Strange Telephone Call
Posted by: cwlh on: 17/03/2011
I’m puzzled. I’ve just had a telephone call purporting to come from the Conservative Party of Canada. I was asked whether I would vote for Mr Harper (the current leader of the Conservative Party and colleague of Bruce Carson who is currently under investigation by the RCMP for influence peddling) as Prime Minister.
Presumably, this was in the event that an election were to be called.
I made it clear that no force in heaven or earth would make me vote for someone who has so mislead Canadians. Mr Harper, fearing an election, brought the word “prorogation” onto everyone’s lips. He issued a handbook to new MPs to tell them how to make parliament dysfunctional (as though it wasn’t already). I could go on, and on, but won’t.
What interested me most was the idea that the Conservative Party believes that ordinary voters vote for the Prime Minister. That’s an interesting idea but not one in the Canadian democratic system.
Working Back
Posted by: cwlh on: 02/01/2011
I have always known that mathematics teaching in high schools is generally disastrous. I suspect that almost all non-specialists and even a majority of specialists could leave a high-school mathematics course with the idea that most mathematicians are dead, those who are alive spend their time doing arithmetic of enormous complexity and that mathematics was complete sometime around the time of Pythagoras (say about 1850). When one points out that most mathematicians who have ever lived are still alive, that one can do a mathematics degree without meeting a number other than 0 and 1 and that there are important mathematical problems that have remained unsolved since the 19th century there is a feeling of incredulity. And, I hope, a feeling of having been cheated by the school system.
Well, over the past few months I’ve had a similar road to Damascus experience with history and feel a great sense of having been cheated. I’ve recently read two sources:
- “Anaximander and the Origins of Greek Cosmology” by Charles H Kahn (ISBN 978-0-87220-255-9)
- “The Official History of Heraclius’ Persian Campaigns” by James Howard-Johnston (included in his book “East Rome, Sasanian Persia and the End of Antiquity”, ISBN 978-0-8607-8992-5)
The former I bought myself, the latter was recommended by Greg Fisher when I had lunch with him at the beginning of December. I await his book on the Sasanians with interest.
What the two books have in common is that they both deduce the existence and contents of documents that have been lost. As Kahn says: “Since the written work of Anaximander is known to us only by a single brief citation in a late author for whom the original was already lost, it may well seem an act of folly to undertake a detailed study of his thought”. But by a process somewhat akin to ded reckoning (“ded” for “deduced” is a term used by pilots) Kahn shews how the analysis of the output of later authors presupposes a common origin for much of the cosmological thought and traces that origin back to Anaximander. A fascinating intellectual journey built on a remarkable knowledge of the later literature.
Howard-Johnston makes a similar journey to deduce the existence of a lost prose/poem created by George of Pisidia from Heraclius’ official dispatches from the battlefield back to the citizens of Constantinople. His deductions start from Theophanes’ Chronographia and work backwards, demonstrating the links in the chain and holding them up for the reader to test their strength, to George of Pisidia. Another intellectual tour de force.
I had a good history teacher at school. All teachers were expected to read some inspirational text in our morning assemblies and I still remember his (he was not invited to do so again and was eventually sacked for his behaviour with a 6th form girl at the end-of-term dance and we had a collection to buy him a crate of beer): “Cromwell said, ‘put your trust in God; but mind to keep your powder dry’”. He was good (I remember his graphic account of what the crowd did with the bodies of Mussolini and his mistress) but not good enough to tell me that history was also the type of deduction that Kahn and Howard-Johnston were doing.
And if we’re misled about mathematics and history, what about the other subjects? Perhaps even biology isn’t totally mind-numbingly boring. Although that seems unlikely.
Text Appeal
Posted by: cwlh on: 21/07/2010
Once again life and literature have co-incided.
Let’s start with life.
A couple of evenings ago, in the gloaming, I was walking through the Bordeleau Park near our house (I pronounce this as “Bordello” but this is apparently not correct). I came across two young people sitting very close together on a bench. As I approached I realised that the girl was pretty and there was a boy sitting by her. Each was ignoring the other and busily typing on some form of mobile device: presumably sending text messages to each other. This is not what we used to get up to on park benches when I was a boy but one must, I assume, keep up with changing times.
