tag:blogger.com,1999:blog-22973357.post6254748815918992898..comments2021-04-17T17:21:32.139-04:00Comments on Sabine Hossenfelder: Backreaction: Elegant proofsSabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-22973357.post-44256911820711642362008-04-14T08:07:00.000-04:002008-04-14T08:07:00.000-04:00Sylvester-Gallai also has, IMO, an elegant proof....<A HREF="http://en.wikipedia.org/wiki/Sylvester%E2%80%93Gallai_theorem" REL="nofollow">Sylvester-Gallai</A> also has, IMO, an elegant proof.<BR/><BR/>"The Sylvester–Gallai theorem asserts that given a finite number of points in the plane, either<BR/><BR/> 1. All the points are collinear; or<BR/> 2. There is a line which contains exactly two of the points."<BR/><BR/>It remained open from 1893Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-25236505169301707142008-04-13T15:25:00.000-04:002008-04-13T15:25:00.000-04:00Parity check! Every domino is 01 or 10. Remove t...Parity check! Every domino is 01 or 10. Remove two squares of the same color to give 00 or 11 residual. No domino can cover it.<BR/><BR/>Order of rotations of a sphere; current, magnetic field, force; Weak Interaction; Cartesian coordinates... Physics assumes isotropic, commutative, abelian conditions then adds exceptions. Perhaps symmetry "breakings" were <I>never</I> unbroken.<BR/><BR/>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-61114876760646261652008-04-13T04:40:00.000-04:002008-04-13T04:40:00.000-04:00Hi Carl, Oleg, dear Bee,yes, the answer is indeed ...Hi Carl, Oleg, dear Bee,<BR/><BR/>yes, the answer is indeed as simple as that - there are 32 white squares and 30 black squares, and each domino covers exactly one white and one black square - hence no complete covering is possible.<BR/><BR/>I didn't know the riddle before, neither this answer. Günter Ziegler in his talk had presented the problem first for a board without the black and white stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-71894216100899944112008-04-12T09:46:00.000-04:002008-04-12T09:46:00.000-04:00Dear Stefan,Interesting post. I vaguely remember I...Dear Stefan,<BR/><BR/>Interesting post. I vaguely remember I came across this triangle proof elsewhere previously but can't recall where. Regarding the dominoes, what Oleg says above sounds good to me, what do you think?<BR/><BR/>Best,<BR/><BR/>B.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-43972258513799765862008-04-12T08:22:00.000-04:002008-04-12T08:22:00.000-04:00Hi Stefan,Nice post and again I find yours’ and Be...Hi Stefan,<BR/><BR/>Nice post and again I find yours’ and Bees access at times both to be wondrous and yet at the same time a little envious. Yet, when I think about it I am grateful that you bring in part some of this experience to life within this blog. The puzzle you present I also find interesting, as to the fact that a proof can be discovered and presented. What I find interesting to Phil Warnellhttps://www.blogger.com/profile/15671311338712852659noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-65581527665477815032008-04-12T08:02:00.000-04:002008-04-12T08:02:00.000-04:00Stefan, Maybe I misunderstand something, but isn't...Stefan, <BR/><BR/>Maybe I misunderstand something, but isn't there a much simpler proof by noting that the two removed squares are both black? Since every domino covers exactly one black and one white square, they can't cover 32 white and 30 black squares.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-619562296313629922008-04-12T07:29:00.000-04:002008-04-12T07:29:00.000-04:00Hi Uncle Al,“Physics routinely chokes on parity - ...Hi Uncle Al,<BR/><BR/>“Physics routinely chokes on parity - right hand rule, gyroscope precession, spacetime torsion... and that little Christmas 1956 experimental embarrassment.”<BR/><BR/>Yes, not only parity yet more importantly symmetry. That is our world is not simply that of the other side of the mirror and therefore just simply a different perspective of reality. For me it has always Phil Warnellhttps://www.blogger.com/profile/15671311338712852659noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-4327525003478807082008-04-11T21:02:00.000-04:002008-04-11T21:02:00.000-04:00Parity check! Parity might falsify General Relati...Parity check! Parity might falsify General Relativity and string theory - parity Eötvös experiment opposing single crystal alpha-quartz enantiomorphs, parity calorimetry experiment opposing single crystal benzil enantiomorphs.<BR/><BR/>Physics routinely chokes on parity - right hand rule, gyroscope precession, spacetime torsion... and that little Christmas 1956 experimental <A HREF="http://Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-44313458034940910332008-04-11T19:56:00.000-04:002008-04-11T19:56:00.000-04:00Hah! An invitation to point out that counting whit...Hah! An invitation to point out that counting white and black squares proves the impossibility.<BR/><BR/>Which reminds me, at the local chess club, a game was discussed where white ended up with two white square bishops. The discussers concluded that there had been a mistake in the play as no pawns had been promoted.<BR/><BR/>So this raises the question. Is it possible to change a white square CarlBrannenhttps://www.blogger.com/profile/17180079098492232258noreply@blogger.com