Archive for the ‘Uncategorized’ Category
There is a short paragraph that has been puzzling me. It comes from the article “The Strangest Numbers in String Theory” by John C Baez and John Huerta, collected in “The Best Writing on Mathematics 2012” which I bought last November in a bookshop in Sydney, Australia—a bookshop of the type that no longer seems to exist in Canada.
The paragraph runs
“A while ago, David Gross, one of the world’s leading experts on string theory, put the odds of seeing some evidence for supersymmetry at CERN’s Large Hadron Collider at 50 percent. Sceptics say they are much less. Only time will tell.”
It is the last sentence that I have been struggling with: the idea of whether time will be able to tell us whether the probability is 50 percent or something much less.
The use of the term “odds” seems to indicate that the authors were thinking of a Bayesian rather the Frequentist model of probability and certainly that would be the only way to compute a prior probability: P(A) = P(A|B}P(B) / P(B|A). However, I still don’t see how to incorporate the time element into the equation.
I have long held a solipsist view and justified it with those moments when there is a continuity error in “reality” that subsequently needs to be justified. My attention wanders and I invoke a discontinuity in the behaviour of the “real” world. Afterwards it has to be justified.
In the past week, two beautiful confirmations have occurred.
Early one morning, I was typing an email to a number of people but primarily to a colleague in Germany. I finished the email just as someone came to my desk to talk to me. I turned back to my desk after the interruption, but still thinking of what was said, and pressed the SEND button on the email. Interestingly, just as my finger was moving towards the SEND key and about a second before I hit it, I saw the out-of-office reply from my German colleague arrive.
The second incident happened yesterday. I was in the office of a colleague here in Ottawa and his window faced west. I noticed that it was snowing quite heavily. I finished the conversation and, somewhat distracted, wandered over to the coffee room which lies on the east side of the building. Someone commented on the weather and I looked out at the clear sky. Certainly no snow.
Now, in a film, these would be “continuity errors”. They can be explained. Indeed they must be explained if I am to believe in an objective reality. The out-of-office email was a very delayed response to an email I had sent the previous evening. The weather really was such that the cloud stopped abruptly over our office building.
But the more likely explanation by far is the solipsist one: my brain wasn’t keeping up with its projection of reality because it was absorbed in other things.
It appears that the British judiciary is about to revert to the process of trial by ordeal. Or perhaps declaring that the earth is flat.
Consider the following. While you are not looking, Ethel tosses a coin and writes on a piece of paper whether it came down heads or tails. She puts the piece of paper in a sealed envelope and leaves it on the table. What is the chance that the piece of paper contains the word “heads”? Before you answer 50%, you must know that, in a court of law in Britain that no longer appears to be true.
The last clause of paragraph 35 in a recent judgement (http://www.bailii.org/ew/cases/EWCA/Civ/2013/15.html) says: “… and to express the probability of some event having happened in percentage terms is illusory”.
The implication is clear: we cannot assign probabilities to something that has already happened. If you think that the answer to Ethel’s piece of paper is 50% then that’s illusory: as Ethel has already sealed the envelope, the probability of the paper containing the word “heads” is either 0% or 100%. It can’t be 50%.
This is really exciting. The Rev Thomas Bayes died in 1761, leaving us with his wonderful formula P(A|B)P(B) = P(B|A)P(A). Clearly this notable historical event hasn’t reached the upper echelons of the British legal system yet. I wonder how long it will take.
And how many witches we will burn before it gets through.
I was fascinated this morning to read a review of Alan Rusbridger’s book Play It Again: An Amateur Against the Impossible. Rusbridger is an editor at the Guardian and information about his quest to learn Chopin’s Ballade No 1 in G minor, Op 23 in a year, while maintaining his day job can be found here:
I shall now buy a copy of the book.
I am interested because almost exactly 10 years ago, I decided that I should tackle Schubert’s Winterreise song cycle. I found a singing teacher and, with my wife, Alison, playing the accompaniments, I’ve been working on those 24 songs for those ten years. I have a 1 hour lesson each week and work at least 30 minutes each evening, either singing or listening to interpretations by different singers. Allowing for our occasional excursions into Die Schoene Muellerin, Schwanengesang and (horror!) Schumann’s Dichterliebe and holidays and business trips, I would estimate that Alison and I have spent at least 2000 hours working on those 24 songs. That’s only 83 hours per song so we have a long way to go.
There’s a long walk between a Chopin Ballade and a Schubert Song Cycle and, not being able to understand how anyone can play the piano’ (I have too much co-ordination to be able to do different things with my left and right hands), I can’t say which is harder. Or which is more rewarding.
The difficulty with the songs is projecting the song while not “living it”. I heard a Canadian singer on the radio just before Christmas. She was being interviewed about the calls that were made on her around Christmas to sing an incredibly syrupy song that I hadn’t heard before called “O Holy Night”. She told the interviewer that her interpretation of it had got a lot better since she stopped being a Christian. The interviewer double-took on this but the singer explained that, if the words mean something directly to the singer, then the singer doesn’t project them correctly to the audience.
My teacher says that to me, too. The trouble is that the songs in Winterreise are written in the first person. I see the signpost indicating the path from which no one has ever returned. It is my tears that fall onto the snow, are carried to the river and glow as they pass my ex-girl’s house. I see the lights on in the bedrooms of the bourgeois as I walk through their town. It is I who seeks out the stony and steep paths. I lost the girl! Not you.
It is easy to get sucked in and finish the song on my knees, hands pressed to my heart with tears pouring from my eyes, drowning the mice in our living room. It is much harder to tell the story and convey that emotion to the audience. Thomas Quasthoff (http://en.wikipedia.org/wiki/Thomas_Quasthoff) can do it. So can Thomas Hampson (http://www.thomashampson.com/), in spades. Perhaps the next 10 years will help me find the way. The way from which no one presumably ever returns.
I provide here a picture of perhaps the worst user interface I have seen for a long time. All of the Metro (nee Loeb) supermarkets in at least the Ottawa area have recently installed these interesting devices for credit and debit card purchases. The cashiers are really annoyed with them because each transaction apparently takes twice as long as it did with the older machines but that is not my gripe.
Firstly, something like 12% of Metro’s male customers cannot distinguish between the red and green buttons at the bottom. I am one of them. If, however, you look closely (very closely) you will see that the button on the right has the digit 0 engraved on it. 0 is used in computing and elsewhere to mean “false” or “no” so it is clear that that button means “no”, isn’t it? Well, actually no. That is the “yes” button.
But it gets better. At one point the system prompts one for the type of bank account: savings or cheque. To select the cheque account one is told to press F1. But when one presses the F key and then the 1 key it doesn’t work. Look more closely. At the top, there is a key marked “F1”. I have asked the cashiers when the F key is used and they don’t know.
So, of course, I complained to Metro. Their response was elegant. “Our pin pads are designed in compliance with the Americans with Disabilities Act (ADA) standard for visually impaired people.” I wrote back pointing out that, except for the obvious fact that everyone between Tierra del Fuego and Baffin Island is an american, I wasn’t an american and I am not disabled and so I couldn’t see what this had to do with the matter. I am still awaiting another response.
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.
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.
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.