Date: Fri, 2 Jan 2004 19:08:39 -0500 (EST) From: Dan Hoey To: math-fun Subject: Re: [math-fun] convex lattice 11-gon of minimum area At last I've got a bound that makes minimizing the area of convex lattice polygons a finite problem. There are two problems. First, the bound isn't terribly good. Second, the proof has a little hand- waving in it. I invite any improvements. Let us choose a convex lattice N-gon of minimum area. As we know, all images of the polygon under SL(2,Z) have the same area. Let us chose the representative polygon P with minimum diameter D. I will show that the area of P is at least D min( (ceiling(N/2)-1)/2, sqrt(1/10)D, 1) . For N>6, this implies that the area is at least D. (partial) Proof: Take vertices G,G' that realize the diameter of P. Using isometries of the plane, take G=(0,0), G'=(a,b), where b >= a >= 0 (i.e., in the second octant of the plane). If a=0, the theorem from 19 December shows that the area is at least D(ceiling(N/2)-1)/2. Otherwise we have b >= a > 0. Consider the transform F: (x,y) |-> (x,y-x) in SL(2,Z). |F((a,b))|^2 = 2aa - 2ab + bb = D^2 + a(a-2b) <= D^2 + a(a-2a) < D^2 . By our choice of P, F(P) must have diameter at least D, so there must be vertices H=(r,s) and H'=(r+c, s+d) for which |F((c,d))| >= d . This turns out to mean that point (c,d) lies outside the ellipse { (x,y) : (T+1)(Tx-y)^2 + (1/(T+1))(x+Ty)^2 = (T+2)D^2 } where T=(sqrt(5)+1)/2 is the golden ratio. In addition, since a^2+b^2 is the diameter of the polygon, we have |(c,d)| <= D, so (c,d) lies inside the circle c^2+d^2 = D^2. These requirements confine (c,d) to two crescent-shaped areas. In particular, HH' has slope at most 1/2. We may assume the slope is finite (d is not zero) by the first paragraph of this proof. Now I come to the point of using Lemma 2 from 19 December: Suppose a convex plane figure meets parallel lines R,S,S' such that the intersection with line R is a line segment of length X, and lines S and S' are at a distance of Y from each other. Then the area of the figure is at least XY/2. Line R will be GG', and lines S, S' will be the lines parallel to R through H, H' respectively. It remains to measure the distance between S and S'. Here I wave my hands to show that the distance is minimized by two cases: Ta > b, where the distance between S and S' is at least sqrt(2/5) D, approached when (c,d) is approximately (sqrt(4/5)D, sqrt(1/5)D). Ta < b, where the distance between S and S' is at least 2, approached when (c,d) is approximately (-1, D-1). I'm fairly sure I could prove this on a good day, but I'm somewhat bogged down in it now. Anyway, this completes the (partial) proof. This shows that if we examine all convex lattice N-gons of diameter at most D, and the minimum area is at most D, then we have found the minimum area N-gon. The reason I think this is not a very good bound is that the bound is based on a polygon that lies within the strip { (x,y) : -1 <= x <= 1 }, which we know has no convex N-gons for N > 6. I think the real bound is proportional to N D, meaning that we should have to search only through N-gons of diameter at most Constant.Area/N . Dan --- Date: Mon, 5 Jan 2004 09:04:15 -0500 (EST) From: Dan Hoey To: "Allan C. Wechsler" Subject: Re: [math-fun] Permutation group problem cc: math-fun "Allan C. Wechsler" wrote about: > [...] the name of the algorithm for determining whether a given > permutation can be expressed as a product of given generators: it's > the Furst-Hopcroft-Luks algorithm. I should probably have responded earlier, when you mentioned you had learned the name from the Rubik's Cube list. I believe I introduced the algorithm there under that name. Since then, I have been reliably informed that the algorithm is more usually and properly known as Sims's algorithm. The paper by Furst, Hopcroft, and Luks was essentially a formalization and analysis of the algorithm that Charles C. Sims described in 1967. I regret the mistaken attribution. Dan --- Date: Tue, 6 Jan 2004 12:15:50 -0500 (EST) From: Dan Hoey To: Eugene Salamin Subject: Re: [math-fun] looking for state-of-knowledge logic puzzles cc: math-fun Eugene Salamin wrote: > --- Joshua Singer wrote: > > As it was originally told to me . . . > > A traveler passes through a small village, each of whose inhabitants > > has a single colored dot .... > > ... As the traveler > > passes through, he casually remarks, "Some people in this village > > have blue dots". Ten days later, .... > This can't be right. The information provided by the traveler was > already known to everybody. In the case of the problem of the > unfaithful wives, the king issues an edict, which starts the clock > ticking. I believe the phrase "he casually remarks" should read "he publically announces," meaning that he states it in a way that (1) everyone hears and believes him, (2) everyone knows that (1) occurs, (3) everyone knows that (2) occurs, (4) everyone knows that (3) occurs, etc. all at the same time. It takes about N such pieces of information to make the clock tick for N days. Dan --- Date: Tue, 6 Jan 2004 17:51:42 -0500 (EST) From: Dan Hoey To: cal@rushg.aero.org Subject: [math-fun] Re; small area convex lattice polygons cc: math-fun@mailman.xmission.com Chris Landauer wrote: > well, the systematic search program i wrote to find minimum area > convex lattice polygons took 20 hours for n=20 and 80 for n=21, with > results as follows.... My understanding is that this still does not establish a lower bound on area even for the 11-gon, unless we can somehow prove that there is a minimum-area 11-gon with no edge more than 10 units long. Given the use of SL(2,Z) to force a unit edge, we would have to prove the existence of an 11-gon with a unit edge _and_ no edge longer than 10. I don't know any way of proving such a thing. I gave an argument earlier that would allow us to establish a lower bound rigorously, though I don't know if it's feasible, and I'd like to improve it. I should note that that argument does not allow us to assume a unit edge (since the transform yielding the unit edge might not yield the minimum diameter). Also, in case it wasn't obvious, I was speaking of Euclidean diameter, rather than the Manhattan diameter that Carl uses in his statistics. I've been looking for the net-accessible materials for help with the problem. Steven Finch has a good survey paper http://people.bu.edu/srfinch/cvxl.pdf though I would quibble with his statement that Barany & Tokushige ... computed that a_n lim --- = 0.0185067... n->oo n^3 via a heuristic solution of ~10^10 constrained maximization problems. The paper, which Finch links to at http://www.renyi.hu/~barany/cikkek.ps/hide.ps is more clear in saying that they prove that the actual value of the limit is the minimum of about 10^10 extremal problems (which are too many to solve), and that their heuristic computations indicate that the minimum is "most likely" 0.0185067.... It's possible that Finch means "heuristic" to imply "most likely", but I would be a lot more comfortable if "computed" were changed to "conjectured". Most surprising, to me at least, is that the minimal area n-gon (when mapped via the appropriate linear transformation) seems to approximate an ellipse (x/c)^2 + (y/d)^2 = 1, with c ~ .003573 n^2 and d ~ 1.656 n. Imagine the minimum eccentricity near n=463 . Another item that may be of interest is the fact that we may take the minimum-area 2n-gon to be centrally symmetric, based on a circular descent argument. Dan --- Date: Wed, 7 Jan 2004 14:48:05 -0500 (EST) From: Dan Hoey To: Chris Landauer Subject: [math-fun] Re: small area convex lattice polygons cc: math-fun@mailman.xmission.com Chris Landauer wrote: > Similary, I noticed that among all of the minimum area polygons that > my program found for even n, all of them were centrally symmetric > (that is, the second half edge directions are the negatives of the > first half ones). I think that there is a simple proof of this > (perhaps less cryptic and subscripty than the one in Barany and > Tokushiga).... Define an "extremal pair of vertices" of a convex polygon to be a pair of vertices that are the intersection of the polygon with two parallel lines. For each vertex v there is at least one vertex v' such that v, v' is an extremal pair; in a centrally symmetric polygon there is exactly one. Consider the extremal pairs (v,v'), taking vertices v in order around the polygon, and taking v' in the same order for each v. Let f(v,v') be the the number of vertices from v to v' (counting in the same order, and counting only one of v,v'). f(v,v') can increase or decrease by at most one from one pair to the next, and f(v,v')+f(v',v)=2n. So there must be some pair for which f(v,v')=n. Take such a pair, cut the polygon in two parts through the line vv', and paste two copies of one part together. This is a centrally convex polygon, and if we never choose the larger of two unequal parts the new polygon will have area at most that of the original polygon. So for any minimal area 2n-gon, we can find a symmetric 2n-gon with the same area. I'm surprised, though, to hear that _all_ minimal 2n-gons were symmetric. I would have expected some chimerae--mismatched pairs of equal area. Perhaps there's something else going on here. I will say that I have not been able to get through even the third page of Barany&Tokushiga. I think they are talking about the relationship between a centrally-symmetric polygon and the convex hull of its edge vectors, but I haven't been able to read it in a way that looks believable. They write "Area P(C)" but I'm not sure what P(C) is supposed to mean; also they write "A(C)" but they only define A(n)--is that supposed to mean Area(C)? Anyone care to explain it? The paper is at http://www.renyi.hu/~barany/cikkek.ps/hide.ps . Dan --- Date: Thu, 8 Jan 2004 14:57:36 -0500 (EST) From: Dan Hoey To: Michael B Greenwald Subject: Re: [math-fun] Secret Santa problem cc: math-fun Thu, 08 Jan 2004 11:18:25 -0800 Marc LeBrun Can you think of a way to generate secret derangements that's about as natural as drawing names from a hat? Thu, 08 Jan 2004 14:44:12 EST Michael B Greenwald Drawing names from two hats? Split the names randomly, partitioning the group into reds and greens.... If the population is odd, partition the group into [n/3] reds, [(n+1)/3] greens, and [(n+2)/3] yellows. Yellows put their names into the red hat, with excess into the green; reds put their names into the green hat, with excess into the yellow; greens put their names into the yellow hat. Then each person draws from their own color of hat. That unfortunately removes the mystery from trios and the red member of quintets. And it spoils the seasonal color scheme. Dan --- Date: Thu, 8 Jan 2004 15:51:23 -0500 (EST) From: Dan Hoey To: Eugene Salamin Subject: Re: [math-fun] Secret Santa problem cc: math-fun Eugene Salamin wrote: > Here is one way to generate derangements with equal probability. Place > numbers 2 to n in a hat. Draw a number; it becomes p(1). Put 1 into > the hat and withdraw 2 if it is not p(1). Draw a number; it becomes > p(2). Replace 2 if it is not p(1), and withdraw 3 if it is not p(1) or > p(2). Draw a number; it becomes p(3). And so on. I think you can derange 1,...,n-1 and have nothing to pick for p(n). Dan --- Making Light: PETA ::: January 14, 2004, 01:05 AM At last I'm drawn out into the blogosphere... I heard on the radio last week about mountain lions out West who have been on the protected species list so long they think humans are wimps. So they tend to hang around town and browse on the house pets now and then, and a few of them have stalked and attacked able-bodied humans. So now the animal controllers deport the ones they find in back yards, and counsel that the greater kindness is to be "mean" to wild critters --drive them off, and make it clear it's not okay to hang with the naked apes. And the ones that bite Rover get shot. Well, this is a blog entry about PETA, and I have to say that the "Fishkill" episode has firmly cemented them in the "not concerned with accuracy" column as far as I'm concerned. Lydy mentioned Raphael's theory that they were not born to looniness, but had it thrust upon them, that "The first lab that PETA busted into was one of the real horror-show DOD labs. What was done there was ... [ awful ]. Raphael's theory is that the experience traumatized them and caused PETA to be a dysfunctional group from their very inception." I