And now literature.
Earlier this year I paid a flying visit to the UK and, on my way back through Heathrow, I bought a copy of Private Eye: the issue for 5th-18th March 2010. This turned up in a pile of paper yesterday and I was thumbing through it and came across a joke on page 4. It shews a man and woman in bed together, each holding a portable (and unattached) device and busily typing text messages.
A Great Week in Court
Posted by: cwlh on: 03/04/2010
- In: General | Software
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This week has seen two significant court cases resolved in a manner which give me increased confidence in the UK’s and the USA’s legal systems (Canada, where I live, works on the principle that if the Prime Minister thinks that a person is a terrorist then that person has to be locked up).
On a more positive note Simon Singh MBE has been cleared in London of libelling the British Chiropractic Association in saying that there was no shred of evidence that their treatments could help treat children with colic, sleeping and feeding problems, frequent ear infections, asthma and prolonged crying. As you will know, there have been online petitions and pressure on the UK government to make the UK’s libel laws more reasonable and thereby cut down on libel tourism to the UK.
The second positive result came from Utah where a jury of people with no knowledge of the travails between SCO, IBM and Novell (with counterpoint from Microsoft and others) regarding UNIX and Linux sat down to determine whether SCO’s predecessor (Santa Cruz) did, or did not, get the UNIX copyrights from Novell back in 1995. I am frankly amazed that 12 people, particularly 12 people from Utah where SCO is based, who knew nothing of the argument could be found for the jury but apparently they could. Of course, Groklaw has changed the way in which technological cases can be analysed by the community, by the people who actually know. SCO felt, however, and I tended to agree, that if they could get the case (already lost elsewhere) in front of a non-technologically adept bunch of Utahians in a jury box then they could win. But they lost. As Novell said:
“Novell is very pleased with the jury’s decision confirming Novell’s ownership of the Unix copyrights, which SCO had asserted to own in its attack on Linux,” a Novell spokesperson said. “Novell remains committed to promoting Linux, including by defending Linux on the intellectual property front.”
So this has been a good week in the courts. At least in the UK and USA. Perhaps next week Mohamed Harkat will be exonerated.
Opus Minus
Posted by: cwlh on: 04/01/2010
One may talk about “being unable to put it down”, but I have actually read few books at one sitting. Possibly a whodunnit or two on a long, boring flight, but nothing else.
Until yesterday.
In Vol. 31 No. 13 · 9 July 2009 of the London Review of Books, the world’s most exciting magazine, Caroline Walker Bynum reviewed a book. Having read the review I added the book to my “Wish List” on Amazon and forgot about it. As if, appropriately, by magic, it turned up in my Christmas stocking and lay with the pages uncut (an affectation, I admit, and according to that link, an inaccurate affectation) until yesterday when I idly picked it up. And read until the last page.
It’s entitled The Natural and the Supernatural in the Middle Ages and was written by Robert Bartlett as a hard copy of the Wiles Lectures he gave at the Queen’s University in 2006. There are four lectures, each copiously footnoted in the book although presumably not during the lectures themselves, and each maintaining the informality of speech in the written word, complete with the odd throw-away joke.
I can’t compete with Bynum’s review that first piqued my interest (all of the LRB reviews and much else are now online for your delight although I won’t be getting rid of my paper copies yet) but I would like to quote Bartlett’s provocative introduction to the fourth lecture:
The trouble with contemporary Western education is that far too little emphasis is placed on science, mathematics and foreign languages, which are the essential foundations of research and which have direct practical benefits. … Especially now, when relations with the Muslim world are so crucial, it is a disgrace that there are so few diplomats trained in the arabic language.
Yes, you guessed, a summary of Roger Bacon’s thoughts, written in 1267.
