Author Archives: Krilling for Company

The Whale’s Way

by in Literature, Poetry, The Sea and tagged , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

“Sea Fever” (1902)

I must go down to the seas again, to the lonely sea and the sky,
And all I ask is a tall ship and a star to steer her by,
And the wheel’s kick and the wind’s song and the white sail’s shaking,
And a grey mist on the sea’s face, and a grey dawn breaking.

I must go down to the seas again, for the call of the running tide
Is a wild call and a clear call that may not be denied;
And all I ask is a windy day with the white clouds flying,
And the flung spray and the blown spume, and the sea-gulls crying.

I must go down to the seas again, to the vagrant gypsy life,
To the gull’s way and the whale’s way, where the wind’s like a whetted knife;
And all I ask is a merry yarn from a laughing fellow-rover,
And quiet sleep and a sweet dream when the long trick’s over.

• John Masefield (1878–1967)

On the M3!

by in Latin, Magistra Mundi, Mathematics and tagged , , , , , , , , , , , , , , , , | Leave a comment

6 = 2 x 3. And 6 = 1 + 2 + 3. But 6 also equals 3!. That is, 6 = 3 x 2 x 1, or factorial three. If you have three different items, you can arrange them in six different ways. There are three posibilities for the first item, two for the second and one for the third.

You can illustrate this linguistically. All languages are governed by mathematics, but maths manifests itself in different ways. Emphasis is an important part of language, for example, but there are different ways to achieve it. English usually does it with stress or by adding an emphatic word. Other languages can do it by varying the order of words. Latin, for example:

  • Mathematica Magistra Mundi
    — Mathematics is Mistress of the World.
  • Mathematica Mundi Magistra
    — Mathematics of the World is Mistress.
  • Magistra Mathematica Mundi
    — Mistress is Mathematics of the World
  • Magistra Mundi Mathematica
    — Mistress of the World is Mathematics.
  • Mundi Mathematica Magistra
    — Of the World Mathematics is Mistress.
  • Mundi Magistra Mathematica
    — Of the World the Mistress is Mathematics.

Elsewhere other-posted:

• Mathematica Magistra Mundi — more on the motto
• Moto-Motto — a variant on the motto

Performativizing Papyrocentricity #23

by in Aesthetics, Art, Astronomy, Biology, Book Reviews, History, Science and tagged , , , , , , , , , , , , , , , , , , , , | Leave a comment

Papyrocentric Performativity Presents:

• Face Paint – A Face to the World: On Self-Portraits, Laura Cumming (HarperPress 2009; paperback 2010)

• The Aesthetics of Animals – Life: Extraordinary Animals, Extreme Behaviour, Martha Holmes and Michael Gunton (BBC Books 2009)

• Less Light, More Night – The End of Night: Searching for Natural Darkness in an Age of Artifical Light, Paul Bogard (Fourth Estate 2013)

• The Power of Babel – Clark Ashton Smith, Huysmans, Maupassant

Or Read a Review at Random: RaRaR

Prime Climb Time

by in Base Behavior, Binary numbers, Digit-sums, Mathematics, Prime numbers and tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The third prime is equal to the sum of the first and second primes: 2 + 3 = 5. After that, for obvious reasons, the prime-sum climbs much more rapidly than the primes themselves:

2, 3, 05, 07, 11, 13, 17, 19, 023, 029...
2, 5, 10, 17, 28, 41, 58, 77, 100, 129...

But what if you use digit-sum(p1..pn), i.e., the sum of the digits of the primes from the first to the nth? For example, the digit-sum(p1..p5) = 2 + 3 + 5 + 7 + 1+1 = 19, whereas the sum(p1..p5) = 2 + 3 + 5 + 7 + 11 = 28. Using the digit-sums of the primes, the comparison now looks like this:

2, 3, 05, 07, 11, 13, 17, 19, 23, 29...
2, 5, 10, 17, 19, 23, 31, 41, 46, 57...

The sum climbs more slowly, but still too fast. So what about a different base? In base-2, the digit-sum(p1..p3) = (1+0) + (1+1) + (1+0+1) = 1 + 2 + 2 = 5. The comparison looks like this:

2, 3, 05, 07, 11, 13, 17, 19, 23, 29...
1, 3, 05, 08, 11, 14, 16, 19, 23, 27...

For primes 3, 5, 11, 19, and 23, p = digit-sum(primes <= p) in base-2. But the cumulative digit-sum soon begins to climb too slowly:

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...

1, 3, 5, 8, 11, 14, 16, 19, 23, 27, 32, 35, 38, 42, 47, 51, 56, 61, 64, 68, 71, 76, 80, 84, 87, 091, 096, 101, 106, 110, 117, 120, 123, 127, 131, 136, 141, 145, 150, 155, 160, 165, 172, 175, 179, 184, 189, 196, 201, 206, 211, 218, 223, 230, 232, 236, 240, 245...

So what about base-3?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59...
2, 3, 6, 9, 12, 15, 20, 23, 28, 31, 34, 37, 42, 47, 52, 59, 64...

In base-3, for p = 2, 3 and 37, p = digit-sum(primes <= p), while for p = 23, 31, 47 and 59, p = digit-sum(primes < p), like this:

2 = 2.
3 = 2 + (1+0).
37 = 2 + (1+0) + (1+2) + (2+1) + (1+0+2) + (1+1+1) + (1+2+2) + (2+0+1) + (2+1+2) + (1+0+0+2) + (1+0+1+1) + (1+1+0+1) = 2 + 1 + 3 + 3 + 3 + 3 + 5 + 3 + 5 + 3 + 3 + 3.