don't believe that theory, but I believe that if PETA found someone who might believe the theory and be swayed by it, they would tell the story. Like Colin Powell's unquestionable evidence for WMDs. (Republicans--the other "L" word.) Anyway, you might suppose that since this is a blog entry about PETA, I'd be interested getting PETA to confront the moral dilemma of dealing with the mountain lion who ate your companion animal. But no, that's not what caught me, not in that sense. I just thought that killing mountain lions was a waste of good predator that could serve a useful purpose if delivered to PETA's headquarters. --- Making Light: PETA ::: January 14, 2004, 01:13 AM Speaking of the kingdomist bigots who spare the animals only to massacre the vegetables, I'm glad I managed to track my memory back to Dave Langford's "Load of Crystal Balls", in which he quotes "that famous SF novel set in 1984, G. K. Chesterton's _The Napoleon of Notting Hill_" ... Mr Mick not only became a vegetarian, but at length declared vegetarianism doomed ("shedding," he called it finely, "the green blood of the silent animals"), and predicted that men in a better age would live on nothing but salt. And then came the pamphlet from Oregon (where the thing was tried), the pamphlet called "Why should Salt suffer?", and there was more trouble. [1904] Yum, the the green blood of the silent animals. --- Making Light: PETA ::: January 14, 2004, 01:15 AM Nix writes: (case in point: snails, er, escargot.) Escargot (Mark-Jason Dominus pointed out) is not a food in itself, but merely a vehicle for conveying the French national foods, garlic and butter. Just as chicken wings are served in upstate New York to eat hot sauce with. And Yorkshire pudding, to help the English savor their suet. --- Making Light: PETA ::: January 14, 2004, 01:24 AM A propos the idea that one should find a good vegetarian restaurant, I hope that Washington, DC residents and visitors will brave the ganglands of Langley Park to sample the remarkable cuisine of "Udupi Palace". I'm a meatie, you bet, but... that food is good! (Most of what I ate was Indian-spicy, but that's because that's what I ordered.) --- Date: Wed, 14 Jan 2004 12:34:04 -0500 (EST) From: Dan Hoey To: "William P. Thurston" Subject: Re: [math-fun] Re: small area convex lattice polygons cc: dpt@math.harvard.edu cc: math-fun cc: cal@rushg.aero.org Chris Landauer wrote: > ... i still can't figure out what B&T mean by ``the minimizing > polygon'', so i have no useful comment about that paper yet. Oops! I forgot to send this reply I wrote to Bill Thurston's note on Thursday. It has some explanation that may help you understand B&T. Bill Thurston wrote: > Another strategy that would probably be revealing and perhaps > algorithmically efficient would be to use some description of polygons > that is invariant by SL(2,Z). Amen, brother. > One way to do it: > (a) for each edge in the polygon, how many lattice points does it > intersect, excluding end points? [is this ever more than 0?] No, not for minimal-area polygons. > (b) Each pair of successive edges defines two vectors that give a > coordinate system for the plane. What are the coordinates of the vector > for the following edge, in this coordinate system? Neat, though I think they might not always be integers. Maybe that's not so important. > Perhaps better, a related invariant description can be given by (1) > the areas of the triangles spanned by any 3 successive vertices, and > (2) the areas of the quadrilaterals spanned by any 4 successive > vertices. This is a sequence of 2n integers, 3 too many --- the 3 > consistency conditions can again be expressed by a matrix product that > has to be the identity. At least these will be half-integers. Here's another approach I got from the Barany&Tokushiga paper ( http://www.renyi.hu/~barany/cikkek/hide.ps -- sorry for the earlier bogus URL ). They take the convex hull C of the edge vectors. They make the important observation that for even n the set V(C) = { (a,b) in C intersect Z^2 : gcd(a,b)=1 } must be exactly the set of edges of the polygon, because otherwise we could replace a pair of vertices of C with the internal primitive pair, giving a smaller area. The problem I had yesterday was that they gave a stealth definition of A(C) = 1/8 sum sum | det(t,u) | t in V(C) u in V(C) which turns out to be the area of the original polygon (by saying a "stealth definition" I mean they didn't say it was a definition, it was just the first use of A(set). I can't complain, I do it myself, usually regrettably.) Anyway, the polygon C has only O(sqrt(n)) vertices, so it's a big improvement. Also, it handles the translation invariance. They deal with SL(2,Z) by taking the "lattice width" of C in the (0,1) direction. They don't define lattice width (citing Kanann&Lovasz in Ann. Math. 128 (1988) 577-602). Not having that, I think this just says to map C to minimize "delta x", though any better insight would be appreciated. Unfortunately, for odd n the convex hull of the edge vectors can include unused primitive vectors. The best I've been able to do for a normal form for that is to take the convex hull of the edge vectors with their negatives, and attach a list of unused primitive vectors. More later, Dan --- Making Light: PETA ::: January 14, 2004, 01:22 PM Teresa Nielsen Hayden: Dan, are you having a manic episode? I don't think I do that, just ADD and depression. What happened is I read this neat blogroll on the way home (still only halfway through) and had a bunch of comments. So I typed them up in emacs while waiting for the home computer to get around to connecting and opening up the page. There was an outage about then where I couldn't get through, so the comments got longer and the hour got later, and I never got around to figuring out that the text was being treated as HTML. On consideration, it would have been more appropriate to put all my comments into one message, but I was learning the mechanics and tried to keep it simple. Perhaps this is better formatted. Thank you for your concern. --- Newsgroups: sci.math From: haoyuep@aol.com (Dan Hoey) Date: 15 Jan 2004 04:30:49 GMT Subject: Re: Any news on odd perfect numbers? On Fri, 9 Jan 2004, Mark Griffith asked: > Anyone know of any recent work on the odd perfect number > question? Oddly enough, a paper claiming to prove the conjecture has appeared, dated Thu, 8 Jan 2004, at http://www.arxiv.org/abs/hep-th/0401052/ I haven't got the background to tell whether it's good or bad. --- Date: Fri, 16 Jan 2004 12:41:45 -0500 (EST) From: Dan Hoey To: math-fun Subject: Re: [math-fun] When liberals do science... > Can you laugh away this graph? .... I can't laugh away the fact that you are helping Gene make math-fun a list I don't want to read. He did, as usual, spew his political credo uninvited and with only his word for support. That's his habitual practice (and the last time I pointed this out, he called it a left-wing rant, which makes him a liar, too). But you can't convince him--he has all the non-facts on his side, and he is his own ultimate authority. So please don't try to debate his issues--the debate is much larger than you can answer on math-fun, unless you turn this into the political list Salamin is slavering for. Dan Hoey@AIC.NRL.Navy.Mil --- Making Light: Housekeeping notes from all over ::: January 21, 2004, 04:58 PM Death to popups, thanks. I agree the author/message connection could be clearer. Can you get your software to put an between comments to keep them apart? And even if not, there's a bit of a problem after the last comment, which transitions into "Note: I hate closing old comment threads..." as if it were part of the comment. I was wondering why the last person on every thread always complained about closing comment threads. --- Making Light: Housekeeping notes from all over ::: January 22, 2004, 01:31 PM Me: ...after the last comment, which transitions into "Note: I hate closing old comment threads..." as if it were part of the comment. Xopher: On my browser (IE 5.5) the Note is on a gray background instead of the white that the comments are on. Oops... I had style sheets turned off. That usually gives me a little better chance at decoding some of the really bad formats out there, but I can't complain if it drops your useful visual cues. In fact, I really like the look with your style sheet, so I'll probably keep it turned on, at least until I visit the next toxic waste site. --- Newsgroups: geometry.research From: haoyuep@aol.com (Dan Hoey) Date: Thu, 22 Jan 2004 19:03:19 +0000 (UTC) Subject: Re: The generalized Schlafli symbol John Berglund wrote: > I have a few questions. What is the notation used when a > flagstone has three different neighbors? In some cases, the lines between rows may have to cross. If you fiddle a bit with row order and the alignment, you can reduce this a bit. In your example, with flags +----------------+ / \ a a | /c c\b b| /d d\e e| / \ f f | + +-----------+ | | g g -' |i i|h h-' | | -' |j j|l l-' | k k | -' +---------+' I'd draw its GSS like this: k *---------* *---------* | | j *---------* *----3----* | | l | *-------* *---------* | | g | | *--3--* *---------* | | | | | h | *-------* *-------* | | | | i *----5----* *-------* | | | 3 | d *---------* *-------* | | | | e | *-------* *-------* | | | | | | f | | *-----* *---------* | | 4 a | | *-----* *---------* | | | | b | *-------* *----3----* | | c *---------* *---------* I wondered for a while why the numbers are sometimes between horizontal lines and sometimes on top of them. I figured out that the numbers are labels for the connected components of the thumb-obscured graph. In these components the vertices all have degree 1 or 2, so the components are either paths or loops. The labels can actually appear anywhere that unambiguously labels the component. For instance, the "5" above labels the long path "kjidc", so it could easily be moved down a row or two. But if it were moved up a row, it could be mistaken for a label on the "lhg" path. The label of a component must be a multiple of half the number of flags in that component, and I think it can only be an odd multiple if the component is a cycle or a single flag. It might be instructive to see how this looks for similarly messy polytopes in four dimensions. Dan --- Making Light: Open thread 17 ::: January 23, 2004, 01:11 PM Steve Taylor: ... a sweatshop in Tijuana full of underpaid gamers generating bashing away at monsters, etc, to gain valuable in-game objects for later sale by their employers I'm as gobsmacked as anyone, but I was wondering why I couldn't parse it. Then I realized Steve probably meant to type "generating & bashing" but forgot to code the "&" as "&". HTML strikes again, and thank Ghu for those previews. WYSINWYG. --- Making Light: Housekeeping notes from all over ::: January 23, 2004, 01:34 PM Patrick Nielsen Hayden: Regarding "spamproofing" your email adddress. Movable Type already encodes your address in a harvesting-resistant form, so that it's not actually out there in plain text... I don't know what you mean by harvesting-resistant--they look pretty plain to me. If you mean the hexadecimal escapes in "mailto:name@isp.com", I'd be surprised if that stops anyone. Perhaps there's a countermeasure I'm not noticing. Or perhaps I'm overestimating the state of the harvesters' er, "art". --- Making Light: Housekeeping notes from all over ::: January 23, 2004, 11:29 PM Patrick: Oh, don't get all huffy with me, for crying out loud. We're non-technical people who're doing our best. Yes, of course Movable Type's rendition of email addresses is only a step away from plaintext. So is putting DONOTSPAM in the middle of your email address. That was my point. I apologize for any huffiness. Please forgive a technical person who has usually seen the &#NN; escapes as a way of making it easier for robots to parse URLs. On further consideration, I'm willing to believe it may help slow down the bad guys. Let me state unequivocally that I appreciate your doing your best. I'm here because the substantive stuff is so damned good. Not that I can criticize the technical stuff, either. Good look. --- Making Light: Free giant shrimp from the oceans of Mars ::: January 29, 2004, 07:53 PM I feel as if I've been dropped into a Heinlein novel. Giant shrimp I can get locally. Now if they put Old One chowder on the menu... Them's good grokkin'. --- Making Light: Free giant shrimp from the oceans of Mars ::: January 30, 2004, 12:18 AM Meanwhile, the Martian Air Force wishes to reassure everyone that the thing in Gusev Crater is a harmless weather balloon. (not to be confused with the plain-text version): Anne loved the story, so I told her about the "Free giant shrimp from the oceans of Mars" thread. "They'll have a hard time delivering," she says. Ever prone to huffiness, I explain, "Well, the freeness of the giant shrimp is from, in the sense of causally arising from, the oceans of Mars... "That is to say, conclusive evidence of oceans on Mars... "Or, perhaps, Mars-related ocean activities...." At which we invoke the twenty-first century version of Godwin's law, and so to bed. I must admit, I'm under the influence of Patricia Marx's "Boswell's Life of Jackson" in this week's New Yorker. "When a boy, he was already fond of other children, and, as you know, he maintained his fondness for them into middle age." Recommended. --- Math Forum From: Dan Hoey Date: Jan 30, 2004 3:03 PM Subject: Re: Is the non-existence of odd perfect number proved? > I'm reading some paper written by Simon Davis, "A proof of odd > perfect number conjecture". I think some people read it already. > I didn't done it yet. If you ever do done it, you may be the first. > But I wonder whether the paper is right or wrong. Is there somebody > who read it and can comment about it? Unknown, but Robin Chapman and others tried to read it and got through parts of it. See http://www.mathforum.org/discuss/sci.math/t/569501 . I found Robin's analysis useful in understanding what the paper was driving at. I haven't heard from anyone who has teased a valid proof out of it. Dan Hoey haoyuep@aol.com --- Making Light: Painful announcement ::: February 18, 2004, 10:16 AM Mitch Wagner: If I ever use a pen name, it will be Norm D. Plume... In case it leads you to reconsider your choice, I should mention that "Norm DePloom" is a prolific Internet author of "stories of tortures used by debauchers" as Tom Lehrer put it. Don't Google it if you're easily squicked. A lot of pen names have been snapped up. "Sue D. Nym" is another porn writer, and I expect "Anna Nimity" and "Jörn Emir" are out there somewhere. I bags "X Hismark" but someone will probably tell me I'm too late. Recalling Lehrer reminded me of the next line: "lurid, licentious, and vile." That sounds like it was borrowed from somewhere, but I haven't found a source. Anyone? --- Making Light: Painful announcement ::: February 18, 2004, 07:04 PM Jonathan: Excerpt from "Smut" by Tom Lehrer: ... I probably didn't make myself clear. I knew the Lehrer lyrics, but I was speculating about whether the phrase "lurid, licentious, and vile" might be a reference to a court decision, as utterly without redeeming social importance is lifted from Roth v. US (1957). I searched through Supreme Court decisions to see if I could find anything. I didn't find what I was looking for, but I did find the case that Lehrer was singing about: Memoirs v. Massachusetts (1966). I found it by searching for "lurid", but it is a treasure trove of words that made up the song--debauchery, licentious, vile, candor, orgy--and some other words and concepts that you couldn't even suggest on TV back then. There's even a long discussion on whether "pandering" is a criterion that can be used in determining obscenity. It looks probable that Tom Lehrer made up "lurid, licentious, and vile" as a reference to this case, but not to a specific phrase. --- Making Light: Pickled dragon ::: February 19, 2004, 09:42 AM Teresa: Pixels are free. He didn't need to skimp on punctuation. It almost looked like he had been administratively disperioded. (Dispointed? Expunctuated?) --- Making Light: Slushkiller ::: February 19, 2004, 11:29 AM Teresa: ... The author has a significant following. An atypical title of theirs gets sold as part of a multi-book contract. The manuscript gets delivered and, my goodness, it certainly is different... I keep wanting this one to end with "after publication they discover the manuscript was submitted by a third party without the author's knowledge or intent." But it would take some serious plot flim-flam to make it work. --- Newsgroups: geometry.research From: haoyuep@aol.com (Dan Hoey) Date: Mon, 23 Feb 2004 20:11:19 +0000 (UTC) Subject: Re: Brussels sprouts Joe Wasserman wrote: > Brussels Sprouts is the same as the original Sprouts game, but > the maximum degree of every node in Brussels Sprouts is 4, rather > than the traditional 3 in Sprouts. No. That is not a correct description of Brussels Sprouts. I quote the summary of Brussels Sprouts from David Molnar's game page: Several plus signs are drawn to start with, and a move consists of drawing an arc connecting two "branches" of plus signs, and then crossing that arc at some point with a small dash, effectively constructing a new plus sign, two of whose branches are already used. This accords with my recollection of the game described in Martin Gardner's column. The key distinction between Brussels Sprouts and Degree-4 Sprouts is that in Brussels sprouts, every spot has predetermined sites (the arms of the plus signs) at which connections can be made. This seemingly minor change makes the game completely different from the usual kind of Sprouts. A true Degree-4 Sprouts game can never end, since each move creates a new spot with two lives, and the next player can connect that spot to itself. We might imagine a game in which the initial spots are small T shapes whose three arms are available for connections, and in which a move consists of connecting two arms with an arc and adding a new arm to the arc (on one side or the other). I imagine that game would have some strategy, though it wouldn't have the stark elegance of regular Sprouts. Another possibility would be for the first player to draw the arcs and the second player to add the arms. That would be a (normal play) win for the second player with one spot; I suspect the first player might win all the other sizes. Dan Hoey haoyuep@aol.com --- Math Forum From: haoyuep@aol.com (Dan Hoey) Date: Feb 25, 2004 1:30 PM Subject: Re: Graph Isomorphism On 22 Feb 2004, Olaf Delgado wrote: >Of course I agree that a planar graph may easily have exponentially >many embeddings. Consequently, checking each embedding separately >will not make for a polynomial time isomorphism algorithm. I >was thinking more along the lines of breaking up the graph into >3-connected pieces and dealing with each of these separately. >I have not worked out the details and am not completely sure if >anyone has.... Yes, they have (and they did it just that way). This was hot stuff thirty years ago. There was even a linear time algorithm: J. E. Hopcroft and J. K. Wong. Linear time algorithm for isomorphism of planar graphs (preliminary report). In Conference Record of Sixth Annual ACM Symposium on Theory of Computing, pages 172-184, Seattle, Washington, 30 April-2 May 1974. http://portal.acm.org/citation.cfm?id=803896&dl=ACM&coll=portal The authors state that this is intended as a theoretical result, since the constant factors are worse than you would see in the n log n algorithms for reasonable sizes of graphs. Also, this doesn't seem to provide a canonical form, which is what you would want for a searchable database of planar graphs. The canonical form requires sorting, so I used to think it couldn't possibly be done in linear time. Now I don't know if radix-sort techniques might be able to do even that. Dan Hoey haoyuep@aol.com --- Making Light: Open thread 18 ::: February 25, 2004, 04:20 PM Kate: ...I'd say that Making Light isn't a fanzine, primarily because of: 3.3.12: Best Fan Writer. Any person whose writing has appeared in semiprozines or fanzines or in generally available electronic media during the previous calendar year. I see that the Fan Writer definition admits the possible existence of electronic media that aren't fanzines. I'd have to reach pretty far to take it as ruling out the existence of fanzines in electronic media. It's much harder to figure out whether Making Light has published at least four issues in its history. I know issues are discussed, but are the discussions published in issues? As for Best Fan Writer, I'm certainly not going to lobby against Teresa, but I might note there is a bit of a tradition there. Perhaps it's time for the tradition to end, but it could make winning more difficult. And something of an admission of failure for WSFS to give up before filling up all his mantelpieces. But I suspect we digress. As I read it, Tom is more amused by stretching the fanzine category than interested in who wins Hugos. Forgive me if that's reading too much into the "constitutional crisis" presentation. --- Newsgroups: geometry.research From: haoyuep@aol.com (Dan Hoey) Date: Sat, 28 Feb 2004 13:13:20 +0000 (UTC) Subject: Re: Brussels sprouts I wrote: > A true Degree-4 Sprouts game can never end, since each move > creates a new spot with two lives, and the next player can > connect that spot to itself. I recently noticed a way that we could define a Degree-4 Sprout- like game that would have some strategy. I got it from David Eppstein's CGT page http://www.ics.uci.edu/~eppstein/cgt/. He glosses Sprouts as "a game invented by Conway and Paterson in which players construct a degree-three planar graph by drawing two-edge ears." I had never heard of "ears" before, but it's clear what he means--add a new spot and connect it to an existing spot or spots with two edges. This makes it easy to generalize to edgier ears. We could define a game in which players construct a degree-four plane graph by drawing three-edge ears. Each move adds four lives and removes six, for a net loss of two, and the last two lives in a region can't be used. So from N spots a game can last at most (4N-2)/2 moves. It should be a challenge for people who find Sprouts too easy. If that isn't enough of a challenge, we could have degree-five Sprouts with three-edge ears, lasting at most 5N-2 moves. Dan Hoey haoyuep@aol.com --- Making Light: Open thread 18 ::: March 03, 2004, 04:52 PM Xopher: I love the Unst Bus Shelter. Particularly the proclamation from the Queen allowing the Hamsters to wear Royal Regalia. You saw a hamster proclamation? I found a proclamation that she had sent the crown jewels in lieu of her personal presence. I wonder if there's a law against forging royal proclamations. It sounds like lese majeste, at least. --- Math Forum From: Dan Hoey Date: Mar 5, 2004 2:40 PM Subject: Re: 4 Points David Eppstein wrote: [ Of four-point configurations in the plane, where we ask how many circumcircles of three points fail to contain the fourth, or "associated", point. ] > With probability 1 the four points have a unique Delaunay > triangulation. > A triangle is Delaunay iff its associated point falls outside it. I think you mean to say a triangle is Delaunay iff its associated point falls outside its circumcircle. The rest of the argument looks good. It's a pity about the original poster's dictionary and other thing. Dan Hoey haoyuep@aol.com --- Newsgroups: sci.math From: haoyuep@aol.com (Dan Hoey) Date: Sat, 6 Mar 2004 05:41:06 +0000 (UTC) Subject: Re: P, NP and coNP On 05 Mar 2004, Craig Feinstein wrote: >I wrote a letter before about the Monty Hall fiasco to Bob. >I don't want to give the impression that I think all of the >experts in mathematics are idiots only because of 20 letters >that were written to Marilyn vos Savant in 1990. The Parade column did not print 20 letters, it printed only excerpts from letters. One or two of those excerpts implied a lack of understanding by their authors. The others may have been from correct letters that pointed out the real errors in vos Savant's analysis of the problem printed in her column. I have never seen any indication that she understands the difference between the problem she posed and one to which her analysis would be applicable. >I really only wanted to >indicate that professional mathematicians are human and make >mistakes. So I apologize if I offended anyone. I doubt many people are offended at your misunderstanding of the MvS fiasco. You are more effective at giving offence in your suggestion that http://arxiv.org/abs/math.NT/0312309 deserves respect as a mathematical paper. I've personally wasted enough time noticing that the first sentence of the "Proof" of Theorem 2 is asserted without support, and that the third sentence of the "Proof" of Theorem 3 incorrectly characterizes Theorem 2. It's hard to tell which error is more effective in evaluating the paper. The first demonstrates a pretense of proving bounds on computation or proof without any mathematical model of the computation or proof process, and the second demonstrates a willingness to engage in proof by misquotation of lemmas. At least these antics have persuaded me that I need not seek for enlightenment in the half of the paper which abandons the pretense of relevance. Dan Hoey haoyuep@aol.com --- Newsgroups: sci.math From: haoyuep@aol.com (Dan Hoey) Date: Tue, 16 Mar 2004 21:36:27 +0000 (UTC) Subject: Re: INTERSECTION OF TWO SQUARES A few weeks ago, some anonymized poster wrote: > Intersection of two squares of equal size can take place in one of > six ways. > 1. the overlap is a triangle > 2. the overlap is a quad... > 6. the overlap is an octa > I see on other cases in which area of overlap is non-zero. This looked like a fairly silly question, but it has a surprising connection. Suppose we take the square S = [-1,1]x[-1,1], and the square T which is S rotated by an angle of theta. Let P be a point in the plane, and we consider the intersection of S with the translate of T whose center is P. If the intersection has positive area, it will be a convex polygon, and we define f(P) to be the number of sides of the intersection. Otherwise, let f(P)=0. Sketching the regions on which f(P) is constant, I found my favorite drawing of a tesseract. Here's an ASCII graphic version, if you view it with a fixed-width font. *--------------------* -'|\ -'|\ -' | \ -' | \ -' | \ -' | \ -' | \ -' | \ -' | \ -' | \ -' | \ -' | \ -' | +' | \ .