Log24

Friday, November 27, 2020

Unreality in Oz

Filed under: General — Tags: , , — m759 @ 11:11 PM

Rebecca Harkins-Cross in Sydney Review of Books  on Nov. 25, 2020 —

Reality at Northfield

Filed under: General — Tags: , — m759 @ 4:34 PM

See also, in memory of a Northfield, Minnesota, professor
of mathematics who reportedly died on October 28 —

Posts tagged Olaf Gate.

Sunday, August 2, 2020

Zero-Sum Theorem

Filed under: General — Tags: — m759 @ 6:41 AM

Sunday, February 23, 2020

The Representation of Reality

Filed under: General — Tags: — m759 @ 1:36 PM

"Although art is fundamentally everywhere and always the same,
nevertheless two main human inclinations, diametrically opposed
to each other, appear in its many and varied expressions. ….
The first aims at representing reality objectively, the second subjectively." 

Mondrian, 1936  [Links added.]

An image search today (click to enlarge) —

Image search for 'Eightfold Cube'

Thursday, February 13, 2020

Zero Sum

Filed under: General — Tags: , , — m759 @ 1:05 PM

The novel Zero Sum Game  by S. L. Huang is reviewed in the
March 2020 Notices of the American Mathematical Society .

For the same novel in this  journal, see posts tagged Berlekamp’s Game.

Wednesday, February 12, 2020

The Reality Bond

Filed under: General — Tags: , — m759 @ 3:33 PM

The plane at left is modeled naturally by
seven types of “cuts” in the cube at right.

Structure of the eightfold cube

 

Wednesday, August 14, 2019

The Mask of Zero

Filed under: General — Tags: , — m759 @ 12:55 PM

For the title, see Zero: Both Real and Imaginary (a Log24 search).

The title was suggested by the previous post, by Zorro Ranch,
by the classic 1967 film The Producers , and by . . .

Related material —

Vanity Fair  on Sept. 8, 2017, celebrated the young actress
who played Beverly Marsh in the 2017 film version of
Stephen King's IT . See a post from her 12th birthday —
"Winter's Game" — that touches upon Maori themes.

More generally, see Bester + Deceivers in this  journal.

And for the Church of Synchronology . . .
See posts related to the above Vanity Fair  date.

Monday, May 20, 2019

The Bond with Reality

Filed under: General — Tags: , , , , — m759 @ 10:00 PM


"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

Tuesday, April 9, 2019

Zero Sum Game

Filed under: General — Tags: , — m759 @ 12:30 AM

Compare and contrast —

Saturday, May 5, 2018

Galois Imaginary

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

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

A related passage —

From The French Mathematician
by Tom Petsinis (Nov. 30, 1998) —

0

I had foreseen it all in precise detail.
One step led inevitably to the next,
like the proof of a shining theorem,
down to the conclusive shot that still echoes
through time and space. 
Facedown in the damp pine needles,
I embraced that fatal sphere
with my whole body. Dreams, memories,
even the mathematics I had cherished
and set down in my last will and testament–
all receded. I am reduced to
a singular point; in an instant
I am transformed to .

i = an imaginary being

Here, on this complex space,
i  am no longer the impetuous youth
who wanted to change the world
first with a formula and then with a flame.
Having learned the meaning of infinite patience,
i  now rise to the text whenever anyone reads 
about Evariste Galois, preferring to remain 
just below the surface, 
like a goldfish nibbling the fringe of a floating leaf.
Ink is more mythical than blood
(unless some ancient poet slit his 
vein and wrote an epic in red):
The text is a two-way mirror 
that allows me to look into
the life and times of the reader. 
Who knows, someday i  may rise
to a text that will compel me 
to push through to the other side.
Do you want proof that i  exist? Where am ?
Beneath every word, behind each letter, 
on the side of a period that will never see the light.

Tuesday, November 24, 2020

Scientism vs. Pure Mathematics

Filed under: General — Tags: , — m759 @ 9:18 PM

In his weblog today, Peter Woit quotes “a remarkable article
entitled Contemplating the End of Physics  posted today at
Quanta magazine [by] Robbert Dijkgraaf (the director of the IAS)”

An excerpt from the quoted remarks by the Institute for
Advanced Study director —

“All of this is part of a much larger shift in
the very scope of science, from studying what is
to what could be. In the 20th century, scientists
sought out the building blocks of reality:
the molecules, atoms and elementary particles
out of which all matter is made;
the cells, proteins and genes
that make life possible;
the bits, algorithms and networks
that form the foundation of information and intelligence,
both human and artificial. This century, instead,
we will begin to explore all there is to be made with
these building blocks.”

Then there are, of course, the building blocks of mathematical  reality:
unit cubes. See building-block.space.

Tuesday, October 6, 2020

Only Connect :  Bulk Apperception* Continues.

Filed under: General — Tags: , — m759 @ 11:49 AM

The above Vanity Fair  article was republished on the Web by VF
on September 3, 2013.  See also this  journal on that date.

