He says, in other words, the math that's taught should be useful. Regarding this more profitable mathematics he asks, "How could the life of man be happily led, nay how could men in a manner consist without it? Truly I may justly say of it as Cicero of Philosophy, it hath taught men to build houses, to live in Cities and walled Towns; it hath taught men to measure and divide the Earth; more facilely to negotiate and trade one with another: From whence was found out and ordered the art of Navigation, the art of War, Engins, Fortifications, all mechanick operations, were not all these and innumerable others the progeny of this never-sufficiently praised Science?"
Webster was a preacher and not a particularly astute scholar. As I pointed out in my last post, he joined many of his contemporaries in believing magic, alchemy, and astrology to be subjects of equal weight with mathematics and natural philosophy (as what we call simply science was then called). In doing so he echoes a man, John Dee, who lived half a century before him and whom he calls a "myrror of manifold learning."[2] In a well-known preface to the first English translation of Euclid's Elements, Dee, like Webster, praises math and science as topics for university study and, just as much, magic, alchemy, and astrology.[3] And, like Webster, he says the application of mathematics is at least as important as is abstract speculation. In his words, "the very chief perfection (almost) of Numbers Practicall use" can be attained by the "mixtyng of speculation and practise."
In the preface Dee catalogs many of math's practical uses — from merchants' reliance on arithmetic, to the tangible uses of algebra[4], and to the many uses of geometry made by surveyors, military commanders, navigators, builders, excise men, and others. With regret Dee says he's been writing against a deadline ("the Printer, hath looked for this Præface, a day or two") and tells us his subject "is so ample and wonderfull, that, an whole yeare long, one might finde fruitfull matter therin, to speake of: and also in practise, is a Threasure endeles."
Despite the passion he shows for his subject in the preface, Dee's life was devoted more to the intangible aspects of math than the material ones. It's true he used Euclidian geometry to solve problems of navigation and trained the crews of ships so they could find their way across the Atlantic in early voyages to North America, but he believed his life's mission to be the uncovering of the spiritual forms underlying the material world. To him math was a language for use in speaking with angels. He associated its abstract beauty with mystical powers of divination which he claimed to possess.
Of the angelical beauty of mathematics he wrote: "All thinges ... do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator. ... By Numbers propertie ... we may ... ascend, and mount up (with Speculative winges) in spirit, to behold in the Glas of Creation, the Forme of Formes, the Exemplar Number of all thinges Numerable: both visible and inuisible, mortall and immortall, Corporall and Spirituall."[5]
The only son of a minor member of the royal court, he had a brilliant career at university and possessed both inclination and sufficient means to extend his education after graduation through extensive travel in Europe. Not himself wealthy, he was able to make himself useful to wealthy members of the aristocracy of England and the European continent. There appears to have been no snobbishness in him however. At a time when "gentles" treated unlettered artisans with contempt, scorn, or — at best — indifference, and when dramatists could be sure to draw laughs by poking fun at men whom they characterized as "rude mechanicals"[6], Dee was unusual in the sympathetic recognition he gave to the emerging class of "Common Artificer."
He closes the Preface by citing advantages of instruction — not in the Latin of the universities but in the English of the shop and street — made available to London tradesmen, many of whom were the first of their families to have acquired the ability to read. Of the book in which the Preface appears — Billingsley's translation of Euclid's Elements (which, as I say, was the first version to be published in English) — he writes: "[H]ow many a Common Artificer, is there, in these Realmes of England and Ireland, that dealeth with Numbers, Rule, & Cumpasse: Who, with their owne Skill and experience, already had, will be hable (by these good helpes and informations) to finde out, and devise, new workes, straunge Engines, and Instrumentes: for sundry purposes in the Common Wealth? or for private pleasure? and for the better maintayning of their owne estate?"
This title page to Billingsley's Euclid depicts some of the practical applications of mathematics to which Dee refers. (It's also, you'll notice, not prudish in depicting naked bodies.)
{The title page of Henry Billingsley's translation of Euclid's Elements (1570), with preface by John Dee; source: wikipedia}
It's generally thought that Dee's Preface and all of Billingsley's Euclid helped set in motion a gradual shift in attitudes toward mathematics and the book's readers appear to have fostered the growth of applied mathematics outside the universities. As a partial result, it's pretty clear that in the century following its appearance mathematical practitioners — the men who employed mathematics in their work as well as the printers and authors of practical math texts, the makers of technical instruments, and the technical advisors who assisted university-trained natural philosophers — became more prosperous and grew somewhat in social standing.[6]
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Some sources:
The Mathematical Practitioners of Tudor and Stuart England by E.G.R. Taylor (Cambridge, 1954)
John Dee's "Mathematicall Praeface": A Sixteenth Century Classification of the Mathematical Arts and Sciences by Charles St. Clair (pdf)
The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara by John Dee from Sir Henry Billingsley's first English version of Euclid's Elements, 1570
"John Dee" by Thompson Cooper in Dictionary of national biography ed. by Leslie Stephen and Sidney Lee (Smith, Elder, & co., 1888)
"John Dee and His Supplication to Queen Mary" by P. Evans Lewin, Woolwich Public Libraries in The Library world, Vol. 5 (Library Supply Co., 1903) Extract: 'Whilst at Cambridge he only slept four hours every night, and spent eighteen hours of the day in study. So great was his knowledge, that his acquaintance was eagerly sought by such men as Gemma Frisius, Mercator, and Gaspar a Mirca, all of whom he visited in his twentyfirst year. Even at this period he was looked on askance, for he relates that in 1547 he "sett forth" at Trinity College a Greek comedy of Aristophanes, "with the performance of the Scarabaeus, his flying up to Jupiter's palace with a man and his basket of victuals on her back, whereat was great wondering and many vain reports spread about." This, probably, was only a piece of stage mechanism suitable to the crude ideas of the time and in keeping with Greene's instructions in "Tamburlaine" — "exit Venus; or if you can conveniently let a chair come down from the top of the stage and draw her up."'