-' | -' \ | \ *-----------------+--*' \ | \ |\ | |\ \ | \ | \ | | \ \ | \ | \ | | \ *--------+-----------* | \ | | \ -'| | -'| | \ | | .+' | | -' | | \ *--+--+--+--+--------* -' | | \ -' \ |-' \ | -' \ -' | | \ -' ++ \| -' +' | | \ -' -' + + -' -' \ | | +' -' |\ ++' -' \ | | -' \ .-' | \ .-| \ -' \ | | -' *--------+--+--+--+--*' \ | | -' | | +' | | \ | | -' | | -' \ | | \ | *-----------+--------*' \ | | \ | \ | \ \ | | \ | \ | \ \| | \| \ | \ +--+-----------------* \ | \ -' | -' \ | +' | -' \ | -' \ | -' \ | -' \ | -' \ | -' \ | -' \ | -' \ | -' \ | -' \ | -' \|.-' \|.-' *--------------------* To calculate f(P), count the number of faces of the tesseract whose image contains P. Dan haoyuep@aol.com --- Newsgroups: sci.math From: haoyuep@aol.com (Dan Hoey) Date: Tue, 16 Mar 2004 22:04:38 +0000 (UTC) Subject: Re: INTERSECTION OF TWO SQUARES I wrote: >Sketching the regions on which >f(P) is constant, I found my favorite drawing of a tesseract. >Here's an ASCII graphic version, if you view it with a >fixed-width font. Unfortunately, some helpful software thought some of my backslashes were attempts to continue long lines. This picture should look better. > *--------------------* > -'|\ -'|\ x > -' | \ -' | \ x > -' | \ -' | \ x > -' | \ -' | \ x > -' | \ -' | \ x > -' | \ -' | \ x > -' | +' | \ x > .-' | -' \ | \ x > *-----------------+--*' \ | \ x > |\ | |\ \ | \ x > | \ | | \ \ | \ x > | \ | | \ *--------+-----------* > | \ | | \ -'| | -'| > | \ | | .+' | | -' | > | \ *--+--+--+--+--------* -' | > | \ -' \ |-' \ | -' \ -' | > | \ -' ++ \| -' +' | > | \ -' -' + + -' -' \ | > | +' -' |\ ++' -' \ | > | -' \ .-' | \ .-| \ -' \ | > | -' *--------+--+--+--+--*' \ | > | -' | | +' | | \ | > | -' | | -' \ | | \ | > *-----------+--------*' \ | | \ | > \ | \ \ | | \ | > \ | \ \| | \| > \ | \ *--+-----------------* > \ | \ -' | -' > \ | +' | -' > \ | -' \ | -' > \ | -' \ | -' > \ | -' \ | -' > \ | -' \ | -' > \ | -' \ | -' > \|.-' \|.-' > *--------------------* Dan haoyuep@aol.com --- Making Light: Is it me -- ::: March 19, 2004, 12:13 AM I occasionally catch flak from people who don't feel up to confronting Patrick. In the pause for laughter this hard-hearted filk just leapt up and I can't get it out of my brame. Patrick's teeth are sharp, Teresa's teeth are sharper. Carp at her: she'll serve filet of carper. Well actually only the first two lines leapt, so I had to grind out a rhyme. Hope it doesn't suck too much. "Sir or madam, will you pub my filk...." --- Making Light: Street cred ::: March 23, 2004, 05:47 PM Kip Manley: ...Points off for huffiness and general mean-spiritedness, but otherwise, O anonymous LDSer who's never had candle salad, I bow to you.... Forgive me for offering a possible reinterpretation, Kip--after all, you are the authority on your own subtext--but I would say you were standing up for the candle virgin. By the way, I started writing this in malaprops--forget me for authoring a remandation...--and I am glad that it has already been done to death in these comments, because it would have been hard work. And even when I don't try, I often find myself skating on too stylistically thin ice and drowning in incomprehensibility. Anyway, "incline" is just too perfect an act to follow. --- Making Light: The miserable Hugo ::: March 25, 2004, 03:32 PM Alex: Jane Austen Doe's whine was simultaneously fruity and bitter, not to mention immature. I suspect that it became spoiled somewhere in the bottling process. That's where these ranters usually fail--neglecting to put the cork in. Meredith: So I'm good if I write the new as long as it is for something else's sake? Like, say, the love of a good cat or to save the spotted subjunctive? The Usher rant could have been poetic with a little more work. For instance, symmetry demands that there be an out for those who write the old, say if it's not for the sake of predictability or nostalgia or, oh anything. Tom: Other Change of Hobbit's closing.... That's so damned depressing, even though I never got there. I think I've been sensitized by seeing Larry Smith's bag at Lunacon, with the Somniorum Mercatores logo from Moonstone Bookcellars. Jill Smith: When I read the title and the first sentence of this post, this flashed through my head: "You don't mean a Hugo winner is now the latest to jump in and moaning about publishing?!" On the way to that very idea, my eye chanced on the second word of the second sentence, and I decided this was another of those high culture moments in Making Light where we get to hear a fine French auctorial whine of the nineteenth century. Eventually I engaged the reading muscles and was otherwise enlightened. "Never mind." Lisa: ...if everyone on the staff agreed to learn to give the cat an injection of insulin. Everyone's hitting my maudlin buttons today. I, too, learned to inject from a cat, now ten years gone. Josh: Perhaps we should invade large printing presses and B&N warehouse distributers and throw doc martins and berkenstocks into the machinery.... Or take a line from Cory Doctorow--invade the presses and warehouses and do their job better (seventh section, "Bitchun wars", and passim). I've become a real Cory fan in the last week. Tom again: The rant included swabbing out the piss that people leave in our entryway.... Another unfair advantage of the dotnets, except that it reminds me of a National Lampoon parody of A Connecticut Yankee that used this as the Achilles heel of the electronic future. I wish I could remember it better. Something about our hero engaging in trial by combat, and single-handedly shorting out the master mainframe using the most convenient fluid. --- Newsgroups: sci.math.research From: Dan Hoey Date: 25 Mar 04 19:36:51 -0500 (EST) Subject: Re: Polinomial representing the sum of r^s On 25 Mar 04 07:08:24 -0500 (EST), Gian Piero Marenco wrote: > I am interested in knowing the result of the finite sum of > P(n,s)= sigma (r=0 to n) r^s You want Bernoulli polynomials. See http://nrich.maths.org/askedNRICH/edited/1632.html and some pages it links to. http://www.uwgb.edu/dutchs/recmath/rmpowers.htm also has a table and a way of calculating the polynomials. Dan Hoey haoyuep@aol.com --- Newsgroups: sci.crypt, sci.math, rec.puzzles From: Dan Hoey Date: 02 Apr 2004 17:51:44 -0500 Subject: Re: How much is Alice worth to Bob? Bob Harris wrote: > What all these solutions have in common is that for a block size of > b with e errors, we need the number of reclaimed bits to satisfy > r = log2 (sum over i=0..e of b choose i) >= b/2 > For e=7 the max b for which this condition holds is 56. It looks > like the next value of e that provides an increase in the rate is > 10, which yields 72 of 82 that gets us up to 1.7561 N. The limit > for this approach appears to be between 7/4 and 9/5 (based on how > the block size is increasing), but I have no proof of that. I will deal with the case that e is a constant fraction of b, say e=cb. Stirling's approximation has n! ~ sqrt(2 pi n) (n/e)^n, so (b choose cb) ~ 1/( sqrt(2 pi b c (1-c)) (c^c (1-c)^(1-c))^b ). For cb large, the sum (b choose cb) + (b choose cb-1) + (b choose cb-2) ... approximates a geometric series to the base c, so we can approximate the sum as (b choose cb)/(1-c). If the number of reclaimed bits is fb (where f = 1/2 in the given problem) this gives us fb ln(2) ~ -1/2 ln(b) - (bc+1/2) ln(c) - (b-bc+3/2)ln(1-c) - ln(2 pi)/2, so b ~ (ln(b) + ln(c) + 3ln(1-c) + ln(2 pi)) / (2 (- f ln(2) - c ln(c) - (1-c)ln(1-c))) . As b increases, the numerator grows slowly and the denominator approaches zero. So in the limit, f ~ -(c ln(c) + (1-c)ln(1-c))/ln(2) . I don't know how to invert this function symbolically, to show the error rate as a function of the compression ratio. But numerical inversion gives us some interesting answers. For instance, in the given case f=1/2, Bob's error rate approaches a fraction c=.110027863 of the bits. This agrees with Bob Harris's estimate of an error rate between .1 and .125 (which he expressed as the score 2(1-e) between 7/4 and 9/5). Here are a few samples for other values of f. Fraction of Bob's limiting message Alice Fraction of worst-case communicates reclaimed bits error rate 1-f f c 1/2 1/2 .110027863 1/3 2/3 .173952331 9/10 1/10 .012986862 eps 1-eps ~.5 - sqrt(eps ln(2)/2) 1-eps eps ~ eps ln(1/eps)/ln(2) I believe this is the same rate achieved by the ECC method. I suspect there may be an information-theoretic way to show this to be optimal over all strategies but I don't see how to prove it. Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Newsgroups: sci.math From: haoyuep@aol.com (Dan Hoey) Date: Tue, 6 Apr 2004 20:24:31 +0000 (UTC) Subject: Re: Winning Strategy? Russell Harper wrote: > For a tolerance of 0.1, I'll always win if I can generate, for > example, the values f = 0.1, 0.3, 0.5, 0.7, and 0.9 from my list, > among many other winning strategies. Is there a way I can construct > a list of integers of finite size, knowing that f = a / b, where a > is the product of some of the elements in the list, and b is the > product of the rest of the elements of the list? If the numbers on the list are rational and you can generate two fractions f, g in this way, then the fraction f/g must be the square of a rational. Subject to this constraint, you can generate any set of target values you like. Suppose the set of targets you must generate is {f_1, f_2, ..., f_n}. Let f_i/f_1 = (a_i/b_i)^2 for i=2,...,n and let f_1=c/d. Then we can take the list to consist of c, d, and two copies each of the numbers a_i and b_i. Then f_1 = (c . Q)/(d . Q) and f_k = (c . a_k . a_k . Q) / (d . b_k . b_k . Q) , where Q is the product of half of the remaining list elements. This works because each remaining list element appears an even number of times. It's not hard to create such a set of targets that covers the unit interval with intervals of any desired tolerance. For the given case, we could take f from {0.1, 0.289, 0.484, 0.676, 0.841, 0.9} and the list could consist of 3, 3, 10, 10, 10, 17, 17, 22, 22, 26, 26, 29, 29 . Dan --- Making Light: Mail ::: April 15, 2004, 05:35 PM The grammar test is pornography for us prescriptivists, and I certainly got my jollies. Being accused of deity was a big boost for a moment, but I almost immediately started questioning my integrity. The crisis was on number #6. "Take" and "bring" mean different things; either may be correct, mostly depending on whether the teacher is in room 22 when she says it. I selected "either" on that basis, but I have come to reject that answer. Only one word can be right, depending on what the teacher is intending to say, so there is no circumstance in which either would be correct.