@@@@@ @ @ @@@@@ @ @ @@@@@@@ @ @ @@@@@ @@@@@ @@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @@@@@ @@@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @@@@@ @ @ @ @ @@@@@ @@@@@ @@@Mt. Holz Science Fiction Society
03/18/05 -- Vol. 23, No. 38 (Whole Number 1274)
Table of Contents
Andre Norton Dies (comments by Mark R. Leeper):
One of the great classic writers of science fiction has died. Andre Norton was 93. Obituaries are at:
http://www.nytimes.com/2005/03/18/books/18norton.html?
Hush Your Mouth (comments by Mark R. Leeper):
Some of you may have heard about the recent diplomatic gaffe with
Sudan. It seems a government website mentioned a nuclear test
that had been conducted in Sudan. The government of Sudan, not
greatly happy with the United States as it is, wanted an
explanation as to the details the nuclear test. In fact what the
website meant to say was the nuclear test was in Sedan, in
Nevada.
http://news.bbc.co.uk/1/hi/world/africa/4338835.stm
The National Security Agency, our cryptology intelligence
organization, actually does have a program called the Middle
Enlisted Career Cryptologic Advancement program. (You can look
it up in your search engine.) I do hope they don't have any
memos around on websites saying that many of their peoples are
going into MECCA. [-mrl]
The Voynich Manuscript (comments by Mark R. Leeper):
In the April 2005 issue of THE MAGAZINE OF FANTASY AND SCIENCE
FICTION is a short article by Bud Webster talking about a fairly
unusual book called the CODEX SERAPHINIANUS by Luigi Serafini.
The book, published in 1981 in several languages, though really
in no language, is a humorous art book. It would appear to be
some sort of medieval manuscript describing a grotesque version
of our world, but the writing is in no script that is
recognizable. In pages and pages of indecipherable script it
seems to be describing the world, but a world that is a strange
and surreal version of our own. There is weird botany with images
of little people who are part machine. A chimerical horse is
shown with a back half that looks like it came from a termite
queen. With no hind legs it has a wheel instead. The cover
chosen from the book by the publisher shows in sequential
pictures a couple making love and transforming into an alligator
that slinks off leaving the bed empty. All this is apparently
described in a script of unknown or indecipherable language.
This book is in itself interesting enough for an article here,
but Webster beat me to it. One thing that Webster does not
mention is that while CODEX SERAPHINIANUS is apparently intended
humorously, it is not the only book like this. (I am going to
beat Webster to publication about the Voynich Manuscript.)
There really is a manuscript written probably in the latter part
of the 15th century that is indecipherable and itself has some
very bizarre illustrations. The book is called the Voynich
Manuscript, after its modern re-discoverer Wilfrid M. Voynich.
It was found in 1912 in the library of a Jesuit college near
Rome. The strange book is filled with odd botanical and
cosmological illustrations and images of human figures. The
style is one an alchemist or herbalist might have used. At least
on first inspection the text looks like it could be a real
language, but nobody has ever been able to make any sense out of
the text. A letter found with the manuscript said that it had
been bought by Rudolph II in 1586 and in the next century at
least two scholars were given the book to decipher. Their
attempts met with failure and the book was simply stored away
until it came to Voynich's attention in 1912. Voynich also tried
to have somebody interpret the language of the book including
cryptographers who examined the manuscript as possibly being in
code or hiding it real message. There was no success. The
Voynich Manuscript eventually made it way to the Beinecke Rare
Book Library of Yale University.
Voynich's discovery itself is maddeningly detailed and complex.
What remains of the book is about 240 pages in vellum. The page
numbering seems to suggest that there were more pages at one time
that were removed. http://www.world-mysteries.com/sar_13.htm
describes the book containing
SCIENTIFIC AMERICAN published an article last year about efforts
to verify what the manuscript really is (http://tinyurl.com/ysp8p).
Writer Gordon Rugg reports the
conclusion is that the book is a clever fake. This conclusion is
based in part on a statistical analysis of the length of the
words.
How does the length of words tell you if the book is written in a
real language or not? This is one for the television detective
show NUMB3RS. There is a problem with writing random words that
are supposed to look like natural language. If you were just
writing strings of letters and you were trying to vary the length
as randomly as possible, you could not help yourself avoid this
or a similar problem without knowing it. The length of nonsense
words you would generate would follow a bell-shaped curve. But
natural human language that evolved from humans talking is not
nearly so regular. Humans do not generate words randomly.
