Log24

Thursday, April 14, 2016

Banach Revisited

Filed under: General — m759 @ 12:00 pm

A  1960  analogy by Max Black —

"Those who see a model as a mere crutch
are like those who consider metaphor
a mere decoration or ornament."

This suggests a search for "Analogies between Analogies" —

“A mathematician is a person who can find analogies
between theorems; a better mathematician is one who
can see analogies between proofs and the best
mathematician can notice analogies between theories.
One can imagine that the ultimate mathematician is one
who can see analogies between analogies.”

— Stefan Banach, according to MacTutor.

Sunday, May 29, 2016

The Ideogram Principle …

Filed under: General,Geometry — Tags: , , , — m759 @ 4:23 pm

According to McLuhan

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

For context, see Cameron McEwen,
"Marshall McLuhan, John Pick, and Gerard Manley Hopkins."
(Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

A relation in four terms —

A : B  ::  C : D   as   Model : Crutch  ::  Metaphor : Ornament —

See also Dueling Formulas and Symmetry.

Tuesday, April 3, 2012

Catholic View

Filed under: General — m759 @ 9:48 am

"When shall we three meet again?"

Left to right— John von Neumann, Richard Feynman, Stanislaw Ulam

The source of the above book's title, "Analogies between Analogies,"
was misattributed in a weblog post linked to here on March 4th, 2012.
It occurs in a quote due not to Stanislaw Ulam but to Stefan Banach—

IMAGE- 'Catholic view' quote in foreword of book 'Analogies between Analogies'

Ulam was Jewish. Banach was not.

From a webpage on Banach—

"On 3 April 1892, he was baptized in the Roman Catholic
 Parish of St. Nicholas in Krakow."

See also…

  1. a post of Sunday, April 2, 2006,
  2. yesterday's Pennsylvania lottery, and
  3. post 585 in this journal. 

(At Los Alamos, Ulam developed the Monte Carlo method.)

Thursday, June 7, 2007

Thursday June 7, 2007

Filed under: General — Tags: — m759 @ 4:15 pm
Framing
truth

On "framing" and "spin"
in journalism:

"… Packaging is unavoidable.
Facts rarely, if ever, 
  speak for themselves."

— Matthew C. Nisbet,  
Assistant Professor
  of "Communication,"
June 6, 2007

If they could, they might
say "We was framed!"

Facts cannot, of course,
speak for themselves
to those who do not
understand their language.

Example:

A picture that appeared in
Log24 on June 7, 2005:

Natural Transformation

Click for details.

Attempt to
frame the picture:

Analogies

"A functor is an analogy."
— Anonymous

  The best mathematicians "see
analogies between analogies."
— Banach, according to Ulam 

For further details,
click on the link
"Analogies" above.

See also the analogies in
the previous entry.

Tuesday, March 30, 2004

Tuesday March 30, 2004

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

Banach’s Birthday

“A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.”

— Stefan Banach, according to MacTutor.

The quotation is perhaps taken from Through a Reporter’s Eyes: The Life of Stefan Banach, by Roman Kauza (a.k.a. Roman Kaluza).

“What we today call ‘Banach spaces’
are called
‘spaces of type (B)’
in Banach’s book.”
— Sheldon Axler

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