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Tuesday, March 26, 2024

Kindergarten Report on Fröbel’s Third Gift:
“Behaves well under group action.”

Filed under: General — Tags: The Prize Shining — m759 @ 8:02 am

From the above: "electronically published on October 6. 2023."

See as well that date in other Log24 posts tagged The Prize Shining.

A co-author of the book reviewed has appeared here previously.

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Wednesday, June 15, 2016

Rubik’s Deathtrap

Filed under: General — Tags: Bloomsday Eve 2016 — m759 @ 7:20 pm

The previous post suggests a search in this journal
for "Deathtrap."

"Rubik’s Cube® used by permission
Rubik’s Brand Ltd. www.rubiks.com."

— Bernd Sturmfels, June-July 2016 Notices
of the American Mathematical Society ,
Volume 63, Number 6, page 605

"Tenser, said the Tensor …." — The Demolished Man

Max von Sydow in Branded (2012)

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Expanding the Spielraum …

Filed under: General — Tags: Bloomsday Eve 2016 — m759 @ 2:40 pm

Continues .

"My AMS invited address at the SIAM Annual Meeting July 11–15
in Boston discusses the extension of eigenvectors and singular
vectors from matrices to higher order tensors."

— Bernd Sturmfels in the June-July 2016 AMS Notices

See also Sturmfels in this journal — for instance, in
"Expanding the Spielraum," a post of Feb. 3, 2015 —

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Thursday, May 12, 2016

But Seriously …

Filed under: General — Tags: Springer — m759 @ 7:31 pm

Google today released on GitHub an English parser,
Parsey McParseface . From Google Research Blog —

"Today, we are excited to share the fruits of our research
with the broader community by releasing SyntaxNet,
an open-source neural network framework implemented in
TensorFlow that provides a foundation for
Natural Language Understanding (NLU) systems.
Our release includes all the code needed to train new
SyntaxNet models on your own data, as well as
Parsey McParseface , an English parser that we have
trained for you and that you can use to analyze English text."

"While the accuracy is not perfect, it’s certainly high enough
to be useful in many applications. The major source of errors
at this point are examples such as the prepositional phrase
attachment ambiguity described above, which require real
world knowledge (e.g. that a street is not likely to be located
in a car) and deep contextual reasoning. Machine learning
(and in particular, neural networks) have made significant
progress in resolving these ambiguities. But our work is still
cut out for us: we would like to develop methods that can
learn world knowledge and enable equal understanding of
natural language across all languages and contexts."

But seriously …

For some historical background, see (for instance) a book by
Ekaterina Ovchinnikova —

Integration of World Knowledge for
Natural Language Understanding ,
Atlantis Press, Springer, 2012.

A PDF of Chapter 2, "Natural Language Understanding
and World Knowledge," is available for download.

The philosophical background is the distinction between
syntax and semantics . See (for instance) …

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Friday, November 27, 2015

Einstein and Geometry

Filed under: General,Geometry — Tags: Dirac and Geometry, Lichtung — m759 @ 2:01 pm

(A Prequel to Dirac and Geometry)

"So Einstein went back to the blackboard.
And on Nov. 25, 1915, he set down
the equation that rules the universe.
As compact and mysterious as a Viking rune,
it describes space-time as a kind of sagging mattress…."

— Dennis Overbye in The New York Times online,
November 24, 2015

Some pure mathematics I prefer to the sagging Viking mattress —

Readings closely related to the above passage —

Thomas Hawkins, "From General Relativity to Group Representations:
the Background to Weyl's Papers of 1925-26," in Matériaux pour
l'histoire des mathématiques au XXe siècle: Actes du colloque
à la mémoire de Jean Dieudonné, Nice, 1996 (Soc. Math.
de France, Paris, 1998), pp. 69-100.

The 19th-century algebraic theory of invariants is discussed
as what Weitzenböck called a guide "through the thicket
of formulas of general relativity."

Wallace Givens, "Tensor Coordinates of Linear Spaces," in
Annals of Mathematics Second Series, Vol. 38, No. 2, April 1937,
pp. 355-385.

