* See Halmos + Tombstone in this journal.
Saturday, September 18, 2021
A Tombstone* for Sinclair
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Sunday, November 11, 2018
Tombstone
See also this journal on the above Catch-22 date — July 16, 2014 —
and a search in this journal for "Halmos + Tombstone."
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Thursday, July 16, 2015
Tombstone
The black rectangle at the end of Example 1.4
is known as the "end-of-proof symbol," "Halmos,"
or "tombstone."
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Thursday, July 14, 2011
Tombstones
Part I: Literal
"Shinin' like a diamond,
she had tombstones in her eyes."
Part II: Figurative
See Halmos Tombstone in this journal.
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Monday, January 8, 2024
The Star Brick
From a post of January 3, 2024 —
"Hello darkness, my old friend.
I’ve come to talk with you again."
The above image was flipped to reverse left and right.
Related reading: Other posts tagged Darkness and …
Related material: Other posts tagged Star Brick and . . .
"And we may see the meadow in December,
icy white and crystalline"
— Song lyric, "Midnight Sun"
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Wednesday, January 3, 2024
Negative Space
A recently coined phrase — "Negative Mathematics" — is related to the
better-known phrase "Negative Space."
The latter is closely related to the proof of the Cullinane diamond theorem.
For the former, see . . .
Related material: The proof symbol, i.e. the Halmos Tombstone.
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Flippant
From the Log24 search in the previous post for "Dimensions" —
"Hello darkness, my old friend.
I’ve come to talk with you again."
The above image was flipped to reverse left and right.
Related reading: Other posts tagged Darkness and …
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Monday, March 12, 2018
“Quantum Tesseract Theorem?”
Remarks related to a recent film and a not-so-recent film.
For some historical background, see Dirac and Geometry in this journal.
Also (as Thas mentions) after Saniga and Planat —
The Saniga-Planat paper was submitted on December 21, 2006.
Excerpts from this journal on that date —
"Open the pod bay doors, HAL."
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Monday, July 18, 2011
Voldemort
Continuing yesterday's lottery meditation…
The NY evening numbers yesterday were 244 and 2962.
The latter suggests Post 2962—
There is no Post 244 here, but a search within this journal for 244 yields…
See also Halmos Tombstone and Death Proof.
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Monday, September 8, 2008
Monday September 8, 2008
Related material:
Tuesday, July 31, 2007Aesthetics for JesuitsJoke The Guardian, July 26, “… inspired satire, laced with Jewish and Christian polemics, sparkling wit and dazzlingly simple effects. For Golgotha a stagehand brings on three crosses. ‘Just two,’ says Jay. ‘The boy is bringing his own.’ Tabori often claimed that the joke was the most perfect literary form.” |
Update at noon,
Sept. 9, 2008:
Tabori, a Jew from Hungary
and former screenwriter
(“No Exit“), died at 93
on July 23, 2007.
For related material on
another Jew from Hungary
click on the black monolith
(also known as
the Halmos tombstone).
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Tuesday, October 10, 2006
Tuesday October 10, 2006
Mate in
Two Seconds
From Oct. 13 last year
(Yom Kippur):
Two Seconds
From Oct. 13 last year
(Yom Kippur):
|
A Poem for Pinter
Oct. 13, 2005 The Guardian on Harold Pinter, winner of this year's Nobel Prize for Literature: "Earlier this year, he announced his decision to retire from playwriting in favour of poetry," Michael Muskal in today's Los Angeles Times: "Pinter, 75, is known for his sparse and thin style as well as his etched characters whose crystal patter cuts through the mood like diamond drill bits." Robert Stone, A Flag for Sunrise (See Jan. 25): "'That old Jew gave me this here.' Egan looked at the diamond…. 'It's worth a whole lot of money– you can tell that just by looking– but it means something, I think. It's got a meaning, like.'
