Concepts of Space —
(From the March 2019 post Back to the Annus Mirabilis , 1905 )
Concepts of Space and Time —
Concepts of Space —
(From the March 2019 post Back to the Annus Mirabilis , 1905 )
Concepts of Space and Time —
See Eightfold Froebel.
"Time is the moving image of eternity." — Plato (paraphrased)
Summary, as an illustration of a title by George Mackey —
A more recent famous saying . . .
"Before time began, there was the Cube." — Optimus Prime
Since it is part of the cube, the square figure above
may be seen as a representation of eternity. (The circle,
familiar to us as a clock face, of course represents time.)
"Before time began . . . ." — Optimus Prime
I noticed this favicon on Sept. 18 (see post) at a publisher's webpage.
It turns out that it is not specific to the publisher, but rather to sites
hosted by Squarespace.com. For instance . . .
See also a post on Christmas Day, 2013.
Related material from the Sept. 18 post mentioned above —
"When things go bonkers, you have to adapt."
— Chris Hemsworth as Dementus in "Furiosa" (2024)
"Before time began, there was the Cube."
— Optimus Prime in "Transformers" (2007)
Today, an animated Transformers opens, with
Chris Hemsworth as the voice of Optimus Prime.
Also today: The new tag "Cubehenge" in this journal.
Click the "timelessness" quote below for the "Bell, Book and Candle" scene
with Kim Novak and James Stewart atop the Flatiron Building.
"Before time began . . . ." — Optimus Prime
"Before time began . . . ." — Optimus Prime
"Before time began, there was the Cube." — Optimus Prime in "Transformers"
This journal at 9 PM ET March 17, 2023 —
The use of binary coordinate systems as a conceptual tool
Natural physical transformations of square or cubical arrays
of actual physical cubes (i.e., building blocks) correspond to
natural algebraic transformations of vector spaces over GF(2).
This was apparently not previously known.
See "The Thing and I."
See as well today's post Geometry for Belgium.
The New York Times today reports the death at 90 of
Peggy Mellon Hitchcock, who arranged for Timothy Leary's
accomodation at the Hitchcock Estate, on April 9, 2024 . . .
Also on April 9 —
A rather different Hitchcock image —
This is from a Log24 search for Hitchcock Cube.
"Before time began . . ." — Optimus Prime.
In memory of the inventor of the Pascal programming language,
who reportedly died on New Year's Day, 2024, an image from
this journal on that date —
"Before time began, there was the Cube." — Optimus Prime
See as well a Pascal that some will prefer, and my own ACM card.
That card gives Warren, PA, as my location… which is no longer
always the case… but Warren is where I learned, and worked, in
computing, after a somewhat belated education in pure mathematics
in New York State.
Some personal background is suggested by…
Epigraph for Cormac McCarthy —
"When I got to high school the first place I went was to the library. It was just a small room with a desk and maybe a thousand books. Maybe not that. But among them was a volume of Berkeley. I dont know what it was doing there. Probably because Berkeley was a bishop. Well. Almost certainly because Berkeley was a bishop. But I sat in the floor and I read A New Theory of Vision. And it changed my life. I understood for the first time that the visual world was inside your head. All the world, in fact. I didnt buy into his theological speculations but the physiology was beyond argument. I sat there for a long time. Just letting it soak in."
— McCarthy, Cormac. Stella Maris (p. 39). |
From this journal on April 18, 2023 —
" NY Times columnist's advice to the recent Harvard donor of $300 million —
'At least make them build you some weird pharaonic monument.' "
Illustration suggested by my own high-school library reading many years ago —
Click to enlarge:
"Before time began, there was the Cube." — Optimus Prime
For a different sort of Lightbox, more closely associated with
the number 13, see instances in this journal of . . .
(Adapted from Encyclopaedia Britannica,
Eleventh Edition (1911), Crystallography .)
"Before time began . . . ." — Optimus Prime
"Before time began . . ." — Optimus Prime
Structures from pure mathematics, by Plato and R. T. Curtis —
* See other "Preform" posts in this journal.
This afternoon's Windows lockscreen is Badlands National Park —
From this morning's post, a phrase from Schopenhauer —
"Apparent Design in the Fate of the Individual."
