Performativizing Papyrocentricity #74

by in Book Reviews, Music and tagged , , , , , , , , , , | Leave a comment

Papyrocentric Performativity Presents…

• A Big Book about Books – The Penguin Classics Book, Henry Eliot (Penguin 2018)

• Wrecks & Drugs & Rock & Roll – Bodies: Life and Death in Music, Ian Winwood (Faber 2022)

• In the Bland of the Blind – An Unexplained Death: The True Story of a Body at the Belvedere, Mikita Brottman (Canongate 2018)

• Hu Thru Mu – The Musical Human: A History of Life on Earth, Michael Spitzer (Bloomsbury 2021)

• A Bit of EngLit – The Power of Delight: A Lifetime in Literature: Essays 1962-2002, John Bayley (Duckworth 2005)

• Chrome Tome – The Secret Lives of Colour, Kassia St Clair (John Murray 2018)

• Cannonball Corpse – AC/DC: The Story of the Original Monsters of Rock, Jerry Ewing (Carlton Books 2015)

• Chimpathy for the Devil? — Oasis: Supersonic: The Complete, Authorised and Uncut Interviews, curated by Simon Halfon (Nemperor 2021)

• D for Deviant, K for Korpse… — Doktor Deviant’s Diary of Depravity: Kandid Konfessions of a Kompulsive Korpse-Kopulator, ed. Dr David Kerekes and Samuel P. Salatta (Visceral Visions 2022)

Or Read a Review at Random: RaRaR

You Sixy Beast

by in Integer sequences, Mathematics, Palindromic numbers, Repdigits, Triangular Numbers and tagged , , , , , , , , , , , , | 2 Comments

666 is the Number of the Beast. But it’s much more than that. After all, it’s a number, so it has mathematical properties (everything has mathematical properties, but it’s a sine-qua-non of numbers). For example, 666 is a palindromic number, reading the same forwards and backwards. And it’s a repdigit, consisting of a single repeated digit. Now try answering this question: how many pebbles are there in this triangle?


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Counting the pebbles one by one would take a long time, but there’s a short-cut. Each line of the triangle after the first is one pebble longer than the previous line. There are 36 lines and therefore 36 pebbles in the final line. So the full number of pebbles = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36. And there’s an easy formula for that sum: (36^2 + 36) / 2 = (1296 + 36) / 2 = 1332 / 2 = 666.

So 666 is the 36th triangular number:


1 = 1
1+2 = 3
1+2+3 = 6
1+2+3+4 = 10
1+2+3+4+5 = 15
1+2+3+4+5+6 = 21
1+2+3+4+5+6+7 = 28
1+2+3+4+5+6+7+8 = 36
1+2+3+4+5+6+7+8+9 = 45
1+2+3+4+5+6+7+8+9+10 = 55
[...]
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36 = 666

But what’s tri(666), the 666th triangular number? By the formula above, it equals (666^2 + 666) / 2 = (443556 + 666) / 2 = 444222 / 2 = 222111. But recall something else from above: tri(6) = 1+2+3+4+5+6 = 21. Is it a coincidence that tri(6) = 21 and tri(666) = 222111? No, it isn’t:


tri(6) = 21 = (6^2 + 6) / 2 = (36 + 6) / 2 = 42 / 2
tri(66) = 2211 = (66^2 + 66) / 2 = (4356 + 66) / 2 = 4422 / 2
tri(666) = 222111 = (666^2 + 666) / 2 = (443556 + 666) / 2 = 444222 / 2
tri(6666) = 22221111
tri(66666) = 2222211111
tri(666666) = 222222111111
tri(6666666) = 22222221111111
tri(66666666) = 2222222211111111
tri(666666666) = 222222222111111111
tri(6666666666) = 22222222221111111111
tri(66666666666) = 2222222222211111111111
tri(666666666666) = 222222222222111111111111
tri(6666666666666) = 22222222222221111111111111
tri(66666666666666) = 2222222222222211111111111111
tri(666666666666666) = 222222222222222111111111111111

