“It often happens that I wake up at night and begin to think about the serious problems afflicting the world and I tell myself, I must talk to the pope about it. Then the next day when I wake up I remember that I am the pope.” — John XXIII
Author: Greg Ross
Ernst’s Paradox
MIT undergraduate Michael Ernst pointed out this problem to philosopher George Boolos during a course on paradox and infinity.
An expression is a finite sequence of symbols. When expression β is appended to expression α, the symbols of α are written in order and then followed immediately by those of β. So, for example, ‘b’ appended to ‘a’ is the two-symbol expression ‘ab’.
The quotation of α is the expression we get when expression α is enclosed in a pair of quotation marks. The quotation of 'Boston' is ''Boston''. The reverse of quotation is denotation: The denotation of ''Boston'' is 'Boston'.
Who could object to any of this? But now consider the nonsense string κ:
b' appended to 'a
And another string, λ:
ab
Let N(α) stand for the number of letters of the English alphabet that alphabetically precede the first letter of expression α. Then N(κ) = 1 (because that string begins with the letter b) and N(λ) = 0 (because that string begins with the letter a).
And now consider μ:
'b' appended to 'a'
μ is the quotation of κ, so the denotation of μ is κ. But look again at μ: By our own definition,
'b' appended to 'a'
is 'ab', and the denotation of μ is λ as we’ve defined it above. So now we find ourselves asserting that 0 = N(λ) = N(the denotation of μ) = N(κ) = 1.
“What has gone wrong?” Boolos writes. “Obviously, the non-identical κ and λ cannot both be the denotation of μ, and unless they are, our demonstration that 0 = 1 fails. How did we conclude that they are identical?”
When Boolos sent Ernst’s observation to Willard Van Orman Quine at Harvard, Quine wrote back, “Dear George, Thanks for Ernst’s paradox. I am delighted with it. But I find I am unable to cope with it, even when I have stopped laughing. Yours, Van.” Ernst himself suggested that perhaps we need two different kinds of quotation marks, syntactic and semantic. See Boolos’ Logic, Logic, and Logic (1998) for his own thoughts on the matter.
(Thanks, Dan.)
Blow by Blow
For Song of the Sky (1954), Guy Murchie collected the names of winds around the world — he calls them “among the least known and most beautiful of words”:
Leste — warm easterly wind of January in the Madeiras
Naalehu — of Hawaii, blowing from the arid interior areas
Soo-oop-wa — bitter sand-laden wind of Southwest Africa
Steppenwind — of Germany blowing from the steppes
Bise — cold wind of France
Southerly burster — of Australia, preceded by an eerie lull
Tramontana — Alpine blast of the Italian east coast
Etesian — of cool summer afternoons in Greece and Levant
Siffanto — up from the hot heel of Italy
Kai — balmy south wind of China
Yamo oroshi — foehn of the steep valleys of Japan
Klod — Balinese wind that blows “downwards to the sea”
Reshabar — lusty and black, out of the high Caucasus
Mistral — down from the Cevennes to the Riviera
Ghost of Gouda — local gust on a calm night, South Africa
Vinds-gnyr — ancient blustery wind of Iceland
Wisper — whistling through narrow Rhine valleys
Imbat — refreshing North African shores
Virazon — cooling Montevideo on summer afternoons
Sz — first faint breeze of the Chinese autumn
Elephanta — of the Malabar coast
“Herodotus tells of the ancient people of Psylli (Tripoli) who became so hysterical when their wells dried up that they actually dclared war on the simoom and marched into the Sahara with clashing cymbals and beating drums until they disappeared forever into a red cloud of whirling sand.”
Tableau
Dinosaur fossils are often found in this dramatic posture, with the head thrown back, the tail extended, and the mouth wide open. The reason isn’t clear. It could be caused by muscle spams during the animal’s death throes, or the contraction of neck ligaments after death, perhaps facilitated by immersion in water. It’s called the opisthotonic death pose.
Weather and Art
In 1970, Penn State meteorologist Hans Neuberger examined 12,000 European paintings to reconstruct historical climate data between 1400 and 1967. He found a marked increase in darkness and cloud cover between 1550 and 1849, corresponding roughly to the Little Ice Age. Painters in the Mediterranean School depicted bluer skies and clearer conditions than their British counterparts, whose paintings showed overcast skies and lower visibility. No English paintings depicted a completely clear sky.
