Log24

Tuesday, January 12, 2016

Lechner’s Beginning

Filed under: General — m759 @ 12:00 AM

Professionally, at least

Click image to enlarge.

See also the previous post, Lechner's End.

For a more up-to-date look at harmonic analysis
and switching functions (i.e., Boolean functions),
see Ryan O'Donnell, Analysis of Boolean Functions ,
Cambridge U. Press, 2014.  Page 40 gives an
informative overview of the history of this field.

Monday, January 11, 2016

Lechner’s End

Filed under: General — m759 @ 11:00 PM

A check on the author of the title illustrated at
the end of today's post Space Oddity yields the fact that
Robert J. Lechner reportedly died on Sept. 16, 2014.

For a synchronicity check, see posts now tagged Lechner's End.

Friday, January 29, 2016

Excellent Adventure*

Filed under: General — Tags: — m759 @ 9:29 PM

(Continued from Dec. 9, 2013)

"…it would be quite a long walk
for him if he had to walk straight across."

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Swiftly Mrs. Who brought her hands… together.

"Now, you see," Mrs. Whatsit said,
"he would be  there, without that long trip.
That is how we travel."

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– A Wrinkle in Time 
Chapter 5, "The Tesseract"

From a media weblog yesterday, a quote from the video below —

"At 12:03 PM Eastern Standard Time, January 12th, 2016…."

This  weblog on the previous day (January 11th, 2016) —

"There is  such a thing as harmonic analysis of switching functions."

— Saying adapted from a young-adult novel

* For some backstory, see a Caltech page.

Monday, January 11, 2016

Space Oddity

Filed under: General,Geometry — Tags: , — m759 @ 3:15 PM

It is an odd fact that the close relationship between some
small Galois spaces and small Boolean spaces has gone
unremarked by mathematicians.

A Google search today for “Galois spaces” + “Boolean spaces”
yielded, apart from merely terminological sources, only some
introductory material I have put on the Web myself.

Some more sophisticated searches, however led to a few
documents from the years 1971 – 1981 …

Harmonic Analysis of Switching Functions” ,
by Robert J. Lechner, Ch. 5 in A. Mukhopadhyay, editor,
Recent Developments in Switching Theory , Academic Press, 1971.

“Galois Switching Functions and Their Applications,”
by B. Benjauthrit and I. S. Reed,
JPL Deep Space Network Progress Report 42-27 , 1975

D.K. Pradhan, “A Theory of Galois Switching Functions,”
IEEE Trans. Computers , vol. 27, no. 3, pp. 239-249, Mar. 1978

Switching functions constructed by Galois extension fields,”
by Iwaro Takahashi, Information and Control ,
Volume 48, Issue 2, pp. 95–108, February 1981

An illustration from the Lechner paper above —

“There is  such a thing as harmonic analysis of switching functions.”

— Saying adapted from a young-adult novel

Tuesday, September 16, 2014

Plan 9

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

(Continued from St. Augustine's Day, 2012)

"Plan 9 deals with the resurrection of the dead."

Epigraph to "No Great Magic," a story by Fritz Leiber:

 To bring the dead to life
Is no great magic.
Few are wholly dead:
Blow on a dead man’s embers
And a live flame will start.


—Graves

Outside Space and Time

Filed under: General — Tags: — m759 @ 7:00 PM

The title phrase appears in today's noon post and also
in a post of October 29, 2007, 'Home from Home.'

Point of Reference

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

A note from the director of the 2014 Scarlett Johansson film Lucy :

Revised version of a post of February 9, 2006, with links repaired:

Space, Time, and Scarlett

 

From last night’s Grammy awards, lyrics:

“a place where there’s no space or time”
– Leon Russell

Aguilera's version wasn't bad, but …

The image “http://www.log24.com/log/pix06/060209-Blondes.jpg” cannot be displayed, because it contains errors.

“Scarlett Johansson does this ‘old Hollywood glam’ look
much better.”

For a reference to the place described in Russell’s lyrics,
see the riff on the number “265″ linked to in last night’s
Midnight in the Garden of the Soul.”

The "point of reference" outside space and time
in the 2006 Johansson post above is of course "265."

For Plato's remarks at this reference point, see Phaedrus
265d and 265e in this morning's post.

Where the Joints Are

Filed under: General,Geometry — Tags: , , — m759 @ 10:00 AM

An image related to the recent posts Sense and Sensibility:

A quote from yesterday's post The Eight:

A possible source for the above phrase about phenomena "carved at their joints":

See also the carving at the joints of Plato's diamond from the Meno :

Image-- Plato's diamond and a modern version from finite geometry

Related material: Phaedrus on Kant as a diamond cutter
in Zen and the Art of Motorcycle Maintenance .

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