From the 18th century until 1909, students at Cambridge University took a compulsory series of examinations, called the Mathematical Tripos, named after the three-legged stool that candidates originally sat on. Until the mid-18th century, these examinations were conducted orally, and only became written examinations over faculty protests. Apparently, not everyone believed that written examinations were the best or fairest way to test mathematical abilities, a view which would amaze many contemporary people – although oral examinations in mathematics are still commonly used in some countries with very strong mathematical traditions, such as Russia and the other states of the former USSR.
The Tripos became a notable annual public event in the 19th century, with The Times newspaper publishing articles and biographies before each examination on the leading candidates, and then, after each examination, the results. There was considerable public interest in the event each year, not just in Cambridge or among mathematicians, and widespread betting on the outcomes.
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Archive for the ‘Religion’ Category
Page 8 of 9
Evil intentions
A commentator on Andrew Sullivan’s blog asks: Where is the Darwinian theory of evil? Because modern biologists this last century or so have been very concerned to avoid teleological arguments, modern biology has still only an impoverished theory of intentionality. Living organisms are focused, in the standard evolutionary account, on surviving themselves in the here-and-now, apparently going through these daily motions unwittingly to ensure those diaphonous creatures, genes, can achieve THEIR memetic goals. Without a rich and subtle theory of intentionality, I don’t believe one can explain complex, abstract human phenomena such as evil or altruism or art or religion very compellingly.
Asking for a theory of intentions and intentionality does not a creationist one make, despite the vitriol often deployed by supporters of evolution. One non-creationist evolutionary biologist who has long been a critic of this absence of a subtle theory of intentionality in biology is J. Scott Turner, whose theories are derived from homeostasis he has observed in natural ecologies. I previously discussed some of his ideas here.
References:
Alfred Gell [1998]: Art and Agency: An Anthropological Theory. Oxford, UK: Clarendon Press.
J. Scott Turner [2007]: The Tinkerer’s Accomplice: How Design Emerges from Life Itself. Cambridge, MA, USA: Harvard University Press.
Speech acts
Thanks to Normblog, I have seen Terry Eagleton’s recent interview on matters of religion, in which he is reported as saying:
All performatives imply propositions. There’s no point in my operating a performative like, say, promising, or cursing, unless I have certain beliefs about the nature of reality: that there is indeed such an institution as promising, that I am able to perform it, and so on. The performative and the propositional work into each other.
Before commenting on the substance here (ie, religion), some words on Eagleton’s evident mis-understanding of speech act theory and the philosophy of language, a mis-understanding that should have been clear if he tested his words against his own experiences of life. His statement concerns performatives — utterances which potentially change the state of the world by their being uttered. Examples include promises, commands, threats, entreaties, prayers, various legal declarations (eg, that a certain couple are now wed), etc. But mere propositional statements (that some description of the world is true) may also change the state of the world by the mere fact of being uttered.
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Nicolas Fatio de Duillier
Nicolas Fatio de Duillier (1664-1753) was a Genevan mathematician and polymath, who for a time in the 1680s and 1690s, was a close friend of Isaac Newton. After coming to London in 1687, he became a Fellow of the Royal Society (on 1688-05-15), as later did his brother Jean-Christophe (on 1706-04-03). He played a major part in Newton’s feud with Leibniz over who had invented the differential calculus, and was a protagonist all his life for Newton’s thought and ideas.
Continue reading ‘Nicolas Fatio de Duillier’
Thinkers of renown
The recent death of mathematician Jim Wiegold (1934-2009), whom I once knew, has led me to ponder the nature of intellectual influence. Written matter – initially, hand-copied books, then printed books, and now the Web – has been the main conduit of influence. For those of us with a formal education, lectures and tutorials are another means of influence, more direct than written materials. Yet despite these broadcast methods, we still seek out individual contact with others. Speaking for myself, it is almost never the knowledge or facts of others, per se, that I have sought or seek in making personal contact, but rather their various different ways of looking at the world. In mathematical terminology, the ideas that have influenced me have not been the solutions that certain people have for particular problems, but rather the methods and perspectives they use for approaching and tackling problems, even when these methods are not always successful.
To express my gratitude, I thought I would list some of the people whose ideas have influenced me, either directly through their lectures, or indirectly through their books and other writings. In the second category, I have not included those whose ideas have come to me mediated through the books or lectures of others, which therefore excludes many mathematicians whose work has influenced me (in particular: Newton, Leibniz, Cauchy, Weierstrauss, Cantor, Frege, Poincare, Pieri, Hilbert, Lebesque, Kolmogorov, and Godel). I have also not included the many writers of poetry, fiction, history and biography whose work has had great impact on me. These two categories also exclude people whose intellectual influence has been manifest in non-verbal forms, such as through visual arts or music, or via working together, since those categories need posts of their own.
