{"id":48390,"date":"2020-08-21T21:39:32","date_gmt":"2020-08-21T20:39:32","guid":{"rendered":"https:\/\/blogs.bmj.com\/bmj\/?p=48390"},"modified":"2020-08-28T19:10:08","modified_gmt":"2020-08-28T18:10:08","slug":"jeffrey-aronson-when-i-use-a-word-laughter","status":"publish","type":"post","link":"https:\/\/blogs.bmj.com\/bmj\/2020\/08\/21\/jeffrey-aronson-when-i-use-a-word-laughter\/","title":{"rendered":"Jeffrey Aronson: When I Use a Word . . . Laughter"},"content":{"rendered":"

Comprehensive though the list of <\/span>phobias<\/span><\/a> in the <\/span>Oxford English Dictionary<\/span><\/i> (<\/span>OED<\/span><\/i>) is, it omits some, notably gelotophobia. Nor does it include gelotophilia, katagelasticism, or gelasmus.<\/span><\/p>\n

The IndoEuropean root KLEG meant to cry out or make a sound, an onomatopoeic form. In Greek <\/span>\u03ba\u03bb\u03b1\u03b3\u03b3\u03ae<\/span>\u00a0<\/span><\/i>(pronounced klang\u0113) meant any sharp noise, such as the twang of a bow or the scream of a bird, specifically a crane. The future of the corresponding verb, \u03ba\u03bb\u03ac\u03b6\u03c9, was \u03ba\u03bb\u03ac\u03b3\u03be\u03c9 (klanx\u014d), I shall scream, from which the makers of an early car horn derived a brand name, Klaxon.<\/span><\/p>\n

In Latin the verb became clangere, from which we get clang and clangor, clack, click, and cluck, clank, clink, and clunk. Clinkum-clankum, later shortened to clink-clank, being a reduplicated form, signified a succession of clinking sounds and hence a senseless jingle.<\/span><\/p>\n

To clink means to make a metallic sound, like the sound a clock might make when its hammer strikes a bell. A clinch or clench was a nail or bolt that would make such a sound when struck with a hammer. A clincher or clinker clinched the bolts in ship-building by bending them back or flattening the points. A clinchpoop may have been one who did that on the poops of vessels, and it then came to mean a rough worker or a boor, just as a clown was originally a peasant, giving us a putative link to laughter, which also comes from KLEG.<\/span><\/p>\n

Latin clangere led to various Northern European forms, such as hlahtar (Old High German), hlakkia (Old Frisian), hlaeja (Old Norse), and hlaehhan (Old English), all meaning to laugh. The Old Irish word cluiche meant a joke. In German gel\u00e4chter means laughter.<\/span><\/p>\n

KLEG is an extended form of the IndoEuropean root KEL, to shout or resound, giving the Greek word for laughter, \u03b3\u03ad\u03bb\u03c9\u03c2. \u0393\u03b5\u03bb\u03c9\u03c4\u03bf\u03c6\u03c5\u03bb\u03bb\u03b9\u03c2 was the Greek name for <\/span>Cannabis sativa<\/span><\/i>, presumably because it was a plant (\u03c6\u03c5\u03bb\u03bb\u03b9\u03c2) that excited laughter.<\/span><\/p>\n

The <\/span>Oxford English Dictionary<\/span><\/i> (<\/span>OED<\/span><\/i>) lists only a few English derivatives of \u03b3\u03ad\u03bb\u03c9\u03c2 and related words. A gelasin is a dimple in the cheeks produced by smiling. Geloscopy, according to Nathaniel Bailey\u2019s <\/span>Dictionarium Britannicum<\/span><\/i> (1730), is \u201ca sort of Divination performed by means of Laughter; or a divining any Persons, Qualities or Character, by observation of the manner of his Laughing\u201d. And a gelotometer is a gauge for measuring laughter. Gelastic means \u201cserving the function of laughter, risible\u201d and gelastics are remedies that act by eliciting laughter, perhaps with Humphry Davy\u2019s laughing gas (nitrous oxide) in mind.<\/span><\/p>\n

