Russell in Your Head-Roe

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world. — Bertrand Russell, “The Study Of Mathematics” (1902)


The title of this incendiary intervention is of course a paronomasia on these lines from Led Zeppelin’s magisterial “Stairway to Heaven”:

“If there’s a bustle in your hedgerow, don’t be alarmed now:
It’s just a spring-clean for the May Queen…”

And “head-roe” is a kenning for “brain”.

Bat out of L

Pre-previously on Overlord-in-terms-of-the-Über-Feral, I’ve looked at intensively interrogated issues around the L-triomino, a shape created from three squares that can be divided into four copies of itself:

An L-triomino divided into four copies of itself


I’ve also interrogated issues around a shape that yields a bat-like fractal:

A fractal full of bats


Bat-fractal (animated)


Now, to end the year in spectacular fashion, I want to combine the two concepts pre-previously interrogated on Overlord-in-terms-of-the-Über-Feral (i.e., L-triominoes and bats). The L-triomino can also be divided into nine copies of itself:

An L-triomino divided into nine copies of itself


If three of these copies are discarded and each of the remaining six sub-copies is sub-sub-divided again and again, this is what happens:

Fractal stage 1


Fractal stage 2


Fractal #3


Fractal #4


Fractal #5


Fractal #6


Et voilà, another bat-like fractal:

L-triomino bat-fractal (static)


L-triomino bat-fractal (animated)


Elsewhere other-posted:

Tri-Way to L
Bats and Butterflies
Square Routes
Square Routes Revisited
Square Routes Re-Revisited
Square Routes Re-Re-Revisited

Performativizing Papyrocentricity #59

Papyrocentric Performativity Presents:

Mobile MetalBattleground: The Greatest Tank Duels in History, ed. Steven J. Zaloga (Osprey Publishing 2011)

Allum’s Album – The Collector’s Cabinet: Tales, Facts and Fictions from the World of Antiques, Marc Allum (Icon Books 2013)

Aschen PassionDeath in Venice and Other Stories, Thomas Mann, translated by David Luke (1988)


Or Read a Review at Random: RaRaR

Tridentine Math

The Tridentine Mass is the Roman Rite Mass that appears in typical editions of the Roman Missal published from 1570 to 1962. — Tridentine Mass, Wikipedia

A 30°-60°-90° right triangle, with sides 1 : √3 : 2, can be divided into three identical copies of itself:

30°-60°-90° Right Triangle — a rep-3 rep-tile…


And if it can be divided into three, it can be divided into nine:

…that is also a rep-9 rep-tile


Five of the sub-copies serve as the seed for an interesting fractal:

Fractal stage #1


Fractal stage #2


Fractal stage #3


Fractal #4


Fractal #5


Fractal #6


Fractal #6


Tridentine cross (animated)


Tridentine cross (static)


This is a different kind of rep-tile:

Noniamond trapezoid


But it yields the same fractal cross:

Fractal #1


Fractal #2


Fractal #3


Fractal #4


Fractal #5


Fractal #6


Tridentine cross (animated)


Tridentine cross (static)


Elsewhere other-available:

Holey Trimmetry — another fractal cross

Alpha Beat a Gamer

Abstract: The game of chess is the most widely-studied domain in the history of artificial intelligence. The strongest programs are based on a combination of sophisticated search techniques, domain-specific adaptations, and handcrafted evaluation functions that have been refined by human experts over several decades. In contrast, the AlphaGo Zero program recently achieved superhuman performance in the game of Go, by tabula rasa reinforcement learning from games of self-play. In this paper, we generalise this approach into a single AlphaZero algorithm that can achieve, tabula rasa, superhuman performance in many challenging domains. Starting from random play, and given no domain knowledge except the game rules, AlphaZero achieved within 24 hours a superhuman level of play in the games of chess and shogi (Japanese chess) as well as Go, and convincingly defeated a world-champion program in each case. — “Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm”, 5/XII/2017.

Tott ist Rot

• Lautlos und fein rann der rostrot gefärbte Sand durch die gläserne Enge, und da er in der oberen Höhlung zur Neige ging, hatte sich dort ein kleiner, reißender Strudel gebildet. — Thomas Mann, Der Tod in Venedig (1912)

• Silently, subtly, the rust-red sand trickled through the narrow glass aperture, dwindling away out of the upper vessel, in which a little whirling vortex had formed. — “Death in Venice” (translated by David Luke)

Oh My Guardian #4

• The past 16 years have involved a lot of questioning and reflecting, both in terms of what it means to be “good”, but also on the various racist myths about Muslims. — Let’s be clear: Muslims are neither good nor bad. We’re just human, Farah in terms of Elahi, The Guardian, 14/xii/2017.


Elsewhere other-available:

Oh My Guardian #1
Oh My Guardian #2
Oh My Guardian #3
Reds under the Thread

Square Routes Re-Re-Revisited

This is an L-triomino, or shape created from three squares laid edge-to-edge:

When you divide each square like this…

You can create a fractal like this…

Stage #1


Stage #2


Stage #3


Stage #4


Stage #5


Stage #6


Stage #7


Stage #8


Stage #9


Stage #10


Animated fractal


Here are more fractals created from the triomino:

Animated


Static


Animated


Static


Animated


Static


And here is a different shape created from three squares:

And some fractals created from it:

Animated


Static


Animated


Static


Animated


Static


And a third shape created from three squares:

And some fractals created from it:

Animated


Static


Animated


Static


Animated


Static


Animated


Static


Animated


Static


Animated


Static


Animated


Static


Animated


Static


Previously pre-posted (please peruse):

Tri-Way to L
Square Routes
Square Routes Revisited
Square Routes Re-Revisited

Toxic Turntable #13

Currently listening…

• Ilm Beogdé, Best Of (1994)
• The Brandywines, Ludlow (1988)
• Murine, A Glass Alga (1997)
• Ichtherion, Et Agnus Vincet (1975)
• Xmode, Giftzwerg (1982)
• Uar Csolt, Marginsur (2010)
• Thomas Skinner Orchestra, Wasidu (1959)
• Elxuve, Howdja (1991)
• Iwri, Iwri 2 (1979)
• Henkerkunst, Gänzehaut (2011)
• Albion Chimes, Soltrip (1969)
• Vihol, F.E.S. (1982)
• Aitmao w Niau, Celebes (2012)


Previously pre-posted:

Toxic Turntable #1#2#3#4#5#6#7#8#9#10#11#12 •