Newsgroups: alt.folklore.urban From: hoey@sun33.aic.nrl.navy.mil (Dan Hoey) Date: 1997/01/10 Subject: Re: Possible UL - cleaning lady/nerve gas? About: > ... a cleaning lady who, by unwittingly mixing two cleaning products > (maybe bleach and ammonia?) managed to generate NERVE GAS, as used > in WWII. rick larson writes: > ... The product is actually chloramine, which is close enough in > volatility and reactivity to chlorine to cause acute and serious > health problems. I've mostly heard this about hydrazine, a volatile neurotoxin that can be absorbed through the skin. It has been suggested that there are enough impurities in the household mix to decompose almost all of the hydrazine, but I wouldn't want to bet on it. I don't know how the neurotoxicity of chloramine compares with hydrazine, but I suspect either of them is harmful in much lower doses than the chlorine. Here's part of an old post from Karl Hahn: ( Newsgroups: sci.chem ) From: h...@lds.loral.com (Karl Hahn) ( Subject: Re: Reacting bleach and ammonia ) Message-ID: <950117123...@are107.lds.loral.com> ( Organization: Loral Data Systems ) Date: Tue, 17 Jan 1995 17:37:57 GMT ... ( 2) When you mix bleach solution with ammonia solution you get an immediate ) reaction. Actually you are getting a number of competing reactions. Under ( carefully controlled conditions, you can get: ) ( 2NH3 + 2ClO- --> 2NH2Cl + 2OH- --> N2H4 + Cl2 + 2OH- ) ammonia bleach chloramine hydrazine ( ) This is one of the commercial methods of producing hydrazine (there's ( another hydrazine process in use as well that involves oxydizing NH3 ) in the presence of acetone, but I've forgotten how that works). In ( order for the above reaction to produce hydrazine in appreciable ) yields, the ammonia has to be in excess and the solutions have to be ( free of metal ions such as Cu or Fe, which catalyze competing ) reactions. You also need to demobilize the solutions by adding ( gelatin or glue to them. Both chloramine and hydrazine are volatile ) and toxic to humans, as is, of course, chlorine gas. ( ) 3) The reaction that competes most vigorously with the above is: ( ) 2NH2Cl + 2OH- + ClO- --> N2 + 3Cl- + 3H2O ( ) due to the great stability of N2. If you simply mix the two household ( solutions, the mixture foams, and the bubbles are mostly nitrogen. But ) enough chlorine and chloramine are blown from the solution by the ( nitrogen that it is hazardous to breathe the effluent. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: hoey@sun13.aic.nrl.navy.mil (Dan Hoey) Date: 1997/01/11 Subject: Re: UL? Stealing electical power with induction coil msm...@tfs.net (Mark E. Smith) writes: > db...@hp8c.nrl.navy.mil (David Ball) wrote: > > Along the lines of: Man lives near high voltage power lines. > > Builds giant induction coil in garage/shed/barn. Sucks enough > > power out of the air to supply his house. > According to power companies -- who naturally have an interesting > in discouraging this kind of activity -- it's trivially easy to > detect a power drain such as you describe. I have been wondering whether this story is some mutation of a well-known (but dimly understood, ALBM) method of sucking power out of "neutral current" or something like that, possibly a technique you can only use if you have three-phase power. That involves having a connection to the power, but the claim was that 1. it bypasses the meter, but 2. the power company will notice, and will collect more from you than you stole. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/01/13 Subject: Re: Tb.Some birds get drunk by eating partly fermented berries/fruits. bmcg...@thenet.co.uk (Brian McGill) writes: > ... DaveHatunen wrote ... > D> ... how do you know they are drunk? I have seen cats act > D> the same way around a catnip ball. > There may be a more direct connection than you think. > In his book "Catwatching" Desmond Morris answers the question Why do cats > react so strongly to catnip? as follows.... And the reason Desmond Morris's books are not accepted as an authority on anything is that his method of science popularization treats the distinction between a "hypothesis" and a "result" as a technical nicety that does not sell books--i.e., by ignoring that distinction. This makes his books quite unsuitable for learning whether a particular bit of folklore is supported by scientific research, as opposed to having been merely investigated--or even merely suspected--by scientists. Consider how much _The Naked Ape_ has fueled the creationists by teaching them that research in human development is best carried out with a vivid imagination and a persuasive pen, unencumbered by all that boring hypothesis-experiment stuff. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/01/19 Subject: Re: Origin of 666 = devil? plkr...@iu.net (Paul and/or Cindy Kruse) write/writes: > Numbers are used in Scripture with very great precision. > You see the same numerical precision in Scripture as you > see in the natural world, where scientists have come to > expect that any new thing can be described with > mathematics.... My late grandfather was greatly interested in computation of Biblical constants. Knowing that I was mathematically inclined, he once asked me to review a manuscript of his that used some extravagant Scriptural comments about the qualities of heavenly light, time, and space to calculate The Speed of Light in Heaven! As I recall, he carried out his calculations to dozens of digits of precision, but ignored some miscellaneous mundane effects, such as that 1. When you calculate the effect of 1/4 of an extra 12-hour day every year (due to leap years), you should include the 1/4 of an extra 12-hour night. (He carried out the calculations of days and nights separately to no purpose I could discern, other than to make this error possible). 2. The 1/4 of an extra day each year is actually closer to 97/400 of a day, as Pope Gregory decreed a few centuries ago. Not being a Roman Catholic, my grandfather might have considered this a papist heresy. But he should have been old enough in 1900 to understand that it was unusual not to have a leap year. 3. The 97/400 of an extra day each year is actually only a reasonable approximation that is off by a few tenths of a second or so, which will necessitate some leap-year modifications several millenia from now. 4. The length of a year actually fluctuates by a few tenths of a second each year due to miscellaneous gravitational and tidal effects. Some of this will even out eventually, though it may require us to insert or delete a leap day now and then. 5. The figure of light speed as 186,000 miles per second is also quite a loose approximation. Thanks to the magic of convenient definitions, that speed is now known to be exactly 39,937 186,282 ------- miles per second. This hasn't stopped the 100,584 people who formerly spent their time calculating the speed of light from continuing with the same sort of experiments, although they are now calculating the length of the meter. I never attempted to attempt to explain all this to him. I seem to recall that Jurgen advised that we should not despise well-intentioned efforts, no matter how bizarrely they may be distorted by future generations. But it can be very difficult sometimes. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: news.admin.net-abuse.sightings Followup-To: news.admin.net-abuse.email From: Dan Hoey Date: 1997/01/27 Subject: [email] UCE from pro1.net spam haven, with possible earthlink involvement Complain-To: jfa...@ee.net,ke...@ee.net Complain-Cc: ab...@earthlink.net Abuse-spotted-in: E-mail Abuse-Subject: (uce) Free Tape "Natural Progesterone" Type-of-Abuse: UCE Description: This is unsolicited commercial bulk e-mail. It is not in response to any request by me, rather my address was taken for this use without my permission. Such use is a social ill of the Internet, and I request that it be stopped. Note an offer to stop sending such materials on request does not mitigate the offense of sending unsolicited bulk e-mail. EE.NET ADMINS: pro1.net and its operators have been reported for this violation many times. They appear to be in the business of access to unsolicited bulk e-mailers and ignoring complaints. Unless you can get them to stop doing this, please stop providing connectivity and DNS service to them. EARTHLINK.NET ADMINS: The headers claim that this came through "pcic.earthlink.net". If your equipment is really being used for this nuisance, please prevent it. 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To remove yourself, eMail: rem...@juice1.net No message required. ---------------- End Included Message ---------------- --- Newsgroups: rec.puzzles From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/02/05 Subject: Re: Question about Rubik's Cube Spoiler eff...