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Elizabeth F. Lewis Phd Thesis

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Elizabeth F. Lewis Phd Thesis PETER GUTHRIE TAIT NEW INSIGHTS INTO ASPECTS OF HIS LIFE AND WORK; AND ASSOCIATED TOPICS IN THE HISTORY OF MATHEMATICS Elizabeth Faith Lewis A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in St Andrews Research Repository at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6330 This item is protected by original copyright PETER GUTHRIE TAIT NEW INSIGHTS INTO ASPECTS OF HIS LIFE AND WORK; AND ASSOCIATED TOPICS IN THE HISTORY OF MATHEMATICS ELIZABETH FAITH LEWIS This thesis is submitted in partial fulfilment for the degree of Ph.D. at the University of St Andrews. 2014 1. Candidate's declarations: I, Elizabeth Faith Lewis, hereby certify that this thesis, which is approximately 59,000 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for a higher degree. I was admitted as a research student in September 2010 and as a candidate for the degree of Ph.D. in September 2010; the higher study for which this is a record was carried out in the University of St Andrews between 2010 and 2014. Signature of candidate ...................................... Date .................... 2. Supervisor's declaration: I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of Ph.D. in the University of St Andrews and that the candidate is qualified to submit this thesis in application for that degree. Signature of supervisor ...................................... Date .................... 3. Permission for publication: In submitting this thesis to the University of St Andrews I understand that I am giving permission for it to be made available for use in accordance with the regulations of the University Library for the time being in force, subject to any copyright vested in the work not being affected thereby. I also understand that the title and the abstract will be published, and that a copy of the work may be made and supplied to any bona fide library or research worker, that my thesis will be electronically accessible for personal or research use unless exempt by award of an embargo as requested below, and that the library has the right to migrate my thesis into new electronic forms as required to ensure continued access to the thesis. I have obtained any third-party copyright permissions that may be required in order to allow such access and migration, or have requested the appropriate embargo below. The following is an agreed request by candidate and supervisor regarding the publication of this thesis: PRINTED COPY Embargo on all or part of print copy for a period of two years on the following ground(s): publi- cation would preclude future publication. Supporting statement for printed embargo request: We submit a request for an embargo on both all of printed copy and electronic copy of this thesis for the same fixed period of two years as publication would preclude future publication. Chapter 2 of this thesis has already been accepted for publication by O.U.P., as a chapter in Mathematicians and their gods, eds. Mark McCartney and Snezana Lawrence. An embargo is also necessary in order to realize plans to publish other material from the thesis after submission. ELECTRONIC COPY Embargo on all or part of electronic copy for a period of two years on the following ground(s): publication would preclude future publication. Supporting statement for electronic embargo request: See statement for printed copy above. Signature of candidate ...................................... Date .................... Signature of supervisor ...................................... Date .................... Embargo granted: on both the printed and electronic copies of this thesis for the requested period of two years from the date the thesis is logged in the university library. Contents Abstract viii Acknowledgements ix Foreword xi 1 An introduction to P. G. Tait 2 1.1 Concise biography 2 1.2 Selected biographical highlights 9 1.2.1 Reputation as a lecturer . 9 1.2.2 The Tait Memorial Movement . 13 1.2.3 Contribution to the Royal Society of Edinburgh . 16 1.2.4 Involvement in controversy . 18 1.2.5 Family life . 19 1.2.6 Spiritual life . 23 2 The Unseen Universe (1875) 24 2.1 Introduction 24 2.1.1 The anonymity game . 25 2.1.2 Balfour Stewart (1828{1887): a biographical sketch . 