“I think it is all right to argue sometimes.”
“I disagree!”
(From Raymond Smullyan.)
“I think it is all right to argue sometimes.”
“I disagree!”
(From Raymond Smullyan.)
George Parker Bidder was born with a surprising gift: He could do complex arithmetic in his head. His feats of calculation would earn for him a university education, a distinguished career in engineering, and fame throughout 19th-century England. In this week’s episode of the Futility Closet podcast, we’ll describe his remarkable ability and the stunning displays he made with it.
We’ll also try to dodge some foul balls and puzzle over a leaky ship.
Imaginary distinctions are often drawn between beliefs which differ only in their mode of expression;– the wrangling which ensues is real enough, however. To believe that any objects are arranged as in Fig. 1, and to believe that they are arranged as in Fig. 2, are one and the same belief; yet it is conceivable that a man should assert one proposition and deny the other. Such false distinctions do as much harm as the confusion of beliefs really different, and are among the pitfalls of which we ought constantly to beware, especially when we are upon metaphysical ground. One singular deception of this sort, which often occurs, is to mistake the sensation produced by our own unclearness of thought for a character of the object we are thinking. Instead of perceiving that the obscurity is purely subjective, we fancy that we contemplate a quality of the object which is essentially mysterious; and if our conception be afterward presented to us in a clear form we do not recognize it as the same, owing to the absence of the feeling of unintelligibility. So long as this deception lasts, it obviously puts an impassable barrier in the way of perspicuous thinking; so that it equally interests the opponents of rational thought to perpetuate it, and its adherents to guard against it.
— Charles Sanders Peirce, “Illustrations of the Logic of Science: How to Make Our Ideas Clear,” Popular Science Monthly, January 1878
In 2014, after receiving dozens of unsolicited emails from the International Journal of Advanced Computer Technology, scientists David Mazières and Eddie Kohler submitted a paper titled “Get Me Off Your Fucking Mailing List.”
To Mazières’ surprise, “It was accepted for publication. I pretty much fell off my chair.”
The acceptance bolsters the authors’ contention that IJACT is a predatory journal, an indiscriminate but superficially scholarly publication that subsists on editorial fees. Mazières said, “They told me to add some more recent references and do a bit of reformatting. But otherwise they said its suitability for the journal was excellent.”
He didn’t pursue it. And, at least as of 2014, “They still haven’t taken me off their mailing list.”
In 1997, Berkeley psychology student Arthur Aron and his colleagues refined a list of 36 questions for “creating closeness.” “One key pattern associated with the development of a close relationship among peers is sustained, escalating, reciprocal, personal self-disclosure,” Aron wrote. “The core of the method we developed was to structure such self-disclosure between strangers.”
Each pair of subjects took turns asking each other questions from this list, in order:
Most of the pairs of strangers left the session with highly positive feelings for each other: “[I]mmediately after about 45 min of interaction, this relationship is rated as closer than the closest relationship in the lives of 30% of similar students” (though, to be sure, “it seems unlikely that the procedure produces loyalty, dependence, commitment, or other relationship aspects that might take longer to develop”).
(Arthur Aron et al., “The Experimental Generation of Interpersonal Closeness: A Procedure and Some Preliminary Findings,” Personality and Social Psychology Bulletin 23:4 [1997], 363-377.)
https://youtu.be/Y2jiQXI6nrE?t=1010s
This is great — Eugene Wigner tells the story of Max Born giving the “two bikes and a fly” puzzle to John von Neumann (it starts at 16:50).
(Via Tamás Görbe, from an old VHS video digitized by Robert Klips.)
In 1986, 89-year-old viewer Jerry Pratt showed up at Minneapolis’s WCCO-TV and told local newsman Don Shelby that he didn’t know how to tie his necktie straight.
“He’s my favorite anchor, and I got sick and tired of looking at the big knot in his tie every night,” Pratt said. “One of the first things people look at is a man’s tie.”
So he showed him something new, the “Pratt knot,” “the first new knot for men in over 50 years.” The Neckwear Association of America confirmed that it didn’t appear in Getting Knotted: 188 Knots for Necks, the trade association’s reference guide.
Some questioned whether it’s entirely original, calling it either a reverse half-Windsor or a variation on a knot called the Nicky, with the narrow end of the tie reversed, the seams and label facing out.
Pratt said he’d invented it on his own 30 years earlier. “I didn’t call it anything,” he said. “I just turned the tie inside out, and there it was.”
“At least something will carry on the family name.”
To find the least common multiple and the greatest common divisor of two natural numbers, construct a billiard table whose side lengths correspond to the two numbers (here, 15 and 40). Set a ball in one corner, fire it out at a 45-degree angle, and let it bounce around the table until it stops in a corner.
Now the least common multiple is the total number of unit squares traversed by the ball (here, 120).
And the greatest common divisor is the number of unit squares traversed by the ball before it reaches the first intersection (here, 5).
A team of mathematicians in Canada and Japan discovered this remarkable polynomial in 1976 — let its 26 variables a, b, c, … z range over the non-negative integers and it will generate all prime numbers:
The snag is that it will sometimes produce negative numbers, which must be ignored. But every positive result will be prime, and every prime can be generated by some set of 26 non-negative integers.
(James P. Jones et al., “Diophantine Representation of the Set of Prime Numbers,” American Mathematical Monthly 83:6 [1976], 449-464.)
When a Western scrub jay discovers the body of a dead jay, it summons other birds to screech over the body for up to half an hour. It’s not clear why they do this — the birds are territorial and not normally social. Possibly it’s a way to share news of danger, concentrate attention to find a predator, or teach young about dangers in the environment.
The gatherings are sometimes called funerals, though we don’t know enough to understand the reasons behind them. But UC Davis student Teresa Iglesias said, “I think there’s a huge possibility that there is much more to learn about the social and emotional lives of birds.”