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.
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.
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)
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.