tag:blogger.com,1999:blog-1227172931607686978.comments2017-12-25T04:46:11.797-05:00Math-Frolic!"Shecky Riemann"http://www.blogger.com/profile/07065658607024191185noreply@blogger.comBlogger236125tag:blogger.com,1999:blog-1227172931607686978.post-71848144551491560642017-12-24T22:57:06.826-05:002017-12-24T22:57:06.826-05:00Math is currently described as being the "sci...Math is currently described as being the "science of patterns"; or the language that describes patterns, ones that exist either in nature or are theorized abstractions.<br /><br />While I do not claim to be a mathematician, you can look at a number as data point related to other points that make up a pattern, that is, a mathematical object.<br /><br />I think this "sensitivity"John CEhttps://www.blogger.com/profile/03629238394162397703noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-86556565691388875752017-10-28T22:33:49.430-04:002017-10-28T22:33:49.430-04:00It feels to me like an argument along the lines of...It feels to me like an argument along the lines of "Nothing is better than eternal happiness, and a ham sandwich is certainly better than nothing." An individual is a combination of atoms, so we'll count every possible combination of atoms as an "individual"...Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-12676662081907715232017-10-28T20:29:12.565-04:002017-10-28T20:29:12.565-04:00Yeah, I’m still confused by the sentence, “If ther...Yeah, I’m still confused by the sentence, “If there are n atoms, there are 2^n - 1 combinations of individuals.” The sentence prior to that makes sense to me, but by their definition, an individual is a “combination of atoms,” so the 2nd sentence really translates to: “If there are n atoms, there are 2^n - 1 combinations of, combinations of atoms.” I can agree there are 2^n - 1 “combinations” ("Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-58247526125908462652017-10-28T20:08:16.927-04:002017-10-28T20:08:16.927-04:00With that definition, I'd quibble with using t...With that definition, I'd quibble with using the word "individual." I can see counting you and me and the moon and the solar system as individuals. But the combination of my right thumb and your left foot? Nope.Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-51244039805383904892017-10-28T16:14:12.177-04:002017-10-28T16:14:12.177-04:00Since for a combination to exist under this assump...Since for a combination to exist under this assumption it is sufficient that its constituents exist, there's no problem..mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-64842594089639631902017-10-28T16:04:45.977-04:002017-10-28T16:04:45.977-04:00Doesn't this argument assume that all possible...Doesn't this argument assume that all possible combinations exist in the universe? If we are missing a few of the possibilities (and we must be, for how could there be more individuals than atoms?), then we can't draw any conclusion.Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-9389184125656627492017-10-25T09:58:25.938-04:002017-10-25T09:58:25.938-04:00
Ahh, thanks for the input and the spelling correc...<br />Ahh, thanks for the input and the spelling correction! (now changed)"Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-57522486439707160022017-10-25T09:13:12.361-04:002017-10-25T09:13:12.361-04:00My own understanding runs as follows:
(a) there a...My own understanding runs as follows:<br /><br />(a) there are a finite number of atoms<br />(b) we define an "individual" as a (non void) group of atoms<br />(c) therefore the total number of individuals must be odd.<br /><br />Of course, if you define a void set of atoms as an individual, the total number becomes even :-)<br /><br />Needless to say, an individual is not a person nor .mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-1115520517676315892017-08-29T09:35:05.953-04:002017-08-29T09:35:05.953-04:00A little history midway through this old piece of ...A little history midway through this old piece of mine: http://bit-player.org/bph-publications/SciAm-1984-01-Hayes-hailstone.pdf. <br /><br />Best source: The Ultimate Challenge: The 3x+1 Problem, ed. by Jeff Lagarias, published by AMS, reprints an article by Collatz himself "On the Motivation and Origin of the (3n+1)-Problem."bit-playerhttps://www.blogger.com/profile/10925013458053903295noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-91749921063476322402017-08-23T07:48:43.210-04:002017-08-23T07:48:43.210-04:00I think I'll use this as a math history assign...I think I'll use this as a math history assignment this semester. Pick a name, make a case! I'll find it difficult to choose, but I think have it narrowed down to Robinson or Thurston.<br /><br />Of course, might be benefits to having a statue of an immigrant as well.John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-53160185150425773642017-02-15T09:38:11.534-05:002017-02-15T09:38:11.534-05:00OK, thanks, he actually does that in a number of h...OK, thanks, he actually does that in a number of his books, which is partly why I think, despite his multi-talents and prolific writing, he never gained the following that Martin Gardner had being a much more succinct, smooth writer.