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Numbers, Accuracy and Precision

Yeats was relatively unconcerned about precision with numbers, which has proved misleading and frustrating for some of his commentators. In particular, with respect to the periods involved in the historical cycles, Yeats seems to have assumed enough familiarity with the astronomical precession and the related astrological idea of the Great Year not to have been as careful as he might in detailing the lengths of his time-periods. Graham Hough, in The Mystery Religion of W. B. Yeats finds that Yeats’s nonchalance undermines the whole of this aspect, and Hazard Adams, in The Book of Yeats’s Vision, remains uncertain about whether his Great Year contains twelve or thirteen months.

There are two particular problems here: those caused by rounding, and those caused by different measurements of the Great Year.

A corollary of the length ascribed to the Great Year, is the length of time between successive incarnations. Yeats never seems to enter into this in much detail, though he had certainly considered the subject in one of the earlier drafts: ‘In a typal man, unfallen man if you will the incarnations in a single cycle were exactly twenty eight, & one symbolical month of the moon & as the sun moves during that time through one sign & the whole of the present phase of human life is considered to make up a single year typal man would go be reincarnated reborn 1000 1536 326 times’ (YVP 4 126-27). After the rejected figures, 326 incarnations (properly, 336 or 12 cycles of 28 separate incarnations, including the non-human Phases 1 and 15) seems almost leisurely, but, placed within a Great Year of 26,000 years, it would imply rebirth every eighty years on average. The older length of year gives an average of 110 years between rebirths. Neither of these gives much time for the processes involved in Yeats’s vision of the after-life, even allowing for life-spans that were often short through much of history.

The rejected figures are also interesting, less because of the arithmetic than because they are more clearly symbolic numbers, 1000 being an nicely cubed total of completion (103), while 1536 is 3 x 29 (512), or 12 x 27 (i.e. 12 doubled 7 times, or 12 times 128), though how Yeats came by this number is unclear.

Rounding of numbers is also behind one of the problems Yeats encountered when trying to fit the Phases of the Moon to the Zodiac. One circuit of the Moon around the Zodiac, its sidereal cycle, takes 27.32 days so that rounding up or down can give either 27 or 28 ‘day’ periods and both counts exist in systems of lunar astrology. However, the average period from New Moon to New Moon, the mean lunation cycle, is 29.53 days, which by rounding can yield 29 or 30. Those mediaeval systems that give interpretations of the ‘days of the moon’ usually give the number as thirty, and the Indian Jyotishi system also numbers the tithis (lunar days) as thirty: twenty-eight plus the Full Moon and the New. Nineteenth-century writers similarly adopt one of the actual round numbers for the lunar month, usually 29 (see astronomy). Yeats, though, takes the number of the simple sidereal cycle and applies it to the synodic cycle of the phases. As noted in the page on astronomy this can be justified by taking the average lunar day, from the culmination of the Moon on successive days, rather than the culmination of the Sun (noon), but Yeats does not bother to justify it.

Again symbolism is as important as accuracy, and twenty-nine and even thirty are numbers which lack mystic resonance. In contrast both twenty-seven and twenty-eight have attractive properties. Twenty-seven is the cube of three and figures as the largest number in the Pythagorean tetractys, the sum of all the others: 1, 2, 3, 4, 8, 9 and 27. Twenty-eight is a ‘triangular’ and a ‘perfect’ number. The development of triangular numbers is attributed to Pythagoras himself and consists simply of those numbers which can be arranged in triangles like a frame of billiard balls or, alternatively, the sum of successive integers from one: thus 28 = 1 + 2 + 3 + 4 + 5 + 6 + 7; perfect numbers are a slightly different group, a special subset of triangular numbers, “integers which are the sum of their positive proper divisors”, including one and excluding themselves, thus 28’s divisors are 1, 2, 4, 7, 14, which have a sum of 28. According to Yeats’s reading of Blake, Blake divided the ecliptic into the ‘Twenty-Seven Heavens’ or Churches of Beulah (see Blake and A Vision). However, given the fundamental fourfold symmetry of much of the System of A Vision, the twenty-eight phases fit far more readily in the Yeatses’ scheme.

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Text and original images copyright © Neil Mann.