KEYNES FOLLOWS EDGEWORTH AMONG THE DACTYLS Geoffrey Fishburn History of Economic Thought Society of Australia 27th Conference, Auckland, N.Z. July 2014 School of Social Sciences University of New South Wales Sydney 2052 Australia. [email protected] 1 The dactyl, a three-syllabic measure (‘foot’) of the form long-short-short, was a staple of Classical (Greek and Roman) poetry, and gives its name to the dactylic hexameter, a line of six feet where the dactyl appears a variable number of times (with its place otherwise most usually being taken by the long-long spondee). Until the end of the Edwardian era, in Britain at least, such a verse form was familiar to economists from their schooldays. Alfred Marshall, for example, wrote of “… a Greek poet, whose hexameters may be rendered thus:…” (Marshall 1919, 790 n1), the last of four attempts by him at this particular verse over a period of some 16 years (Fishburn 2012). But one with far greater skill as a classicist was his contemporary Francis Ysidro Edgeworth, most often known to economists for his seminal contributions in economics and statistics as well as his role as editor of The Economic Journal, but less often appreciated, and certainly largely glossed over in the familiar biographical/obituary notes (Creedy 2008; Keynes 1926; Newman 2004; Price 1926), that this was not the career path for which his undergraduate studies had prepared him, nor on which he had first ventured. Edgeworth’s application in 1875 for a Professorship in Greek at Bedford College, London, was no less than would have been expected of one with a record of achievement such as his in Classics at Trinity College, Dublin, and Oxford. The application, however, was unsuccessful. It would be a few years before his neighbour in Hampstead, W.S. Jevons, would show him the mathematical tools which could be used to fashion a more rigorous version of Political Economy, a subject in which his interest had been stimulated whilst at Oxford by Benjamin Jowett; but in the meantime he first produced, in 1877, his New and Old Methods of Ethics in which, as Maynard Keynes later remarked: Quotations from the Greek tread on the heels of the Differential Calculus, and the philistine reader can scarcely tell whether it is a line of Homer or a mathematical abstraction which is in course of integration. (Keynes 1926, 145)1 It was only natural, then, for Edgeworth, when his mind in time turned to Statistics, to look to the Classics, inter alia, for data. In the last week of June 1885, at the Jubilee Conference of The Statistical Society of London he read a paper in which, as recorded in Nature of that week: A pretty illustration of important principles was afforded by the statistics of a wasp’s nest … As further illustrations of the variety of interests amenable to the general law, he adduced the attendance of the members of a club at a table d’hôte, and the frequency of dactyls in the Latin hexameter. (Anon 1885, 188) From the published paper in the Society’s Journal we read his transitions between these “miscellaneous” subjects: first, “Ex.4. Returning to human society, we shall find that the attendance at a club of its members fluctuates about as much as the coming in and going out of the wasps”, and later, “Ex.5. From London clubs to Latin poetry is a violent transition; significant of the variety of interests which are amenable to the Law of Error.” (Edgeworth 1885a, 210, 211) The data obtained from the Æneid he then uses first to characterise (in a statistical sense) Virgil’s style, and then to propose a distinguishing test: 2 The number of dactyls in the hexameter affords a better example of the mathematical method than might have been expected. I extracted the modulus and Mean for ninety lines, which seemed a fair specimen of the “Æneid,” those at the beginning of the fourth book. The Mean is 1.6, excliusive of the fifth foot; the fluctuation is 1.6 also. We have here a test of the Virgilian style. A passage of N lines is not Virgilian, if the mean differ from 1.6 by two or three times the modulus2 1.6 + ; 1 1 provided that the opening lines of the fourth book may be taken� as�90 a sample � specimen of Virgilian style. (Edgeworth 1885a, 211. In the original a typographical error gives the first term within brackets as .) 