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Mt. Holz Science Fiction Society
08/20/10 -- Vol. 29, No. 8, Whole Number 1611
Table of Contents
Near Escape (comments by Mark R. Leeper):
I am happy that science fiction got the future so wrong. When I was young I look forward to flying cars, personal jet packs, and travel to other solar systems. It was motivation to learn, something to work for. I might have given up back then had I known that the real future was Facebook and Twitter. [-mrl]
Baagh! Baagh! Baagh! (comments by Mark R. Leeper):
Rush Limbaugh professes to be the "the Man Who Runs America." He says in a rant against building a mosque "next to" (sic) the Ground Zero of the September 11 attacks suggests sarcastically that we build a Hindu temple next to Pearl Harbor. You can just see the wheels of his mind asking, "What religion can I associate with the Pearl Harbor attack? Of course, it must have been the Hindus." I am trying to picture the Imperial Japanese Navy made up of Hindus.
(Okay, I can make this a puzzle of the week: Who is the first person who can figure out why I titled this article "Baagh! Baagh! Baagh!"? Incidentally, Limbaugh continued his suggestion by saying we should build a mosque next to the Pentagon. Actually, the Pentagon deals with enough Muslims that they have already built a mosque inside of the Pentagon.) [-mrl]
Very Hard Math Problems (comments by Mark R. Leeper):
The public is finally getting interested in cutting edge mathematics, at least where competition and prize money is concerned. It is for this reason that the Millennium Prize Problems program was instituted. It started with the proof of Fermat's Last Theorem. I think this task of solving great mathematical problems came to public attention in 1995 when Andrew Wiles proved Fermat's Last Theorem.
This was the contention that there are no positive integer solutions to the equation:
A^N + B^N = C^N for N>2.
The conjecture is simply stated, but proving it took more than 350 years.
After this problem was solved the Clay Mathematical Institute instituted the Millennium Prize for solving very difficult mathematics problems. They took seven of the most difficult of the unsolved problems and offered a million-dollar prize for solving any one of them. This would hopefully motivate some people to try to solve these problems, but more importantly it would put questions of mathematics before the media and the public. The media seems to take note when people are trying for a prize of a million dollars. It makes it seem like more of a sport.
In 2003 Grigori Perelman proved the Poincaré Conjecture, becoming the first person to solve one of the designated Millennium problems. This one is a little harder to make simply understandable. Wikipedia quotes it as this: "Every simply-connected, closed 3-manifold is homeomorphic to the 3-sphere."
Now what does that mean? This is sort of a generalization to four dimensions (and higher) of something that seems obvious in three dimensions. I could put a slipknot around a sphere in three dimensions and pull it until it comes off. There is no good way to lasso a crystal ball and be sure it will not slip out of the loop.
On the other hand if I did the same thing with a ring I could put my loop through the center of the ring and around the outside and there is no way it could pull away because it is tied around a piece of the ring. In general, if a thing has a hole in it you can tie it up with a slipknot. If it does not have a hole, you cannot be sure you cannot slip it out without untying the knot. The Poincaré Conjecture is sort of generalizing that observation to higher dimensions where things may not behave so intuitively.
Perelman has been offered the prize $1,000,000, but he does not want to take full credit for integrating other mathematicians' work and adding on enough so that he could write that last part of the proof.
In August of this year a proof has been presented for another Millennium problem that has been unanswered for decades. It seems that P is not equal to NP as many had hoped. The solution is disappointing, because it essentially is a limit on how efficient a computer program can be. It is like the Laws of Thermodynamics for computer programming. Vinay Deolalikar from HP Labs claims to have proven that P is not the same as NP. So what does this mean?
Consider a salesman who has to drive to four cities. He wants the shortest route that will take him to all four cities. He asks his computer. Now the computer has to look at the various paths. He could start at any of the cities so the computer has four choices for the first city visited, three choices for the second, two choices for the third, and only one choice left for the final city. This is four times three times two times one. There are 24 paths that have to be evaluated. That will not take long. But what if there were a million cities. The computer would have a million possible choices for the first city, 999,999 choices for the second, etc. The number of paths would be one-million-factorial. That is a very large number and it would take the computer a very long time to check each case. Suppose we are talking about N cities. It will take N-factorial iterations. The runtime of such a program will be something like a constant times N-factorial. That grows very fast as N gets big.
But is there a way to make the program more efficient so it does not grow like N-factorial but instead grows like a polynomial? N-squared eventually grows very fast, but not nearly as fast as N-factorial since each additional step multiplies it by a larger number. It grows faster than N^5. It grows faster and N^10. Eventually it is growing faster than N^1,000,000. Something that grows like N! eventually grows faster than any polynomial. Can the problem of the salesman and the very big map be solved more efficiently so that the program that looks for the shortest path can with lots and lots of cities grow no faster than a polynomial? That voice you hear is Vinay Deolalikar from HP Labs saying, "no." If you go up to a million cities you will have to take something proportional to 1,000,000-factorial iterations. There are problems that by their very nature take an amount of time that grows faster than any polynomial.
That is sad, but if Vinay Deolalikar has his proof verified, then at least we will know that limitation. And there will still be five more unsolved problems.