However, the OED<\/em> does not refer to gelastic epilepsy, seizures that result in laughter, a term coined in <\/span>1957<\/span><\/a>, nor to gelastic syncope, fainting caused by laughter. When Robin Ferner and I <\/span>reviewed<\/span><\/a> the benefits and harms of laughter in 2013, we found 1335 reports of pathological laughter; many were due to seizures (Table 1). Gelastic syncope is <\/span>rarer<\/span><\/a>.<\/span><\/p>\n

\"\"<\/p>\n

There are other words, not found in the <\/span>OED<\/span><\/i>. Gelotophobia is fear of being laughed at. The earliest hit in PubMed is from <\/span>2010<\/span><\/a>, but earlier instances can be found. For example, in <\/span>1996<\/span><\/a> the German psychoanalyst Michael Titze referred to the Pinocchio Complex as \u201ca phenomenon that refers to those with gelotophobia, … people [who] have never learned to appreciate humor and laughter positively.\u201d He suggested treatments. <\/span>Gelotophilia<\/span><\/a>, joy at being laughed at, is a later coinage, as is <\/span>katagelasticism<\/span><\/a>, joy in laughing at others (Greek \u03ba\u03b1\u03c4\u03ac\u03b3\u03b5\u03bb\u03c9\u03c2, derision or a laughing-stock). And older than any of these is gelasmus, spasmodic laughter; it was listed in the <\/span>Encyclopedia of Aberrations<\/span><\/i>, which was edited by Edward Podolsky in 1953 and described by one <\/span>reviewer<\/span><\/a> as \u201can aberration in encyclopedias\u201d.<\/span><\/p>\n

The Greek word \u03b3\u03b5\u03bb\u03c9\u03c4\u03bf\u03c0\u03bf\u03b9\u03cc\u03c2 meant, and still means, a maker of laughter, a buffoon. <\/span>Gelotopoietic should mean stimulating laughter, but I haven\u2019t found it anywhere. Time to introduce it to describe the quality of stand-up comedians.<\/span><\/p>\n

Finally, back to click-clacking. In French claque means a clap of the hands, and in English an organized body of applauders in a theatre. The claque in the Milan opera house La Scala, the <\/span>loggionisti<\/span><\/i>,<\/span> who occupy the gods, the <\/span>loggione<\/span><\/i>, can make or break an opera singer. Ronald Reagan once told a <\/span>story<\/span><\/a> about Leoncavallo\u2019s opera <\/span>I Pagliacci<\/span><\/i> (\u201cClowns\u201d). A tenor, newly recruited to the company, performed the famous aria \u201cVesti la giubba\u201d (\u201cOn with the motley\u201d). The claque demanded encore after encore: \u201cYou\u2019ll do it until you get it right.\u201d<\/span><\/p>\n

Jeffrey Aronson<\/strong>\u00a0is a clinical pharmacologist, working in the Centre for Evidence Based Medicine in Oxford’s Nuffield Department of Primary Care Health Sciences. He is also president emeritus of the British Pharmacological Society.<\/em><\/span><\/p>\n

Competing interests:<\/strong> None declared.<\/p>\n\n\n\n
\n

This week’s interesting integer: 288<\/strong><\/p>\n

\u2022 <\/strong><\/b>ABA numbers<\/span>
\n\u25cb<\/span> ABA numbers have the form A \u00d7 BA<\/sup>; 288 is an ABA number since it equals 2 \u00d7 122<\/sup>. [Not to be confused with, for example, \u201cDancing Queen\u201d, which is an ABBA number.]<\/span><\/p>\n

