@@@@@ @ @ @@@@@ @ @ @@@@@@@ @ @ @@@@@ @@@@@ @@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @@@@@ @@@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @@@@@ @ @ @ @ @@@@@ @@@@@ @@@Mt. Holz Science Fiction Society
07/01/05 -- Vol. 24, No. 1, Whole Number 1289
Table of Contents
Conflict Resolution (comments by Mark R. Leeper):
We went to a local school to see a program at on the Middle East sponsored by a conflict resolution group. Conflict resolution is a whole subject you can study in colleges. You can major in it. That is a risky career to choose. One thing strikes me. If mathematics had the low success rate that conflict resolution has nobody would study it. I guess it is not that it has such a great success rate, it is amazing it has any success at all.
I hope you are not turned off by mentions of mathematics, as one woman in our discussion group is. This issue is going to mention mathematics a lot. [-mrl]
Mathematics is Discovered, Not Invented (I Think) (comments by Mark R. Leeper):
I am in a book discussion group and our selection for this month is Eric Temple Bell's MEN OF MATHEMATICS. Considering that none of us were mathematicians we quickly got only a question that is very topical among even very good mathematicians. That is the question of whether mathematics is discovered or invented. I suppose I believe that the mathematics itself is discovered; though techniques are invented. I recognize that there is the commonly held belief that mathematics did not pre-exist and that new mathematics is invented. So why do I think it is discovered?
Consider the logical statement:
If one of A or B is true, but A is false, then B must be true.
There is some invention and some arbitrariness in the notation for expressing the idea. There may even be some invention in our rules of manipulating the symbols of the logic. But deep down there is something that we could not get our hands on. There is some truth that preceded us and that we really cannot change. We were not really free to say
((A or B) and not-A) and not-B.
If the universe had been an empty vacuum without any matter nothing that has been invented would exist. Yet the first statement above would have still been true and the second statement would have still been false.
The real truth is not in the letters and punctuation of the first statement; it is the truth behind the statement. The truth exists independent of any invention. The invention consists only in the devices humans have created to express the truth to ourselves and to other people. The real mathematics is not the symbols we put on paper. They only communicate the mathematics and are ways to observe what the mathematics does. Underneath it seems to me is something that is observed and which predates the observer. That is the real mathematics.
Gottfried Leibnitz and Isaac Newton both invented tools to describe motion that we call calculus. They invented different notations. But they had no power to invent the mathematics differently so that their results were inconsistent with each other. They were observing and recording and finding notations for something that was independent of them. All mathematics is consistent if done correctly. Leibnitz and Newton both found the same derivative for x-squared.
Now it is quite possible to conceive of a universe in which there are very different physical laws. Different formulae might describe such a universe. But I do not believe that mathematics would contradict the mathematics of this universe. It would be completely consistent with the mathematics of this universe; it would just be applied to something different.
Let me make that a little easier to understand. The geometry on a globe is different from that on a plane. You cannot have parallel lines on a globe and you can on a plane. Everything you would want to call a line intersects everything else you would want to call a line. Whoa! What do we want to call a line on the surface of a sphere? Well, a line segment is the shortest path between its two endpoints. On the surface of a sphere that is actually a segment of a great circle. A great circle is a circle on the surface of a sphere that is coplanar with the center of the sphere. On the Earth the equator is a great circle. So is the boundary between the Eastern and Western Hemispheres. The lines on the surface of a sphere would correspond to the great circles. But any two great circles on a sphere intersect each other. So on a sphere there is no such thing as parallel lines. That gives you a very different geometry. That does not mean that the laws contradict each other. They are in perfect agreement that parallel lines meet on the surface of a sphere but not in a plane.
So the two geometries disagree on whether parallel lines exist. But they do not contradict each other. They simply start with different assumptions. The mathematics does not say the conclusions are true. The mathematics says that a given set of assumptions leads to a given conclusion. If they lead to two contradictory assumptions, then the assumptions are not consistent. The process of getting to conclusions may vary, but the fact the assumptions lead to a particular conclusion is not.
((A or B) and not-A) leads to the conclusion B is true and not that it is false. Nobody invented that. It is a cold, hard reality of life. [-mrl]
WAR OF THE WORLDS (film review by Mark R. Leeper):
CAPSULE: It is easier to admire than to enjoy Steven Spielberg's adaptation of THE WAR OF THE WORLDS. The film is dark and bleak with little real sense of wonder--the thing that should be Spielberg's forte. The alien technology is not allowed to steal attention away from the human story, but that may not be a good thing. This is a film that is dark in just about every meaning of the word. Rating: low +1 (-4 to +4) or 5/10
When H. G. Wells wrote THE WAR OF THE WORLDS, his intention was to show Britons what it was like to be on the receiving end of an imperialist super-power invading a country. His main interest was on the effect that such an invasion had on the English population. When the public read the book, the strange alien war machines became much more the focus than he had intended. His descriptions of alien war machines captured people's imagination and upstaged the human story. That is a problem that Steven Spielberg carefully prevented when he focused on one family in trouble. But films about families under stress are many and films about tripod alien war machines are few. His film is less in the spirit of earlier versions and more like a big-budget SIGNS.
