polymathematics

With regards ‘Mathematics – Go Figure’ – http://www.prospectmagazine.co.uk/2010/01/go-figure/

Francis Bacon, polymath and scientific theorist, would be proud to read that Timothy Gowers has adopted two of his own techniques in the seeking of an advancement of mathematical learning. The first is what is a sort of linguistic colonialism, that is, the taking of words with specific meanings, and the re-defining of them. Gowers re-draws the word polymath, changing it from a word indicating a wide-ranging (and approaching comprehensive) knowledge into a rather facile pun. Bacon did the same, taking words like ‘form’ and ‘metaphysicke’ and reconceptualising them so that he might bend them to his own will: ‘my Conception & Notion may differ from the Auncient, yet I am studious to keepe the Auncient Termes’.1 Bacon understood that words had power, and that in re-defining them he made them work for him and against their original coiners.

Bacon was also big on collaboration, as demonstrated in his New Atlantis and various other works, but more importantly, he invented what was, within the confines of the available technology, open-source natural philosophy. He was explicit in his suggestion that should a reader find an error in his work, they ought to change it, or at least suggest how to make it better. It worked. In Sylva sylvarum, Bacon write on the imitation of the human voice, noting en passant that ‘I have known a dog, that if one howled in his ear, he should fall howling a great while.’Dutifully, one reader followed Bacon’s earlier prescription, writing these words in the book’s margin:I hav tried this expt, but the dogg must love him who doth it.’2 Wisdom, indeed.

Bacon would, however, also be somewhat disappointed. He lost faith in the genius of his own times, and entrusted his thoughts to the future:knowing well enough the nature of the things that I impart, I deal out work for ages to come.’ Open collaboration, especially at a distance, and the re-meaning of words was something Bacon recommended four hundred years ago, so when Jim Giles writes of Gower’s collaborative ‘polymathematics’ that ‘there are now tentative signs that science is catching on too’, he is just a little behind the times.

The long version:

Francis Bacon would be proud of Timothy Gowers, and for two different reasons. The first, and perhaps most surprising, is for his re-definition of the word ‘Polymath’. Gowers takes a word which has a very specific meaning, and re-uses it as a somewhat facile pun. Francis Bacon hails from an era when being a ‘proper’ polymath, that is, being in possession of large and wide-ranging gobbets of knowledge was still theoretically possible. These enlightened times perhaps make it impossible to be in possession of anything but a tiny percentage of that known – perhaps erudition is all that we can hope for. Far from being critical of this re-drawing of the word’s definition, Bacon would have approved, as one of his tactics in his campaign against the evils of received knowledge was exactly the same. He wrote in his Advancement of Learning (1605) that ‘I vse the word METAPHISICKE, in a differing sense, from that, that is receiued: And in like manner I doubt not, but it will easilie appeare to men of iudgement, that in this and other particulars, wheresoeuer my Conception & Notion may differ from the Auncient, yet I am studious to keepe the Auncient Termes’.3 That is, he kept the word, but changed what it meant. An Early Modern Humpty Dumpty, if you like. But for Bacon it was a serious, not a frivolous business. In re-defining terms used by ancients such as Aristotle and Plato, he not only used language that they recognised, but in making them re-assign new meanings to these old words, he wrestled them from their original context: this was linguistic colonisation.

The second aspect of Gowers’s ‘polymath’ idea is that of collaboration, and the denial of the primacy of the ‘lone genius’. Bacon’s entire philosophical programme, or Instauration as he called it, relied on the brains and hours of many, all working towards the same goal. Like Gowers, Bacon explicitly invited his readers to change his work when they saw errors:

For my own part, if I have wrongly given credit to anything, or grown sleepy or inattentive, or become weary on my way and left the investigation unfinished, I nevertheless make the things plain for all to see, so that my mistakes can be spotted and separated out before the body of science is further infected by them, and also so that my labours can be carried on easily and expeditiously.4

Now, Bacon may have been slightly disingenuous, but the principle was plain – his natural philosophy was open source. Now, the question is whether anyone actually joined in with Bacon’s new way of doing knowing. The example of the Royal Society is perhaps a little simplistic, not least because Bacon’s influence has been over-emphasised over the years. But one just has to look at his Sylva sylvarum, a rather odd (and misunderstood) compendium or collection of natural historical observations and experiments published shortly after his death in 1626 to find evidence for Bacon’s open source natural history bearing fruit – if rather odd fruit. It’s not the fact that Sylva was accompanied by his New Atlantis, the so-called scientific utopia, which contains the ‘blueprint’ for collaborative scientific research, but the margins where the student ought to look. One copy, lodged in the British Library, has marginalia from now fewer than five hands, most of which comment on, correct or cross-reference the printed material. One reader has plainly thought long and hard about the experiments contained within, and has even carried them out: exactly what Bacon intended. Experiment 238 concerns the imitation of the human voice by animals, asserting that only birds can do so, and that apes cannot, before commenting in a sort of aside, that ‘It is true that I have known a dog, that if one howled in his ear, he should fall howling a great while’.5 In the ample margins next to Experiment 238, the diligent, co-operative reader has written the following:

I hav tried this

expt, but the dogg

must love him

who doth it6

Jim Giles writes of this sort of collaboration that ‘there are now tentative signs that science is catching on too’. In his later works, written while disgraced and his hopes for a ‘publically-funded’ scientific institute were dashed, Bacon repeated like a mantra that he was writing ‘to present and future ages’. Indeed, Bacon went further, writing in the late and long-lost Abecedarium novuum naturae that

As for me, I am pretty sure that, because I have little faith in the genius of our times, my own words (as far as the work of instauration is concerned) could be accused of lacking an age or era to match them. […] That is why I am devoted to posterity and put forward nothing for the sake of my name or taste of others, but, knowing well enough the nature of the things that I impart, I deal out work for ages to come.7

Bacon would be overjoyed that Timothy Gowers had adopted both his technique of linguistic colonialism and the idea of open-source science. This Joy, however, might well turn to despair when he realised that they thought it was a new idea.

1 OFB IV, p. 80-1.

2 BL, Sylva sylvarum, 928.f.14, I2r.

3 OFB IV, p. 80-1.

4OFB, XI, p. 21.

5 BL, Sylva sylvarum, 928.f.14, I2r.

6 BL, Sylva sylvarum, 928.f.14, I2r.

7 OFB, XIII, p. 173.

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