@worldaccess.nl (Feico Nater) writes: [ "Lance S. Hopenwasser" asks how to solve the face center twists on Rubik's cube. ] > I understand that you cube is just like Rubik, except that the centers > of each side have marks. > I made such a cube myself, by making each face two-colored. I wonder how much you played with it, since the procedures you give for solving it do not work. > Spoiler follows---------------------------- > 1. Make sure the top is correct. > 2. Make sure the centers of the front, back, left and right are correct. > 2a How to turn the center of the front plane without affecting the top? > 2b Turn front 180 degrees > 2c Turn bottom 180 degrees > 2d Trun front as needed > 2e Turn bottom 180 degrees > 2f Turn front 180 degrees > 3. Move the cubicles on the four edges into position. > I hope this is helpful so far. If your step 3 procedures for moving the edge cubies mess up the face twist, you might have to go back to step 2, and never reach solution. My methods for solving face center twist avoid this problem, because they do not leave any cubies out of position. > If a center cublicle is turned clockwise, there is always another > center cubicle turned anticlockwise, Wrong. You could have two face centers rotated in the same directon, or one center rotated 180 degrees, without any others rotated. In half the face center positions, the total face center rotation will be 180 degrees (modulo 360 degrees), so it is hard to imagine how you could use this procedure without noticing the problem. > Here is a procedure to turn a number of center cublicles: > 1. Turn right plane clockwise > 2. Turn horizontal equator anti clockwise > Repeat seven times. Eight times in all. That will not rotate any face center an odd multiple of 90 degrees. So even if your analysis were correct, this would not be a solution to the position in which one face center is rotated 90 degrees clockwise and another is rotated 90 degrees anticlockwise. The method I found sixteen years ago for solving face centers is at http://www.math.rwth-aachen.de/~mschoene/Cube-Lovers/ Dan_Hoey__The_Supergroup_--_Part_3__A_Super-H_and_Spoilers.html and is also available as part of ftp://ftp.ai.mit.edu/pub/cube-lovers/cube-mail-1.gz if you prefer FTP. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/02/11 Subject: Re: Tires from beyond the grave markandsh...@juno.com (Mark Donaldson) write: > Had it explained to me once as an offshoot of packing theory. Small > objects pack tighter than big objects. But they don't! All spheres pack at the same density. Same for any other shape, providing the small ones are shaped like the big ones. > An extreme example: Tennis balls and sand packed into equal sized > containters: Sand has space in between the grains of sand, the sum of > all that space is less than the sum of space between the tennis balls > packed into the same size container. But it isn't, except near the boundary of the container itself, where the edge effects extend further in for the tennis balls than the sand. If we have a wide field filled with solid sand-size and tennis-ball- size spheres of the same material, the packing density of the two is the same. Something more complicated must be going on. The evil twin speculates.... Perhaps it's the same thing that makes a witch float and a duck drown. I'm surprised nobody noticed that 's remark: >Its called density. The same thing that makes wood float on water >could make tires "float" to the top of the ground.... means that, factitiously speaking, dirt is not really a solid. It is a state of matter that habitual chemistry students refer to as an "amorphous liquid". Just look at a globe: How do you think the Earth got to be wider at the equator than at the poles? And sand is practically dirt, just a little deloaminated, and if you melt the sand.... Dan Hoey eppur si suagge Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: hoey@pooh.tec.army.mil (Dan Hoey) Date: 1997/02/22 Subject: Re: 15-coins game [spoiler] [ This is a revised version of an article I sent last night. That version seems to have evaporated. ] David Madore writes: of a game on a row of coins, in which a move consists of selecting a consecutive subsequence of coins, provided that the rightmost coin of the subsequence is heads, and flipping over each coin of the subsequence in place. The game ends when all the coins are tails, and play is normal--the player who is unable to move loses. > I'm sorry I wasn't clear enough the first time. I hope this time > there is no ambiguity in the meaning of the rules. There never was any ambiguity, but people have to read carefully. The way to evaluate a position is to (mentally) slide the coins slightly out of line, so that they form a profile like the marks on a ruler. If we number the coins sequentially left to right, starting at 1, this means that the odd coins are moved the least, the ones numbered 2 mod 4 slightly more, the 4 mod 8 more, and so forth, with the coins numbered 2^k mod 2^(k+1) moved to mental row k. Thus you should think of the position TTTTHTTHTHHTHTT T T H T T H H T (3 heads in row 0) as if it were shifted to T T H T (1 head in row 1) T T (0 heads in row 2) H. (1 head in row 3) If you haven't got a fixed-pitch font for your newsreader you are out of luck. Draw it yourself. You have lost if there are an even number of heads in each row. If not, you win by moving so there are. In the example there are an odd nubmer of heads in the units, twos, and fours rows, so the winning move is to flip coins 7-11 to form TTTTHTHTHTTTHTT, T T H H H T H T (4 heads in row 0) which we think of as T T T T (0 heads in row 1) T T (0 heads in row 2) T. (0 heads in row 3) Or you could flip coins 1-13, if you prefer. The parity of row k is the 2^k bit of the nim-value of the position. See _Winning Ways_, by Berlekamp, Conway, and Guy, if you don't konw what this means. In fact, this game appears in _WW_ under the name "The ruler game". But I discovered this strategy not by looking it up, but by evaluating all the positions with at most 15 coins (by machine) and analyzing the results. I understand from David Madore that his approach was similar. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: hoey@pooh.tec.army.mil (Dan Hoey) Date: 1997/02/26 Subject: Re: Segment bisection with compass alone. ma...@oban.CS.Berkeley.EDU (Gurmeet Singh Manku) asked: > How do we find the mid-point of a line segment using only a compass? Barry Wolk replied: : I can do it by using the compass seven times. Can this be lowered? Slightly, as in the following modification of your construction. : Let the given segment be AB. The points are located approximately by : the following diagram: : G : C E : : A M B F : : D : H : : Circle 1 has centre A and radius AB. : Circle 2 has centre B and radius BA. : Circle 1 meets circle 2 at points C and D. Circle 4 has centre C and radius CD. Circle 4 meets circle 2 at points D and F. : Circle 5 has centre F and radius FA. : Circle 5 meets circle 1 at points G and H. : Circle 6 has centre G and radius GA. : Circle 7 has centre H and radius HA. : Circle 6 meets circle 7 at points A and M. : Then M is the midpoint of AB. Proof omitted. Note that circle 3 and point E are absent from this construction. Is this six-circle construction optimal? My case analysis of the fourteen possible determinate four-circle constructions suggests so. None of those four-circle constructions includes a circle through M, so no fifth circle could produce an intersection at M. The only problem with this proof is that possible steps like "draw an arbitrary circle through point A intersecting circle C in two points" are not included in my analysis. I doubt such a step would help, but I have no proof. Nor am I sure that Euclid would look favorably on such an operation. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fan.wodehouse From: hoey@sun13.aic.nrl.navy.mil (Dan Hoey) Date: 1997/03/04 Subject: Re: Plum's kindness to a young fan bhurk...@pilot.msu.edu (Augustus Fink-Nottle) writes: > .... To put it simply, would you care to post the contents of the > letters that Plum wrote you? Most of us, I am sure, would appreciate > it greatly. And I am sure the Wodehouse Estate would appreciate it greatly if you do not violate their copyright by posting those letters without their explicit permission. When you are sent a letter, you own the letter itself, but this does _not_ grant permission to publish the contents. Copyright remains with the writer (or his heirs, in this case). I do not wish to reopen the eternal network copyright debate on alt.fan.wodehouse, which is better served by discussing PGW's works. Any questions you might have about copyright law may be answered in a copyright FAQ (http://www.aimnet.com/~carroll/copyright/faq-home.html) or should be posed in the "misc.int-property" newsgroup. Though if you decide that the law is not applicable for some reason, you may be better served by consulting a real attorney instead of relying on the net, since a real attorney can defend you if you are sued for real money. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fan.wodehouse, misc.int-property Followup-To: misc.int-property From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/03/12 Subject: Re: Plum's kindness to a young fan When I warned against posting P.G. Wodehouse's letters without his heirs' permission, I did not do so lightly. I hoped that his heirs might be spared the loss in value of their future publication rights to those letters. I hoped that some Usenet poster might be spared inflicting such a loss upon those heirs. And I hoped that alt.fan.wodehouse might be spared the "eternal network copyright debate" over who believes which myth about copyright. My advice was ignored, and the wrongs have come to pass, and I regret my part in the third wrong out of an attempt to forestall the first two. I will not perpetuate the third wrong by responding to the substantive points raised by Baselight/Heppenstall and HoodArnold/Stoker, save to dismiss them as being the apparent result of complete ignorance of copyright laws. I included a few references in my previous post, and I have included others in e-mail to those respondents. In particular, I listed five sections of the copyright law that contradict the four incorrect statements made by the law student pal, whom I hope manages to learn to give _informed_ advice before she is inflicted on a client. If you wish a copy of those e-mail messages, send e-mail to me--my address is given below. E-mail letters of a non-bulk nature are generally welcome; form letters are not. Note that I will not respond further in alt.fan.wodehouse on this extraneous topic, and I will resent the inconsiderate acts of those who do. Followups are directed to misc.int-property. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban, alt.fan.cecil-adams Followup-To: alt.fan.cecil-adams From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/03/13 Subject: Re: Ring around the ripper meltd...@u.washington.edu (Ulo Melton) wrote of: > ... the current Cecil Adams column at > . > Jabberwocky meets Jack the Ripper. Indeed. Excerpts from Wallace's anagram "research" also appeared in the November 1996 _Harper's_. For a startling illustration of its true significance, I wholeheartedly reccommend the response from Guy Jacobson and Francis Heaney, which appeared in the _Harper's_ February letter column. If it's more convenient, you can also find it at http://dejanews.com. Use the search key ripper & carroll & wallace & harper on the "Old" Usenet database. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/03/20 Subject: Re: I love coffee, I love tea ... brad...@panix.com (Bo Bradham) writes: > Russ Jones wrote: > > H.B. Quoyoon wrote: > >> Does anyone know any of the lines > >> which follow the rhyme: > >> I love coffee, I love tea? > > I love the Java Jive and it loves me. Well, those are some lines that rhyme, but there are others of a somewhat more folkloric nature. The jumprope rhyme archive at lists I love coffee. I love tea. I love the boys And they love me. Tell your mother To hold her tongue. She was the same When she was young. No more coffee. No more tea. No more boys And no more me. (* Jumper exits *) and I love coffee. I love tea. I love (* Names a new jumper *) To jump in with me. Sources for these are given at the web site. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fan.wodehouse Followup-To: poster From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/03/26 Subject: Re: Plum's kindness to a young fan Richard Herring writes: > Every time I see this name I am irresistibly reminded of one of > the Blandings stories, in which Clarence receives some musical > instructions which, surprisingly, were not found in Whiffle (or > even Whipple). Can anyone remind me of the precise form they took? My Dear Mr Herring, Perhaps you are thinking of the short story "Pig-Hoo-o-o-o-ey", in which is presented a pig call variously rendered "Pig-hoo-oo-ey", "Pig-hoo-oo-o-ey", "Pig-hoo-o-o-o-ey", "Pig-HOO-o-o-o-ey", and "Pig-HOOOOO-OOO-OOO-O-O-ey" in the text. Each of these, you may observe, contains the letters of my last name in order, with some extra Os inserted. This is also true of the word "hooey", a slang term meaning nonsense. I am also told there is a military historian named David Hooey. In contrast, my name is supposedly derived from the Gaelic "O'hEochaidh", so the lexical resemblance to these other words is merely one of those superficial coincidences that seem to occur so frequently. Sincerely, Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/03/26 Subject: Re: You're all jealous!! dk...@raspberry.bbn.com (David Karr) writes: > Duncan McKenzie wrote: > >[...] "imagine four intersecting spheres -- what is the > >maximum number of regions they could create?" [...] > >there's a certain level of problem where my mind just gets > >confused, and hers obviously doesn't. > Right. The problem is you think too much. > The obvious answer is that each sphere added in turn can at most > divide all the existing regions in two. So the answer is 16.... Perhaps he was also thinking too rigorously. An added sphere can divide a region into more than two parts. For instance, if three spheres intersect in three-dimensional lune, the fourth sphere could cut the lune into three parts. If so, the fourth sphere won't cut the region exterior to the first three spheres, so perhaps 16 is still an upper bound. But more cases need to be considered if you want a proof. I join in the suspicion that part of what passes for MvS's ability to avoid confusion is a tendency to make plausible guesses instead of addressing the hard parts of a problem. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.theory From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/03/31 Subject: Re: Help on Garey and Johnson Jeff writes (with my emendations): > Could some kind person explain PERMUTATION GENERATION (MS6) to me? > Instance: Permutation f of the integers {1,2,...,N} and a sequence > S1, S2, ...,Sp of subsets of {1,2,...,N} > Question: Can f be expressed as composition f=f1 . f2 . ... . fp, > where for each i, 1<=i<=p, fi is a permutation of {1,2,...,N} that > leaves all elements in {1,2,...,N} - Si fixed? > ... Unfortunately the "reference" G&J refer to is unpublished.... The terminology has been adequately explained, but there is still the problem of the reference. I've been thinking about it off and on for the past week. Garey and Johnson claim a transformation from X3C, but I have not been able to make that work. However, I have come up with a transformation from THREE-DIMENSIONAL MATCHING (3DM). Suppose we have an instance of 3DM: a subset M of W x X x Y, where W, X, Y are disjoint sets of size q. The question is whether there exists a subset M' of M, |M'|=q, such that no two elements of M' agree in any coordinate. I will assume that we have a nontrivial instance, in the sense that every element of W, X, and Y appears as a coordinate in M. I will construct an instance of MS6 based on the permutations of the integers {1,2,...,3m}, where |M|=m. These integers should be considered to stand for the coordinates as they appear in M. In particular, the integers A={1,2,...m} will stand for the W-coordinates, the integers B={m+1,m+2,...,2m} will stand for the X-coordinates, and the integers C={2m+1,2m+2,...,3m} will stand for the Y-coordinates. I will use the map E: (A union B union C) -> (W union X union Y) to refer to this correspondence. Note that E is just a concrete way of expressing the given set M={(E(1),E(m+1),E(2m+1)), (E(2),E(m+2),E(2m+2)), ..., (E(m),E(2m),E(3m))}. The sequence of restriction sets S1,S2,...,Sp will consist of three contiguous subsequences, SS1 = S1, S2, ..., S_3q; SS2 = S_3q+1, S_3q+2, ..., S_3q+2m; and SS3 = S_3q+2m+1, S_3q+2m+2, S_3q+2m+3. While I will temporarily put off their precise definition, I promise that each subset in SS1 and SS3 will be a either a subset of A, a subset of B, or a subset of C, so the corresponding permutations will maintain the segregation of the permuted integers into A, B, and C. The only mixing between the three sets will occur in the permutations corresponding to SS2, in a construction that forms the tricky part of the transformation. The subsets in SS2 are defined as follows: S_3q+1 = {m+1,2m+1}, S_3q+2 = {1,m+1}, S_3q+3 = {m+2,2m+2}, S_3q+4 = {2,m+2}, S_3q+5 = {m+3,2m+3}, S_3q+6 = {3,m+3}, ..., S_3q+2m-1 = {2m, 3m}, S_3q+2m = {m,2m}, It is apparent that any interaction between permutations in SS2 will occur between two adjacent subsets S_3q+2k-1, S_3q+2k. Furthermore, since these subsets are 2-sets, each permutation corresponding to them will be either the identity or a transposition. Thus there are only four possible permutations induced on {k,m+k,m+2k} by the permutations corresponding to SS2: i) I . I = I, ii) I . (k,m+k) = (k,m+k), iii) (m+k,2m+k) . I = (m+k,2m+k), and iv) (m+k,2m+k) . (k,m+k) = (k,m+k,2m+k) The target permutation f will be chosen such that no integer in B is mapped to A (prohibiting case ii) and no integer in C is mapped to B (prohibiting case iii). Therefore the only possible choices of permutations on S_3q+2k-1, S_3q+2k will compose either to the identity or to a three-cycle (k,m+k,2m+k). The rest of the transformation is straightforward. The subsets SS1 are simply the inverse images under E. That is, for each value z in W union X union Y, there is a set E^-1(z) in SS1 consisting of those integers that correspond to the appearance of z as an index in M. The three subsets SS3 are just A, B, and C. To define the target permutation f, let us divide the set A = A1 union A2. The set A1 will consist of one representative from each inverse image of E^-1(W), so that |A1|=q and E:A1->W is surjective (onto). Similarly B1 is a set of representatives of E^-1(X) and C1 is a set of representatives of E^-1(Y), with A2=A\A1, B2=B\B1 and C2=C\C1. Then we define f such that f : A1 -> {m+1, m+2, ..., m+q}, B1 -> {2m+1, 2m+2, ..., 2m+q}, C1 -> {1, 2, ..., q}, A2 -> {q+1, q+2, ..., m}, B2 -> {m+q+1, m+q+2, ..., 2m}, C2 -> {2m+q+1, 2m+q+2, ..., 3m}. To see that this transformation from 3DM to MS6 is faithful, suppose that the given instance of 3DM has a solution. Then the solution to MS6 is found by using permutations on subsets in SS1 to move the elements of A1, B1, and C1 to the 3q integers corresponding to indices in the triples of M'. Those integers are mapped in 3-cycles by permutations on subsets in SS2, while the other integers are held fixed. Finally, permutations on subsets in SS3 are used to move the images of A1, B1, and C1 to the initial part of A, B, and C. Conversely, is not hard to see that this is the only way that one element each of A1, B1, and C1 could be mapped into B, C, and A, respectively, as required by the target permutation f. QED. Dan Hoey posted and e-mailed Hoey@AIC.NRL.Navy.Mil --- Geometry.Net - Theorems_And_Conjectures: Unsolved Problems (1) Prove or disprove that there cannot be distinct colinear arrangements of points with the same multi-set of point-to-point distances. (Reflections are not counted as distinct.) Ref: Distinct Point Sets With Same Distances Variations and Comments on Problem 1 Relation to Golomb Rulers Generating Functions for Point Set Distances SOLVED: 4 Apr 97. Dan Hoey forwarded a couple of messages from John Scholes and Torsten Sillke each giving an example of isospectral sets in one dimension. --- Newsgroups: rec.puzzles From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/04/12 Subject: Re: Puzzle : Striking off sticks. ta...@singnet.com.sg (ghola) writes: > 1 Group 1 (1 stick) > 11 Group 2 (2 sticks) > 111 Group 3 (3 sticks) > 1111 Group 4 (4 sticks) > 11111 Group 5 (5 sticks) > 111111 Group 6 (6 sticks) > How to play: > - 2 players take turn to strike off any number of sticks from any group. > - To strike off 2 or more sticks in a group, the sticks must be side > by side.... > - If striking off one/some of the sticks from in between a group, > then the remaining sticks on the right and on the left are now > consider 2 distinct groups.... > Objective: > - In order to win, you must leave one last stick for your opponent > to strike off. > Question: > - Is there a sure win or higher winning chance strategy? This game (also known as ".777...") appeared on rec.puzzles in 1992, but is not in the latest version of the archives I've seen (1993). David Grabiner showed that this a tame game, played as if it were the same position in Nim (aka ".333..."). That is, it is never necessary to use the ability to split the remnant of a group, and your opponent will not gain by doing so. (Though in misere play, the disjunctive compound of this game with a non-tame game may not admit this simplification). But you were asking... > - If so, how do you do it with you starting first? As in Nim, play to make the nim-sum of the group sizes zero, EXCEPT (since this is misere) when you are leaving no group with more than one stick, when you make the nim-sum one. You calculate the nim-sum (sometimes called the "exclusive-or" or the "GF(2) sum") by writing the numbers in binary notation and adding them together without "carrying" from one bit position to another. (It is not hard to learn to calculate nim-sums in your head. Impress your friends! Confound your opponents!) In the given position, the EXCEPTion is not yet in effect, so you must change the nim-sum from 7 to zero. You do this by nim-adding 7 to the value of some group. Change group 4 to (4 nimsum 7)=3 (x111 or 1x11) since (1 nimsum 2)=3, group 5 to (5 nimsum 7)=2 (xxx11 or 1x111) since (1 nimsum 3)=2, or group 6 to (6 nimsum 7)=1 (xxxxx1 or 11x111) since (2 nimsum 3)=1. You can find out why this strategy works in any of hundreds of books and papers on Nim, but you will learn best from Berlekamp, Conway, and Guy's book _Winning Ways_. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: comp.lang.c From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/04/13 Subject: Re: palindromic program? d...@cwi.nl (Dik T. Winter) writes: > Alas, it is not ANSI. I have two more by Dan Hoey, but they also are > not ANSI. Isn't /**/main(){exit(0);}/*/};)0(tixe{)(niam/**/ ANSI? If not, you should be able to put your favorite ANSI program into this schema. You can even include comments if you indicate them with "/*//**//*/ ... /*//**/", so that they comment in reverse as well. I suspect the non-ANSI program you recall is the palindromic program whose output is the program itself; it had lines that might be too long (is there a maximum line length?), it failed to end with a newline, and it used printf without including stdio (or stdlib or stddef. Do you need them, too?). I've occasionally considered repairing these deficiencies, but I haven't got the whole story on what the requirements are. Dan Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/04/23 Subject: Re: Toes have no names? Mark asks whether to devour a story about someone recently standardizing the names of toes. This is probably related to the _New Scientist_'s column formerly known as ARIADNE (and since renamed "Feedback") in the issue of 6 April 1991. "A doctor at the Yale University School of Medicine has been thinking about the curious affair of the toes. He has written, that unlike the fingers, which all have names --- digitus pollicis, indicis, medius, annularis, and minimus --- the toes are all anonymous, except the big toe, hallux, though they are ignominiously numbered. Unfair, he maintains, and liable to cause confusion. He therefore suggests names, doing away with hallux and substituting porcellus fori. Then the other toes, moving across from the big toe, should become p. domi, p. carnivorus, p. non voratus, and p. plorans domum. "My Latin not being up to this, I was glad to see that he had provided a translation. Porcellus he uses as the diminutive form of porcus, a pig. Light breaks. The toes are then identified as piglet at market, piglet at home, meat-eating piglet, piglet having not eaten, and piglet crying homeward." c...@midway.uchicago.edu (Christine Malcom) was kind enough to note that the 5th and latest edition of _Nomina Anatomica_ doesn't mention any action by the International Congress of Anatomists on this, but that's from 1983, so they could hardly have the latest information. Given the date of the column, I suspect this is all a prank played on or by the _New Scientist_, and that the suggestion that this terminology was adopted is a product of the rumor mill. But perhaps you may get more information from Medline or the kind folks at feedb...@newscientist.com. Dan Hoey [ posted and e-mailed ] Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/04/25 Subject: Re: Toes have no names? About the article on toe-naming in the 6 April 1991 _New Scientist_, c...@midway.uchicago.edu (Christine Malcom) writes: > Don't you look at me like that, Rick Tyler. I was merely trying to point > out that while charming, to be sure, the article was bullocks while not > being confrontational. 