THE MT VOID
Mt. Holz Science Fiction Society
07/01/05 -- Vol. 24, No. 1, Whole Number 1289
El Presidente: Mark Leeper, mleeper@optonline.net
The Power Behind El Pres: Evelyn Leeper, eleeper@optonline.net
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Topics:
Conflict Resolution (comments by Mark R. Leeper)
Mathematics is Discovered, Not Invented (I Think)
(comments by Mark R. Leeper)
WAR OF THE WORLDS (film review by Mark R. Leeper)
This Week's Reading (MEN OF MATHEMATICS) (book comments
by Evelyn C. Leeper)
===================================================================
TOPIC: 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]
===================================================================
TOPIC: 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]
===================================================================
TOPIC: 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]
===================================================================
TOPIC: 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
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"