Performativizing Papyrocentricity #14

Papyrocentric Performativity Presents:

Scheming DemonThe Screwtape Letters, C.S. Lewis (1942)

Ai Wei to HellHow to Read Contemporary Art, Michael Wilson (Thames & Hudson, 2013)

Toxic TwosomeDoll, Peter Sotos and James Havoc (TransVisceral Books, 2013)

Know Your LimaçonsThe Penguin Dictionary of Curious and Interesting Geometry, David Wells (1991) (posted @ Overlord of the Über-Feral)

Pestilent, Pustulent and Pox-Pocked – various books by Dr Miriam B. Stimbers (@ O.o.t.Ü.-F.)


Or Read a Review at Random: RaRaR

The Brain in Pain

You can stop reading now, if you want. Or can you? Are your decisions really your own, or are you and all other human beings merely spectators in the mind-arena, observing but neither influencing nor initiating what goes on there? Are all your apparent choices in your brain, but out of your hands, made by mechanisms beyond, or below, your conscious control?

In short, do you have free will? This is a big topic – one of the biggest. For me, the three most interesting things in the world are the Problem of Consciousness, the Problem of Existence and the Question of Free Will. I call consciousness and existence problems because I think they’re real. They’re actually there to be investigated and explained. I call free will a question because I don’t think it’s real. I don’t believe that human beings can choose freely or that any possible being, natural or supernatural, can do so. And I don’t believe we truly want free will: it’s an excuse for other things and something we gladly reject in certain circumstances.


Continue reading The Brain in Pain

The Hill to Power

89 is special because it’s a prime number, divisible by only itself and 1. It’s also a sum of powers in a special way: 89 = 8^1 + 9^2. In base ten, no other two-digit number is equal to its own ascending power-sum like that. But the same pattern appears in these three-digit numbers, as the powers climb with the digits:

135 = 1^1 + 3^2 + 5^3 = 1 + 9 + 125 = 135
175 = 1^1 + 7^2 + 5^3 = 1 + 49 + 125 = 175
518 = 5^1 + 1^2 + 8^3 = 5 + 1 + 512 = 518
598 = 5^1 + 9^2 + 8^3 = 5 + 81 + 512 = 598

And in these four-digit numbers:

1306 = 1^1 + 3^2 + 0^3 + 6^4 = 1 + 9 + 0 + 1296 = 1306
1676 = 1^1 + 6^2 + 7^3 + 6^4 = 1 + 36 + 343 + 1296 = 1676
2427 = 2^1 + 4^2 + 2^3 + 7^4 = 2 + 16 + 8 + 2401 = 2427

The pattern doesn’t apply to any five-digit number in base-10 and six-digit numbers supply only this near miss:

263248 + 1 = 2^1 + 6^2 + 3^3 + 2^4 + 4^5 + 8^6 = 2 + 36 + 27 + 16 + 1024 + 262144 = 263249

But the pattern re-appears among seven-digit numbers:

2646798 = 2^1 + 6^2 + 4^3 + 6^4 + 7^5 + 9^6 + 8^7 = 2 + 36 + 64 + 1296 + 16807 + 531441 + 2097152 = 2646798

Now try some base behaviour. Some power-sums in base-10 are power-sums in another base:

175 = 1^1 + 7^2 + 5^3 = 1 + 49 + 125 = 175
175 = 6D[b=27] = 6^1 + 13^2 = 6 + 169 = 175

1306 = 1^1 + 3^2 + 0^3 + 6^4 = 1 + 9 + 0 + 1296 = 1306
1306 = A[36][b=127] = 10^1 + 36^2 = 10 + 1296 = 1306

Here is an incomplete list of double-base power-sums:

83 = 1103[b=4] = 1^1 + 1^2 + 0^3 + 3^4 = 1 + 1 + 0 + 81 = 83
83 = 29[b=37] = 2^1 + 9^2 = 2 + 81 = 83

126 = 105[b=11] = 1^1 + 0^2 + 5^3 = 1 + 0 + 125 = 126
126 = 5B[b=23] = 5^1 + 11^2 = 5 + 121 = 126

