Saturday, June 15, 2013

At the Still Point

Filed under: General — m759 @ 1:05 PM

(Continued from yesterday's posts, "Object of Beauty"
and "Amy's Shadow")

A winner of a Nobel Prize for X-ray crystallography stands
at the head of the New York Times  obituary list today.

In memoriam —

X-Ray Vision

"Crystal Engineering in Kindergarten," by Bart Kahr:

"If the reader is beginning to suspect that Froebel’s
philosophy of spiritual crystallography is sometimes
incoherent I can confirm that this is so…."

Click images for some backstories.

Some further background:

The Times  follows yesterday's egregious religious error
with an egregious scientific error:

"The technique developed by Dr. Karle and Herbert A. Hauptman,
called X-ray crystallography, is now routinely used by scientists…."

Karle was reportedly born in 1918, Hauptman in 1917.

Wikipedia on the history of X-ray crystallography:

"The idea that crystals could be used as a 
diffraction grating for X-rays arose in 1912…."

The Nobel Foundation:

"The Nobel Prize in Physics 1914 was awarded to
Max von Laue 'for his discovery of the diffraction of
X-rays by crystals.'"

"The Nobel Prize in Physics 1915 was awarded jointly to
Sir William Henry Bragg and William Lawrence Bragg 
'for their services in the analysis of crystal structure
by means of X-rays.'"

Saturday, May 10, 2008

Saturday May 10, 2008

MoMA Goes to

"… the startling thesis of Mr. Brosterman's new book, 'Inventing Kindergarten' (Harry N. Abrams, $39.95): that everything the giants of modern art and architecture knew about abstraction they learned in kindergarten, thanks to building blocks and other educational toys designed by Friedrich Froebel, a German educator, who coined the term 'kindergarten' in the 1830's."

— "Was Modernism Born
     in Toddler Toolboxes?"
     by Trip Gabriel, New York Times,
     April 10, 1997


Figure 1 —
Concept from 1819:

Cubic crystal system
(Footnotes 1 and 2)

Figure 2 —
The Third Gift, 1837:

Froebel's third gift

Froebel's Third Gift

Froebel, the inventor of
kindergarten, worked as
an assistant to the
crystallographer Weiss
mentioned in Fig. 1.

(Footnote 3)

Figure 3 —
The Third Gift, 1906:

Seven partitions of the eightfold cube in 'Paradise of Childhood,' 1906

Figure 4 —
Solomon's Cube,
1981 and 1983:

Solomon's Cube - A 1981 design by Steven H. Cullinane

Figure 5 —
Design Cube, 2006:

Design Cube 4x4x4 by Steven H. Cullinane

The above screenshot shows a
moveable JavaScript display
of a space of six dimensions
(over the two-element field).

(To see how the display works,
try the Kaleidoscope Puzzle first.)

For some mathematical background, see

1. Image said to be after Holden and Morrison, Crystals and Crystal Growing, 1982
2. Curtis Schuh, "The Library: Biobibliography of Mineralogy," article on Mohs
3. Bart Kahr, "Crystal Engineering in Kindergarten" (pdf), Crystal Growth & Design, Vol. 4 No. 1, 2004, 3-9

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