

Metamorphosis and Metaphor

Filed under: General,Geometry — m759 @ 12:31 pm

"Animation tends to be a condensed art form, using metamorphosis and metaphor to collide and expand meaning. In this way it resembles poetry."

— Harvard's Carpenter Center for the Visual Arts,
description of an exhibition–

FRAME BY FRAME: ANIMATED AT HARVARD

January 28–Feb 14, 2010

For example–

Animation — The Animated Diamond Theorem,
now shown frame by frame for selected frames

Poetry–

Part I — "That Nature is a Heraclitean Fire…."

Part II — Metaphor on the covers of a Salinger book–

Click image for details.

For other thoughts on
metamorphosis and metaphor,
see Endgame.

Comments Off

Saturday, December 5, 2009

Holiday Book

Filed under: General,Geometry — Tags: Aion Art — m759 @ 10:00 pm

Time and Chance, continued…

NY Lottery numbers today–
Midday 401, Evening 717

_________________________________________________

From this journal on 4/01, 2009:

The Cruelest Month

Fictional Harvard professor of symbology Robert Langdon, as portrayed by Tom Hanks

"Langdon sensed she was
toying with him…."

— Dan Brown

___________________________________________

From this journal on 7/17, 2008:

Jung’s four-diamond figure from
Aion — a symbol of the self –

Jung's four-diamond figure showing transformations of the self as Imago Dei

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….”

For related dynamic movements,
see the Diamond 16 Puzzle
and the diamond theorem.

______________________________________________

A piece related to both of the above posts–

"The Symbologist," a review, respectful despite the editor's sarcastic title, of Jung's Red Book in the December 6th New York Times Book Review.

Comments Off