# Author Archives: Krilling for Company

# Ted Said

I thought I knew how depraved and despicable core serial-slayer Ted Bundy was when I began *The Only Living Witness* (1983) for the first time earlier this month.

I was wrong.

Keyly, corely *wrong*.

As I discovered when I reached this putrefactively performative passage:

I wanted to know how Lynda Healy had been taken from her bedroom. “I guess you would have had to dress her?” I ventured.

Ted ignored my use of “you”.

“In that kind of situation,” he replied mechanically, “a person who was alert enough to be able to dress would not be afraid in terms of struggling or crying out. So it would be unlikely that any attempt was made to clothe the girl.” — from chapter 5 of

The Only Living Witness, Stephen G. Michaud and Hugh Aynesworth (revised edition 1989)

It’s always possible to go lower and get worse, it seems. Bundy trained as a lawyer. That’s bad. Bundy used “in terms of”. That’s *worse*. (dot dot dot)

Ted should *of course* have said: “afraid to struggle…” or “afraid about struggling…”

Elsewhere other-engageable:

• Ex-term-in-ate!

• *All Posts* interrogating issues around “in terms of”

• Don’t Do Dot… (also interrogates issues around “core” and “spike”)…

• Heresy, Homotextuality, Hive-Mind…

# Toxic Turntable #18

Currently listening…

• Loxomoxol, *Basilisc d’Or* (2001)

• HēDoNē, *See The Grace Above* (2004)

• Episodic Static, *Ridmik* (1979)

• T-Nor-F, *Ipacuma* (2013)

• Qvo Y Rugr, *By the Rivers of Bangor* (2017)

• Tumultus, *Cat’s Breath* (2001)

• Veulgozir, *Dwelling Beneath* (1998)

• Dan Hadden, *Total (Live in Yeovil)* (2006)

• Los Ombres del Voske, *TuMiNos* (2017)

• VampiriOc, *PlanetOc* (1983)

• Xriqsar, *343813* (2018)

• AzogFoe, *Ghosts of the Hemisphere* (2011)

• Los Magnicidios, *Líquido* (1997)

• Undulatio, *Viva Papua* (2006)

• Ifikh, *Askal Ni Luwo* (1975)

• Esteban Sureño, *Guijarral* (1995)

• W. van Wassenaer, *Concerti Armonici* (2004)

• Tom Vigattsef, *Urneolus* (2013)

Previously pre-posted:

• Toxic Turntable #1

• Toxic Turntable #2

• Toxic Turntable #3

• Toxic Turntable #4

• Toxic Turntable #5

• Toxic Turntable #6

• Toxic Turntable #7

• Toxic Turntable #8

• Toxic Turntable #9

• Toxic Turntable #10

• Toxic Turntable #11

• Toxic Turntable #12

• Toxic Turntable #13

• Toxic Turntable #14

• Toxic Turntable #15

• Toxic Turntable #16

• Toxic Turntable #17

# Nice Von

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” — John von Neumann

This quote is popular on web pages about von Neumann, and about computing and mathematics generally. It is apparently not from a published work of von Neumann’s, but Franz L. Alt recalls it as a remark made from the podium by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947. The exchange at that meeting is described at the end of Alt’s brief article “Archaeology of computers: Reminiscences, 1945–1947”, Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694. Alt recalls that von Neumann “mentioned the ‘new programming method’ for ENIAC and explained that its seemingly small vocabulary was in fact ample: that future computers, then in the design stage, would get along on a dozen instruction types, and this was known to be adequate for expressing all of mathematics…. Von Neumann went on to say that one need not be surprised at this small number, since about 1,000 words were known to be adequate for most situations of real life, and mathematics was only a small part of life, and a very simple part at that. This caused some hilarity in the audience, which provoked von Neumann to say: ‘If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.’ ”

# Colorfool

*Album primo-avrilesque*, meaning *April-Foolish Album*, is a collection of visual jokes published by the French humourist Alphonse Allais (1854-1905) on 1st April 1897. Note that some of the captions can’t be translated fully into English, because they use French idioms that refer to color.

