signs
MANIFOLD readers have been kept informed about the exciting saga of "The Simple Group" ever since an article on the subject in MANIFOLD-2 (which is, unfortunately, out of print). Uninitiated readers may well wonder what all the fuss is about; so we asked one of the Oxford group to explain the rationale behind the seemingly unquenchable search for simple groups. He has also sketched some of the methods used in the search: see later. Since the last issue, incidentally yet another one has been foundl - see later for details.
Also in this issue is a fairly long article on Fuzzy Geometry by Tim Poston. Don't be daunted! It is written in a fairly light-hearted fashion and is easy to read. The material may .look like applied mathematics but it is, in fact, treated very purely: The concept of fuzzy space is due independently to Henri Poincare and Chris Zeeman. Should any applied mathematicians happen to read the article and have any vehement feeling about this enchroachment into forbidden territory we would be pleased to hear from you.
SUDDEN INSIGHTS: No. 1.
Whilst this issue was being typed, Michael Gerzon from Oxford pointed out an improvement of the result in "Meanwhile Back in the Labyrinth". Any natural number can-be expressed in the form, for any x>l:
4 X where 1 ../X] the greatest integer less than choose enough to make it less than 2. Professor Burgess, howeve needs only one 1 using the simple Cornkula sec arctan-c 4n)= I/n+l
You have to be careful how you choose a title for your magazine. A case in point is MAN, the journal of the Royal Anthropological Society. The subscriptions of a certain Indian University are handled by a certain firm of booksellers and importers. Owing to a clerical mix-up, one particular order, for MAN, was dispatched to India.. Unfortunately MAN is also the name of an Australian girlie magazine. To complicate matters, the Indian Customs wouldn't let the copies in, and nobody realized what was happening until several dozen copies of MAN had been dispatched to centres of learning all over the world. Still it's the only way to keep abreast of recent developments...
Our title for a best-selling text- book: Oh! Calculus!
Gordan, by tremendous calculations, proved the existence of a finite system of invariants by actually constructing the beasts. Twenty-two years later Hilbert proved his basis theorem (implying Gordan's result) without any real calculations at all! Whereupon the enraged Gordan cried 'This is not mathematics; it is theology!'
Which statement was echoed by one of the intuitionist school of mathematics, on reading St. John's Gospel: 'This is not theology it is mathematics!
It seems that over 95% of Americans believe in unidentified flying objects (UFOs) and one person in twenty claims to have seen one. Donald I. Warren, a sociologist at the University of Mithigan, recently postulated that flying saucer sightings are related to status frustrations. A status inconsistent person exhibits some dissonance between his age, race, sex, income, education and job classification. Thus blacks and women have high status inconsistency; the latter because of an imposed status from the husband (What about spinsters and liberated women? Ed.) which is ambiguous and anomalous, the former because of white society. Warren eliminated these from the statistics concerning UFOs and was able to verify his hypothesis. But the most amazing find is that the best educated among inconsistents are most susceptible to sighting UFOs - perhaps it is job expectations not living up to educational investment.
Not so long ago, to publicize their new fast inter-city services British Rail had a race against an aeroplane from Manchester to London. The journeys from the centre of each city to the airport proved too much of an obstacle for the plane to overcome. Not to be outdone, a bus raced a car in the United States recently. The route was a fourteen mile journey from Fairfax County in the leafy suburbs of Washington into the heart of the city, close to the White House. Starting at 8.00 a.m. the car raced ahead at the legal maximum speed of 60 m.p.h. along the motorway into the city. The bus, however, arrived at 8.35 a.m. beating the car by 32 minutes, showing the effectiveness of special kerbside bus lanes. Which will no doubt encourage the recent remarkable swing back to public transport in the States. How long before we in Britain, realize the evils of too much progress?
Which reminds us of the new B.R. advertisements. They estimate that a complete motorway system would require 250,000 acres of countryside (which is rapidly diminishing anyway) and 16,000 million pounds; and it would take 43 years to complete. Fortunately, however ......
The Family Planning Association had planned a piece of research on the effectiveness of various contraceptives and sought a group of "experienced women" and a similar number of "inexperienced women". The project had to be abandoned because they were unable to find "a meaningful number of virgins".
MANIFOLD has entered the animal kingdom in that one of a group of snails being bred at llomerton College, Cambridge has been named after thp magazine.
John Horton Conway, fellow of Caius College, Cambridge seems to be becoming a cult figure in mathematics. He first came to fame when he discovered three simple groups (the in-thing to do these days). At the British Mathematics Colloquium most people are content to give a seminar to just one of the various splinter groups. At the last one, Conway gave semninars in algebra, logic and geometry, drawing large crowds. We printed a report of his new game 'Life' in the spring issue. Since then it has caught on in a big way. resulting in a lowdown by the trendy Sunday Times. The report is a little melodramatic: "..if the computer playing the game were big enough, it would in the end throw up on the display screen an object possessing the critical property of life itself: the ability to reproduce." To reproduce what? Conway has heard it estimated that a million dollars of illicit computer time has gone into the game. "Life on earth is vastly more complicated than it needs to be." Conway told the reporter. "We have 92 elements, but you only need 2: on and off. The point which interests me is this. Once you have those little self-reproducing things swimming around on your computer screen do you feel guilty when you switch the machine off?" The reporter admits his bafflement.. "Talking to Conway is like listening to Danny Kaye's French; it sounds fine: you just can't grasp a word of it." We hope to print a more comprehensive report in the next issue. Meanwhile. may we refer you to Barry Pilton's article in MANIFOLD5.