The length of words found in the manuscript fall into a normal
(binomial or Gaussian) distribution. A mathematician graphed the
frequency of the lengths of words in the Voynich manuscript and
the average length was about 5 or 6 letters with the distribution
being that of the famous bell-shaped curve. That pattern would
almost certainly not occur with a naturally-evolved human
language. If one graphs the frequency of words in a language like
English, the curve would be broader and asymmetric because English
words do not come from a random process. There is a greater
frequency of usage of long words than there is in the Voynich
manuscript. Hence it certainly seems a hoaxer was varying the
words more or less by chance and not in the way that a real human
language would. This was not the only analysis used, but it gives
the idea. The analysis is not totally conclusive, but it makes it
seem very unlikely that there is any sense to the words as
written.
Even if the Voynich is a hoax, the book is still one of the most
interesting books in the world.
Sources for the above information include:
The Voynich Manuscript Site:
http://www.voynich.nu/
The Scientific American's article about the mathematical analysis
by Gordon Rugg:
http://tinyurl.com/ysp8p
Wikipedia's article:
http://en.wikipedia.org/wiki/Voynich_manuscript
[-mrl]
Weather Forecasting (letter of comment by Dan Cox):
In response to Mark's comments on weather forecasting (03/11/05),
Dan Cox writes (and Mark responds):
Well, I took two courses in statistics, three if you count high
school, so I'm not a statistician; but this is what I figured
when I thought about this problem:
(1) Track the forecasted percent chance of rain and the results
over a few years.
[That bothers me a little. The forecaster who says 23% every day
and it rains 23% of the days can be shown to be exactly right in
his prediction, even if he is not helpful. There should be some
way to answer if the forecaster who gives varying predictions is
exactly right or not. -mrl]
(3) For each bucket of samples, figure out the percentage of days
that it rained for days that the forecasted percentage falls into
that bucket.
Now, a real statistician would know what to do about the varying
number of samples that fall into each bucket.
I've also read a non-technical article about grading weather
forecasters. They have a scoring system something like taking
your percentage of correct forecasts and subtracting the
percentage that you could have got correct by simply predicting
the most likely weather for your region. The weather forecaster
for Death Valley cannot get much of score under that system, but
you can't win Olympic(tm) figure skating no matter how good your
single-axle jumps are.
[But that goes against the terms of the problem. If the
forecaster says 23% probability you can't tell whether he is
varying from the likely or not based on whether it rains or not.
A prediction of 23% cannot strictly speaking be verified. -mrl]
(Olympic, Olympics, and the 5-ringed Olympic flag are trademarks
of some organization. That organization has lawyers and knows
how to use them. The use of this word to describe other events,
athletic or not, is forbidden without permission. There is no
confirmation that the government of Greece has been asked to
rename a certain mountain.)
And responding to Mark's comments above, Dan continues:
Rounding to the nearest 5% is done so you don't need to wait years
to get enough samples at the various percentages. You can round
to the nearest 1% if you have enough samples, but I don't think
that is what you're looking for either. If you allow your
forecaster to predict probabilities on a continuous scale, then
to use this method you would have to take the limit as the bucket
size approaches zero. It's not obvious (to me at this time) that
such a function is well behaved enough to have a limit. Even if
it becomes obvious, it's at best a more precise way of stating the
problem until the algorithm to take the limit is found.
On further thinking:
(1)
Even in the case of the constant 23% chance of rain forecast,
saying that it is exactly correct after it turns out to happen
that way is incorrect. Suppose I take my 20 sided die and, I
predict a 5% chance of rolling a 20 on each roll, then I start
rolling. After 100 rolls, I get 4 20's. That does not
demonstrate that my prediction was wrong. My prediction was for
the "chance" of rolling a 20 on any single roll. It was not a
prediction that 100 rolls would contain exactly 5 20s.
So even the most likely prediction has only an 18% chance of
coming true.
But closer to the 23% example:
So the forecaster needs a lot of luck to get a perfect score.
