See as well, in this journal, Deathly Hallows, Relativity Problem, and Space Cross.
A related quote: "This is not mathematics; this is theology."
See as well, in this journal, Deathly Hallows, Relativity Problem, and Space Cross.
A related quote: "This is not mathematics; this is theology."
The previous post, on the July 13 death of computer scientist Robert Fano,
suggests a review of "Deathly Hallows" posts in this journal. From that review —
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
For further information, click the image below —
The "eschaton" phrase above is from the works of Robert Anton Wilson.
That Robert A. Wilson should not be confused with
the Robert A. Wilson who is a GL(2,3) enthusiast.
Nor should immanentizing be confused with coordinatizing . . .
"Coordinatizing the Deathly Hallows" —
Related geometric remarks — Hashtag as Well —
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
Another name for the Fano plane design — The Ghostly Hallows.
From a search in this journal for Ghostly —
Hurt’s dies natalis (date of death, in the saints’ sense) was,
it now seems, 25 January 2017, not 27.
A connection, for fantasy fans, between the Philosopher’s Stone
(represented by the eightfold cube) and the Deathly Hallows
(represented by the usual Fano-plane figure) —
Images from a Log24 search for “Holocron.”
The above graphic design is by Noma Bar.
See as well the lamb-in-triangle of the Dec. 27 post
A Candle for Lily —
Related material —
Remarks by Evelyn Lamb on the Deathly Hallows symbol.
The Yale of the title is not the university, but rather the
mathematician Paul B. Yale. Yale's illustration of the Fano
plane is below.
A different illustration from a mathematician named Greenberg —
This illustration of the ominous phrase "line at infinity"
may serve as a sort of Deathly Hallows for Greenberg.
According to the AMS website yesterday, he died on
December 12, 2017:
A search of this journal for Greenberg yields no mention of
the dead mathematician, but does yield some remarks
on art that are pehaps less bleak than the above illustration.
For instance —
Art adapted from the Google search screen. Discuss.
"William Christopher, best known for playing Father Mulcahy
on the hit sitcom M*A*S*H , died Saturday [Dec. 31, 2016] of
lung cancer, his agent confirmed to The Hollywood Reporter.
He was 84.
Christopher died at his home in Pasadena, with his wife by
his bedside, at 5:10 a.m. on New Year's Eve, according to a
statement from his agent."
— 5:59 PM PST 12/31/2016 by Meena Jang
Image reshown in this journal on the midnight (Eastern time)
preceding Christopher's death —
Related material —
From a Log24 search for "Deathly Hallows" —
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
Those who prefer Latin with their theology
may search this journal for "In Nomine Patris."
From an article* in Proceedings of Bridges 2014 —
As artists, we are particularly interested in the symmetries of real world physical objects. Three natural questions arise: 1. Which groups can be represented as the group of symmetries of some real-world physical object? 2. Which groups have actually been represented as the group of symmetries of some real-world physical object? 3. Are there any glaring gaps – small, beautiful groups that should have a physical representation in a symmetric object but up until now have not? |
The article was cited by Evelyn Lamb in her Scientific American
weblog on May 19, 2014.
The above three questions from the article are relevant to a more
recent (Oct. 24, 2015) remark by Lamb:
"… finite projective planes [in particular, the 7-point Fano plane,
about which Lamb is writing] seem like a triumph of purely
axiomatic thinking over any hint of reality…."
For related hints of reality, see Eightfold Cube in this journal.
* "The Quaternion Group as a Symmetry Group," by Vi Hart and Henry Segerman
Omega is a Greek letter, Ω , used in mathematics to denote
a set on which a group acts.
For instance, the affine group AGL(3,2) is a group of 1,344
actions on the eight elements of the vector 3-space over the
two-element Galois field GF(2), or, if you prefer, on the Galois
field Ω = GF(8).
Related fiction: The Eight , by Katherine Neville.
Related non-fiction: A remark by Werner Heisenberg
in this journal on Saturday, June 6, 2015, the eightfold cube ,
and the illustrations below —
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
(A sequel to yesterday's ART WARS and this
morning's De Colores )
“Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind– as Eddington puts it– the colorful tale
of the subjective storyteller mind.” — Hermann Weyl
(Philosophy of Mathematics and Natural Science ,
Princeton, 1949, p. 237)
See also Deathly Hallows.
Comments on two sub-images from yesterday's
The Big Spielraum (image, 1 MB) that may or
may not interest Emma Watson —
The Potter Sub-Image
This is from a link in a July 8, 2011, post:
The above "Childhood's End" link leads to
a midrash on the Harry Potter series:
"After pg. 759 in Harry Potter and the
Deathly Hallows , my childhood ended."
The Carmichael Sub-Image
The number of the last page in the last Harry Potter
book is 759. This number may, for those with
cabalistic tendencies, be interpreted as the
number 3*23*11 from a 1931 mathematics paper:
Oslo artist Josefine Lyche has a new Instagram post,
this time on pyramids (the monumental kind).
My response —
Wikipedia's definition of a tetrahedron as a
"triangle-based pyramid" …
… and remarks from a Log24 post of August 14, 2013 :
Norway dance (as interpreted by an American)
I prefer a different, Norwegian, interpretation of "the dance of four."
Related material: |
See also some of Burkard Polster's triangle-based pyramids
and a 1983 triangle-based pyramid in a paper that Polster cites —
(Click image below to enlarge.)
Some other illustrations that are particularly relevant
for Lyche, an enthusiast of magic :
From On Art and Magic (May 5, 2011) —
|
(Updated at about 7 PM ET on Dec. 3.)
"How about another hand for the band?
They work real hard for it.
The Cherokee Cowboys, ladies and gentlemen."