\u2022 <\/strong><\/b>Achilles numbers<\/span>
\n\u25cb<\/span> A powerful number is one that is divisible by the squares of each of its prime factors.<\/span>
\n\u25cb<\/span> The prime factors of 288 are 2 and 3, and 288 is divisible by both 4 and 9, so 288 is a powerful number.<\/span>
\n\u25cb<\/span> An Achilles number is one that, like the Greek hero Achilles, is powerful but not perfect, i.e. not a perfect power.<\/span>
\n\u25cb<\/span> For example, the powerful number 216, whose prime factors are 2 and 3, is divisible by both 4 and 9. It is also a perfect power, 63<\/sup>, and is therefore not an Achilles number.<\/span>
\n\u25cb<\/span> However, the powerful number 288 = 25<\/sup> \u00d7 32<\/sup>. It is not a perfect power and is therefore an Achilles number.<\/span><\/p>\n

\u2022 <\/strong><\/b>Cunningham numbers<\/span>
\n\u25cb<\/span> A Cunningham number is one that can be expressed as a perfect power \u00b1 one.<\/span>
\n\u25cb<\/span> 288 = 172<\/sup> \u2013 1.<\/span><\/span><\/p>\n

\u2022 <\/strong><\/b>Jordan-Polya numbers and superfactorials<\/span>
\n\u25cb<\/span> The factorial of a number n, denoted by the symbol n!, is the product of n and all smaller numbers:<\/span>
\nn! = n \u00d7 (n\u20131) \u00d7 (n\u20132) \u2026 \u00d7 2 \u00d7 1.<\/span>
\n\u25cb<\/span> Jordan-Polya numbers are products of factorials.<\/span>
\n\u25cb<\/span> 288 = 0! \u00d7 1! \u00d7 2! \u00d7 3! \u00d7 4! [0! = 1 by definition]<\/span>
\n\u25cb<\/span> Because it is the product of consecutive factorials 288 is also called a superfactorial.<\/span><\/p>\n

\u2022 <\/strong><\/b>Pythagorean triples<\/span>
\n\u25cb<\/span> 288 is the perimeter of the right-angled triangle with sides 32, 126, and 130.<\/span>
\n\u25cb<\/span> 288 is the long arm of the following right-angled triangles:<\/span>
\n34, 288, and 290<\/span>
\n84, 288, and 300<\/span>
\n120, 288, and 312<\/span>
\n216, 288, and 360<\/span>
\nand the short arm of the right-angled triangle 288, 540, and 612.<\/span><\/p>\n

\u2022 <\/strong><\/b>Smooth numbers<\/span>
\n\u25cb<\/span> The prime divisors of 288 are the consecutive primes 2 and 3 (288 = 25<\/sup> \u00d7 32<\/sup>). Numbers whose prime factors are all no higher than a specified prime, p, are called p-smooth. Thus, 288 is a 3-smooth number; 3-smooth numbers are also called harmonic numbers. See also <\/span>Interesting integer 270<\/span><\/a>.\u00a0<\/span><\/p>\n

\u2022 <\/strong><\/b>Square manipulations:<\/span>
\n\u25cb<\/span> multiply 288 by the sum of its digits, 18: 288 \u00d718 = 5184, which is a square, 722<\/sup>
\n\u25cb<\/span> divide 288 by the sum of its digits, 18: 288 \/ 18 = 16, which is a square, 42<\/sup>, and a fourth power, 24<\/sup>
\n\u25cb<\/span> multiply 288 by the product of its digits, 128: 288 \u00d7 128 = 36884, which is a square, 1922<\/sup>
\n\u25cb<\/span> multiply 288 by its reverse 882: 288 \u00d7 882 = 254016, which is a square, 5042<\/sup>\u00a0<\/span><\/span><\/span><\/span><\/p>\n