(2)
A problem in my suggested approach:
A high correlation between the predicted chance of rain and the
percentage of times that those days turn out to have rain still
does not indicate a correct prediction. For example, I predict
10% of rain on half of the days, 20% on the other half. On my
10% days it rains 20% of the time. On my 20% days it rains 30%
of the time. I think that gets me a perfect correlation of 1.0,
but not a perfect prediction of the chance of rain. But if I
have a high corellation, the data would probably suggest a smooth
and monotonic mapping function to adjust my predictions to get a
high accuracy. [-dtc]
Weather Forecasting (letter of comment by David Shallcross):
On weather forecasting, David Shallcross also responds:
I am not a statistician, and in particular do not have any
training in non-parametric statistics, which I think is the
relevant sub-field, but I have a few ideas. First, here is an
idea which I think is not good enough. Given probabilities of
rain for each day, we can compute the distribution of the total
number of rainy days. We then observe the actual number of rainy
days. If this is more than the expected number, we look up in
our computed distribution the probability of having this many or
more rainy days. If this is fewer than the expected number, we
look up in the computed distribution the probability of having
this many or fewer rainy days. If, in either case this
probability is sufficiently small, we declare the predictions to
have been bad.
So far this has a serious flaw. We have lost any connection to
the individual days, so we would accept predictions of 0% on
rainy days and 100% on rainless days, if they came in equal
numbers. With this quality measure, we might do best to predict
a constant percentage, based on overall climate.
My second idea is to sort the days by their predicted
probabilities, and divide them into groups. Say, the first group
contains the 10% of the days with the lowest predicted
probabilities, the second group containing the second decile, and
so forth. Now we can compute the probability distribution for
total number of rainy days in each group, and compare with the
observations for the group. Again, declare the predictions bad
if the computed probabilities of weather as far from the
predicted means as the observations are sufficiently small.
Since we have several batched observations to compare against
batched predictions we have to be careful about the meaning of
"sufficiently small". Now we do reward forecasters when it rains
less often on days with low predicted probabilities, and rains
more often on days with high predicted probabilities.
I just had a third idea, which is aesthetically pleasing but
impractical. Given the predicted probabilities of rain for each
of n days, compute the probabilities of each of the 2^n different
outcomes. Sort these outcomes in order of decreasing
probabilities. After observing the n days, look up the predicted
probability of the observations, and add up the total probability
of getting observations of that probability or lower. If this is
sufficiently low, declare the predictions bad. [-ds]
FLIGHT OF THE PHOENIX (letter of comment by Dan Cox):
In response to Mark'sreview of FLIGHT OF THE PHOENIX
(03/11/05), Dan Cox writes (and Mark comments):
I saw the original and enjoyed it.
[The original almost caused a small riot at UMass. The first
time I saw it was on television at the UMass Student Union.
There was a room full of people watching the same movie. About
fifteen minutes before the end (it is a long, long movie)
someone came around and announced they were closing now. It took
him about a minute to decide that that Sunday night the Student
Union would be closing a little late. -mrl]
It included the classic aviation plot of engineers vs. pilots.
[You should see the movie DAM BUSTERS. Although there they
cooperate. -mrl] The same conflict was also featured in THE
RIGHT STUFF, in a scene in which a scientist(*) says something
like "The specimen will ride in this capsule . . ." One of the
astronauts tells him it's "space man". The scientist then
resumes his speech with "The specimen will ride in this capsule .
. ." Through the conversation, the scientists accent is such
that it's not clear if he meant to say "specimen" or "space man",
or if he was deliberately mis-pronouncing it to annoy the
astronauts.
[That, by the way, was Scott Beach playing someone like Werner Von
Braun. Beach was (is?) a popular radio personality in San
Francisco. His program turned me on to old time radio back in the
early 1970s. He has a very distinctive voice. It was Beach who
was riding with a not yet famous George Lucas and told Lucas, "I
think we just hit a wookie." Lucas was puzzled and asked Beach,
"What's a wookie?" "I don't know. I just made the word up."
True story. -mrl]
(*) "Rocket scientists" are more like rocket engineers if you ask
me. Some people might think of that as an insult. I disagree.
If you substitute a space elevator for the airplane, you get a
"Star Trek: Voyager" episode which appears to be a remake of the
original movie. The story does not work as well in a Star Trek
episode, since you know how it's got to end. [You pretty much do
in the film also. -mrl] However, they did do a good job in
choosing Neelix for the role of the "enigmatic passenger who
suggests an unexpected plan for survival". Neelix was always
written as being light on technical knowledge and not easy to
take seriously. [Ribisi is very good in this role. I prefer the
original but by a much more narrow margin than I would have
expected. -mrl]
---- spoiler warning ----
The two key scenes in FLIGHT OF THE PHOENIX (in my memory) are
the "what kind airplanes did you design?" scene, then the scene
in which the pilot tries to start the engine near the end of the
movie. In that scene, the pilot gets to tell the designer "I've
trusted your expertise. Now you've got to trust my expertise."
