Performativizing Papyrocentricity #10

Papyrocentric Performativity Presents:

Sea HereSea Charts of the British Isles: A Voyage of Discovery around Britain & Ireland’s Coastline, John Blake (Conway Maritime Press, 2005)

Art-BanditOutsider II: Always Almost, Never Quite, Brian Sewell (Quartet Books, 2012)

Clarke’s ArksImperial Earth (1976) and Rendezvous with Rama (1972), Arthur C. Clarke

The Joy of ’LeksThe Dalek Handbook, Steve Tribe and James Goss (BBC Books, 2011)

Or Read a Review at Random: RaRaR

Lit Is It

You know, I’m getting worried at my inability to have unmediated experiences. Everything reminds me of something in literature. It reminds me of this passage in Brideshead Revisited (1945):

“Oh, don’t talk in that damned bounderish way. Why must you see everything second-hand? Why must this be a play? Why must my conscience be a Pre-Raphaelite picture?”

“It’s a way I have.”

“I hate it.” (Op. cit.)

He Say, He Sigh, He Sow #12

“There were no bears, but at one point I disturbed an eagle on a ledge — and perhaps have seen nothing more beautiful than the one lazy flap of its wings that set it on a seemingly effortless vertical flight up the sun-warmed cliff behind it.” — the art-critic Brian Sewell describing a Turkish journey in Outsider II: Always Almost, Never Quite (2012).

Neuclid on the Block

How many blows does it take to demolish a wall with a hammer? It depends on the wall and the hammer, of course. If the wall is reality and the hammer is mathematics, you can do it in three blows, like this:

α’. Σημεῖόν ἐστιν, οὗ μέρος οὐθέν.
β’. Γραμμὴ δὲ μῆκος ἀπλατές.
γ’. Γραμμῆς δὲ πέρατα σημεῖα.

1. A point is that of which there is no part.
2. A line is a length without breadth.
3. The extremities of a line are points.

That is the astonishing, world-shattering opening in one of the strangest – and sanest – books ever written. It’s twenty-three centuries old, was written by an Alexandrian mathematician called Euclid (fl. 300 B.C.), and has been pored over by everyone from Abraham Lincoln to Bertrand Russell by way of Edna St. Vincent Millay. Its title is highly appropriate: Στοιχεῖα, or Elements. Physical reality is composed of chemical elements; mathematical reality is composed of logical elements. The second reality is much bigger – infinitely bigger, in fact. In his Elements, Euclid slipped the bonds of time, space and matter by demolishing the walls of reality with a mathematical hammer and escaping into a world of pure abstraction.

• Continue reading Neuclid on the Block

O Apollo

One of Swinburne’s most powerful, but least-known, poems is “The Last Oracle”, from Poems and Ballads, Second Series (1878). A song in honour of the god Apollo, it begins in lamentation:

Years have risen and fallen in darkness or in twilight,
   Ages waxed and waned that knew not thee nor thine,
While the world sought light by night and sought not thy light,
   Since the sad last pilgrim left thy dark mid shrine.
Dark the shrine and dumb the fount of song thence welling,
   Save for words more sad than tears of blood, that said:
Tell the king, on earth has fallen the glorious dwelling,
   And the watersprings that spake are quenched and dead.
Not a cell is left the God, no roof, no cover
   In his hand the prophet laurel flowers no more.

