by John Q on May 31, 2004
Following up my three-way classification of paradoxes,[1] I want to argue that paradoxes involving infinity are always of type-3, that is, the result of ill-posed problems or inappropriate ways of taking limits. (Much the same position is defended in the comments thread by Bill Carone). In fact, I’d argue for the following general principle, applicable to all models relevant to human decisionmakers.
Whenever a result, true for all finite n, is strictly[2] reversed for the infinite case, the problem in question has been posed incorrectly
To defend this, I rely on the premise that we are finite creatures in a finite universe. If a mathematical representation of a decision problem involves an infinite set, such as the integers or the real line, it is only because this is more convenient than employing finite, but very large bounds, such as those derived from the number of particles in the universe. Any property that depends inherently on infinite sets and limits, such as the continuity of a function, can never be verified or falsified by empirical data. Since we are finite, any result that is true for all finite n is true for us.
[click to continue…]
by Chris Bertram on May 31, 2004
On Saturday night we went to a performance of Sheridan’s “The Rivals”:http://www.bibliomania.com/0/6/284/2000/frameset.html at Bristol’s “Old Vic”:http://www.bristol-old-vic.co.uk/ , which has some claim to being the oldest working theatre in Britain (a claim that is carefully qualified to exlude some rivals, though). A very enjoyable evening, complete with a reminder that anxieties about the corrupting effects of new media (internet, the telephone etc) had been fully awakened by the 18th century. Libraries were identified as the cause of moral decline in this exchange between Mrs Malaprop and Sir Anthony Absolute:
bq. Mrs. Mal. There’s a little intricate hussy for you!
bq. Sir Anth. It is not to be wondered at, ma’am,—all this is the natural consequence of teaching girls to read. Had I a thousand daughters, by Heaven! I’d as soon have them taught the black art as their alphabet!
bq. Mrs. Mal. Nay, nay, Sir Anthony, you are an absolute misanthropy.
bq. Sir Anth. In my way hither, Mrs. Malaprop, I observed your niece’s maid coming forth from a circulating library!—She had a book in each hand—they were half-bound volumes, with marble covers!—From that moment I guessed how full of duty I should see her mistress!
bq. Mrs. Mal. Those are vile places, indeed!
bq. Sir Anth. Madam, a circulating library in a town is as an evergreen tree of diabolical knowledge! It blossoms through the year!—And depend on it, Mrs. Malaprop, that they who are so fond of handling the leaves, will long for the fruit at last.
Last week was the centenary of George Formby’s birth. You can hear about his life in a sweet bio-documentary by Russell Davies (probably only for the next couple of days) called (misleadingly) George on George. The best bit concerns Beryl Formby (George’s wife and manager) who, when the South Afrcan Prime Minister phoned her to complain about George’s enthusiam about playing to mixed audiences and apparent colour blindness, shouted “Why don’t you just piss off you horrible little man”, and slammed the phone down. If only more had been like them.
Last week was the centenary of George Formby’s birth. You can hear about his life in a sweet bio-documentary byRussell Davies (probably only for the next couple of days) called (misleadingly) George on George. The best bit concerns Beryl Formby (George’s wife and manager) who, when the South Afrcan Prime Minister phoned her to complain about George’s enthusiam about playing to mixed audiences and apparent colour blindness, shouted “Why don’t you just piss off you horrible little man”, and slammed the phone down. If only more had been like them.