Currently Glistening…

• Tusmørkejuvel, Twilight Jewel (2018)
• Cybernetic Witch Cult, Morlock Rock (2015)
• Bizarra Locomotiva, Homem Máquina (2002)
• Turtle Skull, Monoliths (2020)
• Spotlights, We Are All Atomic (2020)
• Elevators to the Grateful Sky, Nude (2019)
• Egypt, Endless Flight (2015)
• Red Eye, The Cycle (2022)
• Temple Of The Fuzz Witch, Live and Unreleased (2020)
• Compulsion, The Future Is Medium (1996)
• Ultraphallus, First Demo (2004)
• Dunerider, Ascend to the Void (2021)
• Obiat, Emotionally Driven Disturbulence (2005)
• Fuzzthrone, Temple of the Fuzz (2021)
• Kråkslott, The Witchhammer (2021)
• Sludge Terror, Tenebris EP (2018)
• Pitchshifter, Submit (1992)
• The Autumn Spiders, Woe of the World (1987)
• Faster Pussycat, Best Of (2021)

Double-Gweeling


My short-story collection Gweel & Other Alterities has very kindly been re-published by D.M. Mitchell at Incunabula:

Gweel & Other Alterities – Incunabula’s new edition
Once More (With Gweeling) – my short review of the new edition
Incunabula Media — wildness and weirdness in words and more


(click for larger image)

Sprung from the Tongue

• Quot linguas calles, tot homines vales. — attributed to the polyglot Holy Roman Emperor Charles V
• • You’re worth as many people as the languages you speak.
• • The more languages you speak, the more people you are.
• • Speak a new language, be a new person.
• • New language, new person.
• • New tongue, new man.

Lux Legibilis

I wake from dreams and turning
     My vision on the height
I scan the beacons burning
     About the fields of night.

Each in its steadfast station
     Inflaming heaven they flare;
They sign with conflagration
     The empty moors of air.

The signal-fires of warning
     They blaze, but none regard;
And on through night to morning
     The world runs ruinward. — A.E. Housman in More Poems (1936)


There was a young fellow named Bright
Who travelled much faster than light.
     He set off one day,
     In a relative way
And came back the previous night. — Anonymous

Pi in the Bi

Binary is beautiful — both simple and subtle. What could be simpler than using only two digits to count with?


0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 101111, 110000, 110001, 110010, 110011, 110100, 110101, 110110, 110111, 111000, 111001, 111010, 111011, 111100, 111101, 111110, 111111, 1000000...

But the simple patterns in the two digits of binary involve two of the most important numbers in mathematics: π and e (aka Euler’s number):


π = 3.141592653589793238462643383...
e = 2.718281828459045235360287471...

It’s easy to write π and e in binary:


π = 11.00100 10000 11111 10110 10101 00010...
e = 10.10110 11111 10000 10101 00010 11000...

But how do π and e appear in the patterns of binary 1 and 0? Well, suppose you use the digits of binary to generate the sums of distinct integers. For example, here are the sums of distinct integers you can generate with three digits of binary, if you count the digits from right to left (so the rightmost digit is 1, the the next-to-rightmost digit is 2, the next-to-leftmost digit is 3, and the leftmost digit is 4):


0000 → 0*4 + 0*3 + 0*2 + 0*1 = 0
0001 → 0*4 + 0*3 + 0*2 + 1*1 = 1*1 = 1
0010 → 0*4 + 0*3 + 1*2 + 0*1 = 1*2 = 2
0011 → 0*4 + 0*3 + 1*2 + 1*1 = 1*2 + 1*1 = 3
0100 → 1*3 = 3
0101 → 1*3 + 1*1 = 4
0110 → 3 + 2 = 5
0111 → 3 + 2 + 1 = 6
1000 → 4
1001 → 4 + 1 = 5
1010 → 4 + 2 = 6
1011 → 4 + 2 + 1 = 7
1100 → 4 + 3 = 7
1101 → 4 + 3 + 1 = 8
1110 → 4 + 3 + 2 = 9
1111 → 4 + 3 + 2 + 1 = 10

There are 16 sums (16 = 2^4) generating 11 integers, 0 to 10. But some integers involve more than one sum:


3 = 2 + 1 ← 0011
3 = 3 ← 0100

4 = 3 + 1 ← 0101
4 = 4 ← 1000

5 = 3 + 2 ← 0110
5 = 4 + 1 ← 1001

6 = 3 + 2 + 1 ← 0111
6 = 4 + 2 ← 1010

7 = 4 + 2 + 1 ← 1011
7 = 4 + 3 ← 1100

Note the symmetry of the sums: the binary number 0011, yielding 3, is the mirror of 1100, yielding 7; the binary number 0100, yielding 3 again, is the mirror of 1011, yielding 7 again. In each pair of mirror-sums, the two numbers, 3 and 7, are related by the formula 10-3 = 7 and 10-7 = 3. This also applies to 4 and 6, where 10-4 = 6 and 10-6 = 4, and to 5, which is its own mirror (because 10-5 = 5). Now, try mapping the number of distinct sums for 0 to 10 as a graph:

Graph for distinct sums of the integers 0 to 4


The graph show how 0, 1 and 2 have one sum each, 3, 4, 5, 6 and 7 have two sums each, and 8, 9 and 10 have one sum each. Now look at the graph for sums derived from three digits of binary:

Graph for distinct sums of the integers 0 to 3


The single taller line of the seven lines represents the two sums of 3, because three digits of binary yield only one sum for 0, 1, 2, 4, 5 and 6:


000 → 0
001 → 1
010 → 2
011 → 2 + 1 = 3
100 → 3
101 → 3 + 1 = 4
110 → 3 + 2 = 5
111 → 3 + 2 + 1 = 6

Next, look at graphs for sums derived from one to sixteen binary digits and note how the symmetry of the lines begins to create a beautiful curve (the y axis is normalized, so that the highest number of sums reaches the same height in each graph):

Graph for sums from 1 binary digit


Graph for sums from 2 binary digits


Graph for sums from 3 binary digits


Graph for sums from 4 binary digits


Graph for sums from 5 binary digits


Graph for sums from 6 binary digits


Graph for sums from 7 binary digits


Graph for sums from 8 binary digits


Graph for sums from 9 binary digits


Graph for sums from 10 binary digits


Graph for sums from 11 binary digits


Graph for sums from 12 binary digits


Graph for sums from 13 binary digits


Graph for sums from 14 binary digits


Graph for sums from 15 binary digits


Graph for sums from 16 binary digits


Graphs for 1 to 16 binary digits (animated)


You may recognize the shape emerging above as the bell curve, whose formula is this:

Formula for the normal distribution or bell curve (image from ThoughtCo)


And that’s how you can find pi in the bi, or π in the binary digits of 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101…


Post-Performative Post-Scriptum

I asked this question above: What could be simpler than using only two digits? Well, using only one digit is simpler still:


1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111...

But I don’t see an easy way to find π and e in numbers like that.

Lord, What Fuels These Portals Be!


Midnight, one more night without sleeping.
Watching ’til that morning comes creeping.
Green Door: what’s that secret you’re keeping?

There’s an old piano and they play it hot behind the green door!
Don’t know what they’re doing but they laugh a lot behind the green door.
Wish they’d let me in so I could find out what’s behind the green door.

Knocked once, tried to tell ’em I’d been there.
Door slammed — hospitality’s thin there.
Wondering just what’s going on in there.

Saw an eyeball peepin’ through a smoky cloud behind the green door.
When I said “Joe sent me” someone laughed out loud behind the green door.
All I want to do is join the happy crowd behind the green door.



Otra noche mas que no duermo.
Otra noche mas que se pierde.
¿Que habrá tras esa puerta verde?
Suena alegremente un piano viejo
   tras la puerta verde.

Todos ríen y no se que pasa
   tras la puerta verde
No descansaré hasta saber que hay
   tras la puerta verde.

Toqué, y cuando contestaron
dije ¡Ah! que a mí me llamaron.
Risas, y enseguida me echaron.

Sólo pude ver que mucha gente allí se divertía,
y entre tanto humo todo allí se confundía.
Yo quisiera estar al otro lado de la puerta verde.

Otra noche mas que no duermo.
Otra noche mas que se pierde.
¿Que habrá tras esa puerta verde?
¿Que habrá tras esa puerta verde?
¿Que habrá?


Elsewhere Other-Accessible…

“The Green Door” (1956), music by Bob “Hutch” Davie and lyrics by Marvin J. Moore