This Means RaWaR

The Overlord of the Über-Feral says: Welcome to my bijou bloguette. You can scroll down to sample more or simply:

• Read a Writerization at Random: RaWaR


• O.o.t.Ü.-F.: More Maverick than a Monkey-Munching* Mingrelian Myrmecologist Marinated in Mescaline…

• ¿And What Doth It Mean To Be Flesh?

მათემატიკა მსოფლიოს მეფე


*Der Muntsch ist Etwas, das überwunden werden soll.

Terminal Transgressivity

“If this work is about hell,” he says, “it’s not only about hell in terms of content. It’s also about hell in terms of its hellishness in terms of production.” — maximally maverick artist Jake Chapman describes how he and his brother Dinos made the transgressive sculpture Hell (2000), as quoted in Simon Garfield’s In Miniature: How Small Things Illuminate the World (2018)


Elsewhere Other-Accessible

Ex-term-in-nate! — incendiarily interrogating issues around “in terms of”…
All O.o.t.Ü.-F. posts interrogating issues around “in terms of”…


Peri-Performative Post-Scriptum…

Yes, this was an über-ideal quote for posting on the 23rd in terms of the month… But I was so taken with it that I couldn’t delay any longer. And anyway: it is the 23rd of the months in base 11. (I.e., 2111 = 2 * 11 + 1 = 22 + 1 = 23.)

For Flake’s Sake

It caught my eye, it caught my eye,
That fluttering flake of fallen sky.

It rode the wind as cars bored by
And did not die:

And shall not die,
That fluttering flake of fallen sky.


Post-Performative Post-Scriptum

A poem written months ago about a briefly glimpsed blue butterfly flying along — and over — a busy road. I don’t know the species, but Polyommatus icarus seems a reasonable guess.

Octobyss

The deep-sea octopus Vulcanoctopus hydrothermalis, which lives around hydrothermal vents on the floor of the Pacific (image from Octolab)


Elsewhere Other-Engageable

Guise and Molls — review of Front cover of Octopus: The Ocean’s Intelligent Invertebrate: A Natural History (2010)
Magna Mater Marina — review of The Illustrated World Encyclopedia of Marine Fish and Sea Creatures (2007)

There are 719 errors in this sentence

Here’s a famous paradox (or a variant of it at least):

• There are two errers in this sentence.

The only visible error is the misspelt “errers”. But if the sentence claims to have two errors while having only one, that is another error and there are two errors after all.

Now for another variant. I’m not sure if I’ve thought this up for myself, but try this sentence:

• There are three errors in this sentence.

There are no visible errors in the sentence. Therefore it has one error: the claim that it has three errors when there is in fact no error. But if it has one error, it’s in error to claim that it has three errors. Therefore the sentence has two errors. And if it has two errors, again it’s in error, because it claims to have three errors while having only two. Therefore it has three errors after all.

The same reasoning can be applied to any integral number of errors:

• There are five errors in this sentence.
• There are 719 errors in this sentence.
• There are 1,000,000 errors in this sentence.
• There are 1,000,000,000 errors in this sentence.

No matter how large the number of errors, the sentence becomes true instantly, because each time the sentence makes a false claim, it makes another error. But those “times of error” don’t take place in time, any more than this equation does:

• 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16…

So I think these sentences are instantly true:

• There are infinitely many errors in this sentence.
• There are ∞ errors in this sentence.

But there are infinitely many infinities. Ordinary infinity, the infinity of 1,2,3…, is called ℵ0 or aleph-zero. It’s a countable infinity. Above that comes ℵ1, an uncountable infinity. So does this sentence instantly become true?

• There are ℵ1 errors in this sentence.

I’m not sure. But I think I can argue for the validity of sentences claiming fractional or irrational number of errors:

• There is 1.5 errors in this sentence.
• There are π errors in this sentence.

Let’s have a look at “There is 1.5 errors in this sentence”. There are no visible errors, so there’s one error: the claim that sentence contains 1.5 errors. So now there seems to be another error: the sentence has one error but claims to have 1.5 errors. But does it therefore have two errors? No, because if it has two errors, it’s still in error and has three errors. And that generates another error and another and another, and so on for ever. The sentence becomes unstoppably and infinitely false.

So let’s go back to the point at which the sentence contains one error. Now, the difference between 1 error and 1.5 errors is small — less than a full error. So how big is the error of claiming to have 1.5 errors when having 1 error? Well, it’s obviously 0.5 of an error. So the sentence contains 1.5 errors after all.

