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[math-fun] Random thought
by David Wilson 05 Jun '17

05 Jun '17

It's surprisingly difficult to formulate natural-sounding sentences whose acronyms are words, e.g. "Have a nice day" -> hand.

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[math-fun] Climb to a Prime (counterexample)
by Hans Havermann 05 Jun '17

05 Jun '17

A few years ago John H. Conway offered five $1000 problems: http://www.cheswick.com/ches/conway1000.pdf I'll transcribe the fifth one (Climb to a Prime): _____ Let n be a positive integer. Write the prime factorization in the usual way, e.g. 60 = 2^2*3*5, in which the primes are written in increasing order, and exponents of 1 are omitted. Then bring exponents down to the line and omit all multiplication signs, obtaining a number f(n). Now repeat. So, for example, f(60) = f(2^2*3*5) = 2235. Next, because 2235 = 3*5*149, it maps, under f, to 35149, and since 35149 is prime, it maps to itself. Thus 60 -> 2235 -> 35149 -> 35149 -> ..., so we have climbed to a prime, and we stop there forever. The conjecture, in which I seem to be the only believer, is that every number eventually climbs to a prime. The number 20 has not been verified to do so. Observe that 20 -> 225 -> 3252 -> 223271 -> ..., eventually getting to more than one hundred digits without yet reaching a prime! _____ A James Davis contacted me yesterday with word of a counterexample to Conway's conjecture (that every number eventually climbs to a prime) which makes him eligible (I think) for the prize. I told him to write Conway a letter. In the meantime, I'll publish his find here: 13532385396179 -> 13532385396179 -> composite forever James Davis writes: "I'm not a mathematician by any stretch - the search that happened to work was hoping n = x*p=f(x)*10^y+p, where p is the largest prime factor of n. That requires that f(x)/(x-1) terminate and it's decimal expansion be a prime (p). That motivates looking for x of the form x=m*10^y+1 and hoping some common factors cancel between f(x) and (x-1). Turned out to be enough: m=1407 fell out immediately."

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Re: [math-fun] Bill & Rohan's G12 talk
by Henry Baker 05 Jun '17

05 Jun '17

Agreed! Where can I get Minsky's & Trinsky's today ? (Digital version preferred) Will there be a Minsky's & Trinsky's II ? At 09:34 PM 6/1/2017, Robert Smith wrote: >Great talk! > >On Thu, Jun 1, 2017 at 19:56 Bill Gosper <billgosper(a)gmail.com> wrote: > >> https://youtu.be/lXsVWwPa7bc --rwg >> http://www.gathering4gardner.org/g4g12-videos/

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[math-fun] "harmonic-like" series
by Henry Baker 05 Jun '17

05 Jun '17

I've been playing with spreadsheets that have formulae with logs in them. Certain of these spreadsheets effectively approximate logs by summing the inverses of something being counted. So, what I'm *really* doing in these spreadsheets is computing harmonic series. The problem is, the approximation of the standard harmonic series to a log function isn't very good. So, still using a spreadsheet, how can we fiddle with the formulae to better approximate a log function? Idea #1. sum(1/(i+fudge),i,1,n), where fudge is some small constant to be determined. Is there an "optimal" value of fudge that minimizes the error under some error model ? Idea #2. sum(1/(i+fudge[i]),i,1,n), where fudge[i] is an array of small (|fudge[i]|<1) constants that "sample" the function 1/x at somewhat more optimum points ? Any other ideas?

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[math-fun] Number theory question
by David Wilson 04 Jun '17

04 Jun '17

Let !n = 0! + 1! + ... + n! = A003422(n) For integer k, is it true that !a == k (mod a) and !b == k (mod b) together imply !c == k (mod c) where c = lcm(a, b) ?