* I now believe "take" is correct, on the assumption that the teacher does not know whether she is (any more than we know). I immediately accused myself of crass testmanship, choosing my answer for the grade rather than for outright perfection. This tarnished my godhead far more than being called a bastardization (sic) would have done. Now that I know that this kind of godhead is not as absolute as I had assumed, I'm tempted to go back and see if I would have been cast down for a better answer. And no, I didn't notice the typo, either. Some kind of god I'd make. --------------------- * Well, hardly ever! Imagine Chrissy not knowing where the teacher is calling from: the teacher could say "bring" or "take". They are still not equivalent utterances--one tells Chrissy where the teacher is and the other doesn't--but they are both correct. I wish I could remember what a bungerhop is, because I feel that I'm matching slyness with that teacher. --- Newsgroups: sci.math From: haoyuep@aol.com (Dan Hoey) Date: Thu, 15 Apr 2004 18:04:02 +0000 (UTC) Subject: Re: Continuous prime number function On 14 Apr 2004, Peter Webb wrote: >What we need is a continuous function that has f^n(x) defined for all >0<=x<=1 and all n, f^n(0)=0 for all n, but isn't just f(x)=0. I >recall from my calculus days of 30 years ago that such functions >exist. Good on you for remembering. An example is f(x)= exp(-x^2). But this isn't _quite_ enough for Marc Moore's problem, because you also need f^n(1)=0 so that the pieces together. For this, use f(x)=exp(-x^2)(ke - exp(-(1-x)^2)) which interpolates between f(0)=0 and f(1)=k with all derivatives vanishing at the endpoints. It almost seems a shame to make the derivatives zero, since they really only have to match up, and this way the function is bumpier than it has to be. Still, if the twin prime conjecture is true, the derivative will have to hit each point of (0,1/2] infinitely often any way we slice it. Maybe I should ask how low we can keep lim sup f''(x). There's probably a good lower bound based on the prime constellation conjecture. Dan Hoey haoyuep@aol.com --- Making Light: Mail ::: April 16, 2004, 01:37 AM Xopher: Silly, they MEAN different things, but that doesn't mean one is WRONG. I keep telling myself that, but my INTJJJJJ soul says it couldn't possibly be. And the teacher need not be IN the room to say bring; s/he could be anticipating being there when the child arrives. What matters is the deictic center of the action. Well, faux my pas. I gotta think on that, but it might have some bearing on why I was totally convinced the question hinged on whether the teacher was going to be there to receive the book in room 22. And I wrote all that argumentation about losing my integrity over where the teacher was going to be, and then rewrote it about where the teacher said it. The gift of infallibility is more trouble than it's worth. Still, thanks for pointing me to the deictic consideration. Meanwhile, I imagined, "The teacher told Chrissy to bring the book to room 22." Chrissy replied, "What the hell game you playing, Teach? You aren't in room 22, you aren't going to be in room 22, you're never going to go near room 22, and if room 22 ever swam into your deictic center, you'd puke. So are you being dialectic, or informal, or lapsilingual, or erroneous, or are you just trying to mess with my poor prescriptivist mind?" None of the above--the teacher was supplementing her meager income by spreading spyware on commission. Don't cry for me, havoc, just release the gods of grammer. --- Making Light: Mail ::: April 20, 2004, 06:34 PM The best take on Chomsky's sentence I've seen comes from the literary competition to contextualize it so as to make sense. Several examples have been floating around the net since the 1980s. My favorite is It can only be the thought of verdure to come, which prompts us in the autumn to buy these dormant white lumps of vegetable matter covered by a brown papery skin, and lovingly to plant them and care for them. It is a marvel to me that under this cover they are labouring unseen at such a rate within to give us the sudden awesome beauty of spring flowering bulbs. While winter reigns the earth reposes but these colourless green ideas sleep furiously. C. M. Street The earliest mention on the net I've seen is a 1985 ailist digest quoting a message from the Stanford bboard. Several later references say that this was a Stanford literary competition, but I'm not sure whether to believe them. --- Making Light: Open thread 21 ::: April 23, 2004, 06:52 PM fidelio: Based on my experience, the post office will deliver (at first-class rates) anything legal to mail that the envelope is affixed to, provded that it's packed according to their standards. That's a surprise--I read a news story a decade or two ago that said they were no longer going to deliver anything over an ounce in those prepaid envelopes. This was precisely because people were sending bricks (costing the advertisers money) and the Post Awful is in the business of selling "customers" to advertisers. Of course, Edward also wanted this to be legal. I hope I'm also incorrect in my recollection that using those envolopes to send anything other than what they asked for constitutes mail fraud. --- Math Forum From: haoyuep@aol.com (Dan Hoey) Date: May 2, 2004 11:32 AM Subject: Re: Order type of English names of natural numbers On 29 Apr 2004, Stewart Gargis wrote: >But at least we can show your set is well-ordered, because it's a >subset of the set of all strings over a finite alphabet, which is >well-ordered in the lexicographical ordering (since otherwise there >would be a decreasing chain of words, not possible when the space >sorts first). What about the sequence ab, aab, aaab, aaaab, ... ? I think you need to do something like sort the strings by length before lexicographic order to make them a well-ordered set. But I don't see anything that makes the sort order of the space significant. Dan Hoey haoyuep@aol.com --- Making Light: Open thread 22 ::: May 10, 2004, 04:35 PM Jonathan Vos Post: Also, I don't usually quote the bible... Obediah 1 As opposed to the book of Obadiah which no one can find. "...and mightily shall he smite his nephew, and his donkey and his nephew's donkey and anyone in the vicinity of either himself, his donkey or his nephew's donkey that shall grieve him at this time." --- Making Light: Open thread 22 ::: May 18, 2004, 04:18 PM Jonathan: ...To paraphrase [New Scientist], Quicksilver is the first novel in a trilogy ABOUT scientists, but that doesn't make it science fiction. My favorite non-SF science fiction is Andrea Barrett's wonderful collection Ship Fever. I haven't read her other stuff to see if it's a specialty of hers. Reccos, anyone? --- Math Forum From: haoyuep@aol.com (Dan Hoey) Date: May 18, 2004 9:38 PM Subject: Re: smallest disk covering a set of points On 18 May 2004, Carlos Moreno wrote: >Carlos Moreno wrote: >>And no, I don't think it is clear at all that you can do it by >>divide-and-conquer -- how do you merge the results of two subsets? >>Remember, the points are not ordered, so the two convex hulls could >>intersect, not intersect, one entirely included in the other one. >>I'm not sure it is trivial to obtain O(N logN) this way. If you are talking about the smallest disc problem, I don't see any way of doing divide and conquer. If you are talking about calculating the convex hull, divide and conquer works just fine. >Actually, I think I was mistaken on this -- it is probably very easy >to do it by divide-and-conquer; I was concentrating on the fact that >the points are unordered; When the time comes to merge convex hulls, you have ordered the points on the separate convex hulls. That is, you have produced the convex hulls as a list of their vertices in cyclic order. >but the thing is, you still can divide the set into two with a >straight line "in the middle" -- this will guarantee that the two >convex hulls will not intersect (or intersect in just a point). You can divide the set by the median x value in linear time (and if you mean something else by "in the middle" you may not have guaranteed N log N time for the algorithm. But it is not necessary to do this. You can calculate the convex hull of two convex polygons (with their vertices given in cyclic order) in O(V) time, where V is the total number of vertices. This works whether the polygons overlap or not. It even works if they poke out of each other in lots of places. You just take a walk around the polygons in angle order and merge them. Easy. >So yes, what you suggest is a valid approach to obtain the convex >hull in O(NlogN) (and it *is* optimal in terms of big O complexity) It's optimal for finding the convex hull, but not for finding the smallest enclosing disc. I was quite surprised to hear that the smallest enclosing disc could be found in linear time, but there are enough references to Megiddo's 1983 result that I believe it. Unfortunately, the closest I've found to a description of the algorithm online is http://www.personal.kent.edu/~rmuhamma/ Compgeometry/MyCG/CG-Applets/Center/centercli.htm , which unfortunately leaves out a part of the algorithm. Still, the linear time fractioning algorithm is a wonderful idea, and I'm sure the missing part is "a simplified part of the algorithm as a whole", only I can't figure it out. David Eppstein mentioned Bernd Gaertner's software at http://www2.inf.ethz.ch/personal/gaertner/miniball.html , which appears to me to require linear expected time, but I don't know what its worst-case performance is. Dan Hoey haoyuep@aol.com --- Making Light: Hugged it like a brother ::: May 19, 2004, 12:13 AM Jill: I know it's not what you meant, but your title keeps making me think of the old WB Abominable Snowman: "I'm going to love him and hug him and call him George." Isn't that a reference to The sound and the fury? Or some other classic I should have read? Teresa: By the way, I'm wondering whether anyone will spot the provenance of the title. I give up, and I'd sure like to know. Are we there yet? --- Making Light: Bleeping huge security hole ::: May 19, 2004, 01:49 PM Matt McIrvin: This all sounds legit, and More Internet looks like an app I need to get anyway. But it's also worth mentioning to the people out there in Internet-land that if somebody says "There is a security hole in your computer!!! Quick, fix it, now! The way to do it is to download and install the following application..." and you don't at least do a little sanity checking before following directions, then you have a security hole in your brain. I'm very, very paranoid on exactly that issue. Fortunately, you don't have to download any of those tools. You should have Internet Explorer on your OSX (even if you're wise enough not to use it for browsing) and IE's "Protocol helpers" preferences allow you to fix this problem. Just change the "help" and "disk" helpers to an innocuous app like Chess. I wanted to use Calculator, but that doesn't work for some reason, so whatever you use, test it. Thanks to Leif, on Jay Allen's blog, for this fix. --- Making Light: Bleeping huge security hole ::: May 19, 2004, 02:27 PM Jay: I get what you're saying and on principle, I agree with you. However, in this case seeing a hole in my operating system large enough to drive a Mack truck through pretty much gave me enough confidence that it was the right move. It was neither subtle nor theoretical. Oddly enough, it was just this feature of the problem that made me more paranoid than usual. The technique of scaring people into doing something unwise is one of the big malware pumps on the net right now. It might even be more effective than the lures, since it pushes the victims so fast. That's not to say that I have any reason to distrust moreInternet, misfox, or vince, other than the feeling of being pushed at them. But I'm very relieved that Internet Explorer can be used to fix the problem. And I didn't browse from a MacOSX system to search for the fix. --- Making Light: Bleeping huge security hole ::: May 19, 2004, 10:15 PM Teresa, when you wrote ... when I said "he doesn't know a bare pope from a hole full of shinola" I was jamming together several well-known phrases: ... you left out Is the pope Polish? which I acclaim the cream of your jest. If you didn't notice it, I'll tell you that my best puns are not consciously meant, either. els: I can't imagine giving someone advice to lie. That's just so BAD. If