Related religious remarks —

* “Bulk apperception” is a phrase from Westworld. See Log24 notes.

Saturday, August 1, 2020

A Cross for von Sydow

Filed under: General — Tags: — m759 @ 9:59 AM

See also Joseph Malkevitch’s memorial essay on Richard K. Guy,
who reportedly died on March 9, 2020, and Log24 on that date.

Thursday, July 30, 2020

A Picture Show for Quanta Magazine

Filed under: General — Tags: , , , — m759 @ 8:33 AM

An article yesterday at Quanta Magazine  suggests a review . . .

From Diamond Theorem  images at Pinterest —

Some background —

Wednesday, April 1, 2020

Books at Perlego

Filed under: General — Tags: — m759 @ 11:02 AM

Jung's Aion four-diamond diagram vs. recreational mathematics

” How small is the evil that may be safely ignored…? “
— “QBass” at Wikipedia, April 1, 2020

Good question.

Sunday, March 8, 2020

A Tool

Filed under: General — Tags: — m759 @ 2:23 PM

Detail: 

Click on the above date for further details.

Friday, February 14, 2020

Math Woo

Filed under: General — Tags: — m759 @ 6:45 PM

“Pure mathematics is, in its way, the poetry of logical ideas.
One seeks the most general ideas of operation which will
bring together in simple, logical and unified form the largest
possible circle of formal relationships. In this effort toward
logical beauty spiritual formulas are discovered necessary
for the deeper penetration into the laws of nature.”

— Albert Einstein, May 1, 1935, obituary for Emmy Noether
(Quoted in part, without source, in Quanta Magazine  yesterday.)

Friday, May 24, 2019

Stevens and the Hoary Sages

Filed under: General — Tags: — m759 @ 11:05 AM

See also other posts now tagged The Reality Blocks.

Tuesday, May 21, 2019

Inside the White Cube

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

(Continued)

Sunday, May 19, 2019

The Building Blocks of Geometry

Filed under: General — Tags: , , — m759 @ 10:21 PM

From "On the life and scientific work of Gino Fano
by Alberto Collino, Alberto Conte, and Alessandro Verra,
ICCM Notices , July 2014, Vol. 2 No. 1, pp. 43-57 —

" Indeed, about the Italian debate on foundations of Geometry, it is not rare to read comments in the same spirit of the following one, due to Jeremy Gray13. He is essentially reporting Hans Freudenthal’s point of view:

' When the distinguished mathematician and historian of mathematics Hans Freudenthal analysed Hilbert’s  Grundlagen he argued that the link between reality and geometry appears to be severed for the first time in Hilbert’s work. However, he discovered that Hilbert had been preceded by the Italian mathematician Gino Fano in 1892. . . .' "

13 J. Gray, "The Foundations of Projective Geometry in Italy," Chapter 24 (pp. 269–279) in his book Worlds Out of Nothing , Springer (2010).


Restoring the severed link —

Structure of the eightfold cube

See also Espacement  and The Thing and I.
 

Related material —

 
 

Tuesday, April 9, 2019

Old Guy with a Cane

Filed under: General — Tags: , — m759 @ 1:10 AM

From yesterday's post Misère Play —

See as well New York Times  book review of the novel Point Omega .
(The Times 's "Wrinkle in Time" is the title of the review, not of the novel.)

Related material suggested by the publication date — March 27, 2014
of a novel titled Zero Sum Game  —

Monday, September 17, 2018

Lying at the Axis

Filed under: G-Notes,General,Geometry — m759 @ 12:00 AM

Or:  Zero Dark Zero

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

Thursday, May 17, 2018

Leap

Filed under: General — Tags: — m759 @ 9:45 PM

Quoted here on May 5, 2018

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

The page number  229 may also be interpreted, cabalistically,
as the date  2/29, Leap Day.

See Leap Day 2016 among the posts tagged Mind Spider.

Wednesday, May 16, 2018

Church and Temple

Filed under: General — Tags: , , , — m759 @ 10:48 AM

Same Old Story

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

. . . as time goes by.

Tuesday, May 15, 2018

Space Revisited

Filed under: General — Tags: , — m759 @ 11:32 AM

"Well, let's see now "

— Tom Wolfe, July 18, 2009

Thursday, August 31, 2017

A Conway-Norton-Ryba Theorem

Filed under: General,Geometry — Tags: — m759 @ 1:40 PM

In a book to be published Sept. 5 by Princeton University Press,
John Conway, Simon Norton,  and Alex Ryba present the following
result on order-four magic squares —

A monograph published in 1976, “Diamond Theory,” deals with
more general 4×4 squares containing entries from the Galois fields
GF(2), GF(4), or GF(16).  These squares have remarkable, if not
“magic,” symmetry properties.  See excerpts in a 1977 article.

See also Magic Square and Diamond Theorem in this  journal.

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