Teachers & lecturers I have had who have influenced my thinking include: Leo Birsen (1902-1992), Sr. Claver Butler RSM (ca. 1930-2009), Burgess Cameron (1922-2020), Sr. Clare Castle RSM (ca. 1920- ca. 2000), John Coates (1945-2022), Dot Crowe, James Cutt, Bro. Clive Davis FMS, Tom Donaldson (1945-2006), Gary Dunbier, Sol Encel (1925-2010), Felix Fabryczny de Leiris, Claudio Forcada, Richard Gill (1941-2018), Myrtle Hanley (1909-1984), Sr. Jennifer Hartley RSM, Chip Heathcote (1931-2016), Hope Hewitt (1915-2011), Alec Hope (1907-2000), John Hutchinson, Marg Keetles, Joe Lynch, Robert Marks, John McBurney (1932-1998), David Midgley, Lindsay Morley, Leopoldo Mugnai, Terry O’Neill, Jim Penberthy* (1917-1999), Malcolm Rennie (1940-1980), John Roberts, Gisela Soares, Brian Stacey (1946-1996), James Taylor, Frank Torpie (1934-1989), Neil Trudinger, David Urquhart-Jones, Frederick Wedd (1890-1972), Gary Whale (1943-2019), Ted Wheelwright (1921-2007), John Woods and Alkiviadis Zalavras.
People whose writings have influenced my thinking include: John Baez, Ole Barndorff-Nielsen (1935-2022), Charlotte Joko Beck (1917-2011), Johan van Bentham, Mark Evan Bonds, John Cage (1912-1992), Albert Camus (1913-1960), Nikolai Chentsov (1930-1992), John Miller Chernoff, Stewart Copeland, Sam Eilenberg (1913-1998), Paul Feyerabend (1924-1994), George Fowler (1929-2000), Kyle Gann, Alfred Gell (1945-1997), Herb Gintis, Jurgen Habermas, Charles Hamblin (1922-1985), Vaclav Havel (1936-2011), Lafcadio Hearn (1850-1904), Jaakko Hintikka (1929-2015), Eric von Hippel, Wilfrid Hodges, Christmas Humphreys (1901-1983), Jon Kabat-Zinn, Herman Kahn (1922-1983), John Maynard Keynes (1883-1946), Andrey Kolmogorov (1903-1987), Paul Krugman, Imre Lakatos (1922-1974), Trevor Leggett (1914-2000), George Leonard (1923-2010), Brad de Long, Donald MacKenzie, Saunders Mac Lane (1909-2005), Karl Marx (1818-1883), Grant McCracken, Henry Mintzberg, Philip Mirowski, Michel de Montaigne (1533-1592), Michael Porter, Charles Reich (1928-2019), Jean-Francois Revel (1924-2006), Daniel Rose, Bertrand Russell (1872-1970), Pierre Ryckmans (aka Simon Leys) (1935-2014), Oliver Sacks (1933-2015), Gunther Schuller (1925-2015), George Shackle (1903-1992), Cosma Shalizi, Rupert Sheldrake, Raymond Smullyan (1919-2017), Rory Stewart, Anne Sweeney (d. 2007), Nassim Taleb, Henry David Thoreau (1817-1862), Stephen Toulmin (1922-2009), Scott Turner, Roy Weintraub, Geoffrey Vickers VC (1894-1982), and Richard Wilson.
FOOTNOTES:
* Which makes me a grand-pupil of Nadia Boulanger (1887-1979).
** Of course, this being the World-Wide-Web, I need to explicitly say that nothing in what I have written here should be taken to mean that I agree with anything in particular which any of the people mentioned here have said or written.
A more complete list of teachers is here.
Obama Felix
I have never thought much of historian Niall Ferguson’s ideas. For years he has been arguing that America and the West suffer from too little religion, while simultaneously arguing that the Islamic world suffers from too much. One is tempted to ask for this spiritual Laffer Curve to be quantified and differentiated, so that we can determine the optimum level of religion for our society once and for all. At least we could then stop having to accuse him of inconsistency, which surely must wrankle him.
But, despite the shere impossibility of the task, he has managed to plumb even shallower waters. Barack Obama is like Felix the Cat in that firstly . . . ahem, how do I put this without upsetting those of you who’ve been asleep at the back of the class these last few months? . . . apparently, they are both black. Are such superficialities bordering on racism the content of lectures these days at Harvard Business School? Shame that some adult at the FT did not object before publication.