23 = 2 + (1+0) + (1+2) + (2+1) + (1+0+2) + (1+1+1) + (1+2+2) + (2+0+1) = 2 + 1 + 3 + 3 + 3 + 3 + 5 + 3.
31 = 2 + (1+0) + (1+2) + (2+1) + (1+0+2) + (1+1+1) + (1+2+2) + (2+0+1) + (2+1+2) + (1+0+0+2) = 2 + 1 + 3 + 3 + 3 + 3 + 5 + 3 + 5 + 3.
47 = 2 + (1+0) + (1+2) + (2+1) + (1+0+2) + (1+1+1) + (1+2+2) + (2+0+1) + (2+1+2) + (1+0+0+2) + (1+0+1+1) + (1+1+0+1) + (1+1+1+2) + (1+1+2+1) = 2 + 1 + 3 + 3 + 3 + 3 + 5 + 3 + 5 + 3 + 3 + 3 + 5 + 5.
59 = 2 + (1+0) + (1+2) + (2+1) + (1+0+2) + (1+1+1) + (1+2+2) + (2+0+1) + (2+1+2) + (1+0+0+2) + (1+0+1+1) + (1+1+0+1) + (1+1+1+2) + (1+1+2+1) + (1+2+0+2) + (1+2+2+2) = 2 + 1 + 3 + 3 + 3 + 3 + 5 + 3 + 5 + 3 + 3 + 3 + 5 + 5 + 5 + 7.

This carries on for a long time. For these primes, p = digit-sum(primes < p):

23, 31, 47, 59, 695689, 698471, 883517, 992609, 992737, 993037, 1314239, 1324361, 1324571, 1326511, 1327289, 1766291, 3174029

And for these primes, p = digit-sum(primes <= p):

3, 37, 695663, 695881, 1308731, 1308757, 1313153, 1314301, 1326097, 1766227, 3204779, 14328191

Now try the cumulative digit-sum in base-4:

2, 3, 5, 07, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59...
2, 5, 7, 11, 16, 20, 22, 26, 31, 36, 43, 47, 52, 59, 67, 72, 80...

The sum of digits climbs too fast. Base-3 is the Goldilocks base, climbing neither too slowly, like base-2, nor too fast, like all bases greater than 3.

Prime Time #2

by in Mathematics, Prime numbers and tagged , , , , , , , , , , , , , | Leave a comment

“2n2 + 29 is prime for all values of n for 1 to 28.” — The Penguin Dictionary of Curious and Interesting Numbers, David Wells (1986).

• 31, 37, 47, 61, 79, 101, 127, 157, 191, 229, 271, 317, 367, 421, 479, 541, 607, 677, 751, 829, 911, 997, 1087, 1181, 1279, 1381, 1487, 1597.

Elsewhere other-posted:

• Prime Time #1
• Poulet’s Propellor — Musings on Math and Mathculinity
• La Spirale è Mobile

Performativizing Papyrocentricity #22

by in Über-Transgression..., Book Reviews, Civilization, History, Literature, Mathematics, Philosophy of mathematics, Politics, The Sea and tagged , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Papyrocentric Performativity Presents:

• Plates from the Great – Shots from the Front: The British Soldier 1914-18, Richard Holmes (HarperPress 2008; paperback 2010)

• Math for the Mistress – A Mathematician’s Apology, G.H. Hardy (1940)

• Sinister Sinema – Scalarama: A Celebration of Subterranean Cinema at Its Sleazy, Slimy and Sinister Best, ed. Norman Foreman, B.A. (TransVisceral Books 2015)

• Rick Pickings – Lost, Stolen or Shredded: Stories of Missing Works of Art and Literature, Rick Gekoski (Profile Books 2013/2014)

• Slug is a Drug – Collins Complete Guide to British Coastal Wildlife, Paul Sterry and Andrew Cleave (HarperCollins 2012) (posted @ Overlord of the Über-Feral)

Or Read a Review at Random: RaRaR

The Power of Babel

by in Aesthetics, Book Reviews, Clark Ashton Smith, French, History, Latin, Literature, Poetry, Psychology, Weird fiction and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

“…par la suggestive lecture d’un ouvrage racontant de lointains voyages…” – J.K. Huysmans, À Rebours (1884).

The language you know best is also the language you know least: your mother tongue, the language you acquired by instinct and speak by intuition. Asking a native speaker to describe English, French or Quechua is rather like asking a fish to describe water. The native speaker, like the fish, knows the answer very intimately, yet in some ways doesn’t know as well as a non-native speaker. In other words, standing outside can help you better understand standing inside: there is good in the gap. What is it like to experience gravity? Like most humans, I’ve known all my life, but I’d know better if I were in orbit or en route to the moon, experiencing the absence of gravity.

And what is it like to be human? We all know and we’ve all read countless stories about other human beings. But in some ways they don’t answer that question as effectively as stories that push humanity to the margins, like Richard Adams’ Watership Down (1972), which is about rabbits, or Isaac Asimov’s The Gods Themselves (also 1972), which is about trisexual aliens in a parallel dimension. There is good in the gap, in stepping outside the familiar and looking back to see the familiar anew.

Continuing reading The Power of Babel…

The Verm Terms

by in English Usage, In Terms Of, Politics, Quotations and tagged , , , , , , , , , , , , , , , , | Leave a comment

“Our relationship with Saudi Arabia is vitally important for our country in terms of counter-terrorism, in terms of the broader Middle East, in terms of helping in respect of Israel and Palestine.” — Tony Blair hits back at criticism…, BBC News, 15/xii/2006.

Elsewhere other-posted:

• Ex-term-in-ate!