he really believes in his advice, he presumably takes it, and lies. And if he doesn't believe in his advice, he's lying. Is he Epimenides, or is he a Cretan? --- Making Light: Bad advice on cover letters ::: May 19, 2004, 10:26 PM Not to deny Patrick's excellent, even T-shirtable phrase, but... If you're worried about getting stupid on you, you'd better not launch that browser. --- Making Light: Hugged it like a brother ::: May 19, 2004, 10:37 PM Mr Ripley: Dan H-- The slow-witted Abominable Snowman's references to "George" and to "wanting a bunny rabbit" allude, I'd guess, to the Steinbeck novella and play Of Mice and Men, a story nowhere near as kind to the mentally disabled as the Faulkner novel. Just so, and I thank you very much, Mr R. Now I've got two additions to my must-be-read list. So why am I re-reading The Truelove? --- Newsgroups: comp.sys.mac.system From: haoyuep@aol.com (Dan Hoey) Date: 20 May 2004 01:25:40 GMT Subject: Re: Help Viewer vulnerability in Mac OS X 10.3 George Williams wrote: >Sander Tekelenburg wrote: >> It also seems to me that the most elegant solution >> is to disable diskimages-helper by using something >> like LittleSnitch. ... >I noticed you had a problem with MisFox. MoreInternet >doesn't have a dmg helper category (yet), but it can >disable the Help Viewer.... It's worth noting that you don't need to download some random software to disable this. Mac OS X comes with Internet Explorer, and its "Protocol Helpers" preference pane lets you edit the "help" URI helper. I've also created a "disk" URI, and set its helper to an innocuous application, using IE. Does this do everything you would need MoreInternet, MisFox, or vince for? Dan Hoey haoyuep@aol.com --- Making Light: Bleeping huge security hole ::: May 20, 2004, 02:17 PM erik nelson: would simply changing the priveleges of the Help Viewer be a sufficient fix? No, it wouldn't affect the problems with the "disk" and "telnet" URI's at all. Anyway, I'd think running Internet Explorer (for its "Protocol Helpers" preference pane) would be easier for most users. Have people really gone to the trouble of deinstalling IE? Or is there a release of OSX that doesn't install it by default? --- Making Light: Open thread 23 ::: May 21, 2004, 12:03 PM Julai Jones: Most likely scenario is that someone else who has both your addresses in their address book is infected - modern viruses typically forge the address to look as if they come from somewhere else. Yes modern viruses forge the address, but not necessarily out of the infected machine's address book. I doubt that getting sender&receiver addresses out of the same web page or newsgroup is not beyond the state of the art. You'd need to check the headers and trace the IP address the virus came from. In particular, the "Received:" lines describe the trail that the message took from the last non-lying host. It's not beyond a virus to put in extra pebbles to lead you off the track. I've been tracing e-mail spam since 1994, and it just gets trickier. --- Making Light: Taking your own bad advice ::: May 21, 2004, 12:17 PM Xopher: ...But don't worry, I don't think Ellen and I will talk about it too much more...I'll show the diagrams to anyone who wants to know, at Worldcon. Meet at the fan lounge at a specific time? Get a breakout room from programming? I'm sure I know enough people to have a good chance of tracking you down, but my conac is increasingly challenged by the ADD. I don't expect many takers, just so you know. Like the medievalist said, what kind of people do you think read this blog? Just when it was starting to look like something I could make heads or tails from. --- Making Light: Open thread 23 ::: May 21, 2004, 05:56 PM Randall P.: ...As a side note, thank God I live in Canada, because we have two children's networks without any commercials. I don't know how much longer that will last, but I was down in the States for Christmas and could not find one kid's channel without evil commercials directed at kids. I fear for the future generations in the States. Didn't they just figure out that TV is bad for kids? Maybe having ads so distasteful you won't let your kids at the automatic babysitter will save them from having it eat their brains. Anyone with a better memory than mine can prove it by identifying the story about a scientist who figured out that VHF broadcast frequencies were causing cancer/making people stupid/[your disaster here] but couldn't convince anyone to ban it. He decided to fight it by subverting the network programming departments to pump out dreck so unwatchable that TV would be unprofitable. I forget why his plan failed--perhaps the stupidity effect worked too fast. Finally, a subject in which I'm an expert! (I'm also an elementary school teacher). Any questions about children's tv? Please direct them to me. Yeah! So what about TV eating kids' brains? Is that bunk? Or is there a cutoff age at which they become immune? Or has it just all been eaten? I hope this doesn't all come out twice. I tried to post once and it vanished. --- Making Light: Bleeping huge security hole ::: May 24, 2004, 11:51 AM Rachel Reiss: Of course, this raises the question: does the update really fix the problem? Or do we still need the prescribed fixes? The update does not fix the problem. See, for example, secunia.com's advisory: This vulnerability has been confirmed on a fully patched Mac OS X system (including the patch "Security Update 2004-05-24 for Mac OS X" released by Apple, which fixes the "help" URI handler vulnerability). There's more at Sander Tekelenburg's site. Apple is still losing ground on this one. --- Making Light: Bleeping huge security hole ::: May 25, 2004, 04:15 PM Patrick: ...Get RCDefaultApp. (If you already installed More Internet, get rid of it.) Use it to set the following protocols to "disabled"... I'm still missing why you advise RCDefaultApp over More Internet, or either of them over Internet Explorer. I used IE to set the handler for those URIs to a safe application, and the tests John Gruber points to run that application. I think IE is still included in MacOS, isn't it? I'm no fan of IE, but when it's already there, and it seems to do the trick, why download a new tool? --- Making Light: Bleeping huge security hole ::: May 25, 2004, 06:23 PM Patrick, I actually did read John Gruber's page, and didn't get the difference between RCDefaultApp and the other solutions. But he answered his e-mail, and by reading words of few syllables I finally got it. The actual database we have to edit is called "Launch Services", but MSIE, MoreInternet, and MisFox edit a compatibility database called "Internet Config". When you set a URI handler in IC, it writes through to LS, so the vulnerability is patched. But from the IC level you don't see those URIs that have been registered in LS but not IC. That's why you have to create a disks: URI if you're using an IC-based tool. --- Making Light: Harlan and the pirates ::: June 10, 2004, 07:50 PM Am I the only one who mistook authorslawyer for authorslayer? --- Making Light: Open thread 24 ::: June 18, 2004, 06:52 PM NelC: "...capable...to..."? Ha, if they can't spot such errors I'm not sure I'd trust their programming with my precious purple prose, thank you very much. It may be to their advantage to drive off any potential customer who would recognize what a lousy job their software does. But they are probably more stupid than crafty. --- Making Light: Open thread 24 ::: June 18, 2004, 07:25 PM Teresa, on May 21, in "Taking your own bad advice": Oh. Right. "Hugged it like a brother." It's from a novel called Red Sky at Morning, in the episode about the dead horse. Now someone who has a copy to hand is going to tell me I've misremembered it. Thanks, Teresa. I owe you for pointing me at this good read. And you're not misremembering. From the Perennial Classics edition, pp. 52-53: ...When my chest hit the horse about midships it made a noise like an orange being squeezed, and the horse's ribs began a slow caving-in movement. I pushed myself away and my hand went through his skin, surprising me so I took a deep breath without meaning to. Later, still pale and weak-kneed, I told Marcia and Steenie that they didn't need to help me walk and they let go of my arms and stood back. "A real sport," Steenie said. "Just threw himself on that horse and hugged him like a brother." "I didn't realize until now that we've been playing the game wrong all this time," Marcia said. "It doesn't mean a thing until you crawl right into the horse." My only quibble with the relevance to Bush/Rumsfeld is that the latter's correspondence to a decomposing horse is not admidships. --- Making Light: Typesetting: when it changed ::: June 18, 2004, 08:10 PM The internal workings looked like an orrery turned on its side. The system I learned on used mylar strips, one per font, that looked like elongated photo negatives. We got a Mergenthaler brand "Linofilm Superquick" machine as a tax writeoff in 1972 or so. It looked more like a windmill, with four photographic glass plates for vanes. Each plate had about 100 characters, and changes between roman, italic, and bold required the windmill to turn. At about 30 characters/second (plus a half-second for each plate change) we couldn't call it "Superquick" with a straight face, so we called it "Merggy". Initially Merggy ran off paper tape, and managed to avoid the need for memory by reading the tape for each line twice: once to scan for the number of spaces and the amount of linear space to divide up among them, then back up to the beginning of the line and expose film on the second pass through. Later, we interfaced it to a computer so it didn't need paper tape. But the interface gave it the line, then the line in reverse, then the line forward again, just as it would get it from the paper tape. I think we didn't have to give it the whole line in reverse, though, just enough to tell it it got to the beginning of the line. Quel kluge, but it beat paper tape. We set the Faculty Directory on Merggy from 1972 until at least 1976, and I don't know how long after that. I did get a chance to visit the hot-lead plant that we inherited the job from, but I don't remember if their Linotype machine was running at the time. --- Making Light: Typesetting: when it changed ::: June 21, 2004, 05:05 PM Erik: ...Were there by any chance any in-between versions out there? For example, mechanically-controlled moving font films or moving font films controlled by more primitive electronics? On Merggy, the Linofilm Superquick, there were mirrors controlled by stepping motors that acted to guide the light shining through the glass plate onto the correct spot on the photographic paper. The paper didn't move, except that after every line it advanced from source cassette to destination cassette. And the glass plate with the fonts didn't move either, except when switching from one plate to another. --- Making Light: Open thread 24 ::: June 21, 2004, 05:57 PM Sara: Onan is an unfortunate name for a company. I bet you could power a little factory with their stuff. --- Newsgroups: sci.math From: haoyuep@aol.com (Dan Hoey) Date: 23 Jun 2004 01:01:50 GMT Subject: Re: Another twin primes conjecture Jan Kristian Haugland wrote: >In a short article in Normat some 13 (?) years ago, >I conjectured that for every integer n >= 1, the interval > [n(n-1)/2 + 1, n(n+1)/2] >(that is, the nth row of a "triangular table" of the positive >integers) contains an integer u such that 6u-1, 6u+1 are twin >primes (and also an integer v such that 4v^2 + 1 is prime). >These intervals are (in effect) slightly narrower than yours >(although one conjecture doesn't imply the other). ;-) I believe both conjectures are implied by the conjecture mentioned in the OEIS http://www.research.att.com/projects/OEIS?Anum=A091592 that there is a pair of twin primes between n^2 and n^2+1 for every n > 122. Dan Hoey haoyuep@aol.com --- Making Light: Taking your own bad advice ::: June 24, 2004, 01:36 PM Caruso: Everyone here either has been published with tor, has tried to be published with tor, hopes to be published with tor. Stop changing the subject. The question is why you took the "Lie a little" phrase off your web page. You've been waving red-handed herrings ever since the question came up, and it's getting a little tiresome. We'll discuss who works for Tor after you explain your change of advice. --- Making