And ends in exultation:

         For thy kingdom is past not away,
            Nor thy power from the place thereof hurled;
         Out of heaven they shall cast not the day,
            They shall cast not out song from the world.
         By the song and the light they give
         We know thy works that they live;
         With the gift thou hast given us of speech
         We praise, we adore, we beseech,
         We arise at thy bidding and follow,
            We cry to thee, answer, appear,
   O father of all of us, Paian, Apollo,
            Destroyer and healer, hear! (“The Last Oracle”)

The power, grandeur and beauty of this poem remind me of the music of Beethoven. Swinburne is also, on a smaller scale and in a different medium, one of the geniuses of European art. He and Beethoven were both touched by Apollo, but Apollo was more than the god of music and poetry: he also presided mathematics. But then mathematics is much more visible, or audible, in music and poetry than it is in other arts. Rhythm, harmony, scansion, melody and rhyme are mathematical concepts. Music is built of notes, poetry of stresses and rhymes, and the rules governing them are easier to formalize than those governing, say, sculpture or prose.  Nor do poetry and music have to make sense or convey explicit meaning like other arts. That’s why I think a shape like this is closer to poetry or music than it is to painting:

Apollonian gasket (Wikipedia)

(Image from Wikipedia.)

This shape has formal structure and beauty, but it has no explicit meaning. Its name has a divine echo: the Apollonian gasket or net, named after the Greek mathematician Apollonius of Perga (c.262 BC–c.190 BC), who was named after Apollo, god of music, poetry and mathematics. The Apollonian gasket is a fractal, but the version above is not as fractal as it could be. I wondered what it would look like if, like fleas preying on fleas, circles appeared inside circles, gaskets within gaskets. I haven’t managed to program the shape properly yet, but here is my first effort at an Intra-Apollonian gasket:

Apollonian gasket

(If the image does not animate or looks distorted, please try opening it in a new window)

When the circles are solid, they remind me of ice-floes inside ice-floes:

Apollonian gasket (solid)

Simpler gaskets can be interesting too:

five-circle gasket

five+four-circle gasket

nine-circle gasket

Paradigm Lost

Genius schmenius — genetics is sooooo 1950s:

But Paul Martin, a sociologist at the University of Sheffield, UK, is surprised that geneticists are still pursuing this line of research. “I think most people would say that’s the wrong paradigm, when most educational research suggests that social factors are incredibly important,” he says. “Strategically, this seems like something of a throwback.”

Chinese project probes the genetics of genius

See? Sense and decency. That’s because sociology is a proper science. Nearly as proper as psychoanalysis or astrology, in fact.

Spiral Archipelago

Incomplete map of Earthsea

Incomplete map of Earthsea

Ursula K. Le Guin, creatrix of Earthsea, is a much better writer than J.R.R. Tolkien, creator of Middle-earth: much more subtle, skilful and sophisticated. But for me Middle-earth has one big advantage over Earthsea: I can imagine Middle-earth really existing. I can’t say that for Earthsea, an archipelago-world of fishermen, goatherds and wizards. There’s something dead and disconnected about Earthsea. I’m not sure what it is, but it may have something to do with Le Guin’s dedicated political correctness.

For example, despite the northern European climate and culture on Earthsea, a sea-faring world with lots of rain, mist, snow and mountains, most of the people are supposed to have dark skins. The ones that don’t – the white-skinned, blond-haired Kargs – are the bloodthirsty baddies of A Wizard of Earthsea (1968), the first book in the series. Balls to biology, in other words: there’s propaganda to propagate. So it’s not surprising that Le Guin’s father was a famous and respected figure in the mostly disreputable discipline of anthropology. Earthsea is fantasy for Guardian-readers, in short.

But I still like the idea of an archipelago-world: sea and islands, islands and sea. As Le Guin herself says: “We all have archipelagos in our minds.” That’s one of the reasons I like the Ulam spiral: it reminds me of Earthsea. Unlike Earthsea, however, the sea and islands go on for ever. In the Ulam spiral, the islands are the prime numbers and the sea is the composite numbers. It’s based on a counter-clockwise spiral of integers, like this:

 ↓                                               ↑
146 101←100←099←098←097←096←095←094←093←092←091 132
 ↓   ↓                                       ↑   ↑
147 102 065←064←063←062←061←060←059←058←057 090 131
 ↓   ↓   ↓                                  ↑   ↑
148 103 066 037←036←035←034←033←032←031 056 089 130
 ↓   ↓   ↓   ↓                       ↑   ↑   ↑   ↑
149 104 067 038 017←016←015←014←013 030 055 088 129
 ↓   ↓   ↓   ↓   ↓               ↑      ↑   ↑   ↑
150 105 068 039 018 005←004←003 012 029 054 087 128
 ↓   ↓   ↓   ↓   ↓   ↓       ↑   ↑   ↑   ↑   ↑   ↑
151 106 069 040 019 006 001002 011 028 053 086 127
 ↓   ↓   ↓   ↓   ↓   ↓           ↑      ↑   ↑   
152 107 070 041 020 007→008→009→010 027 052 085 126
 ↓   ↓   ↓   ↓   ↓                   ↑   ↑   ↑   ↑
153 108 071 042 021→022→023→024→025→026 051 084 125
 ↓   ↓   ↓   ↓                           ↑   ↑   ↑
154 109 072 043→044→045→046→047→048→049→050 083 124
 ↓   ↓   ↓                                   ↑   ↑
155 110 073→074→075→076→077→078→079→080→081→082 123
 ↓   ↓                                           ↑
156 111→112→113→114→115→116→117→118→119→120→121→122
 ↓                                                   ↑

The spiral is named after Stanislaw Ulam (1909-84), a Polish mathematician who invented it while doodling during a boring meeting. When numbers are represented as pixels and 1 is green, the spiral looks like this – note the unique “knee” formed by 2, 3 (directly above 2) and 11 (to the right of 2):

Ulam spiral

Ulam spiral (animated)

(If the image above does not animate, please try opening it in a new window.)

Some prime-pixels are isolated, like eyots or aits (small islands) in the number-sea, but some touch corner-to-corner and form larger units, larger islands. There are also prime-diamonds, like islands with lakes on them. The largest island, with 19 primes, may come very near the centre of the spiral:


Island 1 = (5, 7, 17, 19, 23, 37, 41, 43, 47, 67, 71, 73, 79, 103, 107, 109, 113, 149, 151) (i=19) (x=-3, y=3, n=37) (n=1 at x=0, y=0)

Here are some more prime-islands – prIslands or priminsulas – in the Ulam-sea that I find interesting or attractive for one reason or other:


Island 2 = (281, 283, 353, 431, 433, 521, 523, 617, 619, 719, 827, 829, 947) (i=13) (x=6, y=-12, n=619)


Island 3 = (20347, 20921, 21499, 21503, 22091, 22093, 22691, 23293, 23297, 23909, 23911, 24533, 25163, 25801, 26449, 27103, 27767, 28439) (i=18) (x=-39, y=-81, n=26449)


Island 4 = (537347, 540283, 543227, 546179, 549139, 552107, 555083, 558067, 561059, 561061, 564059, 564061, 567067, 570083, 573107, 573109) (i=16) (x=375, y=-315, n=561061)


Island 5 = (1259047, 1263539, 1263541, 1268039, 1272547, 1277063, 1281587, 1286119, 1290659, 1295207, 1299763) (i=11) (x=-561, y=399, n=1259047)


Island 6 = (1341841, 1346479, 1351123, 1355777, 1360439, 1360441, 1365107, 1365109, 1369783, 1369787, 1369789, 1374473, 1379167) (i=13) (x=-585, y=-297, n=1369783)


Island 7 = (2419799, 2419801, 2426027, 2426033, 2432263, 2432267, 2438507, 2438509, 2444759, 2451017, 2457283, 2463557) (i=12) (x=558, y=780, n=2432263)


Island 8 = (3189833, 3196979, 3196981, 3204137, 3204139, 3211301, 3211303, 3218471, 3218473, 3218477, 3225653) (i=11) (x=-894, y=858, n=3196981)

Young at Art

Head of a Young English Girl by Fernand Khnopff

Head of a Young English Girl (1895)

Graphische Sammlung Albertina, Vienna.