An apparent design in the philosophy of Optimus Prime —
"Before time began, there was the Cube" —
Click the image for further remarks.
Some background for the exercise of 9/11 —
Vera Pless, "More on the uniqueness of the Golay codes,"
Discrete Mathematics 106/107 (1992) 391-398 —
"Several people [1-2,6] have shown that
any set of 212 binary vectors of length 24,
distance ≥ 8, containing 0, must be the
unique (up to equivalence) [24,12,8] Golay code."
[1] P. Delsarte and J.M. Goethals, "Unrestricted codes
with the Golay parameters are unique,"
Discrete Math. 12 (1975) 211-224.
[2] A. Neumeier, private communication, 1990.
[6] S.L. Snover, "The uniqueness of the
Nordstrom-Robinson and the Golay binary codes,"
Ph.D. Thesis, Dept. of Mathematics,
Michigan State Univ., 1973.
Related images —
"Before time began, there was the Cube."
"Remember, remember the fifth of November"
From a 1964 recreational-mathematics essay —
Note that the first two triangle-dissections above are analogous to
mutually orthogonal Latin squares . This implies a connection to
affine transformations within Galois geometry. See triangle graphics
in this journal.
Update of 4:40 AM ET —
Other mystical figures —
"Before time began, there was the Cube."
— Optimus Prime in "Transformers" (Paramount, 2007)
"And, as with all retold tales that are in people's hearts,
there are only good and bad things and black and white
things and good and evil things and no in-between anywhere."
— John Steinbeck, author's epigraph to The Pearl
From the Season 4 finale of Westworld :
uploading Dolores's pearl at Hoover Dam —
For those who prefer greater theological simplicity . . .
Optimus Prime on a different Hoover Dam figure, that of
the AllSpark: "Before time began, there was the Cube."
Simplifying even more . . .
“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
As above, Black's theology forms a cube.
Continued from April 12, 2022.
"It’s important, as art historian Reinhard Spieler has noted,
that after a brief, unproductive stay in Paris, circa 1907,
Kandinsky chose to paint in Munich. That’s where he formed
the Expressionist art group Der Blaue Reiter (The Blue Rider) —
and where he avoided having to deal with cubism."
— David Carrier,
Remarks by Louis Menand in The New Yorker today —
"The art world isn’t a fixed entity.
It’s continually being reconstituted
as new artistic styles emerge."
(Adapted from Encyclopaedia Britannica,
Eleventh Edition (1911), Crystallography .)
"Before time began, there was the Cube."
— Optimus Prime
See as well Verbum (February 18, 2017).
Related dramatic music —
"Westworld Season 4 begins at Hoover Dam,
with William looking to buy the famous landmark.
What does he consider to be 'stolen' data that is inside?"
" Welcher Art ist die ursprüngliche Einheit,
daß sie sich in diese Scheidung auseinanderwirft,
und in welchem Sinn sind die Geschiedenen
hier als Wesung der Ab-gründigkeit gerade einig?
Hier kann es sich nicht um irgend eine »Dialektik«
handeln, sondern nur um die Wesung des Grundes
(der Wahrheit also) selbst."
"Before time began, there was the Cube." — Optimus Prime
A question attributed to John Horton Conway
about configurations in his Game of Life —
"Indeed, is there a Godlike still-life,
one that can only have existed
for all time . . . . ?"
A simple answer … but not from Conway's Game —
"Before time began, there was the Cube." — Optimus Prime
Related remarks: Ogdoad.
"Before time began, there was the Cube." — Optimus Prime
See also Design Cube.
* According to The Wall Street Journal … and possibly also
dead on October 11th, according to The New York Times .
Miller died on February 7, 2021.
See that date in this journal —
“Before time began, there was the Cube.”
— Hassenfeld Brothers cinematic merchandising slogan.
