Careway to Seven

• დედაბერს შვიდი სოფლის ფიქრი აწუხებდა, იმისი კი არავისა ჰქონდაო.

• • Dedabers shvidi soplis pikri ats’ukhbda, imisi k’i aravisa hkondao.

• • • The old woman worried about seven villages, but nobody cared about her. — A Comprehensive Georgian-English Dictionary, ed. Donald Rayfield et al (2006)


Post-Performative Post-Scriptum…

The title of this incendiary intervention is of course a radical reference to core Black Sabbath platter “Freewheel Burnin'” (2004).

Previously Pre-Posted…

Stare-Way to Hair, Then
Russell in Your Head-Roe
Sampled (Underfoot)

The Belles of El

Title page of Sir Henry Billingsley’s first English version of Euclid’s Elements, 1570, with personifications of Geometria, Astronomia, Arithmetica and Musica as beautiful young women


The Elements of Geometrie of the Moſt Aucient Philoſopher Evclide of Megara.

Faithfully (now first) tranʃlated into the Engliʃhe toung, by H. Billingſley, Citizen of London.

Whereunto are annexed certaine Scolies, Annotations, and Inuentions, of the best Mathematiciens, both of times past, and in this our age.

With a very fruitfull Præface made by M.I. Dee, ʃpecifying the chiefe Mathematicall Sciences, what they are, and wherunto commodious: where, alʃo, are diʃcloʃed certaine new Secrets Mathematicall and Mechanicall, untill theʃe our daies, greatly miʃʃed.

Imprinted at London by Iohn Daye.


The title of this incendiary intervention is a paronomasia on “The Bells of Hell…”, a British airmen’s song in terms of core issues around World War I.

Félosophisme

« Tous les chats sont mortels, Socrate est mortel, donc Socrate est un chat. » — Rhinocéros (1959) par Eugène Ionesco (1931-94)

• “All cats are mortal, Socrates is mortal, therefore Socrates is a cat.”

Wake the Snake

In my story “Kopfwurmkundalini”, I imagined the square root of 2 as an infinitely long worm or snake whose endlessly varying digit-segments contained all stories ever (and never) written:

• √2 = 1·414213562373095048801688724209698078569671875376948073…

But there’s another way to get all stories ever written from the number 2. You don’t look at the root(s) of 2, but at the powers of 2:

• 2 = 2^1 = 2
• 4 = 2^2 = 2*2
• 8 = 2^3 = 2*2*2
• 16 = 2^4 = 2*2*2*2
• 32 = 2^5 = 2*2*2*2*2
• 64 = 2^6 = 2*2*2*2*2*2
• 128 = 2^7 = 2*2*2*2*2*2*2
• 256 = 2^8 = 2*2*2*2*2*2*2*2
• 512 = 2^9 = 2*2*2*2*2*2*2*2*2
• 1024 = 2^10
• 2048 = 2^11
• 4096 = 2^12
• 8192 = 2^13
• 16384 = 2^14
• 32768 = 2^15
• 65536 = 2^16
• 131072 = 2^17
• 262144 = 2^18
• 524288 = 2^19
• 1048576 = 2^20
• 2097152 = 2^21
• 4194304 = 2^22
• 8388608 = 2^23
• 16777216 = 2^24
• 33554432 = 2^25
• 67108864 = 2^26
• 134217728 = 2^27
• 268435456 = 2^28
• 536870912 = 2^29
• 1073741824 = 2^30
[...]

The powers of 2 are like an ever-lengthening snake swimming across a pool. The snake has an endlessly mutating head and a rhythmically waving tail with a regular but ever-more complex wake. That is, the leading digits of 2^p don’t repeat but the trailing digits do. Look at the single final digit of 2^p, for example:

• 02 = 2^1
• 04 = 2^2
• 08 = 2^3
• 16 = 2^4
• 32 = 2^5
• 64 = 2^6
• 128 = 2^7
• 256 = 2^8
• 512 = 2^9
• 1024 = 2^10
• 2048 = 2^11
• 4096 = 2^12
• 8192 = 2^13
• 16384 = 2^14
• 32768 = 2^15
• 65536 = 2^16
• 131072 = 2^17
• 262144 = 2^18
• 524288 = 2^19
• 1048576 = 2^20
• 2097152 = 2^21
• 4194304 = 2^22
[...]