'Let's see,' Egan said, 'what would it mean?' He took hold of Pablo's hand cupping the stone and held his own hand under it. '"The jewel is in the lotus," perhaps that's what it means. The eternal in the temporal….'"
"Modal logic was originally developed to investigate logic under the modes of necessary and possible truth. The words 'necessary' and 'possible' are called modal connectives, or modalities. A modality is a word that when applied to a statement indicates when, where, how, or under what circumstances the statement may be true. In terms of notation, it is common to use a box [] for the modality 'necessary' and a diamond <> for the modality 'possible.'"
Commentary:
"Waka" also means Japanese poem or Maori canoe. (For instance, this Japanese poem and this Maori canoe.)
For a meditation on "bang splat," see Sept. 25-29. For the meaning of "tick tick," see Emily Dickinson on "degreeless noon." "Hash," of course, signifies "checkmate." (See previous three entries.) |
For language more suited to
the year's most holy day, see
this year's Yom Kippur entry,
from October 2.
That was also the day of the
Amish school killings in
Pennsylvania and the day that
mathematician Paul Halmos died.
For more on the former, see
Death in Two Seconds.
For more on the latter, see
The Halmos Tombstone.
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Thursday, October 5, 2006
Thursday October 5, 2006
In Touch with God
(Title of an interview with
the late Paul Halmos, mathematician)
Since Halmos died on Yom Kippur, his thoughts on God may be of interest to some.
And, more simply,
April 28, 2004:
From a 1990 interview:
“What’s the best part of being a mathematician? I’m not a religious man, but it’s almost like being in touch with God when you’re thinking about mathematics. God is keeping secrets from us, and it’s fun to try to learn some of the secrets.”
I personally prefer Annie Dillard on God:
“… if Holy the Firm is matter at its dullest, Aristotle’s materia prima, absolute zero, and since Holy the Firm is in touch with the Absolute at base, then the circle is unbroken. And it is…. Holy the Firm is in short the philosopher’s stone.”
Some other versions of
the philosopher’s stone:
April 28, 2004:
This last has the virtue of
being connected with Halmos
via his remarks during the
“In Touch with God” interview:
“…at the root of all deep mathematics there is a combinatorial insight… the really original, really deep insights are always combinatorial….”
“Combinatorics, the finite case, is where the genuine, deep insight is.”
“Combinatorics, the finite case, is where the genuine, deep insight is.”
See also the remark of Halmos that serves as an epigraph to Theme and Variations.
Finally, it should be noted that
the 4×9 black rectangle
the 4×9 black rectangle
has also served
at least one interpreter
as a philosopher’s stone,
and is also the original
“Halmos tombstone.”
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Wednesday, October 4, 2006
Wednesday October 4, 2006
Paul R. Halmos died
on Yom Kippur, 2006
on Yom Kippur, 2006
“Prof. Paul Halmos died of pneumonia early in the morning of October 2, 2006. He was 90 years old. He is survived by his wife, Virginia Halmos. An obituary may be found at the website of the Mathematical Association of America….”
— Halmos’s home page
at Santa Clara University
For a memorial of sorts, see
Lovely, Dark and Deep.
Update of 8 PM Oct. 4 —
From Google Book Search:
This is the source of the
“Halmos tombstone” symbol,
which has been described in a
different form at Wikipedia:
“The tombstone, or halmos–
symbol ∎ (Unicode U+220E)–
is used in mathematics to denote
the end of a proof.”
This Unicode character is rendered
as an empty square in Explorer
and as a black square in Firefox.
Related material:
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Wednesday, May 17, 2006
Wednesday May 17, 2006
Tombstone
From today's New York Times:
"Jiri Frel, a mercurial and eccentric curator who helped build the J. Paul Getty Museum into a major center for Greek and Roman art but resigned after revelations about unscrupulous acquisition practices, died on April 29. He was 82…. a well-regarded expert in Greek tombstones…."