Tensors (also used by Einstein in 1915) are related to
the theory of line complexes in three-dimensional
projective space and to the matrices used by Dirac
in his 1928 work on quantum mechanics.

For those who prefer metaphors to mathematics —

"We acknowledge a theorem's beauty
when we see how the theorem 'fits' in its place,
how it sheds light around itself, like a Lichtung ,
a clearing in the woods."
— Gian-Carlo Rota, Indiscrete Thoughts ,
Birkhäuser Boston, 1997, page 132

Rota fails to cite the source of his metaphor.
It is Heidegger's 1964 essay, "The End of Philosophy
and the Task of Thinking" —

"The forest clearing [ Lichtung ] is experienced
in contrast to dense forest, called Dickung
in our older language."
— Heidegger's Basic Writings ,
edited by David Farrell Krell,
Harper Collins paperback, 1993, page 441

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Friday, September 19, 2014

Metaphysics for Gilliam

Filed under: General — m759 @ 9:29 pm

See also…

Related remarks: Diederik Aerts at arXiv.org.

See also Aerts (as above) on the metaphysics of entities (1984):

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Friday, December 13, 2013

Outsider Art

Filed under: General — m759 @ 1:23 pm

(Continued from yesterday afternoon)

From yesterday's online New York Times (5:59 PM ET)—

ART REVIEW
A Tension Between the Sacred and the Profane

What exactly are we looking at? Is it the real thing, or is it the promotion of a famous brand gussied up in spectacular, pseudo-sacramental style? Gold or fool’s gold?

This sort of confusion pervades today’s art world, where, so often, the sales pitch comes in the form of quasi-religious rhetoric. It’s a big reason the tribal arts of Africa and other lands — as well as the putatively purely authentic creations of folk artists and so-called outsiders — are held in such high esteem.

— Ken Johnson, review of two exhibitions,
of tribal African art and of Brancusi

"Tenser, said the tensor…"

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Friday, March 23, 2012

Embedding the Stone

Filed under: General,Geometry — Tags: Intake Manifold — m759 @ 8:00 am

"Imbedding the God character in a holy book's very detailed narrative
and building an entire culture around this narrative
seems by itself to confer a kind of existence on Him."

— John Allen Paulos in the philosophy column "The Stone,"
New York Times online, Oct. 24, 2010

A related post from Log24 later that year—

Sunday, November 28, 2010

The Embedding

— m759 @ 6:00 AM

The New York Times Magazine this morning on a seminar on film theory at Columbia University—

"When the seminar reconvened after the break, Schamus said, 'Let’s dive into the Meno,' a dialogue in which Plato and Socrates consider virtue. 'The heart of it is the mathematical proof.' He rose from his seat and went to the whiteboard, where he drew figures and scribbled numbers as he worked through the geometry. 'You can only get the proof visually,' he concluded, stepping back and gazing at it. Plato may be skeptical about the category of the visual, he said, but 'you are confronted with a visual proof that gets you back to the idea embedded in visuality.'"

The Meno Embedding

Plato's Diamond embedded in The Matrix

"Next come the crown of thorns and Jesus' agonized crawl across the stage,
bearing the weight of his own crucifix. And at last, after making
yet another entrance, Mr. Nolan strikes the pose immortalized
in centuries of art, clad in a demure loincloth, arms held out to his sides,
one leg artfully bent in front of the other, head hanging down
in tortured exhaustion. Gently spotlighted, he rises from the stage
as if by magic, while a giant cross, pulsing with hot gold lights,
descends from above to meet him. Mr. Lloyd Webber's churning guitar rock
hits a climactic note, and the audience erupts in excited applause."

— Charles Isherwood, review of "Jesus Christ Superstar" in today's New York Times

Other remarks on embedding —

Part I

Review of a new book on linguistics, embedding, and a South American tribe—

"Imagine a linguist from Mars lands on Earth to survey the planet's languages…."
— Chronicle of Higher Education , March 20, 2012

Part II

The Embedding , by Ian Watson (Review of a 1973 novel from Shakespeare's birthday, 2006)

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