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Re: [math-fun] How does a dull spoon manage to cut a stringy pieceof meat
by Bill Gosper 03 Jun '17

03 Jun '17

Actually, close questioning by Mike Beeler jogged me to remember what is probably a big clue: Somewhat prior to the creeping, I noticed on that shoe the grommetoidoid (occulted, opposite the circled one) in gosper.org/shoe.png can now freely pivot. After the next creep cycle, I'll try gluing it. What the heck are the correct names for grommetoid and (the simply connected) grommetoidoid? On 2017-04-27 13:33, Hilarie Orman wrote: >> From: Bill Gosper <billgosper(a)gmail.com> >> On Sun, Jan 15, 2017 at 4:57 PM, Bill Gosper <billgosper(a)gmail.com> wrote: > >> > while sliding back an forth against the inside of a slippery bowl? --rwg >> > > >> No one took this question seriously, but I claim the phenomenon needs >> explaining. >> It definitely requires some friction with the bowl: Just now I had it work >> improbably >> well on a piece of meat, yet fail on a tenderer but slipperier partially >> stewed tomato >> in the same bowl. > > I did express concern about your diet. > > Tomato skins are tough. The gold standard for a perfect knife blade > is one that with a light touch will cut a tomato skin. > > I've not found any standard measurements for muscle fiber strength. > The usual measure of tenderness relates to compression. Presumably > you are twisting and tearing the fibers with rotational force. > >> OK, on to the next quotidian mystery: For years I've worn the same pair of >> https://ll-us-i5.wal.co/asr/fd205dcf-4974-49eb-b2d2-6166402bc2b3_1.ecc95c27… >> (only with five pairs of grommetoids (discontinued?) >> instead of four). Possibly coincident >> with replacing the original laces with Kiwis >> several weeks ago, a strange phenomenon has emerged: Despite two different >> lacing patterns, the right lace >> creeps rightward an inch or two per week, until it is so lopsided as to >> drag on the ground. This time, I'm >> going to mirror-image the disparity. This happens automatically if you simply juxtapose the aglets before redistributing all the slack to the shorter lace. Evening them is harder. You only want to distribute half the slack. >> Prior to this, both shoes were coming >> untied, until I modified the knot. Circle the thumbnail twice. Pull hard. Works great. (Is this Propp's "mathematician's knot"?) >> The left shoe doesn't creep. Nor has any other shoe in my experience. The >> creep is sufficiently insidious >> that I can't tell if it's while I'm walking or tying. Probably tying. My foot is so narrow that the knot is immobilized between the top two grommetoidoids. --rwg >> --rwg Some Web news service recently ran filler claiming that CIA agents signaled each other with binary patterns in their shoelaces. The practice was discontinued after feminist protests alerted the KGB. > > Does the left lace creep forward when you are in Australia? > > Hilarie

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[math-fun] crossword crystals
by Veit Elser 03 Jun '17

03 Jun '17

I’ve been playing with crossword puzzle variants. Here’s one that Dan A. will like. 1) The puzzle grid is an N by N torus. 2) In each row and column there should be exactly one black square. For example, here is a solved 7 by 7 puzzle (black -> blank): A D E R L E L E D S E A E R L E T T D W A N T E L A D D E R S E N D E R E A T E R H To avoid trivial solutions we should require that the horizontal words are not all the same — as in this one. Still, the solutions I’m finding all have lots of symmetry. Note that the vertical words in this solution match the horizontal words. Now here’s a challenge. Find a solution, with no repeated horizontal words, but where the black squares do not form a backward diagonal. -Veit

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[math-fun] The bathroom square dance
by Bill Gosper 02 Jun '17

