Author Archives: Krilling for Company

Bestia Bestialissima

by in Über-Transgression..., History, Latin, Linguistics, Literature, Mixed Metaphors, Quotations, Theology, Translation and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Auberon Waugh called himself a “practitioner of the vituperative arts”. Perhaps it was a Catholic thing. And unless you know Latin, you won’t understand. Or you won’t understand as much as you might. I don’t know Latin well, but I can appreciate some of the wonderful vituperation in a book of Latin exorcisms I’ve found scanned at Google Books. The title alone is good: Flagellum Daemonum: Exorcismos Terribiles, Potentissimos et Efficaces, which means (I think) The Flail of Demons: Exorcisms Terrible, Most Potent and Effective. Or is the title Fustis Daemonum: Adiurationes Formidabiles, Potentissimas et Efficaces, meaning The Cudgel of Demons: Adjurations Formidable, Most Potent and Effective?

Vituperation from the Flagellum Daemonum (1644)

Vituperation from the Flagellum Daemonum (1644)


Either way, one of the exorcisms contains a good list of curses directed at the Devil. He’s called Bestia Omnium Bestiarum Bestialissima, meaning “Beast of All Beasts the Most Beastly”. Beside that, there are Dux Hæreticorum and Lupus Rapacissimus, “Duke of Heretics” and “Most Rapacious Wolf”. There’s an odd Sus Macra, Famelica, et Immundissima, which means something like “Scrawny, Famished and Most Filthy Hog”. Lovecraft would have liked Nefandissimus Susurrator, “Most Unspeakable Whisperer”, and Draco Iniquissimus, “Most Iniquitous Dragon”.

Pessimus Dux Tenebrarum is “Most Evil Duke of Darkness” and Janua et Vorago Inferni is “Door and Abyss of Hell”. Seminator Zizaniarum, meaning “Sower of Tares”, refers to Matthew xiii, 25: “But while men slept, his enemy came and sowed tares among the wheat, and went his way.” And those are only a few of the curses poured on the Devil’s head. I’ve turned the full list into plain text. As it says in the book that originally led me to the Flagellum Daemonum, “The following is a specimen of one of these vituperative addresses”:

Audi igitur insensate, false, reprobe, et iniquissime Spiritus. Inimice fidei. Adversarie generis humani. Mortis adductor. Vitæ raptor. Justitiæ declinator. Malorum radix. Fomes vitiorum. Seductor hominum. Proditor gentium. Incitator invidiæ. Origo aravitiæ. Causa discordiæ. Excitator malorum. Dæmonum magister. Miserrima Creature. Tentator Homininum. Deceptor malorum Angelorum. Fallax animarum. Dux Hæreticorum. Pater Mendacii. Fatue Bestialis. Tui creatoris Inimicus. Insipiens ebriose. Inique et iniquorum caput. Prædo infernalis. Serpens iniquissime. Lupe rapacissime. Sus macra, famelica, et immundissima. Bestia eruginosa. Bestia scabiosa. Bestia truculentissima. Bestia crudelis. Bestia cruenta. Bestia omnium Bestiarum Bestialissima. Ejecte de Paradise. De gratiâ Dei. De Cœli fastigio. De loco inerrabili. De Societate et consortia Angelorum. Immundissime Spiritus Initium omnium malorum. Trangressor bonæ vitæ. Veritatis et Justitiæ persecutor. Auctor fornicationum. Seminator zizaniarum. Dissipator pacis. Latro discordiæ. Pessime dux tenebrarum. Mortis inventor. Janua et vorago Inferni. Crudelis devorator animarum omniumque malorum causa. Malignissime Dæmon. Spurcissime Spiritus. Nefandissime susurrator. Nequissima Creatura. Vilissime apostata. Scelestissima latro. Impiissima bestia infernalis. Superbissime et ingratissime Spiritus. Iniquissime refuga. Tyranne, Omni bono vacue. Plene omni dolo et fallaciâ. Hominum exterminator. Derisio totius Angelicæ Naturæ. Maledicte Satana a Deo. Excommunicate a totâ cœlesti curiâ. Blaspheme Dei et omnium Sanctorum. Damnate a Deo atque Damnande. Spiritus Acherontine. Spiritus Tartaree. Fili Perditionis. Fili maledictionis æternæ. Rebellis Dei et totius cœlestis curiæ. Serpens crudelissime. Draco iniquissime. Creatura damnata, reprobata et maledicta a Deo in æternum ob superbiam nequitiam tuam.

The first line, Audi igitur insensate, false, reprobe, et iniquissime Spiritus means something like “Hear, then, Senseless, False, Reprobate and Most Iniquitous Spirit”. Then the Devil is called Inimicus Fidei, “Enemy of the Faith”, Adversarius Generis Humani, “Adversary of the Human Race”, Mortis Adductor, “Dragger to Death”, and Vitæ Raptor, “Snatcher of Life”. Then the vituperation really begins.

