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Chapter 1 Neither Indeed Would I Have Put My Selfe to the Labour Of Notes Neither indeed would I have put my selfe to the labour of writing any Notes at all, if the booke could as well have wanted them, as I could easilie have found as well, or better to my minde, how to bestow my time. Marcus Aurelius Antoninus. Chapter 1 1. This description is from Hacking's introduction to the English trans­ lation of Maistrov [1974, p.vii]. 2. Forsaking, in this respect, what is described in the 14th edition [1939] of the Encyclopaedia Britannica as its "career of plain usefulness" [vol. 3, p.596]. A supplementary volume of the Dictionary, soon to be published, will contain a note on Thomas Bayes. 3. See Barnard [1958, p.293]. 4. The note, by Thomas Fisher, LL.D., reads in its entirety as follows: "Bayes, Thomas, a presbyterian minister, for some time assistant to his father, Joshua Bayes, but afterwards settled as pastor of a con­ gregation at Tunbridge Wells, where he died, April 17, 1761. He was F.R.S., and distinguished as a mathematician. He took part in the controversy on fluxions against Bishop Berkeley, by publishing an anonymous pamphlet, entitled "An Introduction to the Doctrine of Fluxions, and Defence of the Mathematicians against the Author of the Analyst," London, 1736, 8vo. He is the author of two math­ ematical papers in the Philosophical Transactions. An anonymous tract by him, under the title of "Divine Benevolence" , in reply to one on Divine Rectitude, by John Balguy, likewise anonymous, attracted much attention." For further comments on this reference see Ander­ son [1941, p.161]. The Winkler Prins Encyclopaedie [1948], in the 394 Notes: chapter 1 entry under "Bayes, Thomas", has only this to say by way of biog­ raphy: "Engels wiskundige (?-1763), omtrent wiens leven wij vrijwel niets weten" [vol. 3, p.396]. It does, however, give a clear and correct discussion of Bayes's Theorem. 5. Anderson [1941, p.160]. If Thomas was born before 25th March (New Year's Day in the old English calendar), the year could be 1701 (old style), though it would be 1702 (new style). The day of his death being the seventh, we find on subtracting the 11 days lost by the calendar reformation of 1752, that his death was on the 27th March 1761 (o.s.). Subtraction of his age at death - viz. 59 - shows that he was either born on or just after New Year's Day 1702 (o.s.), or in 1701 (o.s.). See Bellhouse [1988a]. 6. Hacking [1970] and the 15th edition of the Encyclopaedia Britannica [1980], (vol. I of the Micropaedia). 7. Holland [1962, p.451]. 8. Barnard [1964], Hacking [1970]. 9. Holland [1962, p.452], Pearson [1978, p.355] and Wilson [1814]. Bogue and Bennett [vol. II, 1809] point out that "The necessities of the church may render it proper that men should be ministers, who have not enjoyed the advantages of an academical, or even a liberal educa­ tion" [p.7]. 10. Pearson [1978, p.356] states that this academy was founded by the Congregational Fund Board in 1695. 11. Writing of the course of instruction for the Christian ministry, Bogue and Bennett [vol. III, 1810] say "To mathematics and natural phi­ losophy it has usually been judged proper to apply a portion of the student's time. As they tend to improve the mind, and peculiarly to exercise its powers, and call forth their energies, the general influence of both may be favourable to his future labours, and the hearers as well as the preacher experience their good effects" [p.270]. 12. H.M. Walker, in her biographical notes appended to the 1967 reprint of de Moivre's The Doctrine of Chances, writes " ... Thomas Bayes, with whom he [i.e. de Moivre] is not known to have been associated" [p.367]. An outrageous statement is made by Epstein [1967]: speaking of de Moivre, he writes "His mathematics classes were held at Slaugh­ ter's Coffee House in St. Martin's Lane: one successful student was Thomas Bayes" [p.5]. 13. Holland [1962, p.452]. Proving how little times have changed since then, Kac [1985] in his autobiography says "The way Stan [Ulam] did mathematics was by talking, a work style which goes back to his young days in Lwow, which were spent largely in coffee houses Notes: chapter 1 395 (mainly in Szocka, which is Polish for "Scottish Cafe") endlessly dis­ cussing problems, ideas and conjectures. Great stuff came of this highly unorthodox way of doing mathematics ... " [pp.xx-xxi]. See also Ciesielski [1987]. 14. See Dale [1990]. 15. Holland [1962, p.453]. See also James [1867]. 16. James [1867]. 