In 1995 UCSD psychologist Diana Deutsch was fine-tuning the spoken commentary on a CD when she noticed something odd. When the phrase “sometimes behave so strangely” was repeated on a loop, it came to sound as though it were being sung rather than spoken. When the full surrounding passage was then played in its entirety, this phrase still sounded as though it were being sung (you can hear this here).

The phenomenon is not completely understood, but “the present experiments show that for a phrase to be heard as spoken or as sung, it does not need to have a set of physical properties that are unique to speech, or a different set of physical properties that are unique to song,” the researchers write. “Rather, we must conclude that, assuming the neural circuitries underlying speech and song are at some point distinct and separate, they can accept the same input, but process the information in different ways so as to produce different outputs.”

(Via MetaFilter.)

Humans aren’t the only species that tend to move to a musical beat: Animals that mimic vocally (such as parrots and, here, a sulphur-crested cockatoo) bob their heads and move their feet. Animals that don’t mimic vocally don’t do this. So possibly our urge to move to music is a by-product of our tendency to mimic vocally — it’s a motor response to something we hear.

(Aniruddh D. Patel, et al., “Experimental Evidence for Synchronization to a Musical Beat in a Nonhuman Animal,” Current Biology 19:10 [2009], 827-830; Adena Schachner, et al., “Spontaneous Motor Entrainment to Music in Multiple Vocal Mimicking Species,” Current Biology 19:10 [2009], 831-836.)

                                       1 
                                      1 1 
                                     1 0 1 
                                    1 0 0 1 
                                   1 0 0 0 1 
                                  1 0 0 0 0 1 
                                 1 0 0 0 0 0 1 
                                1 0 0 0 0 0 0 1 
                               1 0 0 0 0 0 0 0 1 
                              1 0 0 0 0 0 0 0 0 1 
                             1 0 0 0 0 0 0 0 0 0 1 
                            1 0 0 0 0 0 0 0 0 0 0 1 
                           1 0 0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
   1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
     1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
      1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
       1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
        1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
          1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
           1 0 0 0 0 0 0 0 0 0 0 1 1 1 9 1 1 1 0 0 0 0 0 0 0 0 0 0 1 
            1 0 0 0 0 0 0 0 0 0 0 1 9 9 9 9 1 0 0 0 0 0 0 0 0 0 0 1 
             1 0 0 0 0 0 0 0 0 0 0 1 9 2 9 1 0 0 0 0 0 0 0 0 0 0 1 
            1 0 0 0 0 0 0 0 0 0 0 1 9 9 9 9 1 0 0 0 0 0 0 0 0 0 0 1 
           1 0 0 0 0 0 0 0 0 0 0 1 1 1 9 1 1 1 0 0 0 0 0 0 0 0 0 0 1 
          1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1  
        1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
       1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
      1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
     1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
    1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
   1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
                           1 0 0 0 0 0 0 0 0 0 0 0 1 
                            1 0 0 0 0 0 0 0 0 0 0 1 
                             1 0 0 0 0 0 0 0 0 0 1 
                              1 0 0 0 0 0 0 0 0 1 
                               1 0 0 0 0 0 0 0 1 
                                1 0 0 0 0 0 0 1 
                                 1 0 0 0 0 0 1 
                                  1 0 0 0 0 1 
                                   1 0 0 0 1 
                                    1 0 0 1 
                                     1 0 1 
                                      1 1 
                                       1
 

Amazingly, this is a prime number. When the digits are assembled into one long string, beginning at the top of the star and reading each row left to right, they form a 1093-digit number whose only factors are 1 and itself.

It was discovered by Australian mathematician Michael Hartley. See more of his prime curios.

In 1894 Francis Galton experimented with conducting addition and subtraction by smell. He designed an apparatus that would produce whiffs of scented air and then memorized their combinations: “I taught myself to associate two whiffs of peppermint with one whiff of camphor; three of peppermint with one of carbolic acid, and so on.”

After practicing sums using the scents themselves, he moved on to doing them entirely in his imagination. “There was not the slightest difficulty in banishing all visual and auditory images from the mind, leaving nothing in the consciousness besides real or imaginary scents. In this way, without, it is true, becoming very apt at the process, I convinced myself of the possibility of doing sums in simple addition with considerable speed and accuracy solely by means of imaginary scents.”

He had similar success with subtraction, but didn’t try multiplication. And some further experiments seemed to show that “arithmetic by taste was as feasible as arithmetic by smell.”

(Francis Galton, “Arithmetic by Smell,” Psychological Review 1:1 [January 1894], 61-62.)

If a tetrahedron is constructed on a base with side lengths 125, 244, 267, then the remaining sides can take the shapes of three right triangles: (44, 240, 244), (44, 117, 125), (117, 240, 267).

And now the sum of the squares of the lengths of each pair of opposite sides in the tetrahedron is the same:

117² + 244² = 125² + 240² = 44² + 267² = 73225

(From Edward Barbeau, Power Play, 1997.)

In 1728 English surgeon William Cheselden removed the cataracts from a 13-year-old boy, producing the first known case of full recovery from blindness:

Having often forgot which was the cat, and which the dog, he was ashamed to ask; but catching the cat, which he knew by feeling, he was observed to look at her steadfastly and then, setting her down said, ‘So, puss, I shall know you another time.’ He was very much surprised, that those things which he had liked best, did not appear most agreeable to his eyes, expecting those persons would appear to be most beautiful that he loved most, and such things to be most agreeable to his sight, that were so to his taste.

Also: “Being shewn his father’s picture in a locket at his mother’s watch, and told what it was, he acknowledged the likeness, but was vastly surprised; asking, how it could be, that a large face could be expressed in so little room, saying, it should have seemed as impossible for him, as to put a bushel of anything into a pint.” A fuller account is here. See also Molyneaux’s Problem.

The smokestack of the local power plant in Turku, Finland, bears the first ten numbers of the Fibonacci sequence in glowing letters seven feet high.

The artist, Mario Merz, had been obsessed with the sequence for nearly 30 years when he added the numbers in 1995; he’d already added them to a chapel in Paris and a spire in Turin.

“It is entirely by accident that the sequence reflects two of the major research fields of the University of Turku, namely, number theory and mathematical biology,” write mathematicians Mats Gyllenberg and Karl Sigmund. “As is well known, Fibonacci introduced the sequence at around AD 1200 to model the growth of a rabbit population.”

(Mats Gyllenberg and Karl Sigmund, “The Fibonacci Chimney,” Mathematical Intelligencer 22:4 [2000], 46.)