Update at noon on Wednesday, June 9, 2021 —
Related material on Frye and deconstruction —
From "The First Major Theoretician? Northrop Frye Towards the end of his career, when it was clear that literary theory had taken hold in the academy, Frye began to reflect on literary theory. In an interview with Deanne Bogdan, Frye laments, “I am feeling out of the great critical trends today”…. Northrop Frye was right that he was “out of fashion,” both in terms of his own theories and his place in literary theory; however, he did seek to reverse the course. Frye hoped to reclaim literary studies from deconstruction, which had become, in a sense, his chief opponent …. |
Also on February Seventh —
Sunday, February 7, 2021
Transformers Continues.“Before time began, there was the Cube.” Et cetera . |
The previous post displayed a photo from November 2014.
Remarks quoted here in November 2014 —
“Before time began, there was the Cube.”
— Optimus Prime
* A weblog motto. See …
http://enowning.blogspot.com/
2007/07/alfred-denkers-dictionary-on-ereignis.html.
That Ereignis post is dated July 3, 2007.
Related material for the Church of Synchronology —
"The deepest strain in a religion is the particular
and particularistic doctrine it asserts at its heart,
in the company of such pronouncements as
‘Thou shalt have no other Gods before me.’
Take the deepest strain of religion away…
and what remains are the surface pieties —
abstractions without substantive bite —
to which everyone will assent
because they are empty, insipid, and safe."
— Stanley Fish, quoted here on July 3, 2007…
The opening date of the film "Transformers."
The opening pronouncement of "Transformers" —
An image from All Souls' Day 2010 —
This is from earlier posts tagged Permutahedron.
See also
Wallace Stevens:
A World of Transforming Shapes.
From that book (click to enlarge) —
"Before time began, there was the Cube."
— Optimus Prime.
Also from earlier posts tagged Permutahedron —
John Horgan in Scientific American magazine on October 8, 2019 —
"In the early 1990s, I came to suspect that the quest
for a unified theory is religious rather than scientific.
Physicists want to show that all things came from
one thing: a force, or essence, or membrane
wriggling in eleven dimensions, or something that
manifests perfect mathematical symmetry. In their
search for this primordial symmetry, however,
physicists have gone off the deep end . . . ."
Other approaches —
See "Story Theory of Truth" in this journal and, from the November 2019
Notices of the American Mathematical Society . . .
More fundamental than the label of mathematician is that of human. And as humans, we’re hardwired to use stories to make sense of our world (story-receivers) and to share that understanding with others (storytellers) [2]. Thus, the framing of any communication answers the key question, what is the story we wish to share? Mathematics papers are not just collections of truths but narratives woven together, each participating in and adding to the great story of mathematics itself. The first endeavor for constructing a good talk is recognizing and choosing just one storyline, tailoring it to the audience at hand. Should the focus be on a result about the underlying structures of group actions? . . . .
[2] Gottschall, J. , The Storytelling Animal , — "Giving Good Talks," by Satyan L. Devadoss |
"Before time began, there was the Cube." — Optimus Prime
"… objects have a notion of 'this' or 'self.' " — Wikipedia
For related notions, see other posts tagged Quark Rock and …
"Before time began, there was the Cube." — Optimus Prime
A link, observablehq.com/demo, (not functioning in my Chrome
browser at the present time but apparently OK in Firefox) in the
previous post suggests . . .
"Physically meaningful observables must also satisfy
transformation laws which relate observations
performed by different observers in different
frames of reference. These transformation laws are
automorphisms of the state space, that is
bijective transformations which preserve certain
mathematical properties of the space in question."
— Wikipedia, Observable
Those who prefer narrative to mathematics may read
"automorphisms" as "auto morphisms."
"Before time began . . . ." — "Transformers" first line, 2007
" … this beautiful love story . . . ."
An image from the previous post:
The above line "From the producer of Transformers " suggests
a story from March 18, 2019 . . .
Misreading the words of di Bonaventura
yields a phrase that might be applied to
the Church of Rome . . .
"A franchise based on release dates."
See dies natalis in this journal.
For the Church of Synchronology, see
the above di Bonaventura date, March 18.
Then there is the Church of Cubism . . .
"Before time began, there was the Cube."
— Optimus Prime, Transformers , 2007
The opening lines of Eliot's Four Quartets —
"Time present and time past
Are both perhaps present in time future,
And time future contained in time past."
Perhaps.