17. Holland [1962, p.453] states that this move of Thomas's was made in 1731, while Barnard [1958, p.293] merely notes that "he was certainly there in 1731". See also Pearson [1978, p.357] and Timpson [1859, p.464]. However, in the Minute Books of the Body of Protestant Dis­ senting Ministers of the Three Denominations in and about the Cities of London and Westminster the following entry may be found: "Oct. 3rd• 1732. List of approved. Ministers of the Presbyterian denomina- tion. MMr. BBayes Jsen:. } Leather Lane." I would suggest therefore r. ayes un. that Thomas Bayes moved to Tunbridge Wells somewhat later than the usually cited date of 1731. 18. Barnard [1958, p.293]. Burr [1766] points out further that "a Methodist meeting-house has also been erected at Tunbridge-Wells since the rise of that deluded sect" [p.104]. 19. The following descriptions of Tunbridge Wells are from Burr [1766]: "Tunbridge-Wells is situated on the southern side of the county of Kent, just on the borders of Sussex, and about thirty-six miles from London. It is partly built in Tunbridge parish, partly in Frant parish, and partly in Speldhurst parish; and consists of four little villages, named Mount-Ephraim, Mount-Pleasant, Mount-Sion, and the Wells" [pp.98-99]. "An excellent bowling-green, the old assembly-room, and a capacious handsome Presbyterian meeting-house, are all situated upon Mount-Sion" [p.104]. For further details see Holland [1962, pp.453-454]. 20. Some doubt as to Ditton's religious convictions exists. The Imperial Dictionary of Universal Biography says "The son [i.e. Humphrey], in opposition to the nonconformist wishes of the father [also Humphrey], entered the English church." On the other hand, in the Dictionary of National Biography we find "The younger Ditton afterwards be­ came a dissenting preacher at his father's desire". The New General Biographical Dictionary is more cautious and merely states "he [i.e. Humphrey] at the desire of his father, although contrary to his own inclination, engaged in the profession of divinity" . 21. Holland [1962, p.455]. 396 Notes: chapter 1 22. Cajori [1919a) writes ''the publication of Berkeley's Analyst was the most spectacular mathematical event of the eighteenth century in England" [p.219). 23. Pearson [1978, p.360) claims that Jurin was the secretary of the Royal Society, and gives his name in the list of secretaries on p.357. But this claim is not supported by the Signatures in the First Journal-Book and the ChaTter-Book of the Royal Society [1912). 24. For further details see Pearson [1978, p.360). 25. Extracts from this tract are given in Holland [1962, pp.455-456): for a detailed discussion of the paper see Smith [1980). The Dictionary of Anonymous and Pseudonymous English Literature cites de Morgan as its source of information on the authorship of this work. 26. Holland [1962) writes "His 1736 tract in defence of the mathematical art was published at an opportune time and was of such merit that it is likely that his election was unanimously agreed to by members of this distinguished body ... We do not believe he obtained election in the manner of some members who contributed nothing of merit but were wealthy enough to pay the high admittance fees and yearly dues" [p.459). See also Hacking [1970, p.531j, Maistrov [1974, p.88j, Pearson [1978, p.356j, Keynes [1973, p.192j, Pearson [1978, p.350) and Timerding [1908, p.44). The last three of these references incorrectly give Bayes's date of election as 1741. Elected at the same time as Bayes were Walter Bowman and Michel Fourmont: see Signatures in the First Journal-Book and the ChaTter-Book of the Royal Society [1912). 27. Quoted in Holland [1962, p.459). 28. One trusts that this last word is not used with the meaning that Chambers Twentieth Century Dictionary assures one it has in book­ sellers' catalogues! 29. Reprinted in Pearson [1978, p.357): for details of the signatories see pp.357-358, op. cit. 30. Pearson [1978, pp.360-361). That Bayes (and his clerical coevals) should have had time to indulge in mathematical and scientific pur­ suits is hardly surprising when one bears in mind the following passage from an editor of Derham's Physico-Theology (first issued in 1713): "The life of a country clergyman is in every respect more favourable to the cultivation of natural science, by experiment and observation, than any other professional employment. He has all the leisure that is requisite to philosophic researches; he can watch the success of his experiments from day to day, and institute long processes without interruption, or record his observations without chasm or discontin­ uation." Not that their professional duties were ignored, however: Notes: chapter 1 397 Bogue and Bennett write "As to the quantity of labour performed by dissenting ministers of evangelical principles (the religious principles of the old nonconformists), they need not blush at a comparison with those of the preceding times.
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