<br /><br />"Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-76037136278972547832017-02-15T08:26:58.449-05:002017-02-15T08:26:58.449-05:00Be warned: I did not appreciate Reflections. It st...Be warned: I did not appreciate <i>Reflections</i>. It startes good, but in the second half of the book Smullyan rambled too much..mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-7736910154782454472017-02-14T04:29:32.050-05:002017-02-14T04:29:32.050-05:00Even if Smullyan published books until last year, ...Even if Smullyan published books until last year, I think his pop fame was in the 80s: this could be a reason why there are so few obituaries. I am startled that the Washington Post did not have one, but as for the other newspapers it's just a matter of "things of the past", rather than canary. After all, I don't think that neither the Donald nor his friends care a damn whether .mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-50306128816195763852016-10-20T23:00:59.869-04:002016-10-20T23:00:59.869-04:00Thanks a lot for motivating. The collection of boo...Thanks a lot for motivating. The collection of books stands at 155 now. My librarian is gracious enough to acquire most of them...JOSEPH VARGHESE Kureetharahttps://www.blogger.com/profile/02019655032384454831noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-27696669425364180212016-09-17T21:32:45.771-04:002016-09-17T21:32:45.771-04:00A bit less work, "next to last".A bit less work, "next to last".Neil Ostrovehttps://www.blogger.com/profile/03638059691645940108noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-82894715544898243032016-09-02T20:10:02.754-04:002016-09-02T20:10:02.754-04:00Not a computer genius here, not by far, but I had ...Not a computer genius here, not by far, but I had a recent problem when I used an ad blocker in a Chrome application. I wanted to open my Outlook work email account using a bookmark of the site.<br /><br />The site was locked, I was blocked, and then immediately a new attempt to reopen was initiated by the computer. The blocking and the re-initiation to open kept going in a cyclic fashion, until MathOughtshttps://www.blogger.com/profile/05020281340534425685noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-7745110449384394752016-08-16T17:29:59.530-04:002016-08-16T17:29:59.530-04:00Agreed. Love Numberphile. Thanks for the other lin...Agreed. Love Numberphile. Thanks for the other links.MathOughtshttps://www.blogger.com/profile/05020281340534425685noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-88095204154438564242016-07-03T22:37:13.094-04:002016-07-03T22:37:13.094-04:00have you had any news on this challenge, i can'...have you had any news on this challenge, i can't seem to find what the challenge even is,<br /><br /><br />thanks,<br /><br />gabegggnoreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-57101081410594299372016-06-15T01:34:34.456-04:002016-06-15T01:34:34.456-04:00Sublime.
Sublime.<br />David Langahttps://www.blogger.com/profile/09034899335717111526noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-27345592046979466612016-06-12T17:46:37.122-04:002016-06-12T17:46:37.122-04:00Thanks. Good seeing this again.
Wonder how many o...Thanks. Good seeing this again.<br /><br />Wonder how many of those math concepts I would identify. MathOughtshttps://www.blogger.com/profile/05020281340534425685noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-38992074886146079072016-06-07T07:53:35.478-04:002016-06-07T07:53:35.478-04:00==> the correct answer is indeed 76. Will Short...<br />==> the correct answer is indeed 76. Will Shortz gives it here:<br />http://tinyurl.com/hp2phtg<br /><br />[the tricky part (to me) is to consider the first set going to a 7-5 outcome rather than a 6-4 outcome]"Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-73990502884317500292016-06-03T18:54:42.407-04:002016-06-03T18:54:42.407-04:00I guess Spanish numbers would go to either 5 (cinc...I guess Spanish numbers would go to either 5 (cinco) or a cycle 4 (cuatro)<->6(seis)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-73189380709075607412016-06-02T21:04:40.726-04:002016-06-02T21:04:40.726-04:00Speaking of fiction, John, reminds me of a novel M...Speaking of fiction, John, reminds me of a novel Martin Gardner highly recommended called "Popco" by British author Scarlett Thomas, that apparently includes lots of recreational mathematics. (I've never read it, but if Gardner highly touts it, it's no doubt good.)<br /><br />Donald Knuth's "Surreal Numbers" also comes to mind.<br /><br /><br />"Shecky Riemann"https://www.blogger.com/profile/07065658607024191185noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-74244567988102710802016-06-02T15:19:34.448-04:002016-06-02T15:19:34.448-04:00Sawyer has several neat older books of problems.
...Sawyer has several neat older books of problems.<br /><br />I'm not sure it's recreational for a general audience, but Professor Posey's Perplexing Problems.<br /><br />Socks Are Like Pants (Rosenfeld and Hamilton) and This is Not a Math Book (Weltman) and Patterns of the Universe (Bellos and Harriss) are some newer ones.<br /><br />What about fiction with math problems, like The John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-1227172931607686978.post-50437585529887255372016-06-02T03:34:00.019-04:002016-06-02T03:34:00.019-04:00Hi, Shecky!
I would add to the latter list some bo...Hi, Shecky!<br />I would add to the latter list some books by Raymond Smullyan (at least <i>The lady or the tiger?</i> and <i>What is the name of this book?</i>.<br /><br />As for mathematical problems, I'd add <i>The Moskow Puzzles</i> by Boris Kordemsky and <i>Mathematical Quickies</i> by Charles Trigg. There are also a lot of books more difficult or too much easy, of course :-)<br />.mau.https://www.blogger.com/profile/09641196427325175260noreply@blogger.com