Those who prefer geometry to rhetoric may also prefer
to Eliot's lines the immortal opening of the Transformers saga —
"Before time began, there was the Cube."
One version of the Cube —
The New Yorker reviewing "Bumblebee" —
"There is one reliable source for superhero sublimity,
and it’s all the more surprising that it’s a franchise with
no sacred inspiration whatsoever but, rather, of purely
and unabashedly mercantile origins: the 'Transformers'
series, based on a set of toys, in which Michael Bay’s
exhilarating filmmaking offers phantasmagorical textures
of an uncanny unconscious resonance."
— Richard Brody on December 29, 2018
"Before time began, there was the Cube."
— Optimus Prime
Some backstory — A Riddle for Davos, Jan. 22, 2014.
The Finkelstein Talisman —
"Before time began, there was the Cube."
— Optimus Prime in "Transformers" (Paramount, 2007)
Wikipedia on Hasbro —
Three American Jewish brothers,[6] Herman, Hillel, and Henry Hassenfeld[7]
founded Hassenfeld Brothers in Providence, Rhode Island in 1923 . . . .
The Hassenfeld Auction —
Also on September 16, 2015 —
The Hindman Image —
The Hood Warenkorb —
Under the Hood —
Megan Fox in "Transformers" (2007) —
This Way to the Egress —
Click to enlarge:
Above are the 7 frames of an animated gif from a Wikipedia article.
* For the Furey of the title, see a July 20 Quanta Magazine piece —
See also the eightfold cube in this journal.
"Before time began . . . ." — Optimus Prime
Related material —
The seven points of the Fano plane within
"Before time began . . . ."
— Optimus Prime
For the late Anne M. Treisman, who reportedly died Friday, Feb. 9:
From "A Feature-Integration Theory of Attention" —
"The controversy between analytic and synthetic theories
of perception goes back many years: the Associationists
asserted that the experience of complex wholes is built
by combining more elementary sensations, while the
Gestalt psychologists claimed that the whole precedes
its parts, that we initially register unitary objects and
relationships, and only later, if necessary, analyze these
objects into their component parts or properties. This view
is still active now . . . ."
— Anne M. Treisman, University of British Columbia,
and Garry Gelade, Oxford University, in
Cognitive Psychology 12, 97-136 (1980)
"Before time began, there was the Cube." — Optimus Prime
The previous post, "Mind," suggests a search for "n+1" in this journal.
From that search —
The above psychoanalytic remarks suggest . . .
See also "Transformers" (2007).
"Before time began, there was the Cube."
— Optimus Prime
Paul Krugman:
Asimov’s Foundation novels grounded my economics
In the Foundation novels of Isaac Asimov …
“The Prime Radiant can be adjusted to your mind, and all
corrections and additions can be made through mental rapport.
There will be nothing to indicate that the correction or addition
is yours. In all the history of the Plan there has been no
personalization. It is rather a creation of all of us together.
Do you understand?”
“Yes, Speaker!”
— Isaac Asimov, Second Foundation , Ch. 8: Seldon’s Plan
“Before time began, there was the Cube.“
See also Transformers in this journal.
From a post of last Friday, June 2 —
See also Transformers in this journal.
"Before time began, there was the Cube."
— Transformers (2007)
"Before time began, there was the Cube." — Transformers (2007)
Plot summary — "An ancient struggle between two Cybertronian races,
the heroic Autobots and the evil Decepticons, comes to Earth, with
a clue to the ultimate power held by a teenager."
* A post suggested by J. D. Salinger's phrase "a fresh impetus"
in "Raise High the Roof Beam, Carpenters" (1955)
"The deepest strain in a religion is
the particular and particularistic doctrine
it asserts at its heart,
in the company of such pronouncements as
‘Thou shalt have no other Gods before me.’
Take the deepest strain of religion away…
and what remains are the surface pieties —
abstractions without substantive bite —
to which everyone will assent
because they are empty, insipid, and safe."
— Stanley Fish, quoted here on July 3, 2007…
The opening date of the film "Transformers."
The opening pronouncement of "Transformers" —
"Before time began, there was the Cube."
Those who prefer Fish's abstractions may consult
the previous post.
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