'tis my shy and retiring way. Well, I'd be glad if you had pointed out the article was bullocks, but you didn't. You noted that the 5th edition of _Nomina Anatomica_ is "that latest on information on what gets used in publication", but the _article_ didn't claim the toe names had been incorporated into the standard, only that someone had suggested the names. As distinct from the article, there is a _rumor_ that those names were submitted to a standards-making body and "accepted". Now the idea that these are the standard names for toes and if you publish an article on toes you'd better call them this, that's bollucks plain and simple. But isn't there a standards-making body saving up new names for body parts until they assemble enough to have a new International Congress of Anatomists and vote on them? I mean, that could have been, "accepted for consideration by the 12th ICA, when and if," after all. For all I know, the International Anatomists may even have decided when they next will have a Congress. Now my observation that this was published in the first week of April (which you snipped, so Rick Tyler could rediscover it on his own) and Ian's observation that the Feedback column is a bespoke bollocks supplier to the pseudoscientific community, these observations tend to suggest an article that is, well, bollocks. But all you did was repeat what you said before, that the 5th edition is currently the standard. It would be nice to know who anatomists are supposed to do tell when they actually do discover a new gobbet of flesh that needs a name. Is there an International Anatomist in the house? (And do you guys have a humerous bone in your body?) I hope you don't consider this confrontational. I just wanted to note which parts of this poisson have been debunked and which are still bunking around. Dan Hoey posted, e-mailed Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fan.wodehouse From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/04/27 Subject: Re: ... in an adage? > > Bertie's reference to the cat in the adage is a line from > > Shakespeare about a cat who let I dare not wait upon I would. > Sorry chaps, I've told you all I know.... Perhaps I can dispell some of the wonderment. It happens the Bard of Avon was writing about this cove M. who was married to this lady named Lady M., and she was trying to Improve him. He was sticking at her plans, because it involved a little bit of rannygazoo along the general lines of regicide. And she was asking him if he was planning to give her plans the miss-in-baulk, considering that it would cause him to sink to the level of some third rate-power in the househod, ``And live a coward in thine own esteem, Letting `I dare not' wait upon `I would,' Like the poor cat i' the adage?'' Given that this cove M. went ahead with her plans, it's a pretty sure bet that _he_ knew how the poor cat i' the adage ended up, and perhaps the Bard figured out that just about anyone ought to know their cats and adages, for he included no explanatory footnotes. Sadly, we in our modern times often have a hard time figuring out just which cat that was and what sort of adage he was i'. Which is where this extremely helpful cove named Bartlett who keeps track of adages for us comes in. In the Eleventh Edition of Bartlett's collection of _Familiar Quotations_ he mentions that this is among the adages collected a bloke named John Heywood, who included ``The cat would eate fish, and would not wet her feete.'' in his _Proverbes_ collection, which was printed in 1546. This in turn has something to do with a MS. from 1250 or so, in Trinity College, Cambridge, in which is written ``Cat lufat visch, ac he nele his feth wete.'' because that was how they wrote their adages back in the 13c. All meaning that if you have a bit of fish and a cat, the way to keep them apart is to interpose a body of water, because the dumb chum will stand on the shoreline mewing piteously and not getting his feet wet. But your plans may come to naught if the cat of the first part is married to a cat of the second part who is ready to reduce the domestic bliss level until the c.o.t.f.p. leaps into the briny and returns with the fish, or on it. We may well regret that in the Sixteenth and current edition of this cove Bartlett's works he (or his postumous redactor) neglects to impart this useful explanation of the cat and adage. And we should be grateful that my fiancee thought to pick up the earlier and more adagious version when she had the opp. Dan (posted and e-mailed) Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.science, alt.folklore.urban Followup-To: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/05/02 Subject: Re: Two engineer-related stories schne...@gold.tc.umn.edu (Mike Schneider) writes: > I found these two stories in sci.engr and was wondering about their > veracity.... [ snip railroad hoax ] > > And the reason we have the QWERTY keyboard was so that early > > typewriters woudl not jam when fast typists caused the keys to hit > > one another as they moved from the semi-circular array toward the > > platen. That's a fairly accurate version of the principle behind the QWERTY design. Unfortunately, your explanation is tends to be misunderstood, due to the Rover phenomenon. When you tell your dog "Bad dog Rover, don't chew the carpet," Rover hears "yadda yadda Rover yadda yadda" and goes on chewing the carpet. A lot of people read that way, too. An example of the Rover phenomenon is mlor...@dns.microsoft.com reading "yadda yadda QWERTY yadda yadda" and deciding you were talking about the widely spread belief that non-QWERTY keyboards are so far superior to QWERTY they would be adopted immediately if we weren't locked in by inertia. He pointed out an article in _Reason_ magazine article (http://www.reasonmag.com/9606/Fe.QWERTY.html) by Liebowitz and Margolis, which argues against that other legend. It has nothing to do with your question. But even people who try to read beyond the first few words of your explanation run into problems, because the geometry of typewriters is not obvious from the explanation. Rover hears "yadda yadda fast typists made the keys jam yadda yadda" which has given rise to a form of the legend that goes "QWERTY was designed to slow down typists so the typewriters wouldn't jam." which is complete nonsense, although it's been spread widely. So to avoid this sort of misunderstanding, I advocate the positive form: "QWERTY was designed to permit faster typing by placing commonly-used pairs of letters far apart, so their type bars would get out of each other's way faster." This is accurate according to the explanation in the the New Hacker's Dictionary, (e.g. http://kcmo.com/text/jargn10.txt), but Eric Raymond unfortunately fails to give sources for the information. This is also supported by other Liebowitz and Margolis articles available http://wwwpub.utdallas.edu/~liebowit/, which you can find referenced from the _Reason_ magazine page. They refer to a number of historical documents, but I did not find direct quotations to original sources about the QWERTY design. I would like more definitive corroboration; I vaguely recall reading supporting excerpts from the Sholes patent, but I don't have access to that now. I notice that Simon Slavin alleged on Monday that QWERTY was designed for separating pairs of keys and _also_ to "make the layout unfamilliar so the user would have to spend longer looking for the next key". I do not believe this to be accurate; I suspect it is a variant of the "slowing down typists" legend. He provided no historical corroboration, of course. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fandom.cons From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/05/06 Subject: Re: MOC-12 === Whatta party!!! Burqess holz...@xochi.tezcat.com (Daniel B. Holzman) writes: > I'm still wondering what you think you do at MOC that folks don't do at > hundreds of cons the world over. Parties are certainly not unique to > MOC. Even sexually explicit parties are not unique to MOC. But an event called "the return of the Bendovahoe tribe"? The title promises a combination of sexual degradation, racism, and general smarminess in a degree that can hardly be approached by any SF con. I hope. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Subject: Re: FILK: Disclave '97... From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/05/29 Newsgroups: rec.arts.sf.fandom,alt.fandom.cons John Pomeranz writes: > John Pomeranz > (who neither confirms nor denies any allegations made in song, but is > nonetheless amused) You may also be amused at a tidbit I found on alt.tv.murder-one. Apparently the episode aired on May 25 (the night after the deluge) includes a law professor named Pomerantz who hanged himself from a sprinkler pipe. Don't do it, John! Dan [ e-mailed and posted ] Hoey@AIC.NRL.Navy.Mil --- Newsgroups: talk.bizarre From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/05/30 Subject: Re: Incident for Solberg klu...