And, as further evidence of his tin-ear for conversation in the public square, his defence is a doubling-down.
Recent reading 2: Spooks
For the record, herewith brief reports of recent reading of books on espionage:
- Michael Holzman [2008]: James Jesus Angleton: The CIA, and the Craft of Counterintelligence. (Amherst, MA, USA: University of Massachusetts Press). A fascinating topic, not given justice in this poorly-written account. Sentence without verbs. Not fond of. I. The author claims to have undertaken interviews with key players (although I only noticed one reference to such an interview), but the book is almost entirely written from secondary sources. This means it has no new insights. On some issues, the book is not up to date – eg, on the Nosenko affair, the author seems not to have seen Bagley’s book (see below), published a year before. The writing is very vague about dates (a rather important failing for a writer of a history book), and lots of information is only provided en passant; for example, we only learn about Angleton’s first child well after its birth. Perhaps that is an editor’s failing, as much as an author’s. There are worse problems: the author appears to have a very unsophisticated understanding of marxism (p. 103), and his description of the Bay of Pigs invasion puts all the blame on Bissell and colleagues (p. 187), when some of it rightly belongs in the White House, including with JFK himself. Relying on secondary sources and without new insights, Holzman could have shown us how Angleton’s literary training helped him in the world of intelligence. Despite repeated claims that his literary education did help, we are not ever shown it doing so, nor given a detailed explanation of how it helped. To show us this, Holzman would have needed to provide a detailed presentation of at least one theory of intelligence and counter-intelligence; this is something that would have been very interesting and very useful in itself, yet is also lacking from the book.
- Tennent H. Bagley [2007]: Spy Wars: Moles, Mysteries, and Deadly Games. (New Haven, CT, USA: Yale University Press). An insider’s account of the Nosenko affair, which I have blogged about here and here. Bagley argues compellingly that Yuri Nosenko was a KGB plant, not a genuine defector. From this he concludes that CIA should not have accepted him as a genuine defector. As I argue, it is not certain that CIA did in fact accept him as such, despite what it looks like, and the benefits of accepting him (or appearing to accept him) may have outweighed the costs. An intelligence agency needs to think through the wider consequences of its beliefs and of what are believed by others to be its beliefs, in addition to considerations of simple truth and falsity.
- S. J. Hamrick [2004]: Deceiving the Deceivers: Kim Philby, Donald Maclean and Guy Burgess. (New Haven, CT, USA: Yale University Press). Hamrick argues that British intelligence knew that Philby, Burgess and Maclean were Soviet agents several years before their public exposures, and during this period used them to securely transmit messages — both information and disinformation — to the Soviet leadership, knowing it would more likely be believed if it came from the Soviets’ own agents. If Holzman’s book about Jim Angleton (above) had included some discussion of theories of intelligence and counter-intelligence, this is just the type of case that such a theory would seek to account for. The (alleged) facts of Hamrick’s book are fascinating, but the book itself is poorly-written, repetitious, acronym-rich and comes with added right-wing tirades. There are even anti-Catholic tirades against the novelist Graham Greene and —for goodness sake! — the poet-priest Robert Southwell SJ (p. 32), who was executed in 1595. These tirades are not only out-of-place here, but replete with errors. One has to wonder at the immense power of a Catholic missionary that he can still provoke such an irrational rant four centuries after his murder by Elizabeth’s police-state. I am certainly one of Southwell’s admirers (see, for example, here), but there cannot be more than a score or two of people alive who even know of him.
- Valerie Plame Wilson [2008]: Fair Game: How a top CIA Agent was betrayed by her own Government. (New York, USA: Simon and Schuster). Published with CIA redactions shown. Very well-written and her life story is fascinating. Shame about her Government.
- Tim Weiner [2007]: Legacy of Ashes: The History of the CIA. (London, UK: Allen Lane). The best single-volume history of CIA, at least as far as an outsider can judge. Well-written and thorough, although I would have liked more on Africa. On page 80, Weiner claims the only two successful CIA-sponsored coups were both executed under Eisenhower, but what of Mobutu Sese Seko in Zaire in 1965 (see Devlin’s book below), and Augusto Pinochet in Chile in 1973 (and perhaps Malcom Fraser in Australia in 1975)?
- Larry Devlin [2007]: Chief of Station, Congo: A Memoir of 1960-67. (New York, USA: Public Affairs). An insider’s account of the role of CIA in putting Mobutu into power in Zaire. Having once met Mobutu, I found this account fascinating, although, of course, I have no idea how honest or comprehensive it is.