# Hour Power

Would it be my favorite fractal if I hadn’t discovered it for myself? It might be, because I think it combines great simplicity with great beauty. I first came across it when I was looking at this rep-tile, that is, a shape that can be divided into smaller copies of itself:

Rep-4 L-Tromino

It’s called a L-tromino and is a rep-4 rep-tile, because it can be divided into four copies of itself. If you divide the L-tromino into four sub-copies and discard one particular sub-copy, then repeat again and again, you’ll get this fractal:

Tromino fractal #1

Tromino fractal #2

Tromino fractal #3

Tromino fractal #4

Tromino fractal #5

Tromino fractal #6

Tromino fractal #7

Tromino fractal #8

Tromino fractal #9

Tromino fractal #10

Tromino fractal #11

Hourglass fractal (animated)

I call it an hourglass fractal, because it reminds me of an hourglass:

A real hourglass

The hourglass fractal for comparison

I next came across the hourglass fractal when applying the same divide-and-discard process to a rep-4 square. The first fractal that appears is the Sierpiński triangle:

Square to Sierpiński triangle #1

Square to Sierpiński triangle #2

Square to Sierpiński triangle #3

[…]

Square to Sierpiński triangle #10

Square to Sierpiński triangle (animated)

However, you can rotate the sub-squares in various ways to create new fractals. Et voilà, the hourglass fractal appears again:

Square to hourglass #1

Square to hourglass #2

Square to hourglass #3

Square to hourglass #4

Square to hourglass #5

Square to hourglass #6

Square to hourglass #7

Square to hourglass #8

Square to hourglass #9

Square to hourglass #10

Square to hourglass #11

Square to hourglass (animated)

Finally, I was looking at variants of the so-called chaos game. In the standard chaos game, a point jumps half-way towards the randomly chosen vertices of a square or other polygon. In this variant of the game, I’ve added jump-towards-able mid-points to the sides of the square and restricted the point’s jumps: it can only jump towards the points that are first-nearest, seventh-nearest and eighth-nearest. And again the hourglass fractal appears:

Chaos game to hourglass #1

Chaos game to hourglass #2

Chaos game to hourglass #3

Chaos game to hourglass #4

Chaos game to hourglass #5

Chaos game to hourglass #6

Chaos game to hourglass (animated)

But what if you want to create the hourglass fractal directly? You can do it like this, using two isosceles triangles set apex to apex in the form of an hourglass:

Triangles to hourglass #1

Triangles to hourglass #2

Triangles to hourglass #3

Triangles to hourglass #4

Triangles to hourglass #5

Triangles to hourglass #6

Triangles to hourglass #7

Triangles to hourglass #8

Triangles to hourglass #9

Triangles to hourglass #10

Triangles to hourglass #11

Triangles to hourglass #12

Triangles to hourglass (animated)

# Möbius Tripping

“In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics. (Some have engaged in it for this reason alone.)” — Stanislaw Ulam (1909-84)

# Square Routes Re-Re-Re-Re-Re-Revisited

For a good example of how more can be less, try the chaos game. You trace a point jumping repeatedly 1/*n* of the way towards a randomly chosen vertex of a regular polygon. When the polygon is a triangle and 1/*n* = 1/2, this is what happens:

Chaos triangle #1

Chaos triangle #2

Chaos triangle #3

Chaos triangle #4

Chaos triangle #5

Chaos triangle #6

Chaos triangle #7

As you can see, this simple chaos game creates a fractal known as the Sierpiński triangle (or Sierpiński sieve). Now try more and discover that it’s less. When you play the chaos game with a square, this is what happens:

Chaos square #1

Chaos square #2

Chaos square #3

Chaos square #4

Chaos square #5

Chaos square #6

Chaos square #7

As you can see, more is less: the interior of the square simply fills with points and no attractive fractal appears. And because that was more is less, let’s see how less is more. What happens if you restrict the way in which the point inside the square can jump? Suppose it can’t jump twice towards the same vertex (i.e., the vertex v+0 is banned). This fractal appears:

Ban on choosing vertex [v+0]

And if the point can’t jump towards the vertex one place anti-clockwise of the currently chosen vertex, this fractal appears:

Ban on vertex [v+1] (or [v-1], depending on how you number the vertices)

And if the point can’t jump towards two places clockwise or anti-clockwise of the currently chosen vertex, this fractal appears:

Ban on vertex [v+2], i.e. the diagonally opposite vertex

At least, that is one possible route to those three particular fractals. You see another route, start with this simple fractal, where dividing and discarding parts of a square creates a Sierpiński triangle:

Square to Sierpiński triangle #1

Square to Sierpiński triangle #2

Square to Sierpiński triangle #3

Square to Sierpiński triangle #4

[…]

Square to Sierpiński triangle #10

Square to Sierpiński triangle (animated)

By taking four of these square-to-Sierpiński-triangle fractals and rotating them in the right way, you can re-create the three chaos-game fractals shown above. Here’s the [v+0]-ban fractal:

[v+0]-ban fractal #1

[v+0]-ban #2

[v+0]-ban #3

[v+0]-ban #4

[v+0]-ban #5

[v+0]-ban #6

[v+0]-ban #7

[v+0]-ban #8

[v+0]-ban #9

[v+0]-ban (animated)

And here’s the [v+1]-ban fractal:

[v+1]-ban fractal #1

[v+1]-ban #2

[v+1]-ban #3

[v+1]-ban #4

[v+1]-ban #5

[v+1]-ban #6

[v+1]-ban #7

[v+1]-ban #8

[v+1]-ban #9

[v+1]-ban (animated)

And here’s the [v+2]-ban fractal:

[v+2]-ban fractal #1

[v+2]-ban #2

[v+2]-ban #3

[v+2]-ban #4

[v+2]-ban #5

[v+2]-ban #6

[v+2]-ban #7

[v+2]-ban #8

[v+2]-ban #9

[v+2]-ban (animated)

And taking a different route means that you can find more fractals — as I will demonstrate.

Previously pre-posted (please peruse):

• Square Routes

• Square Routes Revisited

• Square Routes Re-Revisited

• Square Routes Re-Re-Revisited

• Square Routes Re-Re-Re-Revisited

• Square Routes Re-Re-Re-Re-Revisited

# Tolk of the Devil

I’ve said it before and I’ll say it again: I wish someone would translate *Lord of the Rings* (1954-5) into English. By that I mean (of course) that I wish someone would translate *LOTR* into good English. I’ve looked at Tolkien’s bad English in “Noise Annoys” and “Science and Sorcery”. Here’s another example:

Pippin declared that Frodo was looking twice the hobbit that he had been.

“Very odd,” said Frodo, tightening his belt, “considering that there is actually a good deal less of me. I hope the thinning process will not go on indefinitely, or I shall become a wraith.”

“Do not speak of such things!” said Strider quickly, and with surprising earnestness. –

The Fellowship of the Ring(1954), Chapter 11, “A Knife in the Dark”

Strider should have added: “Or in such a way!” In the second paragraph, Frodo suddenly talks like a *Guardian*-reader. Why on earth did Tolkien use “thinning process”, “indefinitely” and “actually” amid otherwise good, simple English? Thinning is obviously a “process”, so there’s no need to say it is, and “indefinitely” and “actually” are badly out of a place in a fantasy novel, let alone in dialogue there. “Considering” is less bad, but it should go too. I would improve the paragraph like this:

“Very odd,” said Frodo, tightening his belt, “seeing that there is now a good deal less of me. I hope the thinning will not go on much longer, or I shall become a wraith.”

Now there’s nothing incongruous: the only un-English word is “very”, but that doesn’t seem un-English on the tongue or to the eye. The Guardianese is gone, but it should never have been there in the first place. Tolkien should not have written like that in *Lord of the Rings*. And not just as a professional scholar of language: simply as a literate Englishman. H.W. Fowler’s *Modern English Usage* (1926) had been in print for twenty-eight years when *The Fellowship of the Ring* was first published. It’s hard to believe that Tolkien wasn’t familiar with it.