Spielberg directed his version for Dreamworks (the company he partially owns) and for Paramount Pictures (who produced the 1953 George Pal version). The plot is mostly about a divorced father trying to protect his children against a very serious threat. That very serious threat just happens to come from an alien invader. Curiously enough, it is the human relations that get the most attention in the first half of the film. There is one impressive science fictional sequence in the first half, but much that I would have liked to see had been eliminated from the plot. Telling the story of WAR OF THE WORLDS without having cylinders arrive from Mars and be ignored is like trying to tell the story of THE PHANTOM OF THE OPERA without a chandelier scene. Telling WAR OF THE WORLDS without even a mention of Mars is like telling THE PHANTOM OF THE OPERA without a mask. In the second half the alien invasion is more center stage.
In this version Tom Cruise plays dock-worker Ray Ferrier, himself an operator of heavy machinery, who just happens to have custody of his two estranged children on the weekend that the aliens choose to invade. His goal is to get his children to safety and hopefully to find his ex-wife who was headed for Boston. Funny things start happening when odd storms start with new sort of lightning. Its electro-magnetic pulse seems to be killing everything electrical. An SUV nearby dies along everything else electrical, but Ferrier realizes that the problem is probably just a fried solenoid, hence he ends up with a magic SUV that still drives when others have stopped. And so begins a road trip though a country under siege. Spielberg's emphasis is as much on Ferrier's problems dealing with people, both his children and the panicking hordes wherever he goes, than with his problem with the alien invaders.
The film starts with Morgan Freeman's voice reading the quote from the novel that no one would have believed at the end of the century that human events were being scrutinized. That may have been true at the beginning of the 20th century, but at the beginning of the 21st there was a whole tabloid-reading sub- culture that not only would have believed it, they probably did believe it. The film also shows some of the limitation of the alien heat ray, here transformed into more of a disintegration beam. Whatever it was, it did not have nearly the destructive power that terrorists today would have. The tripods are strong, but they hardly qualify as weapons of mass destruction. Other questions I had was why were there avid reporters going around collecting news when it did not seem there was sufficient infrastructure left to broadcast the news they were collecting. The method chosen for delivering the aliens to Earth is original but not logical and leaves too many unanswered questions.
The story is slow to get started with the early part of the film having Cruise's biggest problems being to get through to children that A) something really bad is happening and B) they have to follow his direction. Realistically A is easier than B. Later the script takes more from the situations in the novel. Lines, scenes, and situations are also taken from 1938 radio play produced by Orson Welles and the 1953 film adaptation produced by George Pal. This script owes a debt to all three versions.
I suppose that Steven Spielberg films are known for good special effects. Curiously, the only really striking effect in this film is the tripod war machines. There the film really excels over other versions. While the exact look of the war machines is not memorable, they look as formidable and frightening as any version (including the famous "Classic Illustrated" comic book's interpretation that many of the boomer generation grew up with). Wells never really says how tall a Martian war machine is and Spielberg uses this as license to portray them as very tall and very powerful. The only other really memorable image is a quick view of a destroyed train. The visualization of the aliens themselves is a disappointment with faces that look too human, much more human than the George Pal Martians or the Martians Wells describes. In general the look of the film is dismal, dark, and gray. The action seems to take place under constantly overcast skies.
Somehow Tom Cruise as a dock-worker is just not my vision of the introspective main character in the Wells novel. Dakota Fanning actually manages to out-act Cruise, or at least steal their scenes together. That is no small feat. Justin Chatwin as the son Robby is instantly forgettable. The best actor in the film is Miranda Otto who plays Mary Ann Ferrier, the divorced wife. Unfortunately she is not on the screen long enough make much of a difference.
This WAR OF THE WORLDS is no more faithful to the book than was the 1953 film version. With the exception of the formidable interpretation of Wells's tripod war machines there was no strong reason to make this invasion story an adaptation of the Wells novel. I guess the fact that it was supposedly based on the Wells helped build the audience. It is a nice production with some quality touches but little besides the visual imagery to make it memorable. Disappointedly, I give it a low +1 on the -4 to +4 scale or 5/10. [-mrl]
This Week's Reading (book comments by Evelyn C. Leeper):
Eric Temple Bell's MEN OF MATHEMATICS (ISBN 0-671-62818-6) was the book for our general discussion group this month. I believe that this is considered the classic work of mathematical biography, but its age--and at times lack of scholarship--is showing. For example, no one today would write, "It was the wrong time of the month and Napoleon was enjoying one of his womanish tantrums." [page 244] And Bell first insists that Georg Cantor was "of pure Jewish descent on both sides" [page 558], and later says, "The aggressive clannishness of Jews has often been remarked, sometimes as an argument against employing them in academic work, but it has not been no generally observed that there is no more vicious academic hatred than that of one Jew for another when they disagree on purely scientific matters or when one is jealous or afraid of another. Gentiles either laugh these hatreds off or go at them in an efficient, underhand way which often enables them to accomplish their spiteful ends under the guise of sincere friendship. When two intellectual Jews fall out they disagree all over, throw reserve to the dogs, and do everything in their power to cut one anothers' throats or stab one another in the back."!) [page 562] Amazing today, yet apparently in 1937 the publisher saw no problem with that claim.