175 = 1^1 + 7^2 + 5^3 = 1 + 49 + 125 = 175
175 = 6D[b=27] = 6^1 + 13^2 = 6 + 169 = 175

259 = 2014[b=5] = 2^1 + 0^2 + 1^3 + 4^4 = 2 + 0 + 1 + 256 = 259
259 = 3G[b=81] = 3^1 + 16^2 = 3 + 256 = 259

266 = 176[b=13] = 1^1 + 7^2 + 6^3 = 1 + 49 + 216 = 266
266 = AG[b=25] = 10^1 + 16^2 = 10 + 256 = 266

578 = 288[b=15] = 2^1 + 8^2 + 8^3 = 2 + 64 + 512 = 578
578 = 2[24][b=277] = 2^1 + 24^2 = 2 + 576 = 578

580 = 488[b=11] = 4^1 + 8^2 + 8^3 = 4 + 64 + 512 = 580
580 = 4[24][b=139] = 4^1 + 24^2 = 4 + 576 = 580

731 = 209[b=19] = 2^1 + 0^2 + 9^3 = 2 + 0 + 729 = 731
731 = 2[27][b=352] = 2^1 + 27^2 = 2 + 729 = 731

735 = 609[b=11] = 6^1 + 0^2 + 9^3 = 6 + 0 + 729 = 735
735 = 6[27][b=118] = 6^1 + 27^2 = 6 + 729 = 735

1306 = 1^1 + 3^2 + 0^3 + 6^4 = 1 + 9 + 0 + 1296 = 1306
1306 = A[36][b=127] = 10^1 + 36^2 = 10 + 1296 = 1306

1852 = 3BC[b=23] = 3^1 + 11^2 + 12^3 = 3 + 121 + 1728 = 1852
1852 = 3[43][b=603] = 3^1 + 43^2 = 3 + 1849 = 1852

2943 = 3EE[b=29] = 3^1 + 14^2 + 14^3 = 3 + 196 + 2744 = 2943
2943 = [27][54][b=107] = 27^1 + 54^2 = 27 + 2916 = 2943


Previously pre-posted (please peruse):

Narcissarithmetic #1
Narcissarithmetic #2

Tattoo Your Ears

“The most merciful thing in the world,” said H.P. Lovecraft, “is the inability of the human mind to correlate all its contents.” Nowadays we can’t correlate all the contents of our hard-drives either. But occasionally bits come together. I’ve had two MP3s sitting on my hard-drive for months: “Drink or Die” by Erotic Support and “Hunter Gatherer” by Swords of Mars. I liked them both a lot, but until recently I didn’t realize that they were by two incarnations of the same Finnish band.

Cover of "Die by the..." Swords of Mars
They don’t sound very much alike, after all. But now that I’ve correlated them, they’ve inspired some thoughts on music and mutilation. “Drink or Die” is a dense, fuzzy, leather-lunged rumble-rocker that, like a good Mötley Crüe song, your ears can snort like cocaine. But, unlike Mötley Crüe, the auditory rush lasts the whole song, not just the first half. “Hunter Gatherer” is much more sombre. Erotic Support were “Helsinki beercore”; Swords of Mars are darker, doomier and dirgier. They’ve also got a better name – “Erotic Support” seems to have lost something in translation. Finnish is a long way from English: it’s in a different and unrelated language family, the Finno-Ugric, not the Indo-European. So it lines up with Hungarian and Estonian, not English, German and French. But Erotic Support’s lyrics are good English and “Drink or Die” is a clever title. They’d have been a more interesting band if they’d sung entirely in Finnish, but also less successful, because less accessible to the rest of the world.

Es war einmal eine Königstochter, die ging hinaus in den Wald und setzte sich an einen kühlen Brunnen. Sie hatte eine goldene Kugel, die war ihr liebstes Spielwerk, die warf sie in die Höhe und fing sie wieder in der Luft und hatte ihre Lust daran. Einmal war die Kugel gar hoch geflogen, sie hatte die Hand schon ausgestreckt und die Finger gekrümmt, um sie wieder zufangen, da schlug sie neben vorbei auf die Erde, rollte und rollte und geradezu in das Wasser hinein.