If he wasn’t, that’s a great pity. If he was, the bad prose in *LOTR* becomes even more inexplicable and unforgiveable. Alas for what might have been! Imagine if, *per impossibile*, Tolkien’s masterwork had been edited by the second-greatest Catholic writer of the twentieth-century, namely, Evelyn Waugh.

When bad prose appears in something by Waugh, it’s deliberate:

I had a fine haul – eleven paintings and fifty odd drawings – and when eventually I exhibited them in London, the art critics, many of whom hitherto had been patronizing in tone as my success invited, acclaimed a new and richer note in my work.

Mr. Ryder[the most respected of them wrote]rises like a fresh young trout to the hypodermic injection of a new culture and discloses a powerful facet in the vista of his potentialities … By focusing the frankly traditional battery of his elegance and erudition on the maelstrom of barbarism, Mr. Ryder has at last found himself.–Brideshead Revisited(1945), Book II, “A Twitch Upon the Thread”, ch. 1

Waugh was deliberately mocking the mixed-metaphor-strewn prose and pretensions of modern critics. Waugh paid great attention to language and compared writing to carpentry. It was a craft and good craftsmen do not work carelessly or use bad materials. Nothing in *Brideshead* is careless or casual, as we can see when the narrator, Charles Ryder, first meets the “devilish” æsthete Anthony Blanche, who has “studied Black Art at Cefalù” with Aleister Crowley and is “a byword of iniquity from Cherwell Edge to Somerville”. Blanche has a stutter and Waugh uses the stutter to underline his iniquity. Or so I would claim. Here is Blanche engaging in some papyrocentric performativity:

After luncheon he stood on the balcony with a megaphone which had appeared surprisingly among the bric-à-brac of Sebastian’s room, and in languishing, sobbing tones recited passages from

The Waste Landto the sweatered and muffled throng that was on its way to the river.“’I, Tiresias, have foresuffered all,’” he sobbed to them from the Venetian arches –

“Enacted on this same d-divan or b-bed,

I who have sat by Thebes below the wall

And walked among the l-l-lowest of the dead….”And then, stepping lightly into the room, “How I have surprised them! All b-boatmen are Grace Darlings to me.”

Brideshead Revisited, Book I, “Et in Arcadia Ego”, ch. 1

Talking about the Greek sage Tiresias, who experienced life as both a man and a woman, Anthony Blanche, a man whose surname is the feminine form of the French adjective *blanc*, meaning “white”, stumbles over the initial consonants of three words: “divan”, “bed” and “lowest”. Is it a coincidence that the same consonants, in the same order, appear in the Greek *diabolos*, meaning “devil”?

I don’t think so. If Blanche had stuttered on “surprised” too, I would be even more certain. But the –*s* isn’t essential. After all, it was lost as *diabolos* journeyed from Greek to Latin, from Latin to French, and from French to English, where it appears as “Devil”. And what does Charles Ryder later call Anthony Blanche after Blanche has spent an evening *tête-à-tête* trying to turn Ryder against Ryder’s great friend Sebastian Flyte? You can find out here, as Ryder discusses the evening with Sebastian:

“I just wanted to find out how much truth there was in what Anthony said last night.”

“I shouldn’t think a word. That’s his great charm.”

“You may think it charming. I think it’s devilish. Do you know he spent the whole of yesterday evening trying to turn me against you, and almost succeeded?”

“Did he? How silly. Aloysius wouldn’t approve of that at all, would you, you pompous old bear?” –

Brideshead Revisited, Book I, “Et in Arcadia Ego”, ch. 2

Blanche is “devilish” and his reputation for “iniquity” is well-deserved. That’s why I think the three words over which Blanche stutters were carefully chosen by Waugh from *The Waste Land*. Waugh was a logophile and that is exactly the kind of linguistic game that logophiles like to play.

# Thalassic Classic

(Click for larger)