"ATHENS, May 16 — After four hours of talks here with the Greek culture minister, the director of the J. Paul Getty Museum in Los Angeles said Tuesday that he would press for the return of some of the Getty's most prized ancient artifacts to Greece…. Greece is seeking the repatriation of a… tombstone…."
From a photo accompanying the obituary:
Museum
window
To Aster, from Plato
Asteras eisathreis, Aster emos.
Eithe genoimen ouranos,
'os pollois ommasin eis se blepo.
You gaze at stars, my Star.
Would that I were born the starry sky,
that I with many eyes might gaze at you.
Related material:
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Sunday, October 26, 2003
Sunday October 26, 2003
ART WARS for
Trotsky’s Birthday
Part I:
Symbols
From my entry of July 26, 2003, in memory
of Marathon Man director John Schlesinger:
|
Bright Star and Dark Lady “Mexico is a solar country — but it is also a black country, a dark country. This duality of Mexico has preoccupied me since I was a child.” — Octavio Paz, |
||
|
Bright Star
|
Amen. |
Dark Lady
|
For the meaning of the above symbols, see
Kubrick’s 1x4x9 monolith in 2001,
the Halmos tombstone in Measure Theory,
and the Fritz Leiber Changewar stories.
Part II:
Sunday in the Park with Death
To Leon from Diego —
Details of a mural,
A Dream of a Sunday Afternoon
in Alameda Park,
Fresco, 1947-48,
Alameda Hotel, Mexico City:
Three’s a Crowd:
Symbol:
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Saturday, July 26, 2003
Saturday July 26, 2003
Funeral March
|
John Schlesinger dead at 77; LOS ANGELES – Oscar-winning director John Schlesinger, who daringly brought gay characters into mainstream cinema with Midnight Cowboy and tapped into nightmares with the teeth-drilling torture of Marathon Man, died Friday at 77. The British-born filmmaker…. died about 5:30 a.m…. |
Schlesinger also directed The Day of the Locust, based on a novel by Nathanael West.
See Heaven, Hell, and Hollywood and
From the latter:
“Then you know your body’s sent,
Don’t care if you don’t pay rent,
Sky is high and so am I,
If you’re a viper — a vi-paah.”
— The Day of the Locust,
by Nathanael West (1939),
New Directions paperback,
1969, page 162
This song may be downloaded at
That same site begins with a traditional Mexican song…
“La cucaracha, la cucaracha,
ya no puede caminar,
porque no quiere,
porque le falta
marihuana que fumar.”
(“The cockroach, the cockroach,
can’t walk anymore,
because he doesn’t want to,
because he has no
marihuana to smoke.”)
This suggests an appropriate funeral march for John Schlesinger:
“Ya murió la cucaracha, ya la llevan a enterrar…” – La Cucaracha
Those attending Schlesinger’s wake, as opposed to his funeral, may wish to perform other numbers from the Pot Culture page, which offers a variety of “viper” songs.
|
Bright Star and Dark Lady “Mexico is a solar country — but it is also a black country, a dark country. This duality of Mexico has preoccupied me since I was a child.” — Octavio Paz, |
||
|
Bright Star
|
Amen.
|
Dark Lady
|
For the meaning of the above symbols, see
Kubrick’s 1x4x9 monolith in 2001,
the Halmos tombstone in Measure Theory,
and the Fritz Leiber Changewar stories.
Concluding Unscientific Postscript:
Oh, yes… the question of
Heaven or Hell for John Schlesinger…
Recall that he also directed the delightful
Cold Comfort Farm and see
last year’s entry for this date.
Monday, October 4, 2021
The Stanley Kubrick Award for Novel Engineering*…
Goes to Facebook !
https://www.nytimes.com/2021/10/04/
technology/facebook-down.html —
"Facebook’s global security operations center
determined the outage was 'a HIGH risk to
the People, MODERATE risk to Assets and
a HIGH risk to the Reputation of Facebook,'
the company memo said.
A small team of employees was soon dispatched
to Facebook’s Santa Clara, Calif., data center to
try a 'manual reset' of the company’s servers,
according to an internal memo."