Some Indo-European


Mieleni minun tekevi, aivoni ajattelevi
lähteäni laulamahan, saa’ani sanelemahan,
sukuvirttä suoltamahan, lajivirttä laulamahan.
Sanat suussani sulavat, puhe’et putoelevat,
kielelleni kerkiävät, hampahilleni hajoovat.

Veli kulta, veikkoseni, kaunis kasvinkumppalini!
Lähe nyt kanssa laulamahan, saa kera sanelemahan
yhtehen yhyttyämme, kahta’alta käytyämme!
Harvoin yhtehen yhymme, saamme toinen toisihimme
näillä raukoilla rajoilla, poloisilla Pohjan mailla.

Some Finno-Ugric


All the same, being inaccessible sometimes helps a band’s appeal to the rest of the world: the mystique of black metal is much stronger in bands that use only Norwegian or one of the other Scandinavian languages. Erotic Support haven’t joined that rebellion against Coca-Colonization and tried to create an indigenous genre. They’re happy to reproduce more or less American music using the more or less American invention known as the electric guitar. But amplified music would have appeared in Europe even if North America had been colonized by the Chinese, so I wonder what rock would sound like if it had evolved in Europe instead. It wouldn’t be called rock, of course, but what other differences would it have? Would it be more sophisticated, for example? I think it would. The success of American exports depends in part on their strong and simple flavours. “Drink or Die” has those flavours: it’s about volume, rhythm and power. It’s full of a certain “drug-addled, crab-infested, tinnitus-nagged spirit” — the “urge to submerge in the raw bedrock viscerality of rock”, as some metaphor-mixing, über-emphasizing idiot once put it (I think it was me).

Cover of "II" by Erotic Support

Erotic Support are “beercore”, remember. Beer marks the brain with hangovers, just as tattoos mark the skin with ink. And just as loud music marks the ears with tinnitus. There are various kinds of self-mutilation in rock and that self-mutilation can have unhealthy motives. It can be an expression of boredom, angst, anomie and self-hatred. Unsurprisingly, Finland has the nineteenth highest suicide rate in the world. Beer, tattoos and tinnitus are part of the louder, dirtier and loutier end of rock: unlike Radiohead or Coldplay, Erotic Support sound like a band with tattoos who are used to hangovers. “Drink or Die” is a joke about exactly that. But what if rock had evolved in a wine-drinking culture? Would it be less of a sado-masochistic ritual, more a refined rite? Maybe not: the god of wine is Dionysos and he was Ho Bromios, the Thunderer. His brother Pan induces panic with loud noises. But black metal looks towards northern paganism: it’s music for pine forests, cold seas and beer-drinkers, not olive groves, warm seas and oenopotes.

Erotic Support don’t create soundscapes for Finland the way black metal creates soundscapes for Norway, but they do create beer-drinkers’ music, so they do express Finnishness to that extent. Swords of Mars, being darker, doomier and dirgier, are moving nearer an indigenous Finnish rock, or an indigenous Scandinavian rock, at least. This may be related to the fact that genes express themselves more strongly as an individual ages: for example, the correlation between the intelligence of parents and their children is strongest when the children are adults. Erotic Support create faster, more aggressive music than Swords of Mars, so it isn’t surprising that they’re the younger version of the same band. In biology, the genotype creates the phenotype: DNA codes for bodies and behaviour. Music is part of what Richard Dawkins calls the “extended phenotype”, like the nest of a bird or the termite-fishing-rods of a chimpanzee. A bird’s wings are created directly by its genes; a bird’s nest is created indirectly by its genes, viâ the brain. So a bird’s wings are part of the phenotype and a bird’s nest part of the extended phenotype.

Both are under the influence of the genes and both are expressions of biology. Music (like bird-song) is an expression of biology too, as is the difference between the music of Erotic Support and Swords of Mars. As brains age, the behaviour they create changes. Swords of Mars are older and not attracted to reckless self-mutilation as Erotic Support were: it’s not music to precede hangovers and induce tinnitus any more. Sword of Mars aren’t trying to tattoo your ears but to educate your mind.