Without this scene the pilot would just be a fool who was wrong
throughout the movie. [He still was pretty much. He is less
center-stage in the remake, but you also are more sympathetic to
him. -mrl] [-dtc]
STEAMBOY (film review by Mark R. Leeper):
CAPSULE: A total surprise, this refreshing and enjoyable
alternate history anime film packs quite a lot of action and
adventure in one film. Particularly for fans of Jules Verne this
film is a solid pleasure. Rating: high +3 (-4 to +4) or 9/10
Where do I start? I like adventure films and STEAMBOY is not
only the most action-packed anime adventure film can remember
seeing, it may also be one of the most exciting adventure films
of this decade. STEAMBOY is one of the rare adventure films that
gave me the same kind of excitement I got with the 1977 STAR
WARS. The director is Katsuhiro Otomo who directed one of the
classics of anime (though one that did not impress me nearly as
much), AKIRA. He wrote the original manga "Akira" and directed
the film based on it. He repeated that feat with what is for me
the much more enjoyable STEAMBOY, working on the twenty-million-
dollar film a reported ten years.
STEAMBOY is in a sub-genre sometimes called "steam-punk." That
is it is science fiction set around the time that Jules Verne
wrote about. So how would I compare it to Verne films? Being
anime it can easily beat the amount of action of 20,000 LEAGUES
UNDER THE SEA or JOURNEY TO THE CENTER OF THE EARTH, two films I
much enjoy. Animation is much less restrictive than live action.
The filmmaker is limited only by what the artist can visualize.
This is an adventure that gives and gives some more and gives
still more after that. And still it is just in the early stages.
It is a film on the responsibility of science and of the
scientist that discoveries not be misused. Japanese films have
been examining that theme since GOJIRA in 1954 as well they have
a right to. But in this film, set in 1866 the technology that is
in danger of being misused is steam technology.
In 1866, Ray Steam works in a steam plant in Manchester, England.
He wants some connection to his esteemed forebears. It seems he
is the son and grandson of great steam inventors though he may
not yet have their talent. But Ray does not know even where his
father and grandfather are or what they are doing. He fills a
role as a functionary in a steam plant to try to live up to the
family name. One day a mysterious sort of spherical valve is
delivered to him at his home, addressed to him from his
grandfather. The message is to give it to nobody. But almost
immediately there are two men at his door explaining why they
need to take this odd device. Ray realizes he must protect the
sphere from them and the adventure is off and running. His
prized device will take him to London where the Great Exhibition
of 1866 is soon to take place. The strange ball valve has
something to do with an immense machine being built right next
the Great Exhibition. Somehow involved in all this is a girl
Ray's age named Scarlett. His relationship with her is anything
but steamy. She is a vain and imperious, but Ray may need her as
an ally against The Foundation, the organization trying to steal
his grandfather's sphere. Ray is involved in a war involving
steam-powered suits, steam flying machines, and machines that
dwarf people.
The film is in Japanese with (very good) English subtitles and it
seems odd to hear all these early Victorians speaking Japanese.
Like the film SKY CAPTAIN AND THE WORLD OF TOMORROW this is a
view of the future as it might have been as seen from a point in
the past. STEAMBOY is a large-scale adventure film full of a
sense of wonder at technology and also a discussion of nuclear
weapons in allegory. And it is a lot more. I rate it a high +3
on the -4 to +4 scale or 9/10. [-mrl]
ROBOTS (film review by Mark R. Leeper):
CAPSULE: The same team that made ICE AGE tries again to succeed
in the CGI-animation film. But ROBOTS lacks all the magic of ICE
AGE. The film is entertaining but it is definitely second-rate
as current animated features go. It has some good ideas, but
overall it tanks. Rating: low +1 (-4 to +4) or 5/10
Warning: Minor spoilers follow.
In the competition of computer-animated films there are two
giants vying. Pixar pulled ahead when it made FINDING NEMO and
Dreamworks responded with the much weaker film SHARK TALE. In
third place is Fox Animation Studios. They made ANASTASIA, TITAN
A.E., and (their best) ICE AGE. Their latest entry is ROBOTS, so
it invites comparison to ICE AGE. Just about any measure makes
it seem as if Fox Animation did not understand why their ICE AGE
was so good.
