Knowledge and Belief

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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

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Hoist/Petard

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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.”

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The Love 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:

  1. Given the choice of anyone in the world, whom would you want as a dinner guest?
  2. Would you like to be famous? In what way?
  3. Before making a telephone call, do you ever rehearse what you are going to say? Why?
  4. What would constitute a “perfect” day for you?
  5. When did you last sing to yourself? To someone else?
  6. If you were able to live to the age of 90 and retain either the mind or body of a 30-year-old for the last 60 years of your life, which would you want?
  7. Do you have a secret hunch about how you will die?
  8. Name three things you and your partner appear to have in common.
  9. For what in your life do you feel most grateful?
  10. If you could change anything about the way you were raised, what would it be?
  11. Take four minutes and tell your partner your life story in as much detail as possible.
  12. If you could wake up tomorrow having gained any one quality or ability, what would it be?
  13. If a crystal ball could tell you the truth about yourself, your life, the future or anything else, what would you want to know?
  14. Is there something that you’ve dreamed of doing for a long time? Why haven’t you done it?
  15. What is the greatest accomplishment of your life?
  16. What do you value most in a friendship?
  17. What is your most treasured memory?
  18. What is your most terrible memory?
  19. If you knew that in one year you would die suddenly, would you change anything about the way you are now living? Why?
  20. What does friendship mean to you?
  21. What roles do love and affection play in your life?
  22. Alternate sharing something you consider a positive characteristic of your partner. Share a total of five items.
  23. How close and warm is your family? Do you feel your childhood was happier than most other people’s?
  24. How do you feel about your relationship with your mother?
  25. Make three true “we” statements each. For instance, “We are both in this room feeling … ”
  26. Complete this sentence: “I wish I had someone with whom I could share … ”
  27. If you were going to become a close friend with your partner, please share what would be important for him or her to know.
  28. Tell your partner what you like about them; be very honest this time, saying things that you might not say to someone you’ve just met.
  29. Share with your partner an embarrassing moment in your life.
  30. When did you last cry in front of another person? By yourself?
  31. Tell your partner something that you like about them already.
  32. What, if anything, is too serious to be joked about?
  33. If you were to die this evening with no opportunity to communicate with anyone, what would you most regret not having told someone? Why haven’t you told them yet?
  34. Your house, containing everything you own, catches fire. After saving your loved ones and pets, you have time to safely make a final dash to save any one item. What would it be? Why?
  35. Of all the people in your family, whose death would you find most disturbing? Why?
  36. Share a personal problem and ask your partner’s advice on how he or she might handle it. Also, ask your partner to reflect back to you how you seem to be feeling about the problem you have chosen.

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.)

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A New Knot

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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.”

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Images: Wikimedia Commons
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Arithmetic Billiards

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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).

More details here.

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A Prime Formula

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:

\displaystyle (k+2)(1-\newline [wz+h+j-q]^{2}-\newline [(gk+2g+k+1)(h+j)+h-z]^{2}-\newline [16(k+1)^{3}(k+2)(n+1)^{2}+1-f^{2}]^{2}-\newline [2n+p+q+z-e]^{2}-\newline [e^{3}(e+2)(a+1)^{2}+1-o^{2}]^{2}-\newline [(a^{2}-1)y^{2}+1-x^{2}]^{2}-\newline [16r^{2}y^{4}(a^{2}-1)+1-u^{2}]^{2}-\newline [n+\ell +v-y]^{2}-\newline [(a^{2}-1)\ell ^{2}+1-m^{2}]^{2}-\newline [ai+k+1-\ell -i]^{2}-\newline [((a+u^{2}(u^{2}-a))^{2}-1)(n+4dy)^{2}+1-(x+cu)^{2}]^{2}-\newline [p+\ell (a-n-1)+b(2an+2a-n^{2}-2n-2)-m]^{2}-\newline [q+y(a-p-1)+s(2ap+2a-p^{2}-2p-2)-x]^{2}-\newline [z+p\ell (a-p)+t(2ap-p^{2}-1)-pm]^{2})\newline >0

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.)

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Spreading Word

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.”

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Something Else

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Image: Wikimedia Commons

During a visit to Oxford in May 1931, Albert Einstein gave a brief lecture on cosmology, and afterward the blackboard was preserved along with Einstein’s ephemeral writing. It now resides in the university’s Museum of the History of Science.

Harvard historian of science Jean-François Gauvin argues that this makes it a “mutant object”: It’s no longer fulfilling the essential function of a blackboard, to store information temporarily — it’s become something else, a socially created object linked to the great scientist. The board’s original essence could be restored by wiping it clean, but that would destroy its current identity.

“The sociological metamorphosis at the origin of this celebrated artifact has completely destroyed its intrinsic nature,” Gauvin writes. “Einstein’s blackboard has become an object of memory, an object of collection modified at the ontological level by a social desire to celebrate the achievement of a great man.”

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