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[math-fun] Cliff College
by James Propp 18 Jun '18

18 Jun '18

Does anyone remember a fictional institution called Cliff College that was part of some web-based game back in the 1990s? I recall being surprised to learn that I was listed as a member of the Cliff College math faculty. (I may have the name of the institution wrong.) Jim Propp P.S. I am still hoping to find the original "Poke the Bunny" web-page, or a recreation of it, from the same period. You use your mouse to move a picture of a virtual finger that pokes a virtual bunny a whole lot of times, seemingly without effect, until after some threshold has been crossed the bunny bites the virtual finger and thereafter won't let go.

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Re: [math-fun] A prime factor factory
by Dan Asimov 17 Jun '18

17 Jun '18

Heuristically, the probability of such a chain starting from a given prime p is of the form C_1 * C_2 * C_3 ... where C_k —> 0 as k —> oo. If we then *add* these probabilities over all primes p, we get an infinitesimal that is countable * 1/continuum that is heuristically *greater than* the chance of an infinite Cunningham chain, suggesting it's pretty unlikely. —Dan W. Edwin Clark wrote: ----- This matter seems to be related to Cunningham chains <https://en.wikipedia.org/wiki/Cunningham_chain>--sequences of primes p_i such that p_{i+1} = 2p_{i} + 1. ... ... It is conjectured that there are Cunningham chains of length k for all positive integers k. Is there a reason that one could not have a Cunningham chain of infinite length? -----

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[math-fun] A prime factor factory
by James Propp 17 Jun '18

17 Jun '18

Given any prime p, we can look at all the prime factors of 2p+1, and then perform the same process (double, add 1, find all prime factors) with those primes, and so on; must the process eventually stabilize? E.g.: 2 -> 5 -> 11 -> 23 -> 47 -> 95=5*19 19 -> 39=3*13 3 -> 7 -> 15=3*5 13 -> 27=3*3*3 Done. I looked at a variant where one uses 2p-1 instead of 2p+1; it appears to lead to closure a lot more rapidly. For the 2p-1 version, I was able to check in my head that all primes under 100 lead to closure; for the 2p+1 version, I wasn’t able to do this. Jim Propp

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Re: [math-fun] A prime factor factory
by Dan Asimov 16 Jun '18

16 Jun '18

If true, that would be a colossally cool theorem! Dan W. Edwin Clark wrote: ----- If my program is correct, starting with the n-th prime (n<=10^5) the procedure always ends with {3, 5, 7, 11, 13, 19, 23, 47} which is sequence A020575: (In particular the number of primes obtained will always be finite.) -----

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[math-fun] ft/meter: all threes and ones
by Bill Gosper 16 Jun '18

16 Jun '18

In:= FromContinuedFraction@{3, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1} Quantity@ "ft"/Quantity@"m" Out= 1 --rwg Isn't it weird that to get ft/meter, you divide length(meter) / length(foot) ?

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Re: [math-fun] Schensted's two-dimensional abacus
by Bill Gosper 14 Jun '18

14 Jun '18

Or https://www.youtube.com/watch?v=q7swR8MATA0 --rwg On 2018-06-14 03:35, James Propp wrote: > I know “Ea Ea” is Babylonian, but it brings to my mind the > pseudo-Polynesian “Ea Ea” at the end of the Kellogg’s Puffa Puffa Rice > commercial (does anyone else remember that?). > > Jim Propp > > On Wednesday, June 13, 2018, Allan Wechsler <acwacw(a)gmail.com> wrote: > >> Oh, sorry for not reading this thread more carefully. Somebody else already >> said this. >> >> On Wed, Jun 13, 2018 at 10:58 PM, Allan Wechsler <acwacw(a)gmail.com> wrote: >> >> > Yes, and goes by the name Ea Ea. >> > >> > On Wed, Jun 13, 2018 at 10:50 PM, Hans Havermann <gladhobo(a)bell.net> >> > wrote: >> > >> >> > The Wikipedia page for Craige gives no death date, but uses the past >> >> tense in describing his residency in Portland, Maine. >> >> >> >> I had stated that Craige's mother's obit mentioned two grandchildren so >> I >> >> had hopefully assumed that they might be Craige's kids, he being her >> only >> >> child. I'm fairly certain now that Craige fathered no children and that >> his >> >> mother's grandchildren should more properly have been described as her >> >> step-grandchildren. >> >> >> >> In the search to uncover all this, I unexpectedly discovered that Craige >> >> Schensted is still alive! He's living in Portland, Maine. >> >>