ROBOTS takes place in a world very much like our world today but
one in which there are no humans and only robots. Robots have
evolved to have a society a lot like modern-day America. We
follow Rodney Copperbottom (voiced by Ewan McGregor) from the day
of his birth until he is a young adult. He wants to be an
inventor and a repairer of other robots following the role model
he sees on television, the master inventor Bigweld (Mel Brooks).
However, when he goes to the metropolis of Robot City to find his
fortune he discovers Bigweld's corporation very much rules the
world. And these world rulers are backing a policy that there
will be no more spare parts and inexpensive repairs for robots.
Instead the corporation will back only costly upgrades. The
robots who do cannot afford the expensive upgrades are doomed.
Disillusioned, Rodney discovers that CEO Ratchet (Greg Kinnear)--
urged on by his evil mother Madame Gasket (Jim Broadbent)--has
actually forced Bigweld into an involuntary retirement. Can
Rodney reverse this industrial machine?
A script is by Lowell Ganz and Babaloo Mandel. That is usually
good news. They are the authors of films like PARENTHOOD, CITY
SLICKERS, A LEAGUE OF THEIR OWN, and EDTV. But somehow the
animation medium seems to have thrown them. On the plus side the
script has about four jokes a minute and some hit the mark, but
they rely to a great extent on vulgarity and body humor. This
film may entertain children, but it may not be what all parents
want them to be watching. ICE AGE had almost no body humor. It
takes the time to develop the characters so that we get to know
and care for them. ROBOTS has a more frenetic pace but very flat
characters. The artwork is intricate with a lot of ideas, like a
sort of Rube Goldberg transport system, but much less growth of
the characters. The Robin Williams jokes are a poor substitute
for giving us people/robots the viewer really has affection for.
Perhaps it should not make a difference, but the characters of
ICE AGE are organic. They are soft and covered with fur. The
characters of ROBOTS made of metal. They look like they would
clank rather than have the soft feel of flesh.
In ICE AGE the goal of the heroes was to save the life of a lost
baby by returning him to his father. In this film the goal is
defending the institution of cheap repairs over pricey upgrades.
That is what poor robots can afford. But this theme is a trifle
abstract for an animated film aimed primarily at children. In
ICE AGE the conflict is resolved by the heroes catching up with
the child's father and then bidding a reluctant farewell to the
child they have come to love. Here the conflict is resolved in a
giant fight in which by sheer force the good guys kick the living
rivets out of the villains. Force is what triumphs and not
human/robot values.
ROBOTS is a film that is very industrial, but one with little
light or magic. I rate it a low +1 on the -4 to +4 scale or
5/10. [-mrl]
This Week's Reading (book comments by Evelyn C. Leeper):
Daniel Myers's THE SECOND FAVORITE SON (ISBN 1-877-27044-X) is an
alternate history based on the South winning the American Civil
War (though it starts well before that, during the Revolutionary
War). Though Myers was born in Chicago, he has lived abroad a
lot, most recently in New Zealand. That may be why the
extrapolation doesn't work: the resulting society seems just like
what we had before the Civil Rights movement. I might accept that
in a world that would have been very different with both a United
States and a Confederate States of America there might be
communists, WWI, and a Depression. However, Myers also has
interstates (in our timeline conceived of by Eisenhower for
military purposes), Toyotas, and California as being known for
its gay population (as well as the word "gay" used in this way).
(Without a civil rights movement, would there have been a gay
rights movement? Also, white as a wedding dress color became
common only when Queen Victoria wore it, so the comments about it
during the Revolutionary War era are just plain wrong. I'm not
sure why the author decided to make this an alternate history
rather than a straight contemporary mystery, but that aspect does
not work very well.
A. J. Jacobs's THE KNOW-IT-ALL (ISBN 0-7432-5060-5) is the story
of Jacobs's "quest" to read the Encyclopedia Britannica all the
way through. In a sense, this is similar to Herman Gollob's ME &
SHAKESPEARE (reviewed 02/11/05)--it is a combination of
discussion of the topic and memoir of the author. Unfortunately,
although one of the blurbs describes Jacobs as "self-
deprecating," that is not the impression I got. Indeed, the
title seemed to sum up his personality fairly well. While
reading the Encyclopedia Britannica, he kept correcting people or
inserting weird facts he had learned into conversations. This
would be bad enough, but the problem is that he apparently did
not comprehend what he read very well. And the publisher does
not seem to have had a copy editor for this book, maybe because
they figured that anyone who had just read the Encyclopedia
Britannica would not need copy-editing. Wrong. The first major
mistake is on pages 73-74, when Jacobs says, "[if] a stranger
says he was born any day between October 4 and October 15, 1582,
he's lying. Why? Because there were no such dates. That's when
the world switched to the Gregorian calendar, and they skipped
those ten days." That's just wrong. "The world" did not switch
to the Gregorian calendar, only the Catholic countries did so.