The final digit of 2^p falls into a loop: 2 → 4 → 8 → 6 → 2 → 4→ 8…

Now try the final two digits of 2^p:

02 = 2^1
04 = 2^2
08 = 2^3
16 = 2^4
32 = 2^5
64 = 2^6
• 128 = 2^7
• 256 = 2^8
• 512 = 2^9
• 1024 = 2^10
• 2048 = 2^11
• 4096 = 2^12
• 8192 = 2^13
• 16384 = 2^14
• 32768 = 2^15
• 65536 = 2^16
• 131072 = 2^17
• 262144 = 2^18
• 524288 = 2^19
• 1048576 = 2^20
• 2097152 = 2^21
• 4194304 = 2^22
• 8388608 = 2^23
• 16777216 = 2^24
• 33554432 = 2^25
• 67108864 = 2^26
• 134217728 = 2^27
• 268435456 = 2^28
• 536870912 = 2^29
• 1073741824 = 2^30
[...]

Now there’s a longer loop: 02 → 04 → 08 → 16 → 32 → 64 → 28 → 56 → 12 → 24 → 48 → 96 → 92 → 84 → 68 → 36 → 72 → 44 → 88 → 76 → 52 → 04 → 08 → 16 → 32 → 64 → 28… Any number of trailing digits, 1 or 2 or one trillion, falls into a loop. It just takes longer as the number of trailing digits increases.

That’s the tail of the snake. At the other end, the head of the snake, the digits don’t fall into a loop (because of the carries from the lower digits). So, while you can get only 2, 4, 8 and 6 as the final digits of 2^p, you can get any digit but 0 as the first digit of 2^p. Indeed, I conjecture (but can’t prove) that not only will all integers eventually appear as the leading digits of 2^p, but they will do so infinitely often. Think of a number and it will appear as the leading digits of 2^p. Let’s try the numbers 1, 12, 123, 1234, 12345…:

16 = 2^4
128 = 2^7
12379400392853802748... = 2^90
12340799625835686853... = 2^1545
12345257952011458590... = 2^34555
12345695478410965346... = 2^63293
12345673811591269861... = 2^4869721
12345678260232358911... = 2^5194868
12345678999199154389... = 2^62759188

But what about the numbers 9, 98, 987, 986, 98765… as leading digits of 2^p? They don’t appear as quickly:

9007199254740992 = 2^53
98079714615416886934... = 2^186
98726397006685494828... = 2^1548
98768356967522174395... = 2^21257
98765563827287722773... = 2^63296
98765426081858871289... = 2^5194871
98765430693066680199... = 2^11627034
98765432584491513519... = 2^260855656
98765432109571471006... = 2^1641098748

Why do fragments of 123456789 appear much sooner than fragments of 987654321? Well, even though all integers occur infinitely often as leading digits of 2^p, some integers occur more often than others, as it were. The leading digits of 2^p are actually governed by a fascinating mathematical phenomenon known as Benford’s law, which states, for example, that the single first digit, d, will occur with the frequency log10(1 + 1/d). Here are the actual frequencies of 1..9 for all powers of 2 up to 2^101000, compared with the estimate by Benford’s law:

1: 30% of leading digits ↔ 30.1% estimated
2: 17.55% ↔ 17.6%
3: 12.45% ↔ 12.49%
4: 09.65% ↔ 9.69%
5: 07.89% ↔ 7.92%
6: 06.67% ↔ 6.69%
7: 05.77% ↔ 5.79%
8: 05.09% ↔ 5.11%
9: 04.56% ↔ 4.57%

Because (inter alia) 1 appears as the first digit of 2^p far more often than 9 does, the fragments of 123456789 appear faster than the fragments of 987654321. Mutatis mutandis, the same applies in all other bases (apart from bases that are powers of 2, where there’s a single leading digit, 1, 2, 4, 8…, followed by 0s). But although a number like 123456789 occurs much frequently than 987654321 in 2^p expressed in base 10 (and higher), both integers occur infinitely often.

