23. J.S.Bach, Jack Goldstone, and numbers (10-4-2020)
J.S.Bach, Jack Goldstone, and numbers (10-4-2020)
Written by: Jan Luiten van Zanden
Perhaps the real mystery about Bach is his relationship with numbers. This is a topic that perhaps divides the Bach scholarly community even more than the tempo at which the opening chorus of the Mattheus Passion should be performed. In Bach’s days, it was common to give letters a number: A was 1, B 2, C 3 and by implication H 8, so the numerical equivalent of the name Bach was 1+2+3+8=14. J.S. Bach sums up to 41, Johann Sebastian Bach to 158. The idea is that Bach was aware of this kind of ‘kabbalistic’ thinking, and therefore the number 14 is much more used in his music than 13 or 15. There are, for example, 14 chorals in the Mattheus Passion, and 41 ‘free’ items (apart from the literal quotes from the bible). In 1985 two Dutch authors, Kees van Houten and Marinus Kasbergen, published a book, ‘Bach en het Getal’, based on 13 years of counting and calculating notes, bars, themes, pieces and other dimensions of his work. They presented overwhelming evidence that in their view Bach was, when composing his music, constantly taking all kinds of ‘special’ and ‘holy’ numbers into account. 3, 7, 10, 12 are, for example, also special numbers, but the letters of Christus, or Credo also count up to such numbers. So the fact that the Credo of his last masterpiece the Mass in B minor, has 784 (7 X 112) bars, is no coincidence, as 112 is the number of Christus, and 7 is the number of perfection and completeness. The book gives so many examples, that you almost start believing that they are correct, but at one point, when they ‘demonstrate’ that Bach predicted the day he would die 20 years before the actual date, they clearly go over the top.
The problem with this book is that the authors were making thousands and thousands of calculations of the many special numbers that they ‘identified’, and only reported about the cases that they found ‘something’ (such as the 784 bars of the Credo). They did not report all the calculations they did, and showed that the number of ‘significant’ outcomes was much larger than might be expected on the basis of chance, and they assumed that all significant outcomes were the result of conscious design by the great man himself – and not random. They were so eager and enthusiastic about their revolutionary message, that they did only focus on the evidence that supported it, and ignored the rest. It is highly likely that some of the things they found, were indeed part of the design of the music by Bach, but many other results, and perhaps most, are random.
This is obviously a very general problem: we all have our ideas, pet theories and serious hypotheses, and we tend to be mainly looking at the kind of evidence that confirms them. The same problem recently came up in a discussion with Jack Goldstone about his theory that all pre 1800 growth was cyclical and can best be described as efflorescences – the blooming of economies, always followed by decline. Bas van Leeuwen and I had in our paper in EEH in which we presented the estimates of GDP per capita of Holland in the period 1348-1807 stressed the sustained character of growth, which was underpinned by a regression analysis showing the near stability of per capita growth. In a paper with Sandra de Pleijt we did this in more detail, distinguishing various subperiods – also showing that growth was remarkably stable. But this was not picked up by Goldstone, who had compared estimates from a number of decades, finding more growth before 1700, and decline afterwards. Two things are probably wrong with this. Firstly, this procedure does not take into account the fact that these estimates of GDP per capita are subject to large measurement errors; given this fact, it is likely that sometimes our estimates overstate GDP, and underestimate it in other years. The problem with the Goldstone procedure is that the cyclical character he finds may well be caused by these random fluctuations, especially as he focuses (as a result of his hypothesis) on peak and through years. Secondly, by comparing peak and through years only, a large part of the historical information contained in the estimates is not used. The years in between are simply ignored; estimating trends via regression analysis has the advantage that it does make use of all the annual estimates, all the historical information that is available. In short, Goldstone was in search for evidence for a efflorescence, and found it, but more careful use of the same data, taking into account the large margins of error, leads to a different result (Jutta Bolt and I concluded in our contribution to this discussion dossier).
The takeaway message is perhaps: how often are we trying to find confirmation for our own ideas, and how often are we really prepared to be surprised by the research that we are doing? There are limits to what we are willing to believe – I am not convinced that Bach knew the day he would die in advance, and a good intuition about what is plausible is probably important for academic success. Yet, we aim to develop new insights, new ideas, which go beyond established views. How can we free ourselves from too many prejudices? Perhaps Charles Darwin can help a bit. I once read that he had a special notebook for all the arguments against his theory. The reason was that he had learned that he tended to forget these objections, and in order to be sure that he would discuss them in a new version of his book, he carefully made notes of all critical comments. Perhaps this is not such a bad idea.
And what about Bach? I think he played with numbers occasionally, and when he grew older, and his music became more esoteric and abstract, there was more room for such experimentation and kabbalistic entertainment. But what really counted for him was not the number, but the sound, the structure, the beauty, the emotion it conveyed – fortunately!
Continue reading: Economic History at the frontier (11-4-2020)
Kees van Houten and Marinus Kasbergen, Bach en het Getal. De Walburg Pers, Zutphen, 1985.
The papers by Goldstone and Bolt/Van Zanden will be published in a special issue of Journal of Global History, 2020.