@netcom.com (Scott Dorsey) writes: > There was a science fiction convention in DC this weekend.... Thanks, Scott, for not mentioning the word "Disclave". Not because it would embarass us, but because Louise followed up and _did_ mention the magic word. And I noticed Dejanews missed the original message. So I asked for articles mentioning "sprinkler*". It seems Sunday night after the deluge, a television show named "Murder One" was broadcast. According to alt.tv.murder-one, the episode includes a law professor named Pomerantz who hangs himself from a sprinkler pipe. I don't suppose you knew that the president of WSFA is a law professor named Pomeranz. Dan Posted and e-mailed Hoey@AIC.NRL.Navy.Mil "Bad cop. Soggy donut." --- TRUE CONFESSIONS Dear Cecil: I'm glad to see your discussion of Richard Wallace's anagram "research" in your March 7 column. [Wallace purported to prove that Lewis Carroll was Jack the Ripper by finding sexual anagrams in Jabberwocky, etc. --C. A.] Wallace's book was excerpted in the November Harper's. For a startling depiction of its true significance, you should see the response from Guy Jacobson and Francis Heaney, which appeared in the February Harper's letters column. --Dan Hoey, via the Internet Goodness. Jacobson and Heaney write: "The first paragraph of [Wallace's] article contains a grisly confession." They rearrange the letters of: This is my story of Jack the Ripper, the man behind Britain's worst unsolved murders. It is a story that points to the unlikeliest of suspects: a man who wrote children's stories. That man is Charles Dodgson, better known as Lewis Carroll, author of such beloved books as Alice in Wonderland. and arrive at: The truth is this: I, Richard Wallace, stabbed and killed a muted Nicole Brown in cold blood, severing her throat with my trusty shiv's strokes. I set up Orenthal James Simpson, who is utterly innocent of this murder. P.S. I also wrote Shakespeare's sonnets, and a lot of Francis Bacon's works too. I'm dying, I really am. Guy, Francis, you rock. --CECIL ADAMS This page last modified Wed, Jun 4, 1997. --- Newsgroups: alt.folklore.urban, sci.math Followup-To: sci.math From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/09/05 Subject: Re: Bible codes- Why no psychic prediction?? > Helge Moulding wrote: > >Except that any irrational number has that property: the numbers > >are infinitely long, and they are non-repeating, so that it is a > >trivial matter to prove that any pattern that can be described > >must be found at least once in the string! This is false; even if we consider finite patterns (so we are sure that they "can be described") several counterexamples can be given. Perhaps the simplest is 0.01001000100001000001..., which does not contain the pattern 11. (In case the term "nonrepeating" is confusing anyone, it means only that there is no positive integer P for which the Nth digit is equal to the N+Pth digit for all sufficiently large N. The presence of a digit appearing twice in a row is no bar to irrationality.) A number whose decimal expansion contains every n-digit pattern, and moreover for which each n-digit pattern occurs on average every 10^n places, is called "regular" (to the base 10). It is proven that almost all[*] irrational numbers are regular to every base. With regard to the "interesting" irrational numbers, however--pi, the square root of 2, e, the logarithm of 3, the cosine of 1--we have a much less satisfactory situation. None of them has been proven regular. We must consider it possible that from some point on, pi's decimal digits may all be zeroes and ones. But most mathematicians believe that in fact all of the interesting irrationals are regular to every base, even if we can't prove it. The fact that almost all irrational numbers are regular is no help here, because in fact almost all irrational numbers are "uninteresting" -- so uninteresting that we can't even point them out in a line-up. JoAnne gets close to this problem when she asks > Can stochastic processes be used to generate an irrational number, > or must they be the result of calculation? I wouldn't say that stochastic processes actually generate anything in particular, but the definition of real numbers allows that any sequence of digits defines a number, whether or not we can produce them as a result of a calculation. The numbers that cannot be produced by calculation are sometimes called "ineffable", and include almost all of the irrationals. I'm sorry I can't give you any references for these results, but I believe Martin Gardner had an article or two on these subjects. [*]"almost all" has a precise technical meaning: The set of nonregular numbers has measure 0. Dan Hoey E-mailed and (hopefully) posted. Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fan.wodehouse From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/09/11 Subject: Re: Favorite quotes? apiar...@aol.com (Anne Bannister) writes: > ... What are your favorite quotes, currently? ... Anne's favorite quote--I mean to say, my wife Anne, not any other Anne, such as might be asking the question--is so very subtly good that I read right past it, and didn't notice it until she pointed it out, when I nearly fell over. It's in a bit of dialogue between Madeleine and Bertie in _The Code of the Woosters_ (p. 46): ``Have you sometimes felt in the past, Bertie, that, if Augustus had a fault, it was a tendency to be a little timid?'' I saw what she meant. ``Oh, ah, yes, of course, definitely.'' I remembered something Jeeves had once called Gussie. ``A sensitive plant, what?'' ``Exactly. You know your Shelly, Bertie.'' ``Oh, am I?'' _Code_ is neck-and-neck with _Jeeves in the Morning_ for PGW's peak. It has about a dozen interlocking plots and it's full of these little gems. There's one bit where Sir Watkyn is trying to remember just what he had fined Bertie for at Bosher Street. Sir Watkyn recalls Bertie had pinched a lady's purse, and Bertie says no, it was a policeman's helmet, and Sir Watkyn estimates the two are morally equivalent. It's at that point that Sir Roderick Spode, who had been thoughtfully sucking the muzzle of his shotgun(!) throughout ``this absolute trial of Mary Dugan'' speaks up and says they're not the same thing at all, especially in the youthful good spirits of Boat Race night. All of which is to the point of asking if anyone knows who Mary Dugan was, and what she pinched that made her trial an apt metaphor for Bertie's? Dan Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fan.wodehouse From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/09/11 Subject: Re: Young men in spats john_...@Carleton.xpam.CA (Green Swizzle Wooster) writes: > Spatlet as a diminuitive if you like, but to simply call him "Spat" > would be perfectly etymologically correct. A spat is a baby oyster.... We should not omit to notice that by equivalence of participles, the spat may be the ``spitten image'' of his father. This is the (obscure but most plausible) etymologically correct version of what now more often appears in the pullet surprise versions ``spitting image'' or ``spit and image.'' All of this goes back to a fifteenth century metaphor of a son being as like his father as if the father had spit him out, or as the French say, ``C'est son pere tout crache.'' I might expand (in less mixed company) on whether the spit might itself be a metaphor. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math, sci.math.symbolic, sci.crypt, comp.misc, comp.programming, comp.security.misc, comp.theory Followup-To: comp.programming From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/09/19 Subject: Re: NP-completeness algorithm: errata jhayw...@students.uiuc.edu (jonathan seth hayward) writes: > I now have what I believe to be a polynomial time solution to an > NP-complete problem (specifically, satisfying a propositional > formula expressed in terms of parentheses, variables, negations, > and conjunctions).... > I will post a uuencoded compressed tar.... Posting uuencoded binaries to discussion groups is an abuse of Usenet. You've done this about 14 times now. Please do not do so any more. Posting URL's for your code (as you've done) is a good way of distributing code, and renders posting the targets of those URLs redundant. See news.announce.newusers. Please cancel your own net-abuse, don't wait for Dick Depew. Even if you're not abusive enough for Dick to cancel, it's still abuse. A change to responsible posting would go a long way toward convincing people you're not a crank. Also, posting the same message _separately_ to seven newsgroups is wasteful and potentially abusive. Learn how to crosspost. See news.announce.newusers. This, my response, is crossposted to the seven newsgroups you sent your stuff to. But I've directed the followups to comp.programming, because the programming method you are using does not have mathematical, theoretical, cryptological, or security implications. It's a fairly usual way of program manipulation of Boolean expressions, and does not reduce the complexity of Boolean satisfiability to polynomial time. What you've "discovered" is that any propositional formula on {p,q,r,...