- Markus Wolf and Anne McElvoy [1997]: Man Without a Face: The Autobiography of Communism’s Greatest Spymaster. (New York, USA: Public Affairs). A riveting read, which I read in a single day. Markus Wolf presents himself, I am not sure how sincerely, as a reform Communist, an admirer of Andropov and Gorbarchev.
- David C. Martin [1980]: Wilderness of Mirrors. (Guildford, CT, USA: The Lyons Press). A detailed account of the relationship between Jim Angleton and Bill Harvey. Well-written and an easy read. However, the chronology of the events in the George Blake affair (pp. 100-102) is inconsistent.
- Milt Beardon and James Risen [2003]: The Main Enemy: The Inside Story of the CIA’s Final Showdown with the KGB. (New York, USA: Ballantine Books). Although mostly riveting, I skipped over the history of 1980s Afghanistan. Reading of KGB watching CNN during the attempted coup of August 1991 to learn what has happening was very amusing. The book would have been better if more had been included on the post-1990 period: just when events get interesting, the book ends.
Newton and scientific publication
While on the subject of Isaac Newton, here are several statements by historian Scott Mandelbrote on Newton’s attitude to the public dissemination of his work. The more we know of Newton, the less we should consider him a scientist in the modern meaning of the word.
His [theological investigation] was a voyage of personal discovery; even the Principia required Halley’s exertions as a midwife to bring them to light. Newton might share his religious opinions with other members of the remnant, as he did in his letters to Locke, but he worried about the consequences of their wider dissemination: ‘I was of opinion my papers had lain still & am sorry to heare there is news about them. Let me entreat you to stop their translation & impression so soon as you can for I designe to suppress them.’ Newton’s concern may have reflected fear of being discovered to hold unorthodox opinions, but it was also the product of religious motives. Not everyone could be expected to comprehend ‘strong meat’, which was intended for personal consumption, and which might be wasted on others.” (p.299)
His [Newton’s] theology pervaded his alchemy, in his analysis of the Emerald Tablets of Hermes Trismegistus, and in turn his alchemy suggested to him how matter might be understood physically. A true understanding of the uses of language enabled Newton to introduce astronomical calculation into his chronological writings, and to complete his mathematical arguments with theological references:
[pagebreak]
. . . .
Mathematics was God’s language; the language of the prophets communicated God’s purposes and ‘times’ to men. Newton felt it was his duty to understand and to reconcile the two, to decipher the hieroglyphs which corrupted religion and learning had obscured. The problems of mathematics ended in the solutions of divine majesty, and mathematical language solved the theological problem of describing Newton’s Arian interpretation of the relations within the Trinity:
. . .
Newton’s natural philosophical and theological discoveries removed the obscurities from divine language, in the books of nature and of scripture. In the life of the true believer, the two could not be separated. But most had to be content with the milk for babes, because Newton’s own language was beyond them.” (pp. 300-301).
Reference:
Scott Mandelbrote [1993]: ‘A dute of the greatest moment’: Isaac Newton and the writing of biblical criticism. British Journal of the History of Science, 26: 281-302.
On knowing
I have long thought the many of the members of the cult of militant anti-religionists — people like Richard Dawkins and Christopher Hitchens — have been assailing a straw-man. Their target is religious belief of a particularly narrow, fundamentalist kind, and as Terry Eagleton among others have noted, this target is a gross caricature of most of the people who practice or believe religious ideas. The main argument of the anti-God cult is usually that religious beliefs are held without evidence.
First, as the writer Karen Armstrong discusses today, for most people, religion is about doing, not about knowing. It’s really only philosophers and their street-brawling imitators who obsess over beliefs. Indeed, because doubt and scepticism are integral parts of most of the world’s religions, religious practice may not necessarily start with belief, but in fact end with it: Belief can be what comes after you practice spiritual exercises long enough, not necessarily what causes you to practice them. People do zazen or yoga not because they are already enlightened, but to achieve enlightenment.
Second, the issue of evidence is problematic in these diatribes against religion. It is simply not the case that there is no evidence for religious or spiritual ideas, or that such ideas are only supported by the irrational or the feeble-minded. Most people who proclaim any adherence to religious or spiritual ideas will assert they have evidence for a realm beyond or outside the material world. This evidence is usually of the form of direct personal contact with a spirit world or with spiritual entities, as for example, in the experience of Janet Soskice or the physicist Oliver Lodge. Anyone who has spent any extended period in Africa or in East Asia will know people — sober, rational, and intelligent — who have had, and continue to have, what they experience as direct contact and interaction with spiritual entities.