See http://en.wikipedia.org/wiki/Millennium_problem. [-mrl]
Housing Developments (letter of comment by Evelyn C. Leeper):
In response to Kip Williams's, Tim Bateman's, and Paul Dormer's comments on the naming of housing developments in the 08/13/10 issue of the MT VOID, Evelyn Leeper adds, "Clearly Neal Stephenson did not realize the rule about naming housing developments over what was there before, but I rather like his names in SNOW CRASH: White Columns, The Mews at Windsor Heights, The Heights at Bear Run, Cinnamon Grove, and The Farms of Cloverdelle. There is a similar weirdness in naming shopping centers these days: around here we have 'The Shoppes at Old Bridge", "The Shoppes at North Brunswick", and so on. (I must admit I haven't investigated these thoroughly, because none of the "shoppes" I can see from the road interest me.) I do like the idea of "Crappy Mini-Warehouse Estates". I guess POLTERGEIST was set in Indian Cemetery Hills, and the sequel to the Chekhov play would be Cherry Orchard Cottages. [-ecl]
Mnemonics (letters of comment by Kip Williams and Keith F. Lynch):
In response to the various comments on Pluto and mnemonics in the 08/13/10 issue of the MT VOID, Kip Williams writes:
Last time we were at this (that I can recall) was in 2006, and someone (Amethyst) said we seemed to have two or three new planets, and asked if anybody could come up with a new memory aid. I, of course, was glad to help:
"My Eleven Ripe Cantaloupes Ultimately Return Your Very Evil Nurse Unto Sam's Evil And Rather Tender Hearted Mom's Aunt's Reversible Satanic Jalopy, Unless Plausibly Iterating Twin Elvises Reverse Said Aunt, Turning Ugly Radishes -- Never Ugly Raisins -- And Normally Unusable Salads Nicely Eaten, Provided They Understand Nobody Ever Profited Largely Unless They Overstated Calculated Earnings Reports, Especially Supremely Cretinous Harpies And Robotic Overlords; Nonetheless Everyone Rises In Spain."
Best of all, if you omit "Profited Largely Unless They Overstated," it still makes Just as Much Sense! [-kw]
In response, Keith F. Lynch writes:
Impressive, even though Xena has since been renamed Eris.
I've seen various mnemonics for the digits of pi. Those are easier, since each word only has to have the right number of letters. It doesn't matter what letter it begins with. However, all such mnemonics that I've seen stop short. None of them represent *all* the digits of pi. Perhaps you can remedy that.
When you finish that, please do the same for all other real numbers, such as e, the square root of 2, the seventh root of the log of the cosine of Euler's constant, etc. Thanks.
There's no hurry. I don't need them until tomorrow. [-kfl]
And Evelyn adds, " http://en.wikipedia.org/wiki/Piphilology is all about 'the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant pi'." [-ecl]
This Week's Reading (book comments by Evelyn C. Leeper):
The book-and-movie science fiction group chose THE HITCHHIKER'S GUIDE TO THE GALAXY by Douglas Adams (ISBN 978-1-400-05292-9) for this month, and the film (rather than the radio play, the record, or the television series) for the dramatization part.
Even though the work is very familiar, there are still new comments to be made. "They still think digital watches are a pretty neat idea"--nowadays I think digital watches are in decline, as more and more people are using their cell phones as their timepiece. "Small green pieces of paper" made no sense in a British context--it was only American money that fit that description and even American money seems to be moving away from it. (The movie also seems to be Americanized, with American billions, and "zee" rather than "zed").
[As Keith Lynch pointed out in the 03/19/10 issue of the MT VOID American billions have been the same as British billions since 1974. That is, in both countries a billion is 10^9. That is called the "short" scale. Prior to 1974 as in Britain and in many other countries all along a billion was/is 10^12. That convention is called the "long" scale. See http://en.wikipedia.org/wiki/Long_and_short_scales. -mrl]
The actual "Hitchhiker's Guide to the Galaxy" seems to be an early example of an ebook in fiction.
Was the eponymous character in the film FORD FAIRLANE inspired by Ford Prefect?
One of Adams's distinctive stylistic touches is the use of positive adverbs (e.g., totally, exactly) paired with negative verbs or prepositions (e.g. failed): "more or less exactly failed to please the eye" or "almost entirely, but not quite, unlike tea".
Adams wrote about Prosser being a direct male-line descendent of Genghis Khan well before a geneticist discovered the Genghis Khan Effect, which is that there are approximately 15,000,000 direct descendents of Genghis Khan alive today (though not all in the direct-male line). (See http://en.wikipedia.org/wiki/Genghis_Khan#Descent for details.)
Adams claims that in space you asphyxiate and taking a lungful of air before being ejected helps. Actually, that's backwards-- expelling the air from your lungs is what you want to do.
And I found Alan Rickman's voice far too familiar to use for Marvin; I kept thinking of Rickman as walking around in the Marvin suit.
I also just saw the 1966 John Ford film 7 WOMEN about the women at a mission in western China in 1935. The women are Doctor D. R. Cartwright, Agatha Andrews, Jane Argent, Emma Clark, Florrie Pether, Miss Binns, Mrs. Russell, and Miss Ling. Do you notice anything about that list? [-ecl]
Mark Leeper email@example.com Quote of the Week: When we are born, we cry that we are come to this great stage of fools. -- William Shakespeare, King Lear
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