On this date 15 years ago, other Santa Clara news . . .
* See today's previous post, Bookstores.
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Monday, November 12, 2018
Half Crazy
Douglas Rain, the voice of HAL in Kubrick's 2001 , reportedly
died at 90 on Sunday, Nov. 11, 2018. A piece from the Sunday,
April 1, 2018, print edition of The New York Times recalls that . . .
|
When HAL says, “I know I’ve made some very poor decisions recently, but I can give you my complete assurance that my work will be back to normal,” Mr. Rain somehow manages to sound both sincere and not reassuring. And his delivery of the line “I think you know what the problem is just as well as I do” has the sarcastic drip of a drawing-room melodrama and also carries the disinterested vibe of a polite sociopath. Kubrick had Mr. Rain sing the 1892 love song “Daisy Bell” (“I’m half crazy, all for the love of you”) almost 50 times, in uneven tempos, in monotone, at different pitches and even just by humming it. In the end, he used the very first take. Sung as HAL’s brain is being disconnected, it’s from his early programming days, his computer childhood. It brings to an end the most affecting scene in the entire film.
— Gerry Flahive in the online New York Times , "A version of this article appears in print on , on Page AR13 of the New York edition with the headline: HAL 9000 Wasn’t Always So Eerily Calm." |
This journal on the above online date, March 30, 2018 —
"Program or be programmed."
— A saying by Douglas Rushkoff
See as well the following link from this journal
on Armistice Day, the reported date of Mr. Rain's death —
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Thursday, March 7, 2013
Proof Symbol
Today's previous post recalled a post
from ten years before yesterday's date.
The subject of that post was the
Galois tesseract.
Here is a post from ten years before
today's date.
The subject of that post is the Halmos
tombstone:
"The symbol is used throughout the entire book
in place of such phrases as 'Q.E.D.' or 'This
completes the proof of the theorem' to signal
the end of a proof."
— Measure Theory (1950)
For exact proportions, click on the tombstone.
For some classic mathematics related
to the proportions, see September 2003.
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Tuesday, October 6, 2009
Sunday, October 22, 2006
Sunday October 22, 2006
Ad for "The Prestige":
"Every great magic trick consists of three acts. The first act is called 'The Pledge.' The magician shows you something ordinary, but of course… it probably isn't. The second act is called 'The Turn.' The magician makes his ordinary 'some thing' do something extraordinary. Now if you're looking for the secret… you won't find it. That's why there's a third act, called 'The Prestige.' This is the part with the twists and turns, where lives hang in the balance, and you see something shocking you've never seen before."
The Associated Press
Thought for Today,
Oct. 22, 2006:
Thought for Today,
Oct. 22, 2006:
"You can fool
too many of the people
too much of the time."
— James Thurber,
American humorist
(1894-1961)
For more detail,
click on the above
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Friday, October 20, 2006
Friday October 20, 2006
“Halmos”
For one definition, see
Tombstone (typography)
at Wikipedia.
A halmos, according to
the Wikipedia definition:
For one definition, see
Tombstone (typography)
at Wikipedia.
A halmos, according to
the Wikipedia definition:
Click on the halmos
for further details from
today’s New York Times.
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Sunday, March 9, 2003
Sunday March 9, 2003
Symbols —
Broadway:
The Sound of Silence
|
Hello darkness, my old friend. I’ve come to talk with you again. (See previous entry, Mar. 7, “Lovely, Dark and Deep.) |
And the people bowed and prayed to the neon god they made. (See CNN.com Broadway City Arcade club story of Mar. 9) |
The words of the prophets are written on the subway walls. (See picture in NY Times Book Review, Mar. 9, page 31.) |
See also the footnote on the Halmos “tombstone” symbol in the previous entry, the entry “Dustin in Wonderland” of Feb. 24, the film “Marathon Man,” and the entry “Geometry for Jews” of March 6.
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