29 2.2 The Christian man of science 32 2.2.1 The science versus religion debate: Tait and Stewart's contribution . 34 2.2.2 Tyndall's Belfast address . 35 2.3 The Principle of Continuity 39 2.4 The authors' hypotheses 40 2.4.1 Great First Cause, beginning of the universe and origin of life . 40 i 2.4.2 The end of the visible universe . 43 2.4.3 The existence of an unseen universe . 46 2.4.4 Superior and angelic intelligences . 49 2.4.5 Immortality and the spiritual body . 50 2.4.6 Divine action: miracles, the incarnation and the resurrection . 52 2.4.7 The authors' practical conclusion . 52 2.5 Reception of The Unseen Universe 52 2.6 String theory and M-theory anticipated 56 2.7 Closing remarks 56 3 Tait's statistical models 58 3.1 Introduction 58 3.1.1 Tait's pocket notebook . 58 3.1.2 Tait's contribution to statistics and probability . 60 3.1.3 James Matthews Duncan (1826{1890): a biographical sketch . 62 3.2 Fecundity, Fertility and Sterility (1866) 65 3.2.1 Fertility and fecundity of the mass of wives . 66 3.2.2 Fertility and fecundity of the average individual . 71 3.2.3 Relative fertility and fecundity of different races . 73 3.2.4 Tait's appreciation of good data . 75 3.2.5 The second edition (1871) . 75 3.2.6 Why Tait was writing in French . 79 3.3 Concluding remarks 79 3.3.1 Influence of Tait's Laws . 80 4 Tait's schoolboy introduction to complex numbers 82 ii 4.1 Introduction 82 4.1.1 Schoolboy association with Maxwell . 83 4.1.2 The Tait{Maxwell school-book . 85 4.1.3 Gloag's influence . 86 4.1.4 Significance of a particular school-book entry . 87 4.2 Bishop Terrot 88 4.2.1 Charles Hughes Terrot (1790{1872): a biographical sketch . 88 4.2.2 Devotion to mathematics . 90 4.2.3 Reputation in Edinburgh, contribution to the R.S.E. 92 4.2.4 Associations with the Edinburgh Academy . 93 4.3 Bishop Terrot's 1847 paper 95 4.3.1 Summary of the paper . 95 4.3.2 Tait's notes on Bishop Terrot's paper . 98 4.3.3 Tait's interest in the paper . 99 4.3.4 On priority: John Warren's influence . 101 4.4 Associated historical insights 105 4.4.1 The discovery of quaternions . 105 4.4.2 Warren's reference to Bu´eeand Mourey . 109 4.4.3 Tait's account of the developments . 110 4.5 Coming full circle 110 5 C.-V. Mourey's single science of algebra & geometry 111 5.1 Introduction 111 5.2 C.-V. Mourey: a biographical enigma 112 5.2.1 Self-funded publication . 115 5.2.2 Mourey's identity . 116 iii 5.3 Mourey's mathematics 127 5.3.1 Motivated by algebra, seeking algebraic reform . 127 5.3.2 Definitions and fundamental principles . 130 5.3.3 Applications, including a proof of the F.T.A. 144 5.3.4 Characteristic features of Mourey's mathematics . 165 5.4 Notable references to Mourey 166 5.4.1 Lef´eburede Fourcy (1787{1869): a biographical sketch . 166 5.4.2 Joseph Liouville (1809{1882): a biographical sketch . 167 5.4.3 Dissemination of knowledge of Mourey's contribution . 168 5.4.4 Hamilton and De Morgan's correspondence on Mourey, 1852{1862 . 180 5.5 Benefits of the algebraic perspective 194 Overall final remarks 196 Bibliographical essay 198 Appendices 201 A Family tree report for the Tait family 201 B Tait's poem on the Franco{Prussian War (1870) 225 C Schooldays at the Edinburgh Academy 230 D Transcription of Tait's notes from Terrot's paper 238 E Bu´ee's1806 paper and Gergonne's 2D table 255 F Hamilton's unpublished paper on the F.T.A. 264 G Mourey's terminology and notation: a look-up table 270 iv List of Figures 0.1 Peter Guthrie Tait: an etching by William Brassey Hole, 1884 . 1 1.1 Lieutenant Freddie Tait: a photograph by Marshall Wane, 1896 . 22 2.1 Tait's annotation of a review published in The Glasgow Herald . 27 2.2 Tait's annotation of a review published in The Nation ......... 28 2.3 Balfour Stewart: a sketched portrait . 29 2.4 Tait and Stewart's concentric model of the Great Whole . 48 3.1 Tait's pocket notebook . 58 3.2 An entry in French in Tait's pocket notebook . 59 3.3 Dr. Matthews Duncan: a sketched portrait . 63 3.4 Tait's graph of fecundity at different ages . 68 4.1 Charles Hughes Terrot: a portrait by Mason & Co. 90 4.2 Tait's drawing of the figure to accompany Cotes' theorem . 97 5.1 Title page of the first edition of Mourey . 114 5.2 Mourey's signature . 119 5.3 Technical drawings for Mourey's timber-profiling machine . 120 5.4 Technical drawings for Mourey's saw to cut standing trees .
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