Fragic Carpet

by in Fractals, Geometry, Mathematics, Rep-Tiles and tagged , , , , , , , , , , , , , , , , , | Leave a comment

Maths is like a jungle: rich, teeming and full of surprises. A waterfall here, a glade of butterflies there, a bank of orchids yonder. There is always something new to see and a different route to try. But sometimes a different route will take you to the same place. I’ve already found two ways to reach this fractal (see Fingering the Frigit and Performativizing the Polygonic):

carpet2x2

Fractal Carpet

Now I’ve found a third way. You could call it the rep-tile route. Divide a square into four smaller squares:

square2x2

Add an extra square over the centre:

square2x2_1

Then keep dividing the squares in the same way:

carpet2x2_anim_1

Animated carpet (with coloured blocks)

carpet2x2_anim_2

Animated carpet (with empty blocks)

The colours of the fractal appear when the same pixel is covered repeatedly: first it’s red, then green, yellow, blue, purple, and so on. Because the colours and their order are arbitrary, you can use different colour schemes:

carpet2x2_col1

Colour scheme #1

carpet2x2_col2

Colour scheme #2

carpet2x2_col3

Colour scheme #3

Here are more colour-schemes in an animated gif:

carpet2x2_col

Various colour-schemes

Now try dividing the square into nine and sixteen, with an extra square over the centre:

carpet3x3

3×3 square + central square

carpet3x3_anim

3×3 square + central square (animated)

carpet4x4

4×4 square + central square

carpet4x4_anim

4×4 square + central square (animated)

You can also adjust the size of the square added to the 2×2 subdivision:

carpet2x2_1_2

2×2 square + 1/2-sized central square

carpet2x2_3_4

2×2 square + 3/4-sized central square

Elsewhere Other-Posted:

• Fingering the Frigit
• Performativizing the Polygonic

Toxic Turntable #7

by in Currently Listening..., Music and tagged , , , , , , , , , , , , , | Leave a comment

Currently listening…

• Slow Exploding Gulls, Salmaris EP (1997)
• Dubioso, Codicil LVI (1968)
• Ubair Yex, Weever (1973)
• Dux Tenebrarum, Quinque Fatuae (2012)
• Arctic Midge, Celsius (1992)
• Ijek Mveodeybda, Terë Conuva (1980)
• Schwarzschrein, Du Bist Dunst (1995)

Previously pre-posted:

Toxic Turntable #1 • #2 • #3 • #4 • #5 • #6 •

Polymorphous Pursuit

by in Geometry, Mathematics, Pursuit Curves and tagged , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Suppose four mice are standing on the corners of a large square. Each mouse begins running at the same speed towards the mouse one place away, reckoning clockwise. The mice will meet at the centre of the square and the path taken by each mouse will be what is known as a pursuit curve:

v4_mi1

vertices = 4, mouse-increment = 1

v4_mi1_animated

v = 4, mi = 1 (animated)

As I showed in “Persecution Complex”, it’s easy to find variants on the basic pursuit curve. If mi = 2, i.e. each mouse runs towards the mouse two places away, the mice will run in straight lines direct to the centre of the square:

v4_mi2

v = 4, mi = 2

v4_mi2_animated

v = 4, mi = 2 (animated)

That variant is trivial, but suppose there are eight mice, four starting on the corners of the square and four starting on the midpoints of the sides. Mice starting on the corners will run different pursuit curves to those starting on the midpoints, because the corners are further from the centre than the midpoints are:

v4_si1_mi1

v = 4, si = 1, mi = 1

v4_si1_mi1_extra

If mi = 3, the pursuit curves look like this:

v4_si1_mi3

v = 4, si = 1, mi = 3

v4_si1_mi3_animated

v = 4, si = 1, mi = 3 (animated)

Suppose there are twelve mice, four on each corner and two more on each side. If each mouse runs towards the mouse four places away, then the pursuit curves don’t all meet in the centre of the square. Instead, they meet in groups of three at four points equidistant from the centre, like this:

v4_si2_mi4

v4_si2_mi4_curves

v = 4, si = 2, mi = 4

v4_si2_mi4_animated

v = 4, si = 2, mi = 4 (animated)

v4_si4_mi4_animated

v = 4, si = 4, mi = 4 (animated)

v4_si4_mi4_large

v = 4, si = 4, mi = 4 (zoom)

Now suppose each mouse become sophisticated and runs toward the combined positions of two other mice, one two places away, the other three places away, like this:

v4_si1_mi2_3

v = 4, si = 1, mi = (2, 3)

v4_si1_mi2_3_animated

v = 4, si = 1, mi = (2, 3) (animated)