In 2011, researchers Karen Aplin and Paul Williams quantified the frequency of musical allusions to weather in orchestral music over time. Storms, not surprisingly, were the weather type most frequently represented, followed by wind, cloud, rain, sun, and fog. Of the pieces they chose to study, all those depicting frontal storms were in minor keys, and all those depicting fair weather were in major keys. By a large margin, the most common nationality of weather-depicting composers was British. “This appears to support the stereotypical assumption that people from the UK are more enthusiastic about the weather than their colleagues overseas, although this effect could be due to sampling bias, given that the authors of this paper are both from the UK.”
(Hans Neuberger, “Climate in Art,” Weather 25:2 [February 1970], 46-56; Karen L. Aplin and Paul D. Williams, “Meteorological Phenomena in Western Classical Orchestral Music,” Weather 66:11 [November 2011], 300-306. Here’s a related study looking at popular music.)
Tête-à-Tête
It is related that Anne of Austria one day told Bautree — a councillor of State, poet, and member of the French Academy, but famous for his facetiousness — that she desired to see his wife. Bautree promised to present her. ‘Only, madame,’ he added, ‘she is hard of hearing.’
‘Never mind,’ replied the Queen; ‘I’ll speak loud.’
Bautree hurried home and announced this flattering news to his wife, but at the same time told her to raise her voice, even to the pitch of shouting, as Her Majesty could only hear with difficulty. As soon as the Queen perceived Madame Bautree she began to raise her voice and Madame Bautree shouted back with all her might. The two ladies made a pretty noise between them, and the King, to whom Bautree had confided the audacious hoax, held his sides with laughter.
— “Hoaxes,” Strand, October 1903
Complaint
“Have you noticed … there is never any third act in a nightmare? They bring you to a climax of terror and then leave you there. They are the work of poor dramatists.” — Max Beerbohm
Counterpoint
In 1078, Saint Anselm of Canterbury presented a proof that God exists. We define God as a being than which no greater can be conceived. If God existed only in the mind, then we could conceive of a greater God, one who exists in both mind and reality. Therefore God cannot be merely imaginary — he must exist in reality.
Australian philosopher Douglas Gasking offered this response. The creation of the world is the worthiest achievement imaginable. Its merit is the product of its intrinsic quality and the ability of its creator. The greater the creator’s handicap, the more impressive the achievement. The most grievous handicap would be non-existence. An existent creator would be subordinate to one that does not exist. Therefore, if God is the greatest conceivable being, then he does not exist.
(William Grey, “Gasking’s Proof,” Analysis 60:4 [October 2000], 368-370.)
Perspective
Artist Jeff Lieberman designs “Impossible Corners,” a wall art illusion that exploits the same principle as this mistrustful dragon.
Hobo Ethics
A code of principles proposed at the 1889 National Hobo Convention:
- Decide your own life; don’t let another person run or rule you.
- When in town, always respect the local law and officials, and try to be a gentleman at all times.
- Don’t take advantage of someone who is in a vulnerable situation, locals or other hobos.
- Always try to find work, even if temporary, and always seek out jobs nobody wants. By doing so you not only help a business along, but ensure employment should you return to that town again.
- When no employment is available, make your own work by using your added talents at crafts.
- Do not allow yourself to become a stupid drunk and set a bad example for locals’ treatment of other hobos.
- When jungling [camping] in town, respect handouts and do not wear them out; another hobo will be coming along who will need them as badly, if not worse than you.
- Always respect nature; do not leave garbage where you are jungling.
- If in a community jungle, always pitch in and help.
- Try to stay clean, and boil up wherever possible.
- When traveling, ride your train respectfully. Take no personal chances. Cause no problems with operating crew or host railroad. Act like an extra crew member.
- Do not cause problems in a train yard; another hobo will be coming along who will need passage through that yard.
- Do not allow other hobos to molest children; expose all molesters to authorities – they are the worst garbage to infest any society.
- Help all runaway children, and try to induce them to return home.
- Help your fellow hobos whenever and wherever needed; you may need their help someday.
- If present at a hobo court and you have testimony, give it. Whether for or against the accused, your voice counts!
The convention was held by Tourist Union #63, a union of hobos created in the mid-1800s. Members sought to resist anti-vagrancy laws by representing themselves as itinerant workers rather than idle miscreants.