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.
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 |
"The bond with reality is cut."
— Hans Freudenthal, 1962
Related screenshot of a book review
from the November AMS Notices —
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
“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 …
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