— Ray Price, video, "Danny Boy Mid 80's Live"
Other deathly hallows suggested by today's NY Times—
Click the above image for posts from December 14.
That image mentions a death on August 5, 2005, in
"entertainment Mecca" Branson, Missouri.
Another note from August 5, 2005, reposted here
on Monday—
Happy birthday, Keith Richards.
"Just the facts." — Attributed to Joe Friday
A search in this journal in honor of the late
Christopher Hitchens yields links to two of his reviews—
a review of the author of The Girl with the Dragon Tattoo and
a review of a work by a rather different author—
King Arthur and the Deathly Hallows
BLACK KNIGHT: None shall pass.
ARTHUR: What?
BLACK KNIGHT: None shall pass.
ARTHUR: I have no quarrel with you, good Sir Knight,
but I must cross this bridge.
BLACK KNIGHT: Then you shall die.
ARTHUR: I command you as King of the Britons
to stand aside!
BLACK KNIGHT: I move for no man.
ARTHUR: So be it!
— Monty Python
Above: Anthony Bushell as King Arthur in 1954.
Bushell died on April 2, 1997 (4/2/97).
"Well, she was just seventeen…."
Two Blocks Short of a Design:
A sequel to this morning’s post on Douglas Hofstadter
Photo of Hofstadter by Mike McGrath taken May 13, 2006 |
Related material — See Lyche’s “Theme and Variations” in this journal
and Hofstadter’s “Variations on a Theme as the Essence of Imagination”
— Scientific American October 1982
A quotation from a 1985 book by Hofstadter—
“… we need to entice people with the beauties of clarity, simplicity, precision,
elegance, balance, symmetry, and so on.
Those artistic qualities… are the things that I have tried to explore and even
to celebrate in Metamagical Themas . (It is not for nothing that the word
‘magic’ appears inside the title!)”
The artistic qualities Hofstadter lists are best sought in mathematics, not in magic.
An example from Wikipedia —
Mathematics The Fano plane block design |
Magic The Deathly Hallows symbol— |
Related symbolism from Plato’s Cave—
Recall that Ariadne in “Inception” is played by Ellen Page .
“Show me all the blueprints.”
— Howard Hughes, according to Hollywood
Some fear that the Harry Potter books introduce children to the occult; they are not entirely mistaken.
According to Wikipedia, the “Deathly Hallows” of the final Harry Potter novel are “three fictional magical objects that appear in the book.”
The vertical line, circle, and triangle in the symbol pictured above are said to refer to these three magical objects.
One fan relates the “Deathly Hallows” symbol above, taken from the spine of a British children’s edition of the book, to a symbol for “the divine (or sacred, or secret) fire” of alchemy. She relates this fire in turn to “serpent power” and the number seven:
Kristin Devoe at a Potter fan site:
“We know that seven is a powerful number in the novels. Tom Riddle calls it ‘the most powerfully magic number.‘ The ability to balance the seven chakras within oneself allows the person to harness the secret fire. This secret fire in alchemy is the same as the kundalini or coiled snake in yogic philosophy. It is also known as ‘serpent power’ or the ‘dragon’ depending on the tradition. The kundalini is polar in nature and this energy, this internal fire, is very powerful for those who are able to harness it and it purifies the aspirant allowing them the knowledge of the universe. This secret fire is the Serpent Power which transmutes the base metals into the Perfect Gold of the Sun.
It is interesting that the symbol of the caduceus in alchemy is thought to have been taken from the symbol of the kundalini. Perched on the top of the caduceus, or the staff of Hermes, the messenger of the gods and revealer of alchemy, is the golden snitch itself! Many fans have compared this to the scene in The Order of the Phoenix where Harry tells Dumbledore about the attack on Mr. Weasley and says, ‘I was the snake, I saw it from the snake’s point of view.‘
The chapter continues with Dumbledore consulting ‘one of the fragile silver instruments whose function Harry had never known,’ tapping it with his wand:
The instrument tinkled into life at once with rhythmic clinking noises. Tiny puffs of pale green smoke issued from the minuscule silver tube at the top. Dumbledore watched the smoke closely, his brow furrowed, and after a few seconds, the tiny puffs became a steady stream of smoke that thickened and coiled into he air… A serpent’s head grew out of the end of it, opening its mouth wide. Harry wondered whether the instrument was confirming his story; He looked eagerly at Dumbledore for a sign that he was right, but Dumbledore did not look up.
“Naturally, Naturally,” muttered Dumbledore apparently to himself, still observing the stream of smoke without the slightest sign of surprise. “But in essence divided?”
Harry could make neither head not tail of this question. The smoke serpent, however split instantly into two snakes, both coiling and undulating in the dark air. With a look of grim satisfaction Dumbledore gave the instrument another gentle tap with his wand; The clinking noise slowed and died, and the smoke serpents grew faint, became a formless haze, and vanished.
Could these coiling serpents of smoke be foreshadowing events to come in Deathly Hallows where Harry learns to ‘awaken the serpent’ within himself? Could the snake’s splitting in two symbolize the dual nature of the kundalini?”
and the following
famous illustration of
the double-helix
structure of DNA:
This is taken from
a figure accompanying
an obituary, in today’s
New York Times, of the
artist who drew the figure.
The double helix
is not a structure
from magic; it may,
however, as the Rowling
quote above shows, have
certain occult uses,
better suited to
Don Henley’s
Garden of Allah
than to the
Garden of Apollo.
Similarly, the three objects
above (Log24 on April 9)
are from pure mathematics–
the realm of Apollo, not
of those in Henley’s song.
The similarity of the
top object of the three —
the “Fano plane” — to
the “Deathly Hallows”
symbol is probably
entirely coincidental.
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