Primal Stream

• 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 — A000668, Mersenne primes (primes of the form 2^n – 1), at the Online Encyclopedia of Integer Sequences

• 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281, 77232917, 82589933 — A000043, Mersenne exponents: primes p such that 2^p – 1 is prime. Then 2^p – 1 is called a Mersenne prime. […] It is believed (but unproved) that this sequence is infinite. The data suggest that the number of terms up to exponent N is roughly K log N for some constant K.

• The largest known prime number (as of May 2022) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. — Largest known prime number


« 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.”

Bong of Bongs

Dopelord, Polish stoner-doom band (photo by Marcin Pawłowski)

“Navigator” by Dopelord from Children of the Haze (2017)

Leaf burns to ashes — Hail the Holy Smoke!
Deepspace traveller, folding time with bong;
Green smoke inhaler — space defeated bends.
Skilled time deflector, holding bong in hand
Holding bong in hand…

Slowly he’s dying,
Slowly he’s turning,
Into stones and into ashes:
Slowly gets high.

Galaxy raider flights the mothership;
Mind decompressor on eternal trip;
Green smoke inhaler — space defeated bends.
Skilled time deflector, holding bong in hand
Holding bong in hand…

Elsewhere Other-Accessible…

Dopelord at Bandcamp

Post-Performative Post-Scriptum

The title of this incendiary intervention is a paronomasia on Song of Songs, the Biblical book traditionally ascribed to King Solomon and known in Hebrew as שִׁיר הַשִּׁירִים Šīr hašŠīrīm and in Polish as Pieśń nad Pieśniami. Please note that the Overlord of the Über-Feral abhors and abominates the taking of all and any drugs. Except the purest and most potent: water, language, mathematics and music dot dot dot

Perplexing Purple

We have three sets of cones (or colour sensors) in our retinas, each of which is sensitive to a different part of the colour spectrum; the brain then constructs the rest of the spectrum by extrapolating from the relative strength of these three. In the case of purple, which occurs when the red and blue sensors but not the green ones are triggered, the brain creates a colour to fill the gap. If your brain were more objective, rather than showing you purple, it would display a patch of flickering grey with the words “system error” on it. — Rory Sutherland in Alchemy: The Surprising Power of Ideas That Don’t Make Sense (2019), section 6.2

Fylfy Fractals

An equilateral triangle is a rep-tile, because it can be tiled completely with smaller copies of itself. Here it is as a rep-4 rep-tile, tiled with four smaller copies of itself:

Equilateral triangle as rep-4 rep-tile

If you divide and discard one of the sub-copies, then carry on dividing-and-discarding with the sub-copies and sub-sub-copies and sub-sub-sub-copies, you get the fractal seen below. Alas, it’s not a very attractive or interesting fractal:

Divide-and-discard fractal stage #1

Stage #2

Stage #3

Stage #4

Stage #5

Stage #6

Stage #7

Stage #8

Stage #9

Divide-and-discard fractal (animated)

You can create more attractive and interesting fractals by rotating the sub-triangles clockwise or anticlockwise. Here are some examples:

Now try dividing a square into four right triangles, then turning each of the four triangles into a divide-and-discard fractal. The resulting four-fractal shape is variously called a swastika, a gammadion, a cross cramponnée, a Hakenkreuz and a fylfot. I’m calling it a fylfy fractal:

Divide-and-discard fractals in the four triangles of a divided square stage #1

Fylfy fractal #2

Fylfy fractal #3

Fylfy fractal #4

Fylfy fractal #5

Fylfy fractal #6

Fylfy fractal #7

Fylfy fractal #8

Fylfy fractal (animated)

Finally, you can adjust the fylfy fractals so that each point in the square becomes the equivalent point in a circle:

A Poof in a Porker

The great literary scholar and expert psychoanalyst Dr Miriam B. Stimbers has detected castration, clitoridolatry and communal cannibalism in the novels of Jane Austen. I’m not so ambitious. I merely want to detect a poof in a porker’s poetry. Or rather, I want to detect a poof in the poetry of a peer closely associated with a porker.