As do all other integers. And because stories can be expressed as numbers, all stories ever (and never) written appear in the powers of 2. Infinitely often. You’ll just have to trim the tail of the story-snake.

ზამვარდები

ვარდები

მე, ზამთრისაგან ჯაჭვაწყვეტილი,
ნაცნობ ბაღისკენ მივემართები,
სად ფერად უცხო, ყნოსვად კეთილი,
ზამთარ და ზაფხულ ჰყვავის ვარდები.


Roses

Unchained from winter,
I walk to a long-known garden,
Where, sweet-scented and bright,
Roses grow winter and summer through.

ვარდები, გალაკტიონ ტაბიძე
“Roses”, Galaktion Tabidze — a translation into English

Performativizing Papyrocentricity #71

Papyrocentric Performativity Presents…

Clive DriveUnreliable Memoirs (1980) and Always Unreliable: The Memoirs (2001), Clive James

Nou’s WhoArt Nouveau, Camilla de la Bedoyere (Flame Tree Publishing 2005)

Hit and MistletoeThrough It All I’ve Always Laughed, Count Arthur Strong (Faber & Faber 2013)

Beauties and BeastsShardik, Richard Adams (1974)


Or Read a Review at Random: RaRaR

Genoa Ultramarina

«Il mare è la civiltà», disse [Franco Scoglio] una volta, «il sentimento, la passione, le tempeste, ma l’amore, gli sbarchi, le partenze, il mare è tutto. La follia va di pari passo con il mare». — Ultrà. Il volto nascosto delle tifoserie di calcio in Italia, Tobias Jones (2020)

• “The sea is civilization,” [Franco Scoglio] said once, “sentiment, passion, storms, love, landings, leavings, the sea is everything… madness walks with the sea.” — Ultra: The Underworld of Italian Football, Tobias Jones (2019)


Post-Performative Post-Scriptum

I’m not sure if the Italian is the original Italian or an Italian translation of Jones’s English translation of the original Italian. But it seems to be the former.


Elsewhere other-accessible…

Franco Scoglio en italiano
Franco Scoglio in English

Toxik TikTok

“Libs of TikTok is shaping our entire political conversation about the rights of LGBTQ people to participate in society,” [Ari] Drennen said. “It feels like they’re single-handedly taking us back a decade in terms of the public discourse around LGBTQ rights. It’s been like nothing we’ve ever really seen.” — “Meet the woman behind Libs of TikTok, secretly fueling the right’s outrage machine”, The Washington Post, 19iv22.


Elsewhere other-accessible

Ex-Term-In-Ate! — interrogating issues around “in terms of”…
All posts interrogating issues around “in terms of”…

Bash the Trash

From George Orwell’s “As I Please” for 11th February 1944, Tribune:

THE FOLLOWING lines are quoted in Anthony Trollope’s Autobiography:

When Payne-Knight’s Taste was issued on the town
A few Greek verses in the text set down
Were torn to pieces, mangled into hash,
Hurled to the flames as execrable trash;
In short, were butchered rather than dissected
And several false quantities detected;
Till, when the smoke had risen from the cinders
It was discovered that — the lines were Pindar’s!

Trollope does not make clear who is the author of these lines, and I should be very glad if any reader could let me know. But I also quote them for their own sake — that is, for the terrible warning to literary critics that they contain — and for the sake of drawing attention to Trollope’s Autobiography, which is a most fascinating book, although or because it is largely concerned with money.


Elsewhere Other-Accessible…

Pindar (c. 518-438 BC) at Wikipedia
An Analytical Inquiry Into the Principles of Taste (1806) by Richard Payne-Knight at Archive.org
An Autobiography and Other Writings (1869) by Anthony Trollope at Gutenberg