} can be written as (p & W) | (~p & X) for formulas W and X that do not mention p. So you take the lowest-numbered variable (in some ordering of variables) mentioned in the formula as "p" in this form, and write W and X in this form (for higher-numbered variables), with particular conventions for representing logical TRUE and FALSE. Sharing equivalent structure is expected. This is not rocket science. Your statement of what complement (logical negation) does is a long way of saying Complement( (p & Y) | (~p & X) ) == (p & Complement(Y)) | (~p & Complement(X)) but that's not a problem. The problem comes when you have intersection (logical conjunction), where (in the case that p is the lowest-numbered variable, we have Intersect( (p & Y) | (~p & Z) , W ) == (p & Intersect(Y,W)) | (~p & Intersect(Z,W)). This may or may not be what you described. Your description got so disorganized with attempts to micro-optimize tautologies and equivalent subexpressions I could not tell. Such optimizations do not significantly affect the algorithm's performance because they are rarely applicable when expressions get to a reasonably large size, unless you can prove otherwise. There were a lot of unproven claims about how this or that was the only possible case, but little or no mention of the usual case, in which Y, Z, and W are all nontrivial expressions with no significant sharable substructures. The problem with Intersect() is that your claim that the output is only O(1) plus the size of the inputs is false. Suppose Y and Z have few nodes and W has many nodes. The result has two large terms Intersect(Y,W) and Intersect(Z,W), each of which may easily be large, like W. So by intersecting a small expression with a large expression we have about doubled the total size of the expression. It's clear we can have O(n) small expressions; if we intersect them in one at a time, doubling the size of the large expression each time, we get an expression of size 2^O(n). You may be tempted to try taking advantage of the associativity of Intersect(), but Complement()ing each step before Intersect()ing breaks that idea. You've mentioned in an "errata" posting a requirement that "variables be indexed in order of appearance;" this sounds like an attempt to prevent Y and Z from having higher-numbered variables than W, in hopes of making Intersect(Y,W) and Intersect(Z,W) share a lot of structure (though if your proof relies on this, you're supposed to say so). But the ordering of variables is globally defined, and the ordering of these variables may have been predetermined by an earlier part of the expression than this Intersect() that's blowing up. If you claim you can force a fortuitous variable ordering or structure-sharing you have to prove it. There could conceivably be some way of manipulating these expressions or reordering variables to make them stay small. But finding that way is what me mean by "proving P=NP". To do that, you will have to stop programming and start reading and writing proofs. Writing code and waving hands about it being polynomial is not going to win friends and influence your professor. It is not enough to fail to be obviously wrong, you must find a way to be obviously right. And remember, posting ever newer versions of broken code in half a dozen newsgroups is just going to convince people you're more interested in publicity than in problem solving. The hard part of proving P=NP is not writing code, and it's not getting your code distributed. It's convincing people you can solve the problem and do it in polynomial time. You can discuss and explain your method in words in comp.programming and maybe learn what is hard about NP, or redirect from there to your favorite group (not groups). Or you can continue your binary spam spree and join the years-long parade of clowns. The choice is yours: what do you want to be? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.arts.sf.fandom From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/09/24 Subject: Re: Ross Pavlac Diagnosed With Cancer [ Ross Pavlac's statement ] > > For those who adhere to the Jewish or Christian > > faiths, Ross welcomes prayer. For all the arguments that have been passed around about this request, I'll say I viewed it as simply considerate not to ask for prayer from people who don't consider it appropriate. Just as I don't ask anyone to refrain from praying for me. I don't know enough about Islam to know whether it is appropriate for a member of another faith to request prayers from a Muslim. Wouldn't it be presumptuous? dbe...@nospam.hooked.net (Doug Berry) writes: > Speaking from personal experience, when the doctor looks at your > chart and announces "Cancer", even atheists start asking for help. I'm tempted to object, ``If an atheist claimed it was more often the religious who discard their faith the moment it becomes uncomfortable, he would be thought a bigot,'' except that that level of irony is rather darker than my mood, and quite beyond the ability of Usenet to handle without extraneous punctuation. But I am sure we had all better learn to just get along. My best hopes go with Ross, of course. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/09/29 Subject: Re: Graph Theory Enumeration jhni...@luz.ve (Jose H. Nieto) writes: [ Much good stuff about enumerating graphs. On graph isomorphism: ] > Of course an algorithm does exist! Given two graphs with n vertices > (graphs with different number of vertices aren't isomorphic) check > each bijection between the sets of vertices to see if the adjacency > relationship is preserved. The problem is that there are n! bijections, > so this "brute force" algorithm is impractical except for small n. No > EFFICIENT (i.e. with polinomially bounded execution time) algorithm is > known, and probably it does not exist. A related problem, the SUBGRAPH > ISOMORPHISM problem (i.e. to determine if a graph G contains a subgraph > isomorphic to another given graph H) is known to be NP-complete, so we > are talking of computationally complex problems indeed. Which is generally correct, except that you mustn't use the NP-complete problem SUBGRAPH ISOMORPHISM (S.I.) to argue that GRAPH ISOMORPHISM (G.I.) is difficult. Isomorphism is not what makes S.I. hard--the subgraph to test is can be an empty graph or a clique, for which G.I. is trivial. It's selecting a subset of vertices to induce the subgraph that makes S.I. NP-complete. So calling these problems "related" is misleading. Not that anyone has gotten anywhere near a polynomial-time algorithm for G.I., but neither is anyone near proving it NP-hard (unless something has been accomplished in the last 15 years, which I'd like to hear about). Dan Hoey e-mailed and (hopefully) posted Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.fan.wodehouse From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/11/24 Subject: Pat and Mike (Re: Plumb Lines and Xmas Treats) Gamera writes: > Ooh, a Christmas treat! Shall we have one online, as it were? There > are so many talented folks here, I'm sure we could count on a few to > croon, recite, and/or do "Pat and Mike" bits.... I would like to add my encouragement to anyone who is at all interested in cross-talk, and if anyone were to ask me of that lady with whom they saw me, I would be the first to protest that the person was no lady, but my wife. Still, I hope we may at last dispense with the green beards. This is a somewhat unpleasant topic to raise, for it reveals one of those instances of careless cruelty that the master inherited from his age. I am sure that most people who laugh at it now do not realize the reference, but perhaps a little explanation will make it clear. It is hard for those of us in these civilized times to understand just how terrible the the Irish famines of the 19th century were. Millions of people ekeing out a precarious existence were suddenly deprived of their major food source. The great majority of the population of Ireland was lost, more through starvation than from emigration, at a time that Ireland was a net exporter of food. One of the surviving images is of people eating grass in a vain attempt to stave off starvation, which led to a pronounced greenness about the mouths of the corpses and escapees. I have been persuaded that references to Irishmen with green beards are derived from this sad image. Please understand that I find it quite funny to read of Barmy and Pongo cavorting on the stage in green side-whiskers. I also find it humorous to read in _Psmith Journalist_ [ch 21] of Psmith translating ``Youse can't hoit a coon by soikin' him on de coco, can you?'' as ``Is it possible to hurt a coloured gentleman by hitting him on the head with a stick?'' But I fear these bits of period humor are quite unsuitable for modern re-enactment. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban, alt.radio.networks.npr Followup-To: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/11/28 Subject: Rule of Thumb sighting National Public Radio's news show _All Things Considered_ served up a disappointingly aged chestnut this Thanksgiving evening. They broadcast a listener's letter objecting to their use of the term "rule of thumb" on the grounds that its etymology referred to the size of a stick a man was allowed to beat his wife with, according to "a law in colonial times." Leaving aside the British origin of the phrase (OED's earliest cite is a 1692 use in the context of fencing) you would think some one at NPR would take a bit of time to check this folk etymology, and notice how widely and thoroughly it's been debunked. Or maybe they select for goofy mail, to make their news look more factual. The one good outcome was that I was led to reread Sharon Fenick's marvelous article at http://www.urbanlegends.com/language/etymology/rule_of_thumb.html where she goes over the judicial and urban legend that there ever was such a law (or common law rule, as the legend more frequently goes). Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math, alt.folklore.urban Followup-To: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/12/04 Subject: Re: Chess is Dead [obscene crossposting snecked] bme...@bruce.cs.monash.edu.au writes: > ... There are 32 pieces, of which 30 can be either on or off the > board. 2^30=10^9 When all pieces are on the board (and assuming that > each piece can be at each position), you get 64!/48!=10^61 ways of > arranging them. You're mistaken: 64!/48! ~ 10^28. But that's not important, since the formula you should use is 64!/32! ~ 5 x 10^53. > However, the pawns, knights, castles and rooks are interchangable There is no chesspiece called a "castle". The piece shaped like a castle is called a "rook". > (in the case of rooks not really, but then, they can't > really be at each possible position, either). Presumably you are talking about "bishops" here. > That reduces the number by a factor of 8!*2!*2!*2! for each side, > or 10^11. > Obviously, the number of possible ways of arranging _all_ pieces is > an upper bound for the number of ways of arranging _any set_ of > pieces, so we get an upper limit for the number of positions as > 2*10^9*10^61/(10^11)=2*10^59. Heaven knows where you got the 2 from. Repairing the formulas and arithmetic this should be 2^30 64!/(32! 8!^2 2!^6) ~ 5 x 10^51. But you've left out the possibility of promoting pawns to queens, rooks, bishops, or knights. For instance, after PxP, if two black pawns ans one white pawn are promoted to queens, this method gives us an upper bound of 2^29 64! / (33! 6!^2 3! 2!^7) ~ 2 x 10^52. But we could choose the extra piece to be any of 3 kinds on either of 2 sides, so we get more like 10^53. Promoting the three pawns in all possible ways makes a little over 10^54, according to a short program I wrote. This program also claims that we can't do better with more promotions because they would require more captures. We should multyply by two for which player has the move. It may be claimed that the possibilities of castling add another four bits to each position. This is considerably reduced because the future possibility of castling is usually encoded (in the negative) in the position of the king and rooks. The same argument dispenses with the possibility of capturing _en passant_. At any rate, adding a few factors of two is not not terribly meaningful with such gross estimates as this. > Compare this to the "four in a row" game.... > The difference between these games is a factor of about 10^30, or 2^100.... Comparisons of this type are not meaningful, because the number of _possible_ positions is not well correlated with the number of _sensible_ positions, i.e. those that might appear in competitive play. For instance, 98% of the positions calculated above have exactly one capture and three promotions. Experience suggests that this cannot occur without cooperation between the players. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/12/04 Subject: Re: Snuff films, cont. ang...@mindspring.com (Angus Johnston) writes: > The standard afu definition of snuff involves an onscreen murder > staged as a business enterprise. A few months ago, I argued that > the way the story has evolved in the camcorder age necessitated a > slightly broader definition---snuff being a movie that---a) depicts > a murder, b) was filmed by one of the perpetrators, and c) has been > sold by someone involved in its production for d) entertainment > viewing by a non-participant. This definition places the emphasis > on the production and sale, rather than on the motivation of the > filmmaker.... It seems to me that the "snuff film" urban legend includes at its core a fifth element (more critical that c) or d)) that e) the victim was hired as an actor. This is the fundamental "fear of unknown situations/dangerous professions" cautionary tale that makes it an urban legend. After all, if an urban legend doesn't keep 'em down on the farm, what use is it? Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: alt.folklore.urban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/12/07 Subject: Re: Snuff films, cont. h...@panix.com (Harry MF Teasley) writes: [about my statement that the `snuff film' urban legend includes at its core that the victim was hired as an actor.] > Your requirement is new and interesting to me: have you heard any > specific story where it featured? That's the way I recall first hearing it twenty years ago: unsuccessful aspiring actress accepts a porn role, find herself being murdered. My misty recollection is of reading this as a news story in a magazine. But it's been a long time, so I'm far from sure I've got it right. Dan [posted and e-mailed] Hoey@AIC.NRL.Navy.Mil --- Newsgroups: rec.puzzles From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/12/15 Subject: Re: How many points (9 different queens...) se...@panix.com (Seth Breidbart) writes: About putting the maximum number of nonattacking queens on a chessboard, in the presence of extra wood for blocking: > OK, here's the proof: > Say that a queen poisons the square it's on, and the squares directly > to its right, above it, and diagonally above right. Now each queen > poisons 4 squares, and no square can be poisoned by more than one > queen, so 16 is an upper bound. Bogus proof. Some of those poisoned squares you're counting may not exist. A good proof is to divide the board into 16 2x2 blocks. There can be at most one queen per block (it poisons the rest of the block, if you like) yielding the bound. ObPuzzle: Give a neat proof for at most 32 pawns, 24 if we exclude ranks 1 and 8. Dan Hoey Hoey@AIC.NRL.Navy.Mil posted and e-mailed --- Newsgroups: alt.folklore.suburban From: Hoey@AIC.NRL.Navy.Mil (Dan Hoey) Date: 1997/12/16 Subject: Re: Nomenclature Follies kay.shap...@salata.com (Kay Shapero) writes: > Local legend hath it someone from out of the area came in to map the > place and label all the streets. At one point, he pointed across the > ditch and asked someone what the name of the stret over there was. the > resident replied "Alla?" (meaning "there?") and the guy wrote it down > as the name of the street. What I want to know is if anyone can explain the presence of a street named "Dan Hoey Drive" in Dexter, Michigan. People have brought me photographs, but I still can't help feeling a bit skeptical. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- From hoey@AIC.NRL.Navy.Mil Sat Dec 27 22:32:15 1997 Date: Sat, 27 Dec 97 22:32:12 EST From: Dan Hoey To: kfl@clark.net Subject: Prison Dear KFL, Thanks for writing up your prison experiences. They made very interesting reading. I noticed the following typos, in case you're interested in searching the pages for them--I didn't keep track of where they were. seperated Sheilds flourescent potatos roomate roomate is also a file name/URL tag. Dan Hoey@AIC.NRL.Navy.Mil ---