Log24

Thursday, June 23, 2022

The Nutshell Suite

Filed under: General — Tags: , , , — m759 @ 10:35 am

The above is a summary of 
Pythagorean philosophy 
reposted here on . . .

September 10, 2019.
 

Battle of the Nutshells:

IMAGE- History of Mathematics in a Nutshell

From a much larger nutshell
on the above Pythagorean date—

Now let's dig a bit deeper into history . . .

Bourbaki on arithmetic and geometry

Monday, April 27, 2020

The Cracked Nut

Filed under: General — Tags: , , — m759 @ 1:25 pm

“At that instant he saw, in one blaze of light, an image of unutterable
conviction, the reason why the artist works and lives and has his being –
the reward he seeks –the only reward he really cares about, without which
there is nothing. It is to snare the spirits of mankind in nets of magic,
to make his life prevail through his creation, to wreak the vision of his life,
the rude and painful substance of his own experience, into the congruence
of blazing and enchanted images that are themselves the core of life, the
essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

“… the stabiliser of an octad preserves the affine space structure on its
complement, and (from the construction) induces AGL(4,2) on it.
(It induces A8 on the octad, the kernel of this action being the translation
group of the affine space.)”

— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)

“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside…."

— Joseph Conrad in Heart of Darkness

Thursday, November 17, 2016

Rotman and the Outer Automorphism

Filed under: General,Geometry — Tags: , — m759 @ 11:00 am

This is a followup to Tuesday's post on the Nov. 15 American
Mathematical Society (AMS) obituary of Joseph J. Rotman.

Detail of a page in "Notes on Finite Geometry, 1978-1986,"
"An outer automorphism of S6 related to M24" —

Related work of Rotman —

"Outer Automorphisms of S6," by
Gerald Janusz and Joseph Rotman,
The American Mathematical Monthly ,
Vol. 89, No. 6 (Jun. – Jul., 1982), pp. 407-410

Some background —

"In a Nutshell: The Seed," Log24 post of Sept. 4, 2006:

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