"The Mistaking of 'the Mathematicks' for Magic in Tudor and Stuart England" by J. Peter Zetterberg in The Sixteenth Century Journal, Vol. 11, No. 1 (Spring, 1980), pp. 83-97. Stable URL: http://www.jstor.org/stable/2539477
"Science and Education in the Seventeenth Century: The Webster-Ward Debate" by G. Allen, reviewed by Theodore M. Brown in Isis, Vol. 64, No. 3 (Sep., 1973), pp. 422-424. (The University of Chicago Press) Stable URL: http://www.jstor.org/stable/2297
A general dictionary: historical and critical, in which a new and accurate translation of that of the celebrated Mr. Bayle, with the corrections and observations printed in the late edition at Paris, is included; and interspersed with several thousand lives never before published. The whole containing the history of the most illustrious persons of all ages and nations particularly those of Great Britain and Ireland, distinguished by their rank, actions, learning and other accomplishments. With reflections on such passages of Bayle, as seem to favor scepticism and the Manichee system, Volume 10 by Pierre Bayle, John Peter Bernard, Thomas Birch, John Lockman, George Sale, Alexis Gaudin, Anthelme Tricaud, Pierre Desmaizeaux (Printed by J. Bettenham, 1741)
Billingsley Euclid in Mathematical Treasures by Frank J. Swetz and Victor J. Katz
Shakespeare from the margins by Patricia A. Parker (University of Chicago Press, 1996)
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Notes:
[1] My quotes from John Webster come from his Academiarum Examen: Academiarum examen, or the examination of academies wherein is discussed and examined the matter, method and customes of academick and scholastick learning by John Webster (Calvert, 1654).
[2] My quotes from John Dee come from his The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara by John Dee from Sir Henry Billingsley's first English version of Euclid's Elements, 1570. I have modernized Dee's use of the letter "u" where we would put "v" and given the "long s" (ſ) as "s".
[3] Dee's passion for mathematics leads him to claim (quoting Boetius) that "All thinges (which from the very first originall being of thinges, have bene framed and made) do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator." And further: "By Numbers propertie therefore, of us, by all possible meanes, (to the perfection of the Science) learned, we may both winde and draw our selves into the inward and deepe search and vew, of all creatures distinct vertues, natures, properties, and Formes: And also, farder, arise, clime, ascend, and mount up (with Speculatiue winges) in spirit, to behold in the Glas of Creation, the Forme of Formes, the Exemplar Number of all thinges Numerable: both visible and invisible, mortall and immortall, Corporall and Spirituall."
[4] Of algebra he says: "This Rule, and Arithmetike of Algiebra, is so profound, so generall and so (in maner) conteyneth the whole power of Numbers Application practicall: that mans witt, can deale with nothyng, more proffitable about numbers: nor match, with a thyng, more mete for the divine force of the Soule, (in humane Studies, affaires, or exercises) to be tryed in."
[5] Here's the full quote: "All thinges (which from the very first originall being of thinges, have bene framed and made) do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator. O comfortable allurement, O ravishing perswasion, to deale with a Science, whose Subiect, is so Auncient, so pure, so excellent, so surmounting all creatures, so used of the Almighty and incomprehensible wisdome of the Creator, in the distinct creation of all creatures: in all their distinct partes, properties, natures, and vertues, by order, and most absolute number, brought, from Nothing, to the Formalitie of their being and state. By Numbers propertie therefore, of us, by all possible meanes, (to the perfection of the Science) learned, we may both winde and draw our selves into the inward and deepe search and vew, of all creatures distinct vertues, natures, properties, and Formes: And also, farder, arise, clime, ascend, and mount up (with Speculative winges) in spirit, to behold in the Glas of Creation, the Forme of Formes, the Exemplar Number of all thinges Numerable: both visible and inuisible, mortall and immortall, Corporall and Spirituall."
[6] A Midsummer Night's Dream: Act 3, Scene 2
PUCK[7] Stephen Johnston makes this point. See The identity of the mathematical practitioner in 16th-century England from the proceedings of a 1995 conference in Duisburg: Irmgarde Hantsche (ed.), Der “mathematicus”: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, Duisburger Mercator-Studien, vol. 4 (Bochum: Brockmeyer, 1996), 93-120. It is closely based on material in the introduction to my thesis, and appears here by permission of Universitätsverlag Dr. N. Brockmeyer. See also: The making of the English middle class; business, society, and family life in London, 1660-1730 by Peter Earle (University of California Press, 1989)
6 My mistress with a monster is in love.
7 Near to her close and consecrated bower,
8 While she was in her dull and sleeping hour,
9 A crew of patches, rude mechanicals,
10 That work for bread upon Athenian stalls,
11 Were met together to rehearse a play
12 Intended for great Theseus' nuptial-day.
13 The shallowest thick-skin of that barren sort,
14 Who Pyramus presented, in their sport
15 Forsook his scene and enter'd in a brake
16 When I did him at this advantage take,
17 An ass's nole I fixed on his head:
18 Anon his Thisby must be answered,
19 And forth my mimic comes. When they him spy,
20 As wild geese that the creeping fowler eye,
21 Or russet-pated choughs, many in sort,
22 Rising and cawing at the gun's report,
23 Sever themselves and madly sweep the sky,
24 So, at his sight, away his fellows fly;
25 And, at our stamp, here o'er and o'er one falls;
26 He murder cries and help from Athens calls.
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