Thursday, November 15, 2018


Filed under: General — m759 @ 8:15 AM

"I need a photo opportunity, I want a shot at redemption.
Don't want to end up a cartoon in a cartoon graveyard."
– Paul Simon

From the previous post

From a cartoon graveyard —

See also, in this  journal, Smallest Perfect and Nocciolo .

Wednesday, June 25, 2014


Filed under: General — m759 @ 5:01 AM

In memory of an actor “who as a boy was one of the few Jewish children
in his mostly Italian-American neighborhood in Brooklyn” —

See the link nocciolo  from The Book of Abraham (Oct. 7, 2013).

Monday, June 25, 2018

The Gateway Device

Filed under: General,Geometry — m759 @ 6:24 PM

<title data-rh="true">Frank Heart, Who Linked Computers Before the Internet, Dies at 89 – The New York Times</title>
. . . .
<meta data-rh="true" name="description" itemprop="description" content="Mr. Heart’s team built the gateway device for the Arpanet, the precursor to the internet. Data networking was so new then, they made it up as they went."/>
. . . .
<meta data-rh="true" property="article:published" itemprop="datePublished" content="2018-06-25T19:16:17.000Z"/>

See also yesterday's "For 6/24" and 

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Thursday, January 21, 2016

Dividing the Indivisible

Filed under: General,Geometry — m759 @ 11:00 AM

My statement yesterday morning that the 15 points
of the finite projective space PG(3,2) are indivisible 
was wrong.  I was misled by quoting the powerful
rhetoric of Lincoln Barnett (LIFE magazine, 1949).

Points of Euclidean  space are of course indivisible
"A point is that which has no parts" (in some translations).

And the 15 points of PG(3,2) may be pictured as 15
Euclidean  points in a square array (with one point removed)
or tetrahedral array (with 11 points added).

The geometry of  PG(3,2) becomes more interesting,
however, when the 15 points are each divided  into
several parts. For one approach to such a division,
see Mere Geometry. For another approach, click on the
image below.

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Wednesday, December 16, 2015

The Jewel in the Lotus…

Filed under: General — Tags: , — m759 @ 9:00 PM

Meets the Kernel in the Nutshell.

This post was suggested by the title of Natalie Wolchover's
article in Quanta Magazine today,
"A Fight for the Soul of Science."

The post continues a meditation on the number 6
as the kernel in the nutshell of 15.

For an illustration of the 6 in the 15,
see nocciolo  in this journal.

For an illustration of the jewel in the lotus,
see that  phrase in this journal.

Tuesday, December 1, 2015

The Nutshell

Filed under: General,Geometry — m759 @ 1:13 PM

See a search for Nocciolo  in this journal.

An image from that search —

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Recall also Hamlet's
"O God bad dreams."

Monday, November 11, 2013

The Mystic Hexastigm…

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

Or: The Nutshell

What about Pascal?

For some background on Pascal's mathematics,
not his wager, see

Richmond, H. W., 
"On the Figure of Six Points in Space of Four Dimensions," 
Quarterly Journal of Pure and Applied Mathematics , 
Volume 31 (1900), pp. 125-160,
dated by Richmond March 30,1899

Richmond, H. W.,
"The Figure Formed from Six Points in Space of Four Dimensions,"
Mathematische Annalen , 
Volume 53 (1900), Issue 1-2, pp 161-176,
dated by Richmond February 1, 1899

See also Nocciolo  in this journal.

Recall as well that six points in space may,
if constrained to lie on a circle, be given
a religious interpretation.  Richmond's
six points are secular and more general.

Monday, October 7, 2013

The Book of Abraham

Filed under: General — m759 @ 12:00 AM

On Abraham Nemeth, the developer of Braille
for blind students of mathematics —

"… he began tinkering with the six-dot cell
that is the foundation of Braille."

For a different six-dot cell, see Nocciolo .

"Throughout his life, he dedicated much of his
spare time to creating Braille versions of Jewish
texts, including helping to proofread a Braille
Hebrew Bible in the 1950s." — Nemeth's obituary

Those who prefer entertainment may consult  The Book of Eli.

Thursday, September 5, 2013

Kernel and Glow

Filed under: General — Tags: — m759 @ 11:01 AM

"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,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine."

— Joseph Conrad in Heart of Darkness

Kernel — See Nocciolo.

Glow — See Moonshine and Moonshine II.

See also Cold Open (Jan. 29, 2011) and
Where Entertainment is God (Aug. 25, 2013).

Tuesday, April 2, 2013

Rota in a Nutshell

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

"The proof of Desargues' theorem of projective geometry
comes as close as a proof can to the Zen ideal.
It can be summarized in two words: 'I see!' "

— Gian-Carlo Rota in Indiscrete Thoughts (1997)

Also in that book, originally from a review in Advances in Mathematics,
Vol. 84, Number 1, Nov. 1990, p. 136:

IMAGE- Rota's review of 'Sphere Packings, Lattices and Groups'-- in a word, 'best'

Related material:

Pascal and the Galois nocciolo ,
Conway and the Galois tesseract,
Gardner and Galois.

See also Rota and Psychoshop.

Baker on Configurations

Filed under: General,Geometry — Tags: , — m759 @ 11:11 AM

The geometry posts of Sunday and Monday have been
placed in finitegeometry.org as

Classical Geometry in Light of Galois Geometry.

Some background:

See Baker, Principles of Geometry , Vol. II, Note I
(pp. 212-218)—

On Certain Elementary Configurations, and
on the Complete Figure for Pappus's Theorem

and Vol. II, Note II (pp. 219-236)—

On the Hexagrammum Mysticum  of Pascal.

Monday's elucidation of Baker's Desargues-theorem figure
treats the figure as a 15420configuration (15 points, 
4 lines on each, and 20 lines, 3 points on each).

Such a treatment is by no means new. See Baker's notes
referred to above, and 

"The Complete Pascal Figure Graphically Presented,"
a webpage by J. Chris Fisher and Norma Fuller.

What is new in the Monday Desargues post is the graphic
presentation of Baker's frontispiece figure using Galois geometry :
specifically, the diamond theorem square model of PG(3,2).

See also Cremona's kernel, or nocciolo :

Baker on Cremona's approach to Pascal—

"forming, in Cremona's phrase, the nocciolo  of the whole."

IMAGE- Definition of 'nocciolo' as 'kernel'

A related nocciolo :

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Click on the nocciolo  for some
geometric background.

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