June 2012 - mathfun@mailman.xmission.com

[math-fun] Correction (Re: Venustransit 5th/6th June)
by Robert Munafo 05 Jun '12

05 Jun '12

Sorry, I got it backwards, I was reading the OEIS numbers too fast. It's the other way around: transits sometimes do not occur in pairs: 1275, 1283, 1396, 1518, 1526, ... note the 1396 but no 1388 or 1404. This is why I don't help out with the OEIS more often (-: There's something else odd going on, because the prior solo transit was in 910, but the next one won't be until 3089. That Fred Espenak webpage [3] sort of explains it. On 6/5/12, Robert Munafo <mrob27(a)gmail.com> wrote: > On 6/5/12, Huddleston, Scott <scott.huddleston(a)intel.com> wrote: >> Do Venus transits ever occur in triples? > > Yes, the last triple was in 1275, 1283, and 1396 according to Fred > Espenak [1]. OEIS sequence A171467 [2] gives a list of transit years. > [...] > [2] http://oeis.org/A171467 > [3] http://eclipse.gsfc.nasa.gov/transit/catalog/VenusCatalog.html -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com

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[math-fun] Venustransit 5th/6th June
by Pacher Christoph 05 Jun '12

05 Jun '12

I want to remind you on the last Venus transit that you will ever see (next one in more than 100 years), if you happen to live in a place where it is visible: http://eclipse.gsfc.nasa.gov/OH/transit12.html http://en.wikipedia.org/wiki/Transit_of_Venus,_2012 Wait, did I really send out a wikipedia link? *gg* (Seriously: I just love wikipedia.) Christoph

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Re: [math-fun] a simple problem ?
by Dan Asimov 05 Jun '12

05 Jun '12

The problem sounds reasonable, but I seem to have shown there is no solution. At least if speed is a continuous function of position. Suppose we are on the real line R, headed toward 0, and the velocity at every x <> 0 is given by v(x) <> 0. Then for all x = u we require that the time it will take to reach 0 be 1 unit of time. Then Integral_{u to 0} of (1/v(x)) dx == 1, since that integral gives the time from x to 0. Let F(x) satisfy F'(x) == 1/v(x). Then F(0) - F(u) == 1 (for all u). Hence the function F(x) == const, so by the definition of F we have 0 == F'(x) == 1/v(x) and so v(x) == 1/0. Oops. --------------------------------------------------------- But come to think of it this derivation is not necessary. For if we begin at one hour away from our destination, then any length of traveling will take some positive time, and we must then be that amount *less* than one hour away. Contradiction. --Dan Simon wrote: << I was going back from a place about 100 km away from home and at one point the GPS I have was kind of stuck on a fix time of arrival, which later was corrected I presume. But it made me think of a problem which is the following. Suppose you are at exactly 100 Km from a place going on a straight road at a speed of 100 Km/hour. Obviously, it will take you 1 hour exactly to reach your destination. BUT : what would be your increase in speed or decrease IF , let's say you make a point every kilometer you made so far so that : It would be always 1 hour in time to reach your destination ? In other words, what is the change in speed IF at every kilometer there is always 1 hour left of driving until you reach destination. After 1 min at 100 km/hour, there is 99 kilometers left so if you need to reach destination in 1 hour you need to go at 99 km/hour. Is this a trivial problem ? My impression is that the speed would necessarly decrease to near 0 when you are 1 mm away from your home. In plain english , what is the function of the speed ? If someone has a solution, I would be glad to ear it. >> ________________________________________________________________________________________ It goes without saying that .

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[math-fun] a simple problem ?
by Simon Plouffe 05 Jun '12

05 Jun '12

Hello, I was going back from a place about 100 km away from home and at one point the GPS I have was kind of stuck on a fix time of arrival, which later was corrected I presume. But it made me think of a problem which is the following. Suppose you are at exactly 100 Km from a place going on a straight road at a speed of 100 Km/hour. Obviously, it will take you 1 hour exactly to reach your destination. BUT : what would be your increase in speed or decrease IF , let's say you make a point every kilometer you made so far so that : It would be always 1 hour in time to reach your destination ? In other words, what is the change in speed IF at every kilometer there is always 1 hour left of driving until you reach destination. After 1 min at 100 km/hour, there is 99 kilometers left so if you need to reach destination in 1 hour you need to go at 99 km/hour. Is this a trivial problem ? My impression is that the speed would necessarly decrease to near 0 when you are 1 mm away from your home. In plain english , what is the function of the speed ? If someone has a solution, I would be glad to ear it. Best regards, Simon plouffe

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[math-fun] Computer go via bit-tricks?
by Warren Smith 05 Jun '12