Light: Moving house ::: June 24, 2004, 06:24 PM Mike: "Where does the light come from?" Stefan, you've been around here a while now. Do you actually have to ask that? On the off-chance that you don't mean what I would mean (and since no one seems to have gotten it, if so) She makes it, to feed his illumination. Ain't symbiosis romantic? --- Making Light: Taking your own bad advice ::: June 25, 2004, 07:03 PM Mary Anne: I really don't want to read over the whole thread of responses to find the ones that seem inappropriate; it was more a matter of tone than anything else... Well, I don't much feel like reading them over either, and while I remember some mock-making, there was certainly a lot of well-deserved criticism there. And eventually everyone had enough and it died out. But then the Toddster dropped by, and started telling us that his advice (which he rewrote before he quoted it) wasn't as stupid and evil as it had been, and that we were a bunch of meanyheads for making mock of him, and that we're all Tor toadies, and that he's going to law-sue someone. Oh, and he sent his sock-puppet over to make sure we got the message. Wednesday night's antics reanimated the farce, with nearly as much new mock fuel as the original idiocy. You might as well forget about trying to slow it down--you're about a week too early for that. Just remember who came clowning off in the deep end without his water wings. So Pants-on-fire Pierce has three choices. He can come back and mouth off some more, and see how inventive we can get, or how long before Teresa pulls the plug on the slugfest. He can crawl back under his rock and wait for us to get tired, and eventually we all will get tired and move on. Or perhaps he might actually learn how to apologize, and if he comes off looking human, things might cool down a bit sooner, and someone might actually have some respect for him. I suspect he hasn't found the bottom of his character yet, but I'd be glad to be wrong. --- Math Forum From: Dan Hoey Date: Jun 26, 2004 1:00 AM Subject: Re: Another twin primes conjecture Gerry Myerson wrote: > haoyuep@aol.com (Dan Hoey) wrote: >> Gerry Myerson wrote: >> [...] >> >I sure hope that's a typo. >> I don't see what you mean... >I mean I'll be very surprised if there are ever any twin primes >between n^2 and n^2 + 1. Oooh. Thank you. Indeed, a typo for "between n^2 and (n+1)^2." Sorry. Dan Dan Hoey --- Making Light: Grace ::: June 26, 2004, 01:44 AM Jeremy Leader: My big moment of realization was when I discovered that the "inditements" I heard about on the radio and the "indiktments" in the newspaper were the same thing. I had much the same experience with hearing the Three Stooges say "uh-nile-ate" and sounding out "anna-hilly-ate" from some Heinlein book. And when I found out that what the teacher called the "verb to be" was already a verb I knew about, not some unknown thing waiting to become a verb, I was enlightened again. Whoever decided we could supplant vocalization with visual symbols has a lot to answer for. On the other hand, I now find that surprise is often a good thing --- Making Light: Taking your own bad advice ::: June 28, 2004, 11:15 AM Jeremy Leader: Aw, gee, now I wish I still had a write ring laying around somewhere (from old 9-track tape drives, a write ring was a flexible plastic ring maybe 5 or 6 inches in diameter, about 1/4"x1/4" in cross- section, which when removed from a slot on the back of a 9-track tape reel would tell the drive not to allow writing to that tape. The good thing about ADD is it teaches you to be a packrat (because you never know if you spaced out when you filled the hand that is throwing something away). Fortunately, I was able to find one that wasn't buried too deep. Your description is pretty good, except that the (outside) diameter is closer to 4.3 inches. Somewhere around here, I suspect there's a mother lode of the things. If I find it, perhaps we can have insignias for Noreascon. --- Making Light: Open thread 24 ::: June 30, 2004, 07:35 AM Kip W: Fibonacci forgeries! This reminds me of another forgery. Suppose you select n points on a circle and draw all segments between pairs of points. Be sure you select the points so that no three segments cross in a point. Then count the number of regions that the disc is divided into. This is a suprisingly good forgery for 2^n, but there's a good reason for that. I'll explain later if there's interest. --- Making Light: Open thread 24 ::: June 30, 2004, 08:02 AM Kip W: Oh, I meant to add, I tripped over that while I was trying to find out if anybody had researched series that were like the Fibonacci numbers except that they started from two other 'seeds' than (0,1). This has been investigated in some depth by Clark Kimberling. Take all such sequences that don't have a common divisor--each pair of relatively prime integers appears as adjacent terms in just one of the sequences. The Wythoff Array is one way of organizing them. I think there's another way involving a less vanilla geometry, but I can't get to those files at the moment. --- Making Light: Grind ::: July 01, 2004, 11:18 AM Kate: Patrick: time to bribe interns with *really* *good* pizza?... In 1989, I moved house with the help of several fans, including Erica van Dommelen. She was working at some magazine--Biology Today? -- and brought in an ad they ran for a Smithsonian Institution summer program. The Smithsonian was asking for help moving one of their collections from a downtown repository to one in the suburbs. Anyone who could pony up $1500 was welcome to spend three weeks moving artifacts. Erica suggested that perhaps I should have asked the volunteers to buy the pizza. --- Making Light: Grind ::: July 01, 2004, 11:52 AM Xopher: Now, with all the devotion your heart can muster, say "Om Ganesha ya nama" 108 times. The mantra I learned is Om Gum Ganapatayei Namaha, for which I find the translation "Om and salutations to the remover of obstacles for which Gum is the seed." "Gum" is a sound that evokes the deity of Ganesh. There used to be an audio version of this at http://www.globalword.net/concerts.htm, but that seems to be gone. After several tries, the obstacles to http://solo.abac.com/streamrdr/mantra/mantra.html fell away, and I found an audio presentation. This information is for comparative purposes, not necessarily as a recommendation. I've still got a lot of obstacles. --- Making Light: Grind ::: July 02, 2004, 11:15 AM Xopher: ...getting people to get its/it's right is very, very important, and telling them "possessive pronouns in English NEVER, NEVER have apostrophes!!!" is a really good way of helping them remember. I'd say getting people to use conformant lexicography is an important good thing, but that getting people to use non-conformant lexicography is not a good way to accomplish that good thing. Maybe helping them to fully accept that rules for English grammar never, never lack exceptions is worthwhile in itself. --- Making Light: Open thread 24 ::: July 02, 2004, 02:46 PM I was only partly right about the table of all Fibonacci sequences. The Wythoff Array actually lists all of them (not just the relatively prime ones). As the link points out, though, there are infinitely many such tables. The other table I was thinking of is the inverse Wythoff array, which for each (x,y) gives the row of the Wythoff array that contains the sequence ... 2x-y, y-x, x, y, x+y, x+2y, .... The inverse Wythoff array has some fairly interesting geometrical structure that I don't think I can post here. Send e-mail if you want to know about it. --- Making Light: Open thread 25 ::: July 09, 2004, 02:13 PM Dorothy--I like The Bowery and Harlem Nocturne. Separately. Together, they're like toothpaste and cereal. --- Making Light: Open thread 25 ::: July 10, 2004, 05:51 PM Marilee -- Rhapsody in Blue reminds me of An American in Paris, but that's different. --- Making Light: Prophetable colors ::: July 15, 2004, 02:30 PM julia: check out how many names there are for purpley maroon and maroony purple. When you draw three-dimensional objects in Mathematica, the color model it uses makes them mostly come out in shades of purple. Hence the maxim, "You can have any color of graph you like, as long as it's mauve." Randall P.: They had some style back in the depression. I've officially decided that no one from the years 1930 to 1945 dressed poorly. Yes, but the style was ecologically unsustainable. Consider the extinction of the zoots, eh, pachuco? Randall P.: "Coppertunity" rules! Can I put that on a t-shirt? Probably, for a modest royalty, or an ambush lawsuit. --- Making Light: Open thread 25 ::: July 20, 2004, 11:21 AM Alex: At the risk of being overly pedantic, a monotonic function is one that never increases or never decreases; it does not necessarily always decrease or increase. Frex, [1, 1, 1, 2] is a monotonically increasing sequence. The first derivative will never change sign, but can be zero. At the risk--or perhaps the hope--of extrapedantificication, I'll note that careful writers would call your sequence monotonically nondecreasing, and reserve monotonically increasing for sequences or functions that neither decrease nor remain constant (nor pass through incomparable elements of a partially-ordered set, should that arise). To make the distinction explicit, we often call the function strictly monotonic. The first derivative has no relevance to your sequence, but I'll mention that in the continuous case, the derivative being zero does not preclude strict monotonicity. For instance, the function f(x)=x^3 is strictly monotonic, but f'(0)=0. I seem to recall there's a name for a function whose derivative is positive everywhere, but I don't remember it. --- Making Light: Open thread 25 ::: July 21, 2004, 03:45 PM It seems ricercars go back to the sixteenth century. And micing has been the cats' job even longer than that. --- Making Light: Open thread 25 ::: July 21, 2004, 04:32 PM Xopher: Mousing, usually? Usually, and perhaps always. Google finds one Usenet message from a gardening person who plans to turn her kitten into either a micer or a moler. But perhaps she and I are both mistaken. Mouser it is. --- Making Light: Prophetable colors ::: July 22, 2004, 02:32 PM Paula: monkeysh*t green As in "Monkey see, monkey doo". Or is that a corruption of "do"? --- Making Light: Prophetable colors ::: July 23, 2004, 01:08 PM Elise: ...I pick out stuff that's not popular yet, but is going to be eventually -- but by then, either I'm tired of it or I've worn it to pieces. [...] if I could only figure out which of the things I'm craving are the ones that are going to hit in a while, and (more importantly) exactly when they're going to hit, it could come in handy. If T. Pettys Shadwell, the most despicable of living men, should make you an offer, don't take it. Read Avram Davidson's "The Sources of the Nile". --- Making Light: Prophetable colors ::: July 24, 2004, 01:37 AM I: If T. Pettys Shadwell, the most despicable of living men, should make you an offer, don't take it. Read Avram Davidson's "The Sources of the Nile". which (I neglected to inform) you will find, a gem in a trove, in The Avram Davidson Treasury, edited by our own fair hostrix, for which and whom Huzzah! Huzzah! Huzzah! and, let us not stint, Huzzah! --- Making Light: USA Today notices ::: July 30, 2004, 02:22 PM His Son: However, if you have bothered even further to figure out what I am saying, then 994031614864, 4565962889937912832 29989027451691 108800789304590768 29903936707828 .... I can't tell whether 108800789304590768 was just a Badenov to be a cryptoespionological reference, or whether it's a typo for 108800789304590764. But what could you mean by 4565962889937912832? 4565962889940629932 is Hammingly nearby, but the sense is more like 4565962889962995973. Please, 2500660720059408197920 91110995576726. --- Making Light: USA Today notices ::: July 30, 2004, 02:43 PM JVP: ...And then he wrote and ran a program that converts bases of even larger number. 