Know Your Limaçons

Front cover of The Penguin Dictionary of Curious and Interesting Geometry by David WellsThe Penguin Dictionary of Curious and Interesting Geometry, David Wells (1991)

Mathematics is an ocean in which a child can paddle and an elephant can swim. Or a whale, indeed. This book, a sequel to Wells’ excellent Penguin Dictionary of Curious and Interesting Mathematics, is suitable for both paddlers and plungers. Plumbers, even, because you can dive into some very deep mathematics here.

Far too deep for me, I have to admit, but I can wade a little way into the shallows and enjoy looking further out at what I don’t understand, because the advantage of geometry over number theory is that it can appeal to the eye even when it baffles the brain. If this book is more expensive than its prequel, that’s because it needs to be. It’s a paperback, but a large one, to accommodate the illustrations.

Fortunately, plenty of them appeal to the eye without baffling the brain, like the absurdly simple yet mindstretching Koch snowflake. Take a triangle and divide each side into thirds. Erect another triangle on each middle third. Take each new line of the shape and do the same: divide into thirds, erect another triangle on the middle third. Then repeat. And repeat. For ever.

A Koch snowflake (from Wikipedia)

A Koch snowflake (from Wikipedia)

The result is a shape with a finite area enclosed by an infinite perimeter, and it is in fact a very early example of a fractal. Early in this case means it was invented in 1907, but many of the other beautiful shapes and theorems in this book stretch back much further: through Étienne Pascal and his oddly organic limaçon (which looks like a kidney) to the ancient Greeks and beyond. Some, on the other hand, are very modern, and this book was out-of-date on the day it was printed. Despite the thousands of years devoted by mathematicians to shapes and the relationship between them, new discoveries are being made all the time. Knots have probably been tied by human beings for as long as human beings have existed, but we’ve only now started to classify them properly and even find new uses for them in biology and physics.

Which is not to say knots are not included here, because they are. But even the older geometry Wells looks at would be enough to keep amateur and recreational mathematicians happy for years, proving, re-creating, and generalizing as they work their way through variations on all manner of trigonomic, topological, and tessellatory themes.


Previously pre-posted (please peruse):

Poulet’s Propeller — discussion of Wells’ Penguin Dictionary of Curious and Interesting Numbers (1986)

Persecution Complex

Imagine four mice sitting on the corners of a square. Each mouse begins to run towards its clockwise neighbour. What happens? This:

Four mice chasing each other

Four mice chasing each other

The mice spiral to the centre and meet, creating what are called pursuit curves. Now imagine eight mice on a square, four sitting on the corners, four sitting on the midpoints of the sides. Each mouse begins to run towards its clockwise neighbour. Now what happens? This:

Eight mice chasing each other

Eight mice chasing each other

But what happens if each of the eight mice begins to run towards its neighbour-but-one? Or its neighbour-but-two? And so on. The curves begin to get more complex:

square+midpoint+2

(Please open the following image in a new window if it fails to animate.)

square+midpoint+3

You can also make the mice run at different speeds or towards neighbours displaced by different amounts. As these variables change, so do the patterns traced by the mice:

• Continue reading: Persecution Complexified

Poulet’s Propeller

The Penguin Dictionary of Curious and Interesting Numbers (1986) is one of my favourite books. It’s a fascinating mixture of math, mathecdote and math-joke:

2·618 0333…

The square of φ, the golden ratio, and the only positive number such that √n = n-1. (pg. 45)


6

Kepler discussed the 6-fold symmetry of snowflakes, and attempted to explain it by considering the close packing of spheres in a hexagonal array. (pg. 69)


39

This appears to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number to have the property of being uninteresting.