Now for “There are π errors in this sentence”. There are no visible errors, so there’s one error: the claim that the sentence contains π errors. Therefore it contains one error. But it claims to have π errors, so it has another error. And if it has 2 errors and claims to have π errors, it has another and third error. But if it has three errors and claims to have π error, it’s still in error. But only slightly — it’s now committing a small amount of an error. How much? It can only be 0.14159265… of an error. Therefore it’s committing 3.14159265… = π errors and is a true sentence.

Now try:

• There is -1 error in this sentence.

What is a negative error? A truth. So I think that sentence is valid too. But I can’t think of how to use i, or the square root of -1, in a sentence like that.

Pteric Ptosis

Uncle, whose inventive brains
Kept evolving aeroplanes,
Fell from an enormous height
Upon my garden lawn last night.
Flying is a fatal sport:
Uncle wrecked the tennis court. — Harry Graham (1874-1936)


Peri-Performative Post-Scriptum

Pteric means “of or like a wing”; ptosis meant “fall, falling” in ancient Greek and is now used in medicine to mean “drooping of the eyelid; sagging or lowering of an organ”, etc.

I Like Aix

Mandarin duck, Aix galericulata (Linnaeus 1758) (from the In-Terms-in-ator)


Peri-Performative Post-Scriptum

“I Like Aix” corely references “I Like Ike”, a slogan for Dwight “Ike” Eisenhower’s presidential campaign in the 1950s. Aix galericulata means “crested aix”, the word αἴξ, aix, being used by Aristotle for an unknown variety of water-bird. In Greek, it would have been pronounced something like “aye-ks”, which is what I’ve used in the title of this incendiary intervention. But “ay-ks” is probably better in modern English.

Young Out to Dry

“I am sick to death of people saying that we’ve made 11 albums that sound exactly the same. In fact we’ve made 12 albums that sound exactly the same.” — Angus Young of AC/DC


Elsewhere other-accessible

Bon and Off — a rogue review at Papyrocentric Performativity of Two Sides to Every Glory: AC/DC: The Complete Biography

H₂Oenometry

You have two glasses each filled with exactly the same amount of liquid. One contains water, the other contains wine. First, take a teaspoon of water from the water glass and pour it into the wine glass. Next stir the wine and water until well mixed. Then take a teaspoon of the water-and-wine mixture and pour it into the glass of water.

The question now is: Is there more wine in the water glass than water in the wine glass, or is there less? (from World’s Most Baffling Puzzles, Charles Barry Townsend, Sterling, New York, 1991)

(Scroll down for answer)


Post-Performative Post-Scriptum

Oenometry means “wine-measurement”, from ancient Greek οἶνος, oinos, “wine”, + μετρία, metria, “measurement”. Its standard pronunciation would be “ee-NOM-ett-ry”, but you could conceivably say “oh-een-NOM-ett-ry” or “oi-NOM-ett-ry”.


Discussion of the answer

The original question is fair but worded to send you astray. By using the words “glass” and “teaspoon”, it creates distinct images in your mind: those of an unvarying teaspoon and of two glasses with identical-but-varying amounts of wine and water in them. So you’re guided away from considering that the contents of the glasses can be measured in teaspoons too. If you think not in teaspoons but in unspecified units (of liquid measure), it’s easier to see the truth.

If the two glasses each contain n units of liquid, by transferring water to the wine you’re adding 1 unit of water to n units of wine.

Therefore the wine glass contains n+1 units of mixed wine-and-water, of which n units are wine and 1 unit is water. Let’s say n+1 = n1.

Consider that 1 unit of that mixture contains n/n1 parts of wine and 1/n1 parts of water: n/n1 + 1/n1 = (n+1)/n1 = n1/n1 = 1 unit.

Now, if one unit of the mixture is transferred to the water glass, you take n/n1 units of wine from n units of wine in the wine glass: n – n/n1 = n-1 + 1/n1. You also take 1/n1 units of water from 1 unit of water in the wine glass: 1 – 1/n1 = (n1-1)/n1 = n/n1. So the wine glass now contains n-1 + 1/n1 units of wine and n/n1 of a unit of water.

When you add that unit to the (n-1) units of water in the water glass, it will contain (n-1) + 1/n1 units of water and n/n1 of unit of wine:

Wine glass: n-1 + 1/n1 units of wine and n/n1 of a unit of water
Water glass: n-1 + 1/n1 units of water and n/n1 of a unit of wine

Therefore, however much water and wine you start with, in the end there will be as much water in the wine glass as there is wine in the water glass. For some concrete examples:

Example #1

1. Start

Water glass: 2 teaspoons of water
Wine glass: 2 teaspoons of wine

2. Transfer water to wine glass and mix:

Water glass: 2 tsp of water – 1 tsp = 1 tsp of water
Wine glass: 2 tsp of wine + 1 tsp of water = 3 tsp of which 2/3 is wine, 1/3 is water