05 Jun '12

> Warren D. Smith: > I assume you all know the rules of "go" on an NxN board. > If N<=21 (where 21 is the board size contemplated for > future professional play in case the current size 19 is ever > deemed inadequate) then an entire row of the go board > would fit in a single 64-bit word using 3 bits per location. > Actually 2 bits would suffice in principle because each location > is either BLACK, WHITE, or EMPTY, but I'm granting you > one extra bit for fooling around. > > This stores the board considerably more compactly than if > you used a 2D array, hence fast board-copying; and it also allows > "bit tricks" using word-wide parallelism to speed up common operations. > > The QUESTION is how fast can you implement the following: > > 1A. Find & count all board-locations connected via a chain of > horizontal and/or vertical adjacencies to a given location X and > where all these locations are required to contain WHITE. > 1B. Find & count all board-locations connected via a chain of > horizontal and/or vertical adjacencies to a given location X and > where all these locations are required to contain BLACK. > 1C. Also count all board-locations containing EMPTY and adjacent > to the location-set found by 1A (also ditto for 1B). > > 2A. Find and count all EMPTY board-locations > connected via a chain of EMPTYs to WHITE. > 2B. Find and count all EMPTY board-locations > connected via a chain of EMPTYs to BLACK. > > If these things can be made fast enough, then go program fancy board > data structures, > could be replaced with simple ones (but with somewhat complicated > bit-trick algorithms). --I did some initial thinking about this. It is unclear to me which is the faster approach in practice: conventional data structures or bitboard. If a 64-bit word stores a row of the board as follows: 19 bits: EMPTY(1) vs not (0) 1 zero bit as buffer 19 bits: BLACK(1) vs not (0) 1 zero bit 19 bits: WHITE(1) vs not (0) that's 59 bits consumed with 5 left over. Also you can do 21-21-21 with 1 bit left over, for a 21x21 go board (no buffer bits). An array of 19 such words stores the entire 19x19 go board. A typical initial set of bitboard operations could then include * copy * test equality * AND * OR * XOR * bit-complement * reverse colors * shift NORTH, SOUTH, EAST or WEST: The last by means of wordwide left-shift followed by ANDing with a predefined mask. The first by shifting the array 1 hop. * count black (AND with mask, then apply "popcount") * count white * count empty * compute hash function: A multiplicatively-weighted sum of all row-words regarded as binary numbers, done modulo a fixed prime modulus. * write something to board location (x,y): AND array[y] with PredefinedBitMask<<x, then OR with another. * read board location (x,y): AND (array[y]>>x) with PredefinedBitMask. * print board A key trick is this: for many operations like "find the black connected region containing a given point" you actually can perform three independent such operations in parallel using 3 black/not-bitboards stored in the same 19-array of 64-bit words. This factor-3 speedup is a big reason bitboards might be better. In "1 dimensional go," which also has some interest as a computer programming problem (not as a game) we can ask: QUESTION: What is the fastest way to compute the string of consecutive 1-bits in a 64-bit word W, which contain a given location X? Here X is a 64-bit word containing a single 1-bit. POSSIBLE ANSWER (untested): Z = X-1; if(Z==0){ Y = (W+1) XOR W; }else{ Y = ((1<<(64-CountLeadingZeros(Complement(W) AND Z))) + W) XOR W; } return( Y AND (Y>>1) ); I do not know a fast way if X is a non-singleton set and we ask for all the strings of 1s in W which contain some overlap with X.

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Re: [math-fun] Name of board game
by Dan Asimov 05 Jun '12

05 Jun '12

Right, the game is Teeko, invented by John Scarne (a magician and card sharp, if memory serves). My parents knew a friend of a friend of Scarne, so I ended up with a set as a kid. --Dan << There was a board game played (I think) on a 5 by 5 board. Each player had 4 blots which they alternately placed on empty squares on the board. After all pieces were placed, players alternately moved one piece as a king in chess, to an empty square. The object was to be first to form either a straight line of four adjacent blots, horizontally, vertically, or diagonally, or place the blots at the corners of a square. I seem to think it was called "teco" or something similar. >> ________________________________________________________________________________________ It goes without saying that .