It is therefore also the first number to be simultaneously interesting and uninteresting. (pg. 120)

David Wells, who wrote the Dictionary, “had the rare distinction of being a Cambridge scholar in mathematics and failing his degree”. He must be the mathematical equivalent of the astronomer Patrick Moore: a popularizer responsible for opening many minds and inspiring many careers. He’s also written books on geometry and mathematical puzzles. But not everyone appreciates his efforts. This is a sideswipe in a review of William Hartston’s The Book of Numbers:

Thankfully, this book is more concerned with facts than mathematics. Anyone wanting to learn more about [π] or the Fibonacci sequence should turn to the Penguin Dictionary of Curious and Interesting Numbers, a volume which none but propeller-heads will find either curious or interesting. (Review in The Independent, 18th December 1997)


Continue reading: Poulet’s Propeller

Narcissarithmetic #2

It’s easy to find patterns like these in base ten:

81 = (8 + 1)^2 = 9^2 = 81

512 = (5 + 1 + 2)^3 = 8^3 = 512
4913 = (4 + 9 + 1 + 3)^3 = 17^3 = 4913
5832 = (5 + 8 + 3 + 2)^3 = 18^3 = 5832
17576 = (1 + 7 + 5 + 7 + 6)^3 = 26^3 = 17576
19683 = (1 + 9 + 6 + 8 + 3)^3 = 27^3 = 19683

2401 = (2 + 4 + 0 + 1)^4 = 7^4 = 2401
234256 = (2 + 3 + 4 + 2 + 5 + 6)^4 = 22^4 = 234256
390625 = (3 + 9 + 0 + 6 + 2 + 5)^4 = 25^4 = 390625
614656 = (6 + 1 + 4 + 6 + 5 + 6)^4 = 28^4 = 614656
1679616 = (1 + 6 + 7 + 9 + 6 + 1 + 6)^4 = 36^4 = 1679616

17210368 = (1 + 7 + 2 + 1 + 0 + 3 + 6 + 8)^5 = 28^5 = 17210368
52521875 = (5 + 2 + 5 + 2 + 1 + 8 + 7 + 5)^5 = 35^5 = 52521875
60466176 = (6 + 0 + 4 + 6 + 6 + 1 + 7 + 6)^5 = 36^5 = 60466176
205962976 = (2 + 0 + 5 + 9 + 6 + 2 + 9 + 7 + 6)^5 = 46^5 = 205962976

1215766545905692880100000000000000000000 = (1 + 2 + 1 + 5 + 7 + 6 + 6 + 5 + 4 + 5 + 9 + 0 + 5 + 6 + 9 + 2 + 8 + 8 + 0 + 1 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0)^20 = 90^20 = 1215766545905692880100000000000000000000

Patterns like this are much rarer:

914457600 = (9 x 1 x 4 x 4 x 5 x 7 x 6)^2 = 30240^2 = 914457600

3657830400 = (3 x 6 x 5 x 7 x 8 x 3 x 4)^2 = 60480^2 = 3657830400

I haven’t found a cube like that in base ten, but base six supplies them:

2212 = (2 x 2 x 1 x 2)^3 = 12^3 = 2212 (b=6) = 8^3 = 512 (b=10)
325000 = (3 x 2 x 5)^3 = 50^3 = 325000 (b=6) = 30^3 = 27000 (b=10)
411412 = (4 x 1 x 1 x 4 x 1 x 2)^3 = 52^3 = 411412 (b=6) = 32^3 = 32768 (b=10)

And base nine supplies a fourth and fifth power:

31400 = (3 x 1 x 4)^4 = 13^4 = 31400 (b=9) = 12^4 = 20736 (b=10)
11600 = (1 x 1 x 6)^5 = 6^5 = 11600 (b=9) = 6^5 = 7776 (b=10)

Then base ten is rich in patterns like these:

81 = (8^1 + 1^1) x (8 + 1) = 9 x 9 = 81

133 = (1^2 + 3^2 + 3^2) x (1 + 3 + 3) = 19 x 7 = 133
315 = (3^2 + 1^2 + 5^2) x (3 + 1 + 5) = 35 x 9 = 315
803 = (8^2 + 0^2 + 3^2) x (8 + 0 + 3) = 73 x 11 = 803
1148 = (1^2 + 1^2 + 4^2 + 8^2) x (1 + 1 + 4 + 8) = 82 x 14 = 1148
1547 = (1^2 + 5^2 + 4^2 + 7^2) x (1 + 5 + 4 + 7) = 91 x 17 = 1547
2196 = (2^2 + 1^2 + 9^2 + 6^2) x (2 + 1 + 9 + 6) = 122 x 18 = 2196

