# Tête avec Texte

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:

Couleur des yeux

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

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

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

“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

# Fernandhörer

Fernand Khnopff, En écoutant du Schumann / Listening to Schumann (1883)

• Fernhörer, “telephone receiver”, “earphone” ← Fern, “far”, + -hörer, “listener”, “receiver”

# Chatalogue des Choses

Cats divide inanimate objects into two great classes:

1. Things they are frightened of.

2. Things they can climb inside.

From How it Works: The Cat (Ladybirds for Grown-Ups 2016)