Of course, such direct, personal evidence is usually not replicable at will, nor observable to others. That makes it invalid as the basis of science, which is a shared undertaking, but does not make it invalid as evidence for personal beliefs or actions. Knowledge of the existence of things unseen can be obtained by merely being in the presence of such entities, as the Sufi philosopher and founder of Illuminationism, Shahab al-Din Suhrawardi (1155-1191) argued in the 12th century. Knowledge-from-being-in-the-presence-of is a valid form of knowing, just as knowledge-from-tasting is. Our subjective personal tastes in food and drink, say, or our subjective experience of being in love, are also not observable to others, but that does not invalidate them as evidence for our beliefs or as a rational basis for our actions. When I say I prefer coffee to tea, this is an inference based (usually) on my personal, subjective reactions to the tastes of the two different liquids. Only I know whether this inference is based on true reactions or not; if I am a sufficiently-clever actor, no one will ever be able to conclude anything about my reactions to the respective tastes other than what I claim.
It may be that experiences understood subjectively as contact with spiritual entities can be replicated in the laboratory by stimulating particular parts of the brain, as recent experiments appear to show. But it does not follow from such research that all religious experiences are due to similar mental stimulation, just as using implanted electrodes to create the subjective experience of the taste of coffee would not thus imply the non-existence of coffee.
In closing then, I wonder which is more rational: to commit to certain religious beliefs (or undertake a spiritual practice) based on one’s personal subjective experiences with the divine OR to devote one’s career to studying mathematical models of additional space-time dimensions, dimensions for which there is as yet no evidence whatsoever, not even any subjective personal experience? If Dawkings and Hitchens were really worried about irrational beliefs, they should be attacking the practitioners of String Theory and M-Theory.
References:
Mehdi Amin Razavi [1996]: Suhrawardi and the School of Illumination. London, UK: Routledge.
POSTSCRIPT (2017-06-04): In a New Yorker profile of business author Clayton Christensen, he is quoted regarding his daily reading of The Book of Mormon:
One evening in October, 1975, as I sat in the chair and opened the book following my prayer, I felt a marvelous spirit come into the room and envelop my body. I had never before felt such an intense feeling of peace and love. I started to cry, and did not want to stop. I knew then, from a source of understanding more powerful than anything I had ever felt in my life, that the book I was holding in my hands was true.” (Page 90)
Larissa MacFarquhar [2012]: When Giants Fail. The New Yorker. 14 May 2012, pp.84-95.
The Supremes
While on the subject of the US Supreme Court nominations, the New Yorker’s Jeff Toobin has a nice historical analysis of diversity on the US Supreme Court here.
In making nominations to the Supreme Court, Presidents care about diversity, which is a relatively new term for an idea that is nearly as old as the Court itself. In the early days of the republic, when regional disputes were the foremost conflict of the era, nominees were generally defined by their home turfs. So Presidents came to honor an informal tradition of preserving a New England seat, a Virginia seat, a Pennsylvania seat, and a New York seat on the Court. In the nineteenth century, as a torrent of European immigrants transformed American society, religious differences took on a new significance, and Presidents used Supreme Court appointments to recognize the new arrivals’ growing power. In 1836, Andrew Jackson made Roger B. Taney the first occupant of what became known as the Catholic seat on the Court, and that tradition carried forward intermittently for more than a century, with Edward White, Joseph McKenna, Pierce Butler, Frank Murphy, and William J. Brennan, Jr., occupying the chair. In 1916, Woodrow Wilson nominated Louis D. Brandeis, establishing the Jewish seat, which later went, with brief overlapping periods, to Benjamin N. Cardozo, Felix Frankfurter, and Abe Fortas.
. . .
At the Court, as in American life, the rules of diversity have changed. Regional differences faded long ago. The fact that two Arizonans, O’Connor and William H. Rehnquist, served together for almost a quarter century mattered little to anyone. Religious tensions have also cooled. By the time Bill Clinton named Ruth Bader Ginsburg and Stephen G. Breyer to the Court, the fact that both are Jewish (and replaced non-Jewish predecessors) was little more than a curiosity. If Sotomayor is confirmed, there will be six Catholics on the Court, which is also of minor significance. George W. Bush appointed John G. Roberts, Jr., and Samuel A. Alito, Jr., because they are conservative, not because they are Catholic. (The Catholic Brennan was the Court’s greatest liberal.) More than anything, it seems clear that the President saw in Sotomayor a kindred spirit—a high achiever from a humble background who reflects, as best as can be determined, his own brand of progressivism.”