\u2022 <\/strong><\/b>288 is the sum of:<\/span>
\n\u25cb<\/span> 2 consecutive primes: 139 + 149<\/span>
\n\u25cb<\/span> 11 consecutive non-primes: 20 + 21 + 22 + 24 + 25 + 26 + 27 + 28 + 30 + 32 + 33<\/span>
\n\u25cb<\/span> 2 consecutive odd numbers: 143 + 145<\/span>
\n\u25cb<\/span> 4 consecutive odd numbers: 69 + 71 + 73 + 75<\/span>
\n\u25cb<\/span> 6 consecutive odd numbers: 43 + 45 + 47 + 49 + 51 + 53<\/span>
\n\u25cb<\/span> 8 consecutive odd numbers: 29 + 31 + 33 + 35 + 37 + 39 + 41 + 43<\/span>
\n\u25cb<\/span> 12 consecutive odd numbers: 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35<\/span>
\n\u25cb<\/span> 16 consecutive odd numbers: 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33<\/span>
\n\u25cb<\/span> 3 consecutive integers: 95 + 96 + 97<\/span>
\n\u25cb<\/span> 9 consecutive integers: 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36<\/span>
\n\u25cb<\/span> 288 is therefore a trapezoidal number twice over (see Interesting integer <\/span>278<\/span><\/a> and <\/span>279<\/span><\/a>); this also shows that 288 is the difference between two triangular numbers in two different ways:<\/span>
\nT97<\/sub> \u2013 T94<\/sub> = 4753 \u2013 4465 = 288<\/span>
\nT36<\/sub> \u2013 T27<\/sub> = 666 \u2013 378 = 288<\/span>
\n\u25cb<\/span> eight consecutive non-primes: 32 + 33 + 34 + 35 + 36 + 38 + 39 + 40<\/span>
\n\u25cb<\/span> 15 consecutive non-primes: 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 22 + 24 + 25 + 26 + 27 + 28<\/span>
\n\u25cb<\/span> 3 cubes: 23<\/sup> + 43<\/sup> + 63<\/sup>
\n\u25cb<\/span> 3 fourth powers: 24<\/sup> + 24<\/sup> + 44<\/sup>
\n\u25cb<\/span> 2 distinct powers of 2: 25<\/sup> + 28<\/sup><\/span><\/span><\/span><\/p>\n

\u2022 <\/strong><\/b>285 is a Harshad number (see Interesting integer <\/span>280<\/span><\/a>), since it is divisible by the sum of its digits (18).<\/span><\/p>\n

\u2022 <\/strong><\/b>288 is divisible by each of its digits; such numbers are called nude numbers.<\/span><\/p>\n

\u2022 <\/strong><\/b>288 is a refactorable number (or a tau number), i.e. one that is divisible by its number of divisors. Here\u2019s how you calculate the number of divisors of a number, including the number itself. First express it as the product of all its prime factors: 288 = 25<\/sup> \u00d7 32<\/sup>. Now add one to each of the indices of the prime factors (in this case 5 and 2) and multiply them: 6 \u00d7 3 = 18. So 288 has 18 divisors. And 18 divides 288 exactly (288\/18 = 16).<\/span><\/p>\n

\u2022 <\/strong><\/b>288 is a self-number. Many numbers can be generated from other numbers in the following way: add the generating number to the sum of its digits. For example, in base 10, 265 can be generated from 254, since 265 = 254 + 2 + 5 + 4. However, there is no number that generates 288 in this way; in this sense it is by itself. Self-numbers are also called Colombian numbers and Devlali numbers.<\/span><\/p>\n

\u2022 <\/strong><\/b>Like <\/span>262<\/span><\/a>, <\/span>268<\/span><\/a>, and <\/span>276<\/span><\/a>, 288 is an untouchable number, an integer that cannot be expressed as the sum of all the proper divisors of any other number. For example, the proper divisors of 9 are 1 and 3, whose sum is 4; therefore 4 is a touchable number, since it is the sum of the proper divisors of 9. There is no integer whose proper divisors add up to 288. Untouchable numbers are also called non-aliquot numbers.<\/span><\/p>\n

\u2022 <\/strong><\/b>288 is the ninth pentagonal pyramidal number, having the form n2<\/sup>(n + 1)\/2, where n = 8.<\/span><\/p>\n

\u2022 <\/strong><\/b>288 is the 53rd<\/sup> entry in <\/span>Aronson\u2019s sequence<\/span><\/a>.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Comprehensive though the list of phobias in the Oxford English Dictionary (OED) is, it omits some, notably gelotophobia. Nor does it include gelotophilia, katagelasticism, or gelasmus. The IndoEuropean root KLEG […]<\/p>\n

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