And it came as a shock to find my namesake, St Christopher, portrayed as a doghead. I frequently saw a less cynocephalic interpretation of him carrying the baby across the river in St Mary’s church in Huntingdon when, as a small child, I accompanied my father in stoking the boiler there. I would have run screaming from the one depicted in the book (and on the web site above). The story of carrying a load that gets increasingly heavy as time passes, particularly resonates with me.
Barlett’s book presents not only an authoritative discussion of the balance between the natural and the supernatural but also poses deep questions that need to be answered today; the primary of these being how we relate to people with beliefs that we do not share. This is posed in the context of understanding the reasoning of the medieval mind but also, I suppose, covers my reprehensible behaviour in encouraging Jehovah’s Witnesses into the house so that I can tease them.
By the way, if you want them to grow well, make sure that your olive trees are planted by virgins and use sealskin to protect them against lightning.
Cartesian Gliding
Posted by: cwlh on: 25/10/2009
I have come across two thought-provoking notices over the last few days.
I am informed, by a normally reliable witness, that the first appears in the women’s toilet in the Chapters Bookshop on the corner of Rideau Street and Sussex Drive. It is inscribed on the wall and reads
I think, therefore I am. Aristotle.
The second appears more openly in the window of a hairdresser on Beechwood (a street in Vanier, Ottawa rather than a bosky grove). It says
Say ‘NO’ to thermal abuse.
I have no recollection of ever having said “yes” to thermal abuse and, as a glider pilot, I have abused many. I remember one of my instructors saying that it was incredible how I had been able to fly across the floor of a valley in central Wales, missing every one of the thermals. The problem, of course, is that if you catch the edge of a thermal with your wing, it lifts the wing and tends to throw you away from the thermal. The trick is to detect the tiny upward movement of the wing and immediately turn into the thermal. Thereby gaining lift.
It it still a puzzle why anyone would be that worried about thermals but the quotation from Aristotle is even more thought-provoking.
I assume that the versions of Aristotle that we have, translated and interpreted by people like Abū ‘Alī al-Ḥusayn ibn ‘Abd Allāh ibn Sīnā’ (OK, I looked Avicenna’s real name up in Wikipedia), have had his sceptical side suppressed. It is good to see that someone, and someone who is female and who frequents Chapters, has a more accurate version.
Pancakes and Ham Sandwiches
Posted by: cwlh on: 21/06/2009
Browsing in our excellent, local second-hand bookshop a week or so ago I came across a book I should have known but didn’t: The Mathematical Experience (Study Edition) by Davis, Hersh and Marchisotto. Browsing in that book today I came across a theorem I should have known but didn’t: the “pancake theorem”, the two-dimensional version of the “ham sandwich theorem”.
The pancake theorem says that, given any two closed curves in the plane, there is a single straight line that bisects the area of both of them. The proof is straight-forward if you accept the concept of continuous functions and I see from the link above that it also appears in Courant and Robbins, an old favourite of mine.
However, the point of demonstrating the proof was that there is one step at which students tend to balk. They eat the lemma and the definition of two functions p(theta) and q(theta) and then the next step is “define r(theta) = p(theta) – q(theta)” and this is where they suddenly dig in their heels.
Of course, at heart you can’t argue with a definition. If I want to define r to be (p – q) then that’s what it is. What fascinates the author of the article is why the students block at that point. And, of course, it’s the arbitrariness of it in what he calls “proof by coercion” that causes the sticking point. As it says in the Mathematician’s Miscellany: “but please Sir, what if x is not the number of sheep in the field?”
The author then describes a different proof that avoids the arbitrary definition and reports on much greater success with students when using it.
I think that it’s a slightly different issue. Although I’d never seen the original proof (the one with r = (p – q)) before, I found that, when I was about 25% of the way through, I could see where it was going and only needed to skim-read the rest before I felt comfortable I could reproduce it: it fell into a well-known pattern and I didn’t need the details. For a student coming to this type of proof for the first time, the “let r = p – q” must feel like another item to be pushed onto an already over-loaded stack.