1215 = (1^3 + 2^3 + 1^3 + 5^3) x (1 + 2 + 1 + 5) = 135 x 9 = 1215
3700 = (3^3 + 7^3 + 0^3 + 0^3) x (3 + 7 + 0 + 0) = 370 x 10 = 3700
11680 = (1^3 + 1^3 + 6^3 + 8^3 + 0^3) x (1 + 1 + 6 + 8 + 0) = 730 x 16 = 11680
13608 = (1^3 + 3^3 + 6^3 + 0^3 + 8^3) x (1 + 3 + 6 + 0 + 8) = 756 x 18 = 13608
87949 = (8^3 + 7^3 + 9^3 + 4^3 + 9^3) x (8 + 7 + 9 + 4 + 9) = 2377 x 37 = 87949

182380 = (1^4 + 8^4 + 2^4 + 3^4 + 8^4 + 0^4) x (1 + 8 + 2 + 3 + 8 + 0) = 8290 x 22 = 182380
444992 = (4^4 + 4^4 + 4^4 + 9^4 + 9^4 + 2^4) x (4 + 4 + 4 + 9 + 9 + 2) = 13906 x 32 = 444992

41500 = (4^5 + 1^5 + 5^5 + 0^5 + 0^5) x (4 + 1 + 5 + 0 + 0) = 4150 x 10 = 41500
3508936 = (3^5 + 5^5 + 0^5 + 8^5 + 9^5 + 3^5 + 6^5) x (3 + 5 + 0 + 8 + 9 + 3 + 6) = 103204 x 34 = 3508936
3828816 = (3^5 + 8^5 + 2^5 + 8^5 + 8^5 + 1^5 + 6^5) x (3 + 8 + 2 + 8 + 8 + 1 + 6) = 106356 x 36 = 3828816
4801896 = (4^5 + 8^5 + 0^5 + 1^5 + 8^5 + 9^5 + 6^5) x (4 + 8 + 0 + 1 + 8 + 9 + 6) = 133386 x 36 = 4801896
5659875 = (5^5 + 6^5 + 5^5 + 9^5 + 8^5 + 7^5 + 5^5) x (5 + 6 + 5 + 9 + 8 + 7 + 5) = 125775 x 45 = 5659875


Previously pre-posted (please peruse):

Narcissarithmetic

Pestilent, Pustulent and Pox-Pocked

I’m sorry, but let’s face facts: you cannot consider yourself a keyly committed core component of the counter-cultural community unless you own at least three copies — a reading copy, a prominent-shelf-of-the-bookcase copy and a wrap-carefully-in-brown-paper-put-away-in-a-cupboard-and-never-touch-or-look-at-again copy — of each of these toxic’n’tenebrose titles:

Can the Cannibal? Aspects of Angst, Abjection and Anthropophagy in the Music of Suzi Quatro, 1974-1986 (University of Nebraska Press 2004).

Doubled Slaughter: Barbarism, Brutalism and Bestial Bloodlust in the Music of Simon and Garfunkel, 1965-2010 (Serpent’s Tail 2007)

Re-Light My Führer: Nausea, Noxiousness and Neo-Nazism in the Music of Take That, 1988-2007 (U.N.P. 2013)

Base Citizens Raping: Revulsion, Repulsion and Rabidity in the Music of the Bay City Rollers, 1972-2002 (U.N.P. 2014)

Underground, Jehovahground: Ferality, Fetidity and Fundamentalist Phantasmality in the Music of the Wombles, August 1974-January 1975 (forthcoming)

All are by Dr Miriam B. Stimbers, of course. And what can I say about them? Simply this: these books hold an uncompromising mirror up before the pestilent, pustulent and pox-pocked features of so-called Western so-called society and say: “Look. That’s you, that is.” Dr Stimbers’ ruthlessly radical research and sizzlingly psychoanalytic scholarship will overturn your preconceptions so hard that, in some cases, they won’t appear to change at all.