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[math-fun] Game of go -- bit tricks?
by Warren Smith 04 Jun '12

04 Jun '12

I assume you all know the rules of "go" on an NxN board. If N<=21 (where 21 is the board size contemplated for future professional play in case the current size 19 is ever deemed inadequate) then an entire row of the go board would fit in a single 64-bit word using 3 bits per location. Actually 2 bits would suffice in principle because each location is either BLACK, WHITE, or EMPTY, but I'm granting you one extra bit for fooling around. This stores the board considerably more compactly than if you used a 2D array, hence fast board-copying; and it also allows "bit tricks" using word-wide parallelism to speed up common operations. The QUESTION is how fast can you implement the following: 1A. Find & count all board-locations connected via a chain of horizontal and/or vertical adjacencies to a given location X and where all these locations are required to contain WHITE. 1B. Find & count all board-locations connected via a chain of horizontal and/or vertical adjacencies to a given location X and where all these locations are required to contain BLACK. 1C. Also count all board-locations containing EMPTY and adjacent to the location-set found by 1A (also ditto for 1B). 2A. Find and count all EMPTY board-locations connected via a chain of EMPTYs to WHITE. 2B. Find and count all EMPTY board-locations connected via a chain of EMPTYs to BLACK. If these things can be made fast enough, then go program fancy board data structures, could be replaced with simple ones (but with somewhat complicated bit-trick algorithms). -- Warren D. Smith http://RangeVoting.org

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Re: [math-fun] Wiki article on Circumscribed_circle
by Henry Baker 04 Jun '12

04 Jun '12

Thanks, Robert, for your excellent & helpful suggestions. But I still think there is a place in the world for a WikiProofia, where math results (new or old) can be submitted together with a proof that eventually could be mechanically checked. In the mean time, a human-readable proof would suffice, because math readers who didn't buy the proof given could request additional details. I would also love for there to be an online version of "Proofs without Words", or "Picture Proofs". (Yes, I know, Bourbaki will be spinning in its/his/her/their grave(s).) I had thought that Wikipedia might be the germ of such a resource, but its current rules make that impossible. Since it doesn't appear that those rules will be changing any time soon, it's probably time to start anew. At 09:54 PM 6/2/2012, Robert Munafo wrote: >Unfortunately, the only effective way to contribute on Wikipedia is to >publish it elsewhere and wait for lots of people who happen to also >read Wikipedia to think that your stuff is important. Sometimes "wait" >means "more than 5 years". > >It also helps to think of Wikipedia people as being kind of a niche >audience. The real audience is people who use search engines like >Google and Bing. > >I also think that if you link from your article to other related >articles online, the process is quicker. Link to other related >content, such as the external links presently used by that Wikipedia >article, or be more creative and do your own Google/Bing searches to >find other useful articles on circumscription (sic?) > >That means turning your .txt into a .html (hint: you can put "<pre>" >around most of it) and submit its URL to Google and Bing (see [1] and >[2]). You should do that to all of your publshed content, at the very >least adding title and keywords tags, which will get your work noticed >much more effectively than being linked on Wikipedia. > >- Robert > >[1] http://www.google.com/submityourcontent/website-owner/ > >[2] https://ssl.bing.com/webmaster/SubmitSitePage.aspx > >On 6/2/12, Henry Baker <hbaker1(a)pipeline.com> wrote: >> Does anyone know how to deal with Wikipedia? >> >> I tried this morning to make a very modest edit to the Circumscribed_circle >> article, and someone else keeps reverting it back. [...] >> >> http://home.pipeline.com/~hbaker1/FAQ-circumcircle.txt >> >> [...] > >-- > Robert Munafo -- mrob.com > Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - >mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com

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Re: [math-fun] Wiki article on Circumscribed_circle
by Dave Dyer 04 Jun '12

04 Jun '12

>On Sat, Jun 2, 2012 at 2:07 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> Does anyone know how to deal with Wikipedia? Wiki is infested with content nazis who are intent on enforcing "the rules". Overall, it's probably a necessary affliction to prevent it from becoming just another platform for spam.

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Re: [math-fun] Wiki article on Circumscribed_circle
by Henry Baker 04 Jun '12