When a good pianist comes to sight-read a page of music she knows immediately what notes can be left out while retaining the musicality of the whole. I can’t remember ever having been taught how to read a proof—it was always assumed that one started at the top and worked through line by line until one reached the end. And arbitrary things like “let r = p – q” were meaningless and annoying: “WHY!?”. My basic mathematical education took place a long time ago and the book originally came out in 1981. Perhaps things are a lot better in secondary school mathematics these days.
Anyway, I think the term “study edition” in the title means that the book includes questions. And there’re a couple at the back that would reward some thought:
- “Suppose you were able to travel back in time to meet some like Polya, Descartes or Pythagoras. Suppose he was discouraged and was considering giving up the pursuit of mathematics. How would you encourage him?”
- “Discuss the relationship between belief and information.”
The British Chiropractic Association: Quack, Quack
Posted by: cwlh on: 05/06/2009
I imagine everyone who reads this blog (indeed everyone who can read) has by now heard of the terrible injustice being done to Simon Singh in Britain’s law courts by the British Chiropractic Association. If not, there are plenty of articles about the case on almost every science-based blog and even some of the better newspapers (e.g., Discover and The Guardian). I have nothing but outrage to add but wanted to post this so that I could include the button:
Deus ex Machina (literally)
Posted by: cwlh on: 21/04/2009
Well, it appears that I angered the new gods yesterday.
We’ve had a very dry Spring in Ottawa this year with cloudless skies for days on end. Last night I went to a student’s home to do some private groundschool teaching and, unexpectedly, it started to pour with rain. When I left 90 minutes later it was still pouring and even now, 14 hours later, it’s still raining.
I was wondering what had caused this when I realised my terrible sin: in an attempt to find my student’s house I had asked Google for directions. And then I didn’t follow them. I thought up a better route for myself and thereby displeased Google.
Lands of Priests and Caliphs
Posted by: cwlh on: 28/02/2009
- In: General
- 2 Comments
I walked out of a cafe about half an hour ago after lunch, climbed into my car and turned on the radio. On CBC radio 2 the opera from the New York Metropolitan Opera House is broadcast on Saturday afternoons and on radio 1 a programme entitled “Definitely Not The Opera” runs in parallel. My radio was tuned to radio 1 and I was pitched into the middle of an interview with an artist from Winnipeg.
He said that he had been thinking about frozen rivers (it’s that time of the year when I begin to wonder whether there is any other sort but the dynamiting of the Rideau River outside our house did begin today—the harbinger of Spring) and how the ice was just frozen water. The river had effectively been stopped (frozen?) in time. He said that books contained ideas frozen in time and he had therefore constructed a work of art combining the two. I missed the part of the interview where the art work was described but it presumably included books on the Assiniboine River.
That statement about books containing ideas frozen in time jarred with me. Many, many years ago I read a book (by Anthony Hopkins?) on music that described Sonata Form. He likened the form to walking through a house that you don’t know but are thinking of buying. You enter the hall and get a first impression. You then tour the rest of the house and end up back in the hall. You see the hall again (the recapitulation) but because you now know the rest of the house you see it in a different way. In a sonata you hear the theme again during the recapitulation but, because of the journey you’ve made in the meantime, it means more to you: the notes are the same (more-or-less) but the context is different.
Surely books are the same: their ideas are not frozen because ideas have to be interpreted. At the moment I’m rereading Gerald Priestland’s autobiography, “Something Understood” which I last read at least 15 years ago and Dimitri Gutas’ “Greek Thought, Arabic Culture: The Graeco-Arabic Translation Movement in Baghdad and Early Abbasid Society” which I last read about 6 months ago.
In each case, the ideas I read during this recapitulation are new, not because the words have changed, but because I have been through other rooms and can now see these books in a new light. The words are the same but the context is different.
And it’s not just the ideas that the books contain. Sometimes I pick up a book from my shelves and find the unmistakable signs that, at some time in the past, I dropped it in the bath (I spend hours lying in the bath reading and sometimes books suffer). That too is part of the context that I bring to the next reading.
At the risk of being accused (by one particular colleague whom I won’t name) of being a relativist, the idea that books are ideas frozen in time really seems indefensible.