These polypursuits, as they could be called, can have complicated central regions:

v4_si2_mi1_4

v = 4, si = 2, mi = (1, 4)

v4_si2_mi1_4_animated

v = 4, si = 2, mi = (1, 4) (animated)

v4_si_va_mi_va

v = 4, si = various, mi = various

And what if you have two teams of mice, running towards one or more mice on the other team? For example, suppose two mice, one from each team, start on each corner of a square. Each mouse on team 1 runs towards the mouse on team 2 that is one place away, while each mouse on team 2 runs towards the mouse on team 1 that is two places away. If the pursuits curves of team 1 are represented in white and the pursuit curves of team 2 in green, the curves look like this:

2v4_mi1_mi2

v = 4 * 2, vmi = 1, vmi = 2

2v4_mi1_mi2_green

v = 4 * 2, vmi = 1, vmi = 2

2v4_mi1_mi2_animated

v = 4 * 2, vmi = 1, vmi = 2 (animated)

Now suppose the four mice of team 1 start on the corners while the mice of team 2 start at the centre of the square.

v4_c4_vmi1_cmi2_white

v = 4, centre = 4, vmi = 1, cmi = 2 (white team)

v4_c4_vmi1_cmi2_green

v = 4, centre = 4, vmi = 1, cmi = 2 (green team)

v4_c4_vmi1_cmi2_both

v = 4, centre = 4, vmi = 1, cmi = 2 (both teams)

v4_c4_vmi1_cmi2_animated

v = 4, centre = 4, vmi = 1, cmi = 2 (animated)

Here are more variants on pursuit curves formed by two teams of mice, one starting on the corners, one at the centre:

v4_c4_vmi0_1_cmi0

v = 4, centre = 4, vmi = (0, 1), cmi = 0

v4_c4_vmi0_2_cmi0

v = 4, centre = 4, vmi = (0, 2), cmi = 0

v4_c4_vmi0_3_cmi0

v = 4, centre = 4, vmi = (0, 3), cmi = 0

2v4_mi1_mi2_both

White Rites

by in Blancmange Curves, Fractals, Geometry, Mathematics and tagged , , , , , , , , , , , , , , , | Leave a comment

The blancmange curve is an interesting fractal formed by summing a series of zigzags. It
takes its name from its resemblance to the milk-pudding known as a blancmange
(blanc-manger in French, meaning “white eating”):

blanc_solid

Blancmange curve

In successive zigzags, the number of zags doubles as their height halves, i.e. z(i) = z(i-1) * 2, h(i) = h(i-1) / 2. If all the zigzags are represented at once, the construction looks like this:

blanc_all

Zigzags 1 to 10

blancmange_all

Zigzags 1 to 10 (animated)

Here is a step-by-step construction, with the total sum of zigzags in white, the present zigzag in red and the previous zigzag in green:

blanc1

Blancmange curve stage 1

blanc2

Stage 2

blanc3

Stage 3

blanc4

Stage 4

blanc5

Stage 5

blanc6

Stage 6

blanc7

Stage 7

blanc8

Stage 8

blanc9

Stage 9

blanc10

Stage 10

blancmange

Blancmange curve (animated)

It’s easy to think of variants on the standard blancmange curve. Suppose the number of zags triples as their height is divided by three, i.e. z(i) = z(i-1) * 3, h(i) = h(i-1) / 3:

blanc_x3_solid

Blancmange curve for z(i) = z(i-1) * 3, h(i) = h(i-1) / 3

Continue reading “White Rites”…

Bash the Pash

by in English Usage, Guardianistas, Quotations and tagged , , , , , , , , , , , , , , | Leave a comment

An heretical Guardianista keyly critiquizes a core component of Guardianese:

I recently considered nominating for a board position on a professional association to which I belong, so I had a look at the biographical statements of the incumbents. One claimed to be “passionate about helping individuals, businesses, and communities thrive”, another declared “a particular passion for thought leadership and executive profiling”, and another revealed “a passion for social inclusion”. Yet another claimed “a passion about creating valuable career development opportunities for the profession”. The best was the one that stated, without irony, “a passion for working on meaningful projects”.

In days gone by, job applicants listed hobbies. These days, it appears candidates are expected to declare, not merely interests or things they like doing, but things they are allegedly passionate about. — Being enthusiastic is no longer enough. Now we must all be passionate, Paul Begley, The Guardian, 13/vii/2016.

