A Short History of Infinity

 

    Brian Clegg. A Short History of Infinity (2003) The title describes the book, and Clegg does a good job of introducing the “interested reader” to the mathematical concepts of infinity, and the many mathematicians who contributed to and developed the modern concepts of countable and uncountable infinities (terms he doesn’t use).
      The basic ideas are in fact simple: two sets are the same size (cardinality) if you can match them element for element with no exceptions and none left over. Using this rule you discover that the set of whole numbers is the same size as the set of  square numbers, or any other set whose elements can be defined in terms of some operation on the whole numbers.
      The trouble starts when you are stuck at the stage of thinking of numbers as somehow real, just as kittens and trees are real. Not a problem with the whole numbers or the rational fractions: you see five pies on the kitchen counter, each cut into six pieces, so you 30 pieces of pie, or 30/6ths of a pie. But in the 15th  and 16th centuries mathematicians began to work with numbers that you couldn’t point to in this way. We need and use “imaginary” numbers because they work, they enable us to solve problems in both pure and applied math that we couldn’t deal with otherwise. Clegg needs us to accept the weirdness of infinite numbers, so he spends several chapters on imaginary numbers.
     The first of these was negative numbers. Here Clegg  (who is above all a compiler of information) seems to have missed something: a negative number can be pointed to: if you have -5 dollars, then you owe $5 to someone. Negative numbers may have been discovered as points on the number line, enabling solutions to otherwise insoluble equations, but bookkeepers made them real.
     The square root of -1 (i) was the next “imaginary” number to be discovered (or invented:  the verb you use reveals your metaphysics). Clegg makes a big thing of this one, too, but he asks us to accept on faith his assurance that it is used every day by engineers. A couple of examples would have been helpful.
     Finally, he comes to Cantor, whose mental health was fragile, and whose feud with Kronecker (his erstwhile mentor and sponsor) triggered the final crisis. Cantor applied the axioms of set theory to infinite sets, and in doing so showed that “infinity” was a viable mathematical concept. In particular, it helped clarify the differences between rational, irrational, and transcendental numbers.
     A good book, its flaws are minor and don’t interfere with understanding infinity. Clegg likes explaining things, and has a neat talent for potted biographies that give us both the facts essential to understanding the subject’s place in the central story, but also enough quirks to make the people real. What you make of other questions about infinity (such as whether the Universe is infinite or not) is left up to you. Recommended. ***

A Certain Justice (P. D. James, 1997)

    

P. D. James. A Certain Justice (1997) A murder in Chambers, office politics and rivalries, past evils and desires for present revenges, quite ordinary desires for security and love, and children loved too much or not loved enough make up this typically complex mix of character study and police procedural. One murder is solved, the one that prompted it will never be prosecuted because there will never be enough evidence to warrant laying a charge. In this late Adam Dalgleish, James allows herself room to meditate on the nature of evil, and our inability to achieve more than a limited justice. I'm a fan, so I rate this ****

Malice Domestic 9

     Joan Hess, ed. Malice Domestic 9 (2000) A nice collection of purpose-written stories paying homage to Agatha Christie. In the last one, “Oliphants can Remember”, a nasty actor-manager is murdered because he seduced and abandoned a young actress, something he did regularly, but the girl killed herself. His murder recalls Murder on the Orient Express, so does the story succeed? Yes, as a puzzle, as pastiche, and as homage to Christie. Good collection, great for travelling, when you want the occasional fiction bon-bon, not a complete meals ** to ****

Night Train to Munich (1940)

     Night Train to Munich (1940) [D: Carol Reed. Margaret Lockwood, Rex Harrison, Paul Henreid (as Paul von Henried)]
     Agent Gus Bennett (Harrison) plays a German army officer in order to rescue Dr Bomasch, who was recaptured by the Nazis after an arranged escape of his daughter Anna (Lockwood) from a concentration camp. Henreid plays Karl Marsen, the evil Gestapo officer who tricked Anna into revealing her father’s location. Well plotted, but the slow narrative rhythm of the time allows us to see the holes. Harrison is in top form playing the stereotype he became famous for, the man who doesn’t take things seriously yet manages to outsmart and outfight all his adversaries, besides attracting the female lead who falls for him despite herself.
     A well done main feature, but even for the times the painted and model sets are a bit too obviously fake. The narrative pace is slow by today’s standards, which means that the story nicely fills its 95 minutes.  Radford and Wayne appear as Charters and Caldicott, the hapless and comically dense English tourists, who supply some levity and a crucial plot point. One of the earliest WW2 patriotic movies, and one of the best. Available for free download, and worth watching. ***

UP (2009) Movie Review

     UP (2009) [D: Peter Docter, Bob Peterson. Voiced by Ed Asner, Jordan Nagai, Christopher Plummer, et al].
     After a long and happy marriage, Carl loses his wife Ellie, and almost his will to live. About to be evicted from his house, he lofts it with a bunch of balloons and sets out for Paradise Valley, as planned long ago with Ellie. Russell, a Wilderness Explorer seeking a Helping a Senior badge, inadvertently hitches a ride. They do make it to Paradise Valley somewhere in South America, where they meet Charles Muntz, a childhood hero of Carl’s. But Muntz turns out to be a fame-obsessed sociopath who lives in a dirigible with a pack of servant dogs, one of whom takes a shine to Carl. Muntz wants Kevin, a 13 foot tall flightless bird that looks like a cross between a peacock and an emu. In the end Carl and Russell defeat Muntz. Russell gets his Helping a Senior medal, too.
     Nicely twisted plot, well done animation, and a less sentimental tone than one might infer from the plot summary. The movie won an Oscar, deservedly. ***

Lisa Wojna. The Bathroom Book of Canadian Quotes

     Lisa Wojna. The Bathroom Book of Canadian Quotes (2005) Just what it says, and better than I expected. Some of the political have become history, but most are still relevant. Eg, Governments are like underwear. They start smelling pretty bad if you don’t change them once in a while. (Ma Murray)
     A keeper. Probably out of print. ****

R. D. Wingfield. Frost at Christmas

 

R. D. Wingfield. Frost at Christmas (1984) The first Jack Frost novel, with a cutesy title, published in Canada by PaperJacks. My copy is a much-read 2nd hand one I bought at Bearly Used Books in Parry Sound. The title refers only to the time of year. Several crimes interlace, complex plotting is one of Wingfield’s strengths. He’s pretty good on character, too, creating series characters with all the traits that were developed so well in the TV series. Ambience focusses on weather (awful) and work (mixed, with nicely done satire of careerists), and the mean and suburban streets.
     A girl is missing, she turns up murdered by accident. A bank heist, blackmail, an ancient crime, miscellaneous misdemeanours, and a rookie DC who is the Chief Constable’s nephew complicate Frost’s life and enrich the novel with the kind of detail that persuades us we are in a real world.  Frost suffers a gunshot wound, but will survive. According to the Wiki entry, Wingfield wanted this tale to be a one-off, but was persuaded to leave Frost’s survival open. Good decision for fans of Frost, and for the TV series, one of the best ever. ***