02 Jun '17

I get _strong_ twisting from http://www.math.brown.edu/~rkenyon/gallery/squarespiral.gif (vs squarespiral2), and ascribed it to differential fatigue of my motion receptors. (Generalized moving bar illusion.) On 2017-06-01 09:21, Fred Lunnon wrote: > At second attempt, I did detect a slight twisting effect. > > I imagine this is the same mechanism that causes the room apparently > to rotate in the reverse direction after one suddenly ceases spinning about > a vertical axis (how do ballerinas cope, I wonder?); or the floor to roll and > pitch after one disembarks from a small boat. For many hrs after a local (1989, Richter 7) quake, the ground felt gelatinous. I assumed it was objectively measurable seismicity. Perhaps not. --rwg > > I doubt whether retinal cell configuration has any part to play in > such effects, > which are manifestations of a general mental process, occurring at many > levels, which seeks to filter out constant background from our perception, > leaving us conscious only of any unpredictable variation. > > I once encountered a spectacular example of this phenomenon, involving > hearing rather than sight. Standing beside the Victorian wall clock in the > hall of my home late one quiet night, I failed to hear its customary loud tick, > and concluded that it must have broken down. Visual inspection however > revealed that the pendulum continued to swing; and as I stared at it in some > perplexity, over several seconds its tick gradually faded in to become once > more clearly perceptible. > > Similarly as Sarah Silverman recently pointed out, it is impossible > to register > one's own body odour, whatever olfactory violence one may inadvertantly be > perpetrating upon one's neighbours. The distinctive feature of sight in this > context is that relative motion possesses sign, making its (sudden) absence > more directly contrasted with presence. > > Fred Lunnon > > > On 6/1/17, Bill Gosper <billgosper(a)gmail.com> wrote: >> What's supposed to happen after 20 sec? >> >> You're supposed to quickly redirect your stare to top left of your screen. >> >> >> (That's my sixties cred shot to pieces.) WFL >> >> >> Or just your retinal cone cells. If you do not see disturbing, startling >> twisting, >> >> consider an ophthalmological consult. --Bill >> >> >> >> On 5/31/17, Bill Gosper <billgosper(a)gmail.com> wrote: >> >> On 2017-05-29 10:55, Stuart Anderson wrote: >> >> To make the tiles really dance ... >> >> Danny Caligari >> >> ; >> >> >> https://www.google.com.au/amp/s/lamington.wordpress.com/2013/01/13/kenyons-… >> >> >> Bad URL there. Use >> >> http://www.math.brown.edu/~rkenyon/gallery/squarespiral2.gif >> >> >> While you're there, stare at >> >> http://www.math.brown.edu/~rkenyon/gallery/squarespiral.gif >> >> for ~20 secs, then the top corner of your screen. --rwg >>

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[math-fun] Edwards book on Integration
by Bill Gosper 02 Jun '17

02 Jun '17

Not(?) to be confused with https://archive.org/details/treatiseonintegr01edwauoft . --rwg On 2017-06-02 06:49, Hans Havermann wrote: > Guy Haworth: "His father was a Professor of Mathematics (hence the > 'Professor' above) and wrote a book on Integration solutions - my > school had a copy (with hard, orange covers)." > > The man was Reginald Walter Kenrick (RWK) Edwards (born 1862), > educated at Cambridge and taught at King's College, London. He > authored The Mermaid of Inish-Uig (1898), Dick Vaughan's First Term > (1901), A Radial Area-Scale (1904), and An Elementary Text-Book of > Trigonometry (1911). I can't find the Integration book to which you > refer but I'll note that Sir Alfred Lodge authored Integral Calculus > for Beginners (1905) about which is written (The Mathematical > Gazette): "The most novel feature of the book is perhaps the seventh > chapter dealing with approximate methods of integration. Here, after > the well-known rules of Simpson and Weddle, approximate formulae, > recently devised by Mr. R. W. K. Edwards and Professor Lodge himself, > are given, for dealing with the case in which the curvilinear boundary > of a required area cuts the axis at right angles; a case for which, as > is well known, rules of the Simpson type are not well fitted." >

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[math-fun] Bill & Rohan's G12 talk
by Bill Gosper 02 Jun '17

02 Jun '17

https://youtu.be/lXsVWwPa7bc --rwg http://www.gathering4gardner.org/g4g12-videos/

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