[Georg Cantor is the mathematician who found proof that there are precisely as many integers as even integers or rational numbers, but there are actually a lot more real numbers. -mrl]
If you don't recall reading this, or can't find it in your copy, that's because current editions (since about 1965) have been bowdlerized to change this to "When two academic specialists disagree violently on purely scientific matters, they have a choice, if discretion seems the better part of valor, of laughing their hatreds off and not making a fuss about them, or of acting in any of the number of belligerant ways that other people resort to when confronted with situations of antagonism. One way is to go at the other in an efficient, underhand manner, which often enables one to gain his spiteful end under the guise of sincere friendship. Nothing of the sort here! When Cantor and Kronecker fell out, they disagreed all over, threw reserve to the dogs, and do everything but slit the other's throat." Note that whoever changed this removed all references to religion. You can even tell what was changed, because the font for that part of the paragraph that was replaced has noticeably thinner lines than the rest!
In fact, searching for other changes based on ink color turns up two more. On page 559, Bell had referred to Cantor's brother's becoming a German army officer, saying "what a career for a Jew!" This has been changed to "very few Jews ever did." And on page 560, the editor was unable to come up with something that would take up exactly the same (or slightly less) space as the original, and has the change sticking out into the margin! The original reads, "Cantor could not see that the old man [his father] was merely rationalizing his own greed for money." The changed text says, " Cantor could not see that the old man [his father] was merely rationalizing his own absurd ambition."
The whole question of Cantor's Jewishness has been a subject for debate. For quite a while, it seemed as though Bell had made this up. However, in footnote 3 on the web page http://www.jinfo.org/Computer_Scientists.html, it says, "In MEN OF MATHEMATICS, Eric Temple Bell described Cantor as being 'of pure Jewish descent on both sides,' although both parents were baptized. In a 1971 article entitled 'Towards a Biography of George Cantor,' the British historian of mathematics Ivor Grattan-Guinness claimed (ANNALS OF SCIENCE 27, pp. 345-391, 1971) to be unable to find any evidence of Jewish ancestry (although he conceded that Cantor's wife, Vally Guttmann, was Jewish). However, a letter written by Georg Cantor to Paul Tannery in 1896 (Paul Tannery, MEMOIRES SCIENTIFIQUE 13, CORRESPONDANCE, Gauthier-Villars, Paris, 1934, p. 306) explicitly acknowledges that Cantor's paternal grandparents were members of the Sephardic community of Copenhagen. In a recent book, THE MYSTERY OF THE ALEPH: MATHEMATICS, THE KABBALAH, AND THE SEARCH FOR INFINITY (Four Walls Eight Windows, New York, 2000, pp. 94, 144), Amir Aczel provides new evidence in the form of a letter, recently uncovered by Nathalie Charraud, that was written by Georg Cantor's brother Louis to their mother. This letter seems to indicate that she was also of Jewish descent, as Bell had claimed originally."
However, in any case, Bell agrees that Cantor's mother was born a Roman Catholic, which would make Cantor non-Jewish by Jewish law. One suspects Cantor is using the definitions of the Nuremberg Laws instead. Bell's description of Galois's life is also considerably off the mark--see http://www.maa.org/devlin/devlin_aug.html for a refutation.
Still, Bell's off-hand remarks are sometimes quite *on* the mark. On page 221, he says, "Shortly after his seventh birthday [1784] Gauss entered his first school, a squalid relic of the Middle Ages run by a vile brute . . . whose idea of teaching the hundred or so boys in his charge was to thrash them into such a state of terrified stupidity that they forgot their own names. More of the good old days for which sentimental reactionaries long."
Bell's explanations of the mathematics is not as clear as other have been. (Mark recommends William Dunham's JOURNEY THROUGH GENIUS [ISBN 0-140-14739-X] as a better alternative.) I actually skipped a lot of the mathematics while reading Bell (and we also read only selected chapters); I was reading more for the external forces on these mathematicians. (For example, Queen Christina may have had many good qualities, but she basically killed Rene Descartes by insisting he tutor her at five in the morning in an unheated room.) This may still be the classic work, but if you are going to read only one such work, it may not be the best one. [-ecl]
[See my comments in the 04/16/04 issue of the MT VOID on the modifications made to TEN LITTLE INDIANS for more on removing ethnic slurs from older works of literature. (http://www.geocities.com/evelynleeper/2004/VOID0416.htm#reading. -ecl]
Mark Leeper
mleeper@optonline.net
Quote of the Week:
Science is a match that man has just got alight.
He thought he as in a room--in moments of devotion,
a temple--and that his light would be reflected
from and display walls inscribed with wonderful
secrets and pillars carved with philosophical
systems wrought into harmony. It is a curious
sensation, now that the preliminary splutter is
over and the flame burns up clear, to see his hands
and just a glimpse of himself and the patch he
stands on visible, and around him, in place of all
that human comfort and beauty he anticipated--
darkness still.
-- H. G. Wells, "The Rediscovery of the Unique"
Go to my home page