So we’ve looked at tri(36) = 666 and tri(666) = 222111. Let’s go a step further: tri(222111) = 24666759216. So 666 appears again. And the sixiness carries on here:


tri(36) = 666
tri(3366) = 5666661
tri(333666) = 55666666611
tri(33336666) = 555666666666111
tri(3333366666) = 5555666666666661111
tri(333333666666) = 55555666666666666611111
tri(33333336666666) = 555555666666666666666111111
tri(3333333366666666) = 5555555666666666666666661111111
tri(333333333666666666) = 55555555666666666666666666611111111
tri(33333333336666666666) = 555555555666666666666666666666111111111
tri(3333333333366666666666) = 5555555555666666666666666666666661111111111
tri(333333333333666666666666) = 55555555555666666666666666666666666611111111111
tri(33333333333336666666666666) = 555555555555666666666666666666666666666111111111111
tri(3333333333333366666666666666) = 5555555555555666666666666666666666666666661111111111111
tri(333333333333333666666666666666) = 55555555555555666666666666666666666666666666611111111111111

Tête avec Texte

by in Aesthetics, Literature, Photography, Poetry, Post-Weird and tagged , , , , , , , , , , , , , , , , , , , , | Leave a comment


Above you can see the Peacock on a Platter, or Robert de Montesquiou posing as the severed head of John the Baptist and flanked by relevant lines of his own poetry. But there’s a better version of the poetry, as you can see by comparing the photo with this:

J’aime le jade,
Couleur des yeux
D’Hérodiade

Et l’améthyste,
Couleur du sang
De Jean-Baptiste. — from “Robert de Montesquiou: The Magnificent Dandy” (1962) by Cornelia Otis Skinner

I love jade,
Color of the eyes
Of Herodias

And amethyst,
Color of the blood
Of John the Baptist.

Elsewhere Other-Accessible…

• Portrait of a Peacock — Cornelia Otis Skinner’s excellent essay on Montesquiou
• Le Paon dans les Pyrénées — review of Julian Barnes’ not-so-good book partly about Montesquiou

Agogic Arithmetic

by in Base Behavior, Integer sequences, Mathematics, Triangular Numbers and tagged , , , , , | Leave a comment

This is one of my favorite integer sequences:

• 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, ... — A000217 at OEIS


And it’s easy to work out the rule that generates the sequence. It’s the sequence of triangular numbers, of course, which you get by summing the integers:

1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
28 + 8 = 36
36 + 9 = 45
[...]

I like this sequence too, but it isn’t a sequence of integers and it’s much harder to work out the rule that generates it:

• 1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520, 7381/2520, 83711/27720, 86021/27720, 1145993/360360, 1171733/360360...

But you could say that it’s the inverse of the triangular numbers, because you generate it like this:

1
1 + 1/2 = 3/2
3/2 + 1/3 = 11/6
11/6 + 1/4 = 25/12
25/12 + 1/5 = 137/60
137/60 + 1/6 = 49/20
49/20 + 1/7 = 363/140
363/140 + 1/8 = 761/280
761/280 + 1/9 = 7129/2520
[...]

It’s the harmonic series, which is defined at Wikipedia as “the infinite series formed by summing all positive unit fractions”. I can’t understand its subtleties or make any important discoveries about it, but I thought I could ask (and begin to answer) a question that perhaps no-one else in history had ever asked: When are the leading digits of the k-th harmonic number, hs(k), equal to the digits of k in base 10?

hs(1) = 1
hs(43) = 4.349...
hs(714) = 7.1487...
hs(715) = 7.1501...
hs(9763) = 9.76362...
hs(122968) = 12.296899...
hs(122969) = 12.296907...
hs(1478366) = 14.7836639...
hs(17239955) = 17.23995590...
hs(196746419) = 19.6746419...
hs(2209316467) = 22.0931646788...

Do those numbers have any true mathematical significance? I doubt it. But they were fun to find, even though I wasn’t the first person in history to ask about them:

• 1, 43, 714, 715, 9763, 122968, 122969, 1478366, 17239955, 196746419, 2209316467, 24499118645, 268950072605 — A337904 at OEIS, Numbers k such that the decimal expansion of the k-th harmonic number starts with the digits of k, in the same order.

Moz on Mogz

by in Cats, Morrissey, Quotations and tagged , , , , , , , , , , | 2 Comments

“The basic fascination I have with cats is nothing unusual. I find them very intelligent and very superior. And I feel entranced by them. If I see one in the street I feel immediately drawn to the cat. I have a friend, Chrissie Hynde [the singer with The Pretenders], she’s exactly the same. You can be walking with her along the street, she sees a cat, she walks away. You continue to walk on, talking to no one. You look around and she’s crouched down with a cat in a hedge. I’m exactly the same way. I’m fascinated by them.” — “Morrissey on… privacy, the Queen and The Smiths”, The Daily Telegraph, 17vi11