Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation of the above
seven partitions of the eightfold cube:
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Related mathematics:
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The use of binary coordinate systems
Natural physical transformations of square or cubical arrays See "The Thing and I." |
and . . .
Related entertainment:
Or Matt Helm by way of a Jedi cube.
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"For all their wealth of content, for all the sum of history and social institution vested in them, music, mathematics, and chess are resplendently useless (applied mathematics is just higher plumbing, a kind of music for the police band). They are metaphysically trivial, irresponsible. They refuse to relate outward, to take reality for arbiter. This is the source of their witchery."
— George Steiner on chess in “A Death of Kings,” |
Steiner says that mathematics refuses "to relate outward,
to take reality for arbiter."
Related reading . . .
"The bond with reality is cut."
— Hans Freudenthal, 1962
From this journal last Sunday morning . . .
From this journal this morning . . .
"In conclusion: what an axiomatic presentation of a piece of mathematics
conceals is at least as relevant to the understanding of mathematics
as what an axiomatic presentation pretends to state." — Gian-Carlo Rota
As for noir . . .
Consider how Apple TV recently created "brutal, exaggerated worlds
that originated in actual locations" and also created a villainous
private company named Axiom .
Some relevant history of mathematics . . .
"The bond with reality is cut." — Freudenthal on axiomatics .
New York Review of Books , Dec. 16, 2021 issue —
Lorrie Moore on the documentary series "Couples Therapy" —
"Few of the people sitting on the couch avoid the cliché of
one person (a man) playing fruitlessly with a plastic puzzle
while the other speaks tearfully and avails herself of a
Kleenex box. In season 1, there is literally a Rubik’s cube,
and no one ever solves it, an unfortunate but apt metaphor.
During one session, when the cube has been placed out of reach,
one of the husbands gets up to look for it, finding it on a shelf."
See also . . .
"The bond with reality is cut." — Hans Freudenthal
Hans Freudenthal in 1962 on the axiomatic approach to geometry
of Fano and Hilbert —
"The bond with reality is cut."
Some philosophical background —
For Weyl's "few isolated relational concepts," see (for instance)
Projective Geometries over Finite Fields , by
J. W. P. Hirschfeld (first published by Oxford University Press in 1979).
Weyl in 1932 —
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Mathematics is the science of the infinite , its goal the symbolic comprehension of the infinite with human, that is finite, means. It is the great achievement of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. The intuitive feeling for, the quiet unquestioning acceptance of the infinite, is peculiar to the Orient; but it remains merely an abstract consciousness, which is indifferent to the concrete manifold of reality and leaves it unformed, unpenetrated. Coming from the Orient, the religious intuition of the infinite, the apeiron , takes hold of the Greek soul in the Dionysiac-Orphic epoch which precedes the Persian wars. Also in this respect the Persian wars mark the separation of the Occident from the Orient. This tension between the finite and the infinite and its conciliation now become the driving motive of Greek investigation; but every synthesis, when it has hardly been accomplished, causes the old contrast to break through anew and in a deepened sense. In this way it determines the history of theoretical cognition to our day. — "The Open World: Three Lectures on the Metaphysical Implications of Science," 1932 |
From posts tagged “The Empty Quarter” —
Related tune suggested today by Peter J. Cameron —
The Beatles, “I Me Mine,” from the “Let It Be” album.
That album, and an image from Log24 on Feb. 23 —
From the previous post:
“… all things, whether below or above appearance,
are one and that it is only through reality, in which
they are reflected or, it may be, joined together,
that we can reach them.”
See also “The Bond with Reality.”
"The bond with reality is cut."
— Hans Freudenthal, 1962
Related screenshot of a book review
from the November AMS Notices —
Recent posts now tagged Paycheck suggest . . .
Related material —
See too “The Bond with Reality” in posts tagged Voids.
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
"The bond with reality is cut."
— Hans Freudenthal, 1962
From page 180, Logicomix — It was a dark and stormy night …
_regarding_the_discovery_of_Quaternions_multiplication_by_Sir_William_Rowan_Hamilton.jpg)
"In this way the eight quaternions came into being."
— Legend adapted from Richard Wilhelm.
See as well The Bond with Reality (20th of May, 2019).
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