Elsewhere other-engageable:

• Ex-term-in-ate!
• Reds under the Thread
• Titus Graun — Heresy, Homotextuality, Hive-Mind
• Oh My Guardian

Performativizing Papyrocentricity #49

by in Book Reviews, Geology, Literature, Morrissey, Music, Science and tagged , , , , , , , , , , , , , , , , | Leave a comment

Papyrocentric Performativity Presents:

• Clarke’s Sparks – The Collected Stories, Arthur C. Clarke (Victor Gollancz 2000)

• Deeper and Down – Blind Descent: The Quest to Discover the Deepest Place on Earth, James M. Tabor (Random House 2010)

• Manchester’s Mozzerabilist Messiah – Morrissey: The Pageant of His Bleeding Heart, Gavin Hopps (Continuum Books 2012)

• Or Read a Review at Random: RaRaR

Toxic Turntable #6

by in Currently Listening..., Music and tagged , , , , , , , , , , , , , , , , , | Leave a comment

Currently listening…

• Anaïd, Magna Est (1969)
• Linnet, Venussong (1977)
• Šrúsma, Ðrioso (1994)
• Milchstraße, Der Schwarze Zwerg (2001)
• Ser, Acanthocalycium (1989)
• Zélote, Lac d’Angoisse (1992)

Previously pre-posted:

Toxic Turntable #1 • #2 • #3 • #4 • #5 •

Get Your Ox Off

by in Clark Ashton Smith, Integer Sequences, Mathematics, Prime numbers, Reciprocals and tagged , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Boustrophedon (pronounced “bough-stra-FEE-dun” or “boo-stra-FEE-dun”) is an ancient Greek word literally meaning “as the ox turns (in ploughing)”, that is, moving left-right, right-left, and so on. The word is used of writing that runs down the page in the same way. To see what that means, examine two versions of the first paragraph of Clark Ashton Smith’s story “The Demon of the Flower” (1933). The first is written in the usual way, the second is written boustrophedon:

Not as the plants and flowers of Earth, growing peacefully beneath a simple sun, were the blossoms of the planet Lophai. Coiling and uncoiling in double dawns; tossing tumultuously under vast suns of jade green and balas-ruby orange; swaying and weltering in rich twilights, in aurora-curtained nights, they resembled fields of rooted servants that dance eternally to an other-worldly music.

Not as the plants and flowers of Earth, growing peacefully
.iahpoL tenalp eht fo smossolb eht erew ,nus elpmis a htaeneb
Coiling and uncoiling in double dawns; tossing tumultuously
;egnaro ybur-salab dna neerg edaj fo snus tsav rednu
swaying and weltering in rich twilights, in aurora-curtained
ecnad taht stnavres detoor fo sdleif delbmeser yeht ,sthgin
eternally to an other-worldly music.

Boustrophedon writing was once common and sometimes the left-right lines would also be mirror-reversed, like this:

You could also use the term “boustrophedon” to describe the way this table of numbers is filled:

primes_table

The table begins with “1” in the top left-hand corner, then moves right for “2”, then down for “3”, then right-and-up for “4”, “5” and “6”, then right for “7”, then left-and-down for “8”, “9” and “10”, and so on. You could also say that the numbers snake through the table. I’ve marked the primes among them, because I was interested in the patterns made by the primes when the numbers were represented as blocks on a grid, like this:

primes_large

Primes are in solid white (compare the Ulam spiral). Here’s the boustrophedon prime-grid on a finer scale:

primes

(click for full image)

And what about other number-tests? Here are the even numbers marked on the grid (i.e. n mod 2 = 0):

mod2

n mod 2 = 0

And here are some more examples of a modulus test:

mod3

n mod 3 = 0

mod5

n mod 5 = 0

mod9

n mod 9 = 0

mod15

n mod 15 = 0

mod_various

n mod various = 0 (animated gif)

Next I looked at reciprocals (numbers divided into 1) marked on the grid, with the digits of a reciprocal marking the number of blank squares before a square is filled in (if the digit is “0”, the square is filled immediately). For example, in base ten 1/7 = 0.142857142857142857…, where the block “142857” repeats for ever. When represented on the grid, 1/7 has 1 blank square, then a filled square, then 4 blank squares, then a filled square, then 2 blank squares, then a filled square, and so on:

recip7_base10

1/7 in base 10

And here are some more reciprocals (click for full images):

recip9_base2

1/9 in base 2

recip13_base10

1/13 in base 10

recip27_base10

1/27 in base 10

recip41_base10

1/41 in base 10

recip63_base10

1/63 in base 10

recip82_base10

1/82 in base 10

recip101_base10

1/101 in base 10

recip104_base10

1/104 in base 10

recip124_base10

1/124 in base 10

recip143_base10

1/143 in base 10

recip175_base10

1/175 in base 10

recip604_base8

1/604 in base 8

recip_various

1/n in various bases (animated gif)