04 Jun '12

As in everything else, Feynman was prescient when he talked of "Cargo Cults": http://neurotheory.columbia.edu/~ken/cargo_cult.html "In the South Seas there is a cargo cult of people. During the war they saw airplanes with lots of good materials, and they want the same thing to happen now. So they've arranged to make things like runways, to put fires along the sides of the runways, to make a wooden hut for a man to sit in, with two wooden pieces on his head to [simulate] headphones and bars of bamboo sticking out like antennas--he's the controller--and they wait for the airplanes to land. They're doing everything right. The form is perfect. It looks exactly the way it looked before. But it doesn't work. No airplanes land." This is also a description of Wikipedia after the inmates have taken over the asylum. No planes land; no new articles are created or _can_ be created. Those HTML headphones look right, but no sound comes out. Wikipedia has itself become a "cargo cult"! All organizations go through transitions similar to those that people themselves go through, but at different rates. People go through infancy, adolescence, early adulthood, middle age, old age, death. Adolescent organizations are very brash but vibrant; their exuberance carries them through a number of mistakes that would cost older organizations their lives. Early adult organizations are very competent, and have usually learned from the excesses of their youthful indiscretions. Middle and older age organizations start becoming extremely conservative -- even reactionary, and are unwilling to take the kinds of risks that they must in order to survive the significant changes occurring about them. Finally, having no new blood, and no new ideas in years/decades, the organization succumbs to the next significant change without even putting up a fight. The amazing thing about the age of the internet is how quickly organizations have been aging. The kinds of risk-averse behavior that traditionally took 20-30 years to develop are now overtaking organizations less than 10 years old. The only good news is the speed of development of new organizations to pick up the mantle from the older organizations that decide to stop changing & innovating. At 07:31 PM 6/3/2012, Thane Plambeck wrote: >Awhile ago I noticed that someone created this page on the Wikipedia >that refers both to a paper I wrote, and a web site I maintain. > >http://en.wikipedia.org/wiki/Indistinguishability_quotient > >However, the page is almost nonsensical and I've been tempted more >than once to rewrite it from scratch. > >But I doubt I'll ever do it, because I couldn't bear to see someone >officiously revert my extensive corrections to the original (lame) >version that is there now. And I assume that it would raise the >suspicions of editors, since I'm the only person whose work is >referred to on the page. > >Has anyone else had an experience like this? I've contributed little >to Wikipedia except the current photo of JHC, Elwyn Berlekamp, Vi >Hart, and Richard Guy. I'd happily rewrite it if I knew it wouldn't >be wiped out. > >On Sun, Jun 3, 2012 at 6:45 PM, Charles Greathouse ><charles.greathouse(a)case.edu> wrote: >>> But I still think there is a place in the world for a WikiProofia, where >>> math results (new or old) can be submitted together with a proof that >>> eventually could be mechanically checked. >> >> Perhaps metamath.org? Of course that's mechanically checked, not just >> potentially mechanically checked. >> >> Charles Greathouse >> Analyst/Programmer >> Case Western Reserve University >> >> On Sun, Jun 3, 2012 at 1:10 AM, Henry Baker <hbaker1(a)pipeline.com> wrote: >>> Thanks, Robert, for your excellent & helpful suggestions. >>> >>> But I still think there is a place in the world for a WikiProofia, where >>> math results (new or old) can be submitted together with a proof that >>> eventually could be mechanically checked. In the mean time, a human-readable >>> proof would suffice, because math readers who didn't buy the proof given could >>> request additional details. >>> >>> I would also love for there to be an online version of "Proofs without Words", >>> or "Picture Proofs". (Yes, I know, Bourbaki will be spinning in its/his/her/their >>> grave(s).) >>> >>> I had thought that Wikipedia might be the germ of such a resource, but >>> its current rules make that impossible. >>> >>> Since it doesn't appear that those rules will be changing any time soon, it's >>> probably time to start anew. >>> >>> At 09:54 PM 6/2/2012, Robert Munafo wrote: >>>>Unfortunately, the only effective way to contribute on Wikipedia is to >>>>publish it elsewhere and wait for lots of people who happen to also >>>>read Wikipedia to think that your stuff is important. Sometimes "wait" >>>>means "more than 5 years". >>>> >>>>It also helps to think of Wikipedia people as being kind of a niche >>>>audience. The real audience is people who use search engines like >>>>Google and Bing. >>>> >>>>I also think that if you link from your article to other related >>>>articles online, the process is quicker. Link to other related >>>>content, such as the external links presently used by that Wikipedia >>>>article, or be more creative and do your own Google/Bing searches to >>>>find other useful articles on circumscription (sic?) >>>> >>>>That means turning your .txt into a .html (hint: you can put "<pre>" >>>>around most of it) and submit its URL to Google and Bing (see [1] and >>>>[2]). You should do that to all of your publshed content, at the very >>>>least adding title and keywords tags, which will get your work noticed >>>>much more effectively than being linked on Wikipedia. >>>> >>>>- Robert >>>> >>>>[1] http://www.google.com/submityourcontent/website-owner/ >>>> >>>>[2] https://ssl.bing.com/webmaster/SubmitSitePage.aspx >>>> >>>>On 6/2/12, Henry Baker <hbaker1(a)pipeline.com> wrote: >>>>> Does anyone know how to deal with Wikipedia? >>>>> >>>>> I tried this morning to make a very modest edit to the Circumscribed_circle >>>>> article, and someone else keeps reverting it back. [...] >>>>> >>>>> http://home.pipeline.com/~hbaker1/FAQ-circumcircle.txt >>>>> >>>>> [...] >>>> >>>>-- >>>> Robert Munafo -- mrob.com >>>> Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - >>>>mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com > >-- >Thane Plambeck >tplambeck(a)gmail.com >http://counterwave.com/

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