For what it’s worth: In 2015 University of Wisconsin psychologists Megan Savage and Charles Snowdon considered that music might appeal better to other species if it used the same tempos and frequency ranges that they use to communicate.

Accordingly they got musician David Teie to compose three songs that ought to appeal to felines and tried them out on 47 domestic cats, comparing their reactions to Bach’s “Air on a G String” and Fauré’s “Elegie.” The cat music was pitched about an octave higher than human voices, and its tempos replicated purring and suckling rather than a human heartbeat.

The cats showed no interest in the music intended for humans, but they showed a “significant preference for and interest in” Teie’s cat-targeted songs, approaching the speakers and often rubbing their scent glands on them. Also, for some reason young and old cats seemed to like the cat music better than middle-aged ones.

Savage and Snowdon conclude that these results “suggest novel and more appropriate ways for using music as auditory enrichment for nonhuman animals.” Here’s a sample to try on your own cat:

(Charles T. Snowdon, David Teie, and Megan Savage, “Cats Prefer Species-Appropriate Music,” Applied Animal Behaviour Science 166 [May 2015], 106–111.) (Thanks, Noah.)

These are called Borwein integrals, after David and Jonathan Borwein, the father-and-son mathematicians who first presented them in 2001.

Engineer Hanspeter Schmid writes, “[W]hen this fact was recently verified by a researcher using a computer algebra package, he concluded that there must be a ‘bug’ in the software. It is not a bug, though; this series of integrals really only results in π/2 up to a certain point, and then breaks down. This astonishes most mathematically educated readers, as especially those readers mentally extrapolate the sequence shown above and find it surprising that something fundamental should change when the factor sinc(x/15) is introduced.” He gives a graphic explanation of what’s happening.

(David Borwein and Jonathan M. Borwein, “Some Remarkable Properties of Sinc and Related Integrals,” Ramanujan Journal 5:1 [March 2001], 73–89.) (Thanks, Dan.)

In his 2008 book Impossible?, Julian Havil presents an argument offered in Massachusetts in 1854 contending that foreigners were more likely to be insane than native-born Americans. These figures were offered:

Whole Population
	Insane	Not Insane	Totals
Foreign-Born	625	229375	230000
Native-Born	2007	892669	894676
Totals	2632	1122044	1124676

The probability that a foreign-born person was deemed insane was 625/230000 = 2.7 × 10^-3, and for a native-born person the probability was 2007/894676 = 2.2 × 10^-3, which seems to support the claim.

But we get a different story when we divide the data by social hierarchy, into what were called the pauper and independent classes:

Pauper Class
	Insane	Not Insane	Totals
Foreign-Born	182	9090	9272
Native-Born	250	12513	12763
Totals	432	21603	22035

Independent Class
	Insane	Not Insane	Totals
Foreign-Born	443	220285	220728
Native-Born	1757	880156	881913
Totals	2200	1100441	1102641

In the pauper class the probability of a foreign-born person being deemed insane is 182/9272 = 0.02, which is the same as that for a native-born person (250/12763 = 0.02). And the same is true in the independent class, where both probabilities are 2.0 × 10^-3. Havil writes, “So, if an adjustment is made for the status of the individuals we see that there is no relationship at all between sanity and origin” (an example of Simpson’s paradox).