1 Edgeworth then applies this test to a more substantial extract from09 Virgil. The table of observations is for convenience omitted here; but attention is drawn to evidence that Edgeworth was no mere statistical bean-counter but was aware of the nuances of his data- base and, as a classicist, well able to appreciate such: To determine this question I observed 6003 additional hexameters taken from the sixth book. The following table gives the results of the whole set of Virgilian observations:-- [… …] This table conveys many valuable lessons. First we learn that the test above found is fairly accurate. It suffices to discriminate the Virgilian from the Ovidian hexameter; which has an average of 2.2 and modulus 1.8.iv But the test must not be pressed too far, or we should find Virgil himself violating the canon of Virgilian style. … If we had taken the last thirty lines of the passage under consideration, viz., “Æneid” VI, 434-464, we should have found a still more marked exception to the general canon. Those thirty lines pathetically describe the "plains of woe" where dwell unhappy lovers :-- “Lugentes campi, sic illos nomine dicunt.” “The line too labours and the words move slow.” 5 The gusts of passion to which the rhythm is accommodated cannot be treated as perfectly fortuitous. Nevertheless it appears that the causes at work are sufficiently numerous and independent to fulfil the conditions required for the elimination of chance. (Edgeworth 1885a, 211-212.) Maynard Keynes did not read Classics at university, but was similarly a product of a school system which, for those who could afford it, comprised little else. On 3 May, 1902 he read before the Eton Literary Society (which he had revived) a paper on the long 12th century poem De contemptu mundi (“Scorn for the World”) by the monk Bernard of Cluny.6 On the poem’s style he said: 3 The metre of the poem is probably better known than the poem itself; it is technically known as ‘Leonini cristati trilices dactylici’; Bernard himself refers to it as ‘tum dactylicum continuum exceptis finalibus, tum etiam sonoritatem leonicam servans’.7 It consists of couplets of pure dactylic hexameters with a two-syllable rhyme at the end of the line, while in each single line the last two syllables of the second foot rhyme with the last two of the fourth. A year later, on 1 February 1903, he read before the Appenine Literary Society of King’s College a paper on another 12th century figure, Peter Abelard. Describing the structure of some hymns (Hymnarius Paraclitensis) written by Abelard for the convent which he had founded, and of which Heloise was abbess, he says: The first series (2 lines of 4 iambic feet followed by 2 of 5) . and later: After 9 cantos he changes to a dactylic metre and finally: In the next series he describes the infancy of Christ, beginning in an awkward metre of 2 spondees followed by 2 dactyls: but he soon falls into a more conventional form. So, as we now know, Keynes could be relied on to know a dactyl when he saw one. We next, after this commendable post-schoolboy effort, hear from Keynes on the matter of dactyls in his A Treatise on Probability (1921). In a characteristic passage Professor Edgeworth has applied these theories to the frequency of dactyls in successive extracts from the Aeneid. The mean for the line is 1.6, exclusive of the fifth foot, thus sharply distinguishing the Virgilian line from the Ovidian, for which the corresponding figure is 2.2. … That Edgeworth should have put forward this example in criticism of Lexis’s conclusions, and that Lexis should have retorted that the explanation was to be found in Edgeworth’s series not consisting of an adequate number of observations, indicates, if I do not misapprehend them, that these authorities are at fault in the principles, if not of probability, of poetry. The dactyls of the Virgilian hexameter are, in fact, a very good example of what has been termed connexité, leading to subnormal dispersion. The quantities of the successive feet are not independent, and the appearance of a dactyl in one foot diminishes the probability of another dactyl in that line. It is like the case of drawing black and white balls out of an urn, where the balls are not replaced. (Keynes 1921, 437, 438. Italic original.) 4 This then leaves us with two questions: the validity of Keynes’ criticism of Edgeworth in a statistical context; and the validity of his understanding of the practice of Latin poetic composition. As a preliminary we begin with a discussion of a concept which touches on both questions: “connexité, The quantities of the successive feet are not independent, and the appearance of a dactyl in one foot diminishes the probability of another dactyl in that line.”8 Keynes offers no evidence in support of this notion; but curiously, it is from Edgeworth elsewhere that he could have found such support, for this is along the lines of what Edgeworth establishes, not in the paper under consideration by Keynes, but in another read later in the same year before Section F of the British Association for the Advancement of Science, and like the earlier paper published in the Journal of the Statistical Society of London (Edgeworth 1885b).