The porker is Bill Bunter, the fat, lazy and greedy public schoolboy whose misadventures at Greyfriars School were chronicled, under the pseudonym Frank Richards, by the highly prolific Charles Hamilton (1876-1961). One of Bunter’s schoolfellows was the languid and apparently effete peer Lord Mauleverer, who contributed this poem to The Greyfriars Holiday Annual for 1928:

“The Song of the Slacker”, by Lord Mauleverer

Tell me not, in mournful numbers,
Life was meant for toil and hustle;
It was meant for soothing slumbers,
Which relax both mind and muscle.

Life is lovely! Life is topping!
When you lie beneath the shade,
With the ginger-beer corks popping,
And a glorious spread arrayed.

Not enjoyment, and not sorrow,
Is our destined end or way;
But to put off till to-morrow
Work that should be done today!

In the world’s broad field of battle
All wise soldiers take their ease;
And they lie asleep, like cattle,
Underneath the shady trees.

Trust no Future, trust no Present,
Let the dead Past bury its dead!
The only prospect nice and pleasant
Is that of “forty winks” in bed!

“Life is short!” the bards are bawling,
Let’s enjoy it while we may;
On our study sofas sprawling,
Sleeping sixteen hours a day!

Lives of slackers all remind us
We should also rest our limbs;
And, departing, leave behind us,
“Helpful Hints for Tired Tims!”

Helpful hints, at which another
Will, perhaps, just take a peep;
Some exhausted, born-tired brother––
They will send him off to sleep!

While the hustlers are pursuing
Outdoor sports, on land and lake;
Let us, then, be up and doing––
There are several beds to make. – The Greyfriars Holiday Annual for 1928 (1927), Howard Baker abridged edition 1971

I liked the poem when I first read it, but I didn’t spot the parody as soon as I should. It was unexpected, you see, but then it dawned on me that “The Song of the Slacker” must be a parody of a famous poem by the poof-poet A.E. Housman (1859-1936):


Wake: the silver dusk returning
Up the beach of darkness brims,
And the ship of sunrise burning
Strands upon the eastern rims.

Wake: the vaulted shadow shatters,
Trampled to the floor it spanned,
And the tent of night in tatters
Straws the sky-pavilioned land.

Up, lad, up, ’tis late for lying;
Hear the drums of morning play;
Hark, the empty highways crying
“Who’ll beyond the hills away?”

Towns and countries woo together,
Forelands beacon, belfries call;
Never lad that trod on leather
Lived to feast his heart with all.

Up, lad: thews that lie and cumber
Sunlit pallets never thrive;
Morns abed and daylight slumber
Were not meant for man alive.

Clay lies still, but blood’s a rover;
Breath’s a ware that will not keep.
Up, lad: when the journey’s over
There’ll be time enough to sleep. – A Shropshire Lad (1896), Poem IV

The meter of the two poems is the same, the period is right, and the sentiments of Housman’s call to energy and effort are turned neatly on their heads in Lord Mauleverer’s call to sleep and slackness. And it’s a clever parody, although it’s a little too long. I’m glad to have come across “The Song of the Slacker”, which the second-best parody of Housman I’ve read. Here’s the best:

What, still alive at twenty-two,
A clean, upstanding chap like you?
Sure, if your throat ’tis hard to slit,
Slit your girl’s, and swing for it.

Like enough, you won’t be glad,
When they come to hang you, lad:
But bacon’s not the only thing
That’s cured by hanging from a string.

So, when the spilt ink of the night
Spreads o’er the blotting-pad of light,
Lads whose job is still to do
Shall whet their knives, and think of you.

Hugh Kingsmill’s famous parody of A.E. Housman

Absolutely Sabulous

The Hourglass Fractal (animated gif optimized at ezGIF)

Performativizing Paronomasticity

The title of this incendiary intervention is a paronomasia on the title of the dire Absolutely Fabulous. The adjective sabulous means “sandy; consisting of or abounding in sand; arenaceous” (OED).

Elsewhere Other-Accessible

Hour Re-Re-Re-Re-Powered — more on the hourglass fractal
Alas, Pour Horic — an earlier paronomasia for the fractal