John Constable’s Salisbury Cathedral from the Bishop’s Grounds (1825, Frick Collection)

Elsewhere other-engageable…

• Discussion of Salisbury Cathedral from the Bishop’s Grounds (1823) at Wikipedia

Tri Num Sum

The Sum of ten consecutive Triangular Numbers:

Starting with T0 = 0, in base 10,

The sum of the first 10 triangular numbers from T0 to T9 = 165
The sum of the next 10 triangular numbers from T10 to T19 = 1165
The sum of the next 10 triangular numbers from T20 to T29 = 3165
The sum of the next 10 triangular numbers from T30 to T39 = 6165
The sum of the next 10 triangular numbers from T40 to T49 = 10165
The sum of the next 10 triangular numbers from T50 to T59 = 15165

and so on.

The same pattern is evident in other bases [when summing T0 to Tbase-1 and so on].

• As submitted by Julian Beauchamp, 9v19, to Shyam Sunder Gupta’s “Fascinating Triangular Numbers”.

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”…


“The Garden of Prosperpine”

By Algernon Charles Swinburne

Here, where the world is quiet;
         Here, where all trouble seems
Dead winds’ and spent waves’ riot
         In doubtful dreams of dreams;
I watch the green field growing
For reaping folk and sowing,
For harvest-time and mowing,
         A sleepy world of streams.

I am tired of tears and laughter,
         And men that laugh and weep;
Of what may come hereafter
         For men that sow to reap:
I am weary of days and hours,
Blown buds of barren flowers,
Desires and dreams and powers
         And everything but sleep.

Here life has death for neighbour,
         And far from eye or ear
Wan waves and wet winds labour,
         Weak ships and spirits steer;
They drive adrift, and whither
They wot not who make thither;
But no such winds blow hither,
         And no such things grow here.

No growth of moor or coppice,
         No heather-flower or vine,
But bloomless buds of poppies,
         Green grapes of Proserpine,
Pale beds of blowing rushes
Where no leaf blooms or blushes
Save this whereout she crushes
         For dead men deadly wine.

Pale, without name or number,
         In fruitless fields of corn,
They bow themselves and slumber
         All night till light is born;
And like a soul belated,
In hell and heaven unmated,
By cloud and mist abated
         Comes out of darkness morn.

Though one were strong as seven,
         He too with death shall dwell,
Nor wake with wings in heaven,
         Nor weep for pains in hell;
Though one were fair as roses,
His beauty clouds and closes;
And well though love reposes,
         In the end it is not well.

Pale, beyond porch and portal,
         Crowned with calm leaves, she stands
Who gathers all things mortal
         With cold immortal hands;
Her languid lips are sweeter
Than love’s who fears to greet her
To men that mix and meet her
         From many times and lands.

She waits for each and other,
         She waits for all men born;
Forgets the earth her mother,
            The life of fruits and corn;
And spring and seed and swallow
Take wing for her and follow
Where summer song rings hollow
         And flowers are put to scorn.

There go the loves that wither,
         The old loves with wearier wings;
And all dead years draw thither,
         And all disastrous things;
Dead dreams of days forsaken,
Blind buds that snows have shaken,
Wild leaves that winds have taken,
         Red strays of ruined springs.

We are not sure of sorrow,
         And joy was never sure;
To-day will die to-morrow;
         Time stoops to no man’s lure;
And love, grown faint and fretful,
With lips but half regretful
Sighs, and with eyes forgetful
         Weeps that no loves endure.

From too much love of living,
         From hope and fear set free,
We thank with brief thanksgiving
         Whatever gods may be
That no life lives for ever;
That dead men rise up never;
That even the weariest river
         Winds somewhere safe to sea.

Then star nor sun shall waken,
         Nor any change of light:
Nor sound of waters shaken,
         Nor any sound or sight:
Nor wintry leaves nor vernal,
Nor days nor things diurnal;
Only the sleep eternal
         In an eternal night.


Here are the natural numbers or counting numbers:

• 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, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77... — A000027 at the Online Encyclopedia of Integer Sequences (OEIS)

Here are the prime numbers, or numbers divisible only by themselves and 1:

• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271... — A000040 at the OEIS

Here are the palindromic prime numbers, or prime numbers that read the same both forwards and backwards:

• 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181... — A002385 at the OEIS

Finally, here are the repunit primes, or palindromic primes consisting only of 1s:

• 11, 1111111111111111111, 11111111111111111111111, 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111, 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111... — A004022 at the OEIS (see A004023 for numbers of 1s in each repunit prime)

It’s obvious that there are more counting numbers than primes, isn’t it? Well, no. There are in fact as many primes as counting numbers. And there may be as many palindromic primes as primes. And as many repunit primes as palindromic primes.

Lavoro di Leonardo?

I first came across this quote about cats in French:

« Le plus petit des félins est une œuvre d’art. »
• “The smallest of felines is a work of art.”

It’s widely attributed to Leonardo da Vinci, but I can’t find any proof that he ever said it. Here it is in a fuller Italian version:

« Anche il più piccolo dei felini, il gatto, è un capolavoro. »
• Même le plus petit des félins, le chat, est un chef-d’œuvre.
•• Even the smallest of felines, the cat, is a masterpiece.

It’s a good quote, wherever it comes from. But the attribution to Leonardo reminds of another saying in Italian: Se non è vero, è ben trovato — “If it’s not true, it’s a happy invention.”

(From Pinterest)

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
An Autobiography and Other Writings (1869) by Anthony Trollope at Gutenberg