3251605731127812162770237369792172852520139962792814076268399225- 5065438348398854256993399674613874355849356440914605955745903081- 8150436092546650900931935947509390302010545059841678979329004798- 9233468357680168834138829197669212783263924980986114031723784281- 1399468677816136808742589264371119044327848573756949373110982858- 8521299716422911284267704860756176608419053190357861207604156324- 5241318700809425895674173661322835101766881025004729092981432065- 1675848704 --- Making Light: Open thread 26 ::: August 09, 2004, 09:06 PM Stefan: This is really odd. A flash cartoon, in poorly translated English, that seems to be an advert for a line of toys from the Insane Asylum for Abused Plush Animals. I hesitate to ask, but, since it's more than a cartoon--did you effect any cures? I've never had the slightest inclination towards being a therapist before, but this is enchanting. I'm looking forward to seeing what Dolly's progress is like. If you don't know what I'm talking about, you may only have watched the intro. Maybe it's OS-dependent--for egs, I know the game works on OSX, and I've seen it not work on W98. By the way, can anyone see a rationale for the sequence of toys? Why the bolo, and why not? --- Making Light: Open thread 26 ::: August 13, 2004, 10:59 AM Bruce Adelsohn: Conversely, what are the books you own (or try to) multiple copies of for the express purpose of being able to give them away? We've managed to accumulate three copies of Poetry for Cats, mostly with the intention of giving them away. --- Making Light: Open thread 26 ::: August 14, 2004, 12:20 AM Andy Perrin: ...I misread the Hurricane Charlie headline "Storm heads for Florida" as "Storm hunts for Florida." Closer to home, I misread the previous thread's title today (after reading it right so many times) as Prepared nectarine salad. Some sort of performance art food, made of nectarines that have been hollowed out, leaving only the skin and pit? --- Making Light: Tracking Nielsen Haydens in their habitat ::: August 16, 2004, 02:32 PM Jonathan Vos Post: The amazing Eric W. Weisstein (who was sued by his own publisher when he posted his own material on his website.... As far as I can tell, he had contracted with the publisher, CRC, not to publish the work elsewhere, a restriction that CRC believed was violated by his putting it on the web. I can't really fault CRC for suing to enforce the arrangement they had purchased. It is hard to tell who is being sinned against, given that details of the disagreement are only available through one of the parties. I'm somewhat more concerned about the possible results of the arrangement between Weisstein and his new sponsor, given Wolfram's track record with regard to suppression of research. --- Making Light: Tracking Nielsen Haydens in their habitat ::: August 16, 2004, 03:19 PM Xopher: Andy, I meant the person who stays on Earth is also predicted to be older than the one who flies at a significant fraction of C. Relative to the frame of reference of the one who flies off, the Earthbound twin is moving at a significant fraction of C. It's called the Twins Paradox because each twin ages more (and less) rapidly with respect to the other. Now, if I misunderstand that, I'm ready to be corrected. But that's how I had it explained to me.... I think the disconnect is that Andy was describing relativity without mentioning the twin paradox, and you're describing the twin paradox. ... Mere one-sided time dilation doesn't strike me as paradoxical, or is my sensibility just too post-Einstein to see it as such? I agree that the idea that two equally valid reference frames can disagree on which frame is time-dilated seems paradoxical. I guess that's why Heinlein got it wrong in Time for the Stars, if I remember right. Though I don't how it should have worked, except possibly that it shouldn't have worked. Nor ansibles neither. They're just weird scifi ideas, ginned up to make plots more interesting than "They left and we never heard from them again." --- Making Light: Tracking Nielsen Haydens in their habitat ::: August 16, 2004, 04:08 PM Xopher: ...And I thought it had now (thought not when LeGuin wrote those novels) been demonstrated that in fact information can travel faster than light? I think you're talking about Aspect's work. I don't believe that's been demonstrated in a generally accepted way. And there's a serious credibility hurdle to overcome: If there's a FTL rate of information transfer that works in all inertial frames, then there's information transfer into the past. I don't know how you can (nonfictionally) fix the grandfather paradox. --- Making Light: Tracking Nielsen Haydens in their habitat ::: August 16, 2004, 04:49 PM Dan Blum: The Twins Paradox is in fact not actually a paradox, but a common misunderstanding of Special Relativity.... I understand it from a standpoint of Special Relativity. But that doesn't stop it from being a paradox, any more than Zeno's paradox stops being a paradox when you understand continuity. It's true, it's explainable, it's understandable, but I call it paradoxical. To summarize - the twin on the spaceship definitely ages more slowly. I don't believe that's an accurate summary. From an SR standpoint, the twin on the spaceship measures the Earther as aging more slowly, then (in another reference frame) as being suddenly older, then aging more slowly. After the round trip, the Earther is older, but except during turnaround he's going just as much slower with respect to the traveler as vice versa. --- Making Light: Bad advice on cover letters ::: August 18, 2004, 02:53 PM Xopher: That idiot didn't even read the links you gave him, obviously.... Why would he? It hasn't changed much since June, and look how riled up he got then. Or am I being naïve in supposing that no one but a sock puppet would pretend to be one? --- Making Light: Tracking Nielsen Haydens in their habitat ::: August 28, 2004, 12:14 AM Chad: That sounds pretty dodgy to me-- being "suddenly older," in particular, strikes me as unlikely (discontinuous jumps are not common in real systems). The "suddenness" is entirely an artifact of how suddenly the traveling twin adopts a new inertial frame at the turnaround. All that happens is that the traveler's calculation of what "now" is on Earth has advanced by a significant amount. There is no discontinuous jump in any observed quantity, only in what is calculated to be simultaneous in a distant place. The only good textbook description I have of what each twin sees at each point in the journey is one that also includes the time-of-flight delays of light signals sent from one to the other (in which case, they each "see" slower aging at first (in the sense of annual signals from one to the other arriving more slowly), followed by a burst of rapid aging at the end of the round trip. I think you are remembering a description equivalent to the short one already cited. However, the "burst of rapid aging" is what the traveling twin "sees" happening to the earthbound twin when turning around (and adopting a new inertial frame) in the middle of the round trip (the turnaround), not the end. That aging is of course not directly observed, since the twins are far apart when it occurs. The earthbound twin does not change frames, and so does not observe any "rapid aging" in the traveler. On the web page, the burst of "rapid" (or "sudden") aging is shown in the right-hand diagram, where "Joe 2" in one frame becomes "Joe 6" in the other. As for your other remarks, I don't find acceleration to be necessary to resolving the paradox, I don't believe I'm applying formulae blindly, and I don't believe I'm confused. But you may feel free to disagree. --- Making Light: Tracking Nielsen Haydens in their habitat ::: September 02, 2004, 06:23 PM After writing: As for your other remarks, I don't find acceleration to be necessary to resolving the paradox, I don't believe I'm applying formulae blindly, and I don't believe I'm confused. But you may feel free to disagree. I've been feeling a bit... guilty? unreconstructed? I mean, that was pretty huffy, and I know I have a tendency toward unwarranted verbal antagonism. So let me apologize for treating Chad's remarks as being dismissive, which he almost certainly didn't intend. While I've been able to do all the reasoning I need about the twin paradox and FTL=time travel without going out of a few inertial frames, I imagine I might learn something by examining an accelerating frame. And if anyone wants to talk about relativity, perhaps it would be better on an open thread. --- Making Light: A brief note on linguistic markers ::: September 21, 2004, 06:17 PM Lenora: "Hopes and Dreams", of course, is directly linked to the Turkey City lexicon entry for "pushbutton words": 'Words used to evoke a cheap emotional response without engaging the intellect or the critical faculties....' There's a classic term for that kind of emotional button-pushing: argumentum ad hominem. Unfortunately, the term is now misused, almost universally, for distrusting people who have a record of unreliability. The latter is actually not a logical error, though habitually unreliable people would have you believe it is. If you don't believe me, don't bother to tell me until you look it up. --- Making Light: Open thread 30 ::: October 17, 2004, 02:17 AM Re The art of coding porn in Particles, I'll mention that the jargon of video porn is somewhat less choate than for the written stuff. I learned this a while ago when I tracked down the meaning of an "RCA scene". Turns out there's a fair glossary on rame.net, though not recommended for the faint of heart, pure of soul, nor good of taste (nor safe of work, of course). --- Newsgroups: sci.math From: Dan Hoey Date: 21 Oct 2004 18:49:16 -0400 Subject: Re: Cute little next-to-nothing. le...@PROBE.MITRE.ORG (Keith A. Lewis) wrote: > w.tay...@math.canterbury.ac.nz (Bill Taylor) wrote: > >This is doubtless well-known to all graph theorists and many others, > >but I just noticed it recently and thought it was rather cute. > >The fully transitive 3x3 lattice, naturally embedded in a torus... > > d e f > > : : : > > | | | > >a ...---*------*------*---... a > > | | | > > | | | > > | | | > >b ...---*------*------*---... b > > | | | > > | | | > > | | | > >c ...---*------*------*---... c > > | | | > > : : : > > d e f ...is SELF-COMPLEMENTARY! > Are you saying that if you redraw the graph with all the connections > flipped, it's the same graph? > . . . . > \ / \ / \ / > * * * > / \ / \ / \ > X X > \ / \ / \ / > * * * > / \ / \ / \ > X X > \ / \ / \ / > * * * > / \ / \ / \ > . . . . > I see how they're isomorphic, but why worry about the torus? The > complementary edges cross each other where the originals don't. That's only because you drew it with edges crossing. It's always possible to avoid crossing edges if the graph is embeddable, and in this case it's quite easy: g h.j k m.n p r.q a /' / /' / /' a .* / .* / .* / b'/ / .'/ / .'/ / b / /.' / /.' / /.' c /' / /' / /' c .* / .* / .* / d'/ / .'/ / .'/ / d / /.' / /.' / /.' e /' / /' / /' e .* / .* / .* / f'/ / .'/ / .'/ / f g h j k m n p r q Dan Hoey Hoey@AIC.NRL.Navy.Mil --- Making Light: The Holy Spirit gets around ::: November 26, 2004, 05:55 PM Sajia: Um, I don't. Intone the words like rolling thunder; nevermore have cause to wonder. Or google it (like I did to make sure my guess was right). --- Newsgroups: geometry.puzzles From: haoyuep@aol.com (Dan Hoey) Date: Wed, 29 Dec 2004 23:17:34 +0000 (UTC) Subject: Re: problem 726 On 25 Feb 1993 18:49:33 GMT, Stan Wagon wrote: >[from Stan Wagon's problem mailing list] >#726: >Take a triangle ABC and place D on AB and E on AC so that DE is >parallel to the base BC. But do not draw the line DE. Draw lines BE >and CD and let them intersect in F. Given that triangle BCF has area >4 and that quadrilateral ADEF has area 4, determine the area of >ABC. > --suggested by Loren Larson, St. Olaf College When Area(BCF)=Area(ADEF) the problem has a nice solution with medians. But in general, if x=Area(BCF) and y=Area(ADEF), I get Area(ABC) = (2x + y + Sqrt((8x+y)y))/2 . Algebraically, we would expect the negative square root to provide another solution, but then Area(ABC) DavidG wrote: >> Imagine an irregular polygon that contains several points. >> I would like to find the coordinates of the points that form >> a second polygon that is completely contained within the >> first polygon, such that this second polygon has maximum >> area. Is there an algorithm that can perform this task? > I must be missing something.... The way I understand the problem, we require the second polygon's vertices to be a subset of a given finite set of points. If the first polygon is convex, the answer is the convex hull of the point set. If not, I wouldn't be surprised if this is NP-hard. Dan Hoey haoyuep@aol.com ---