3. Transfer wine-and-water mixture to water glass:

One tsp of wine-and-water mixture = 2/3 tsp of wine + 1/3 tsp of water

Therefore:

Wine glass: 2 tsp of wine – 2/3 tsp of wine = 1 and 1/3 tsp of wine; 1 tsp of water – 1/3 tsp of water = 2/3 tsp of water
Water glass: 1 tsp of water + 1/3 tsp of water = 1 and 1/3 tsp of water; 0 tsp of wine + 2/3 tsp of wine = 2/3 tsp of wine

4. Finish

Wine glass contains: 1 and 1/3 tsp of wine, 2/3 tsp of water
Water glass contains: 1 and 1/3 tsp of water, 2/3 tsp of wine


Example #2

1. Start

Water glass: 10 teaspoons of water
Wine glass: 10 teaspoons of wine

Transfer water to wine glass and mix:

Water glass: 10 tsp of water – 1 tsp = 9 tsp of water
Wine glass: 10 tsp of wine + 1 tsp of water = 11 tsp of liquid of which 10/11 is wine, 1/11 is water

Transfer wine-and-water mixture to water glass:

One tsp of wine-and-water mixture = 10/11 tsp of wine + 1/11 tsp of water

Therefore:

Wine glass: 10 tsp of wine – 10/11 tsp of wine = 9 and 1/11 tsp of wine; 1 tsp of water – 1/11 tsp of water = 10/11 tsp of water
Water glass: 9 tsp of water + 1/11 tsp of water = 9 and 1/11 tsp of water; 0 tsp of wine + 10/11 tsp of wine = 10/11 tsp of wine

4. Finish

Wine glass contains: 9 and 1/11 tsp of wine, 10/11 tsp of water
Water glass contains: 9 and 1/11 tsp of water, 10/11 tsp of wine

RevNumSum

If you take an integer, n, and reverse its digits to get the integer r, there are three possibilities:


n > r (e.g. 85236 > 63258)
n < r (e.g. 17783 < 38771)
n = r (e.g. 45154 = 45154)

If n = r, n is a palindrome. If n > r, I call n a major number. If n < r, I call n a minor number. And here are the minor and major numbers represented as white squares on an Ulam-like spiral (the negative of a minor spiral is a major spiral, and vice versa — sometimes one looks better than the other):

b=2 (minor numbers)


b=3


b=4


b=5


b=6


b=7 (major numbers)


b=8 (minor numbers)


b=9 (mjn)


b=10 (mjn)


b=11 (mjn)


b=12 (mjn)


b=13 (mjn)


b=14 (mjn)


b=15 (mjn)


b=16 (mjn)


b=17 (mjn)


b=18 (mjn)


b=19 (mjn)


b=20 (mjn)


Minor numbers, b=2..20 (animated)


Now let’s look at a sequence formed by summing the reversed numbers, minor ones, major ones and palindromes. Here are the standard integers:


1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17...

If you sum the integers, you get what are called the triangular numbers:


1 = 1
3 = 1 + 2
6 = 1 + 2 + 3
10 = 1 + 2 + 3 + 4
15 = 1 + 2 + 3 + 4 + 5
21 = 1 + 2 + 3 + 4 + 5 + 6
28 = 1 + 2 + 3 + 4 + 5 + 6 + 7
36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
45 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
55 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
66 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11
78 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12
91 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13
105 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14
120 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15
136 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16
153 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17
171 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18
190 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19
210 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20

But what happens if you reverse the integers before summing them? Here side-by-side are the triangular numbers and the underlined revnumsums (as they might be called):


45 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
45 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
55 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
46 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1
66 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11
57 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11
78 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12
78 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21
91 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13
109 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31
105 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14
150 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 + 41
120 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15
201 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 + 41 + 51
136 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16
262 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 + 41 + 51 + 61
153 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17
333 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 + 41 + 51 + 61 + 71
171 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18
414 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 + 41 + 51 + 61 + 71 + 81
190 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19
505 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 + 41 + 51 + 61 + 71 + 81 + 91
210 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20
507 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 11 + 21 + 31 + 41 + 51 + 61 + 71 + 81 + 91
+ 2

Unlike triangular numbers, revnumsums are dependent on the base they’re calculated in. In base 2, the revnumsum is always smaller than the triangular number, except at step 1. In base 3, the revnumsum is equal to the triangular number at steps 1, 2 and 15 (= 120 in base 3). Otherwise it’s smaller than the triangular number.

And in higher bases? In bases > 3, the revnumsum rises and falls above the equivalent triangular number. When it’s higher, it tends towards a maximum height of (base+1)/4 * triangular number.