Britain did not switch until September 1752; Russia did not
switch until after the Revolution in 1918. (See my long
discussion of this in my review of Mary Gentle's 1610 in the
02/20/04 issue.) Then on page 104, Jacobs refers to "M. Night
Shamalan" (it should be "Shyamalan"), and on page 120, to
"Finnegan's Wake" (it should be "Finnegans Wake"--no apostrophe).
Ironically, on page 127, he says, "I make mistakes rarely--maybe
once every four hundred pages"! Given all this, plus Jacobs'
tendency to gratuitously insult various pop figures, I found
myself thinking that my time could have been better spent reading
the Encyclopedia Britannica.
Oliver Sacks's THE MAN WHO MISTOOK HIS WIFE FOR A HAT (ISBN
0-684-85394-9) is a collection of essays about various peculiar
neurological syndromes. The title essay is about a patient with
the inability to interpret visual images: show him a rose and he
cannot identify it as a rose, but let him smell it and he has no
problem. "The Lost Mariner" is about a man with retrograde
amnesia (a.k.a. Korsakov's syndrome). I can't remember if it
used the term, but that is what the film MEMENTO is about. I
would be surprised if the writer of that was not at least
partially inspired by Sacks. And this is not the only pop
culture derivative of Sacks's work. Just a few weeks ago, the
"B" story on "House, M.D." was almost precisely the case
described in "Cupid's Disease". (And the writers of "Medical
Investigation" seemed to have taken their pilot episode from
Berton Roueche's "Eleven Blue Men". This seems to be the season
for taking television plots from classic medical case histories.)
Michael Nyman has even written an opera based on Sacks's title
essay. At times the writing is a bit dense, but still readable.
(Roueche, mentioned earlier, wrote for a wider audience and is
somewhat easier to read. Paul de Kruif, with his MICROBE HUNTERS
and MEN AGAINST DEATH, predates both of them in this genre.)
The consensus among our book discussion group, however, was that
the descriptions of the cases were far more interesting than
Sacks's philosophizing about them. [-ecl]
[Actually the victims in MEMENTO and the Sacks book have different
types of amnesia. The victim that Sacks writes about has amnesia
that is both anterograde and retrograde. Those words sound fancy,
but it just refers to whether the person forgetting things that
occurred before or after the onset of the amnesia. In MEMENTO
Leonard Shelby has anterograde amnesia. He remembers things
before his injury but nothing for long after. Sacks's patient
made it to the 1980s without problems, then suddenly started
forgetting things both before and after the onset. He thought he
was back in 1945 and still remembered nothing after 1945. His
amnesia went both forward with short-term memory loss and backward
forgetting things of the past. Charles Rainier in James Hilton's
RANDOM HARVEST has retrograde amnesia. He has lost his entire
past. (Fear not. A second injury restores his memory which is a
great literary device and I am told makes absolutely no sense
medically. How many things do you know that break if you hit them
once but repair themselves if you hit them a second time?)
Incidentally, my review of MEMENTO recommended THE MAN WHO MISTOOK
HIS WIFE FOR A HAT. -mrl]
Go to my home page
(2) Round percentages to the nearest 5% (or maybe 10%) so you
have a reasonable number of buckets.
(4) Now you have some predicted percentages and some actual
percentages. Dust off the statistics book and compute the
correlation between the two numbers.
P(5 20's in 100 rolls of a 20 sided die) =
0.05 ^ 5 * 0.95 ^ 95 * (100! / (5! * 95!)) =
approximately 0.180
P(25 4's in 100 rolls of a 4 sided die) =
0.25 ^ 25 * 0.75 ^ 75 * (100! / (25! * 75!)) =
approximately 0.0918
Mark Leeper
mleeper@optonline.net
Quote of the Week:
A sound American is simply one who has put
out of his mind all doubts and questionings,
and who accepts instantly, and as
incontrovertible gospel, the whole body of
official doctrine of his day, whatever it may
be and no matter how often it may change. The
instant he challenges it, no matter how
timorously and academically, he ceases by that
much to be a loyal and creditable citizen of
the republic.
--H. L. Mencken