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[math-fun] Terse ratfitter
by Bill Gosper 14 Jun '18

14 Jun '18

Out[551]= {3, 5, 28/5, 165/28, 91/15, 68/11, 570/91, 253/40, 325/51, 609/95, 496/77} In[552]:= fitrat@% Out[552]= 3 + (-1 + n)/(1/2 + (-2 + n)/(26/7 + (-3 + n)/(203/2 + 28 (-4 + n)))) In[553]:= FullSimplify@% Out[553]= 3/4 (9 + 1/(1 - 2 n) - 4/n) fitrat[L_List, v_: (n - 1)] := If[MemberQ[#2 - #, 0] || #2 == {}, #, # + v/fitrat[Range[Length@#2]/(#2 - #), v - 1]] &[L[[1]], Rest@L] Has anyone a nice explanation of why this works? --rwg

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[math-fun] Schensted's two-dimensional abacus
by James Propp 14 Jun '18

14 Jun '18

Oops; this thread needs a subject-line. On Sun, Jun 10, 2018 at 9:00 PM, James Propp <jamespropp(a)gmail.com> wrote: > According to Martin Gardner's piece "Napier's Abacus" (chapter 8 in > "Knotted Doughnuts and Other Mathematical Entertainments"): > > Craige Schensted was inspired by Napier's device to invent a chessboard > computer on which many astonishing calculations can be made. The basic idea > is to allow the columns to be labeled with the powers of one base and the > rows to be labeled with the powers of a different base. Each cell > represents the product of its row and column numbers. It would require a > long chapter to do justice to the elegant ways Schensted found for using > such a board to solve problems that otherwise would be difficult. > Does anyone know anything about this? > > I wonder whether the only extant account of Schensted's device is in > Gardner's files of correspondence. I assume that these files are available > to scholars. Perhaps someone should seek to publish those letters that > contain contributions to mathematics that would otherwise be lost to > posterity? > > Jim Propp >

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[math-fun] Minimum number of swaps to sort a permutation of {1, 2, 3, ..., N}
by Dan Asimov 13 Jun '18

13 Jun '18

Consider all algorithms for sorting a permutation of {1, 2, 3, ..., N}, say given as a filled array arr[1], ..., arr[N], such that each step of the algorithm is of the form if (arr[I] > arr[J]) swap(arr[I], arr[J]); where I and J are actual numbers, and no other steps are allowed. For instance, If x[1], x[2], x[3] is any permutation of {1, 2, 3} then this program will always sort it: ----- if (x[1] > x[2]) swap(x[1], x[2]); if (x[2] > x[3]) swap(x[2], x[3]); if (x[1] > x[2]) swap(x[1], y[2]); ----- Among those that sort all permutations of {1, 2, 3, ..., N}, what is the minimum number of comparisons that sort the worst-case permutation(s)? Let this number be C(N). I'd like to have an asymptotic expression for C(N), or at least upper and lower bounds. —Dan

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[math-fun] Draft of June 2018 blog post
by James Propp 13 Jun '18

13 Jun '18

I started writing a new draft titled "Why Does Exploding Dots Work?" and would love to get your comments, whether I receive them before or after I publish the essay on my blog (late on the 16th or early on the 17th). As usual, I prefer to get responses via email, since then I'll know who you are and can respond if I have follow-up questions. Thanks! Jim Propp <https://mathenchant.wordpress.com?p=2354&shareadraft=5b214e16a08c9> Title: Why Does Exploding Dots Work? Beginning: A few months from now, if James Tanton and his Global Math Project co-conspirators have their way, ten million schoolchildren will take a huge mathematical step backward from the twenty-first century into the Bronze Age: instead of using a gadget with a state-of-the-art interface (say, a telepathic ... Read more: https://mathenchant.wordpress.com?p=2354&shareadraft=5b214e1 6a08c9

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