July 2010 - mathfun@mailman.xmission.com

Re: [math-fun] RE : RE : King walk on a square grid to write 0 to 100
by Seb Perez-D 22 Jul '10

22 Jul '10

On Thu, Jul 22, 2010 at 03:20, Eric Angelini <Eric.Angelini(a)kntv.be> wrote: > > I have 20 cells: > 29378 > 78154 > 60291 > 54360 But where is 10? Best, Seb

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Re: [math-fun] A Scientist Takes On Gravity
by Steve Witham 22 Jul '10

22 Jul '10

>Subject: Re: [math-fun] A Scientist Takes On Gravity Frederick W Kantor's 1977 book _Information Mechanics_ says that energy must correspond to information, and then works out consequences of that in ways I didn't understand when I had a copy. But I do remember his explaining gravity in terms of information: http://books.google.com/books?ei=AtFHTLjPN4H98AaX-NiaBQ&ct=result&id=VaKBAA… "That is, energy and information are released when two objects are brought nearer each other. From this, I next construct a picture for gravity." Here's a paper from 1974 introducing information mechanics: http://www.gravityresearchfoundation.org/pdf/awarded/1974/kantor.pdf --Steve

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Re: [math-fun] RE : King walk on a square grid to write 0 to 100
by Robert Munafo 22 Jul '10

22 Jul '10

Thanks for the clarification Eric. So it's a word search puzzle where you need to find the 10 single digits, plus 45 two-digit pairs where the two digits differ. The need for 45 pairs places a lower limit on the size of the grid, since each vertical, horizontal and diagonal line is one unique pair. I thought about it for a bit, and I didn't improve on the 4x8 grid size but at least found a more orderly pattern. Here I have deliberately left redundant digits in (such as the upper-left 1) to show the pattern. Using a mono-space font, the lines represent pairs of adjacent digits: 1-2-3-4-5-6-7-8 |x|x|x|x|x|x|x| 4-5-6-7-8-9-0-1 |x|x|x|x|x|x|x| 8-9-0-1-2-3-4-5 |x|x|x|x|x|x|x| 1-2-3-4-5-6-7-8 On Wed, Jul 21, 2010 at 19:24, Eric Angelini <Eric.Angelini(a)kntv.be> wrote: > > Hello Robert, > sorry to be unclear, > the "words" alone have to be found, > not the path linking them. > So you can find "0", of course, > "1", "2", etc. And "10", "11", "12"... > But for "19" (in my example) you > have to add an extra digit "1"... > Hope I'm more clear now, > E. > > > What would be a "minimal king's-tour spelling matrix" showing all > integers > > from 0 to 100? > > > > Double digits can be accomodated by the rule that a cell may be counted > > twice. > > > > The attempt below is for sure not minimal (minimal = quantity of cells = > > 24, here): > > > > 9 2 3 4 7 8 9 > > 4 7 8 0 5 3 . > > 0 6 1 2 9 1 . > > . 5 4 3 6 4 . > -- Robert Munafo -- mrob.com

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Re: [math-fun] Nicole Oresme in the year 1350 and Zeta[1]
by Dan Asimov 21 Jul '10

21 Jul '10

Rich wrote: << H(2n) - H(n) -> log2 = .693... for large N. The H difference can be thought of as the area of a staircase, with steps of width 1/n and height n/k from the x-axis, as k goes from n+1 to 2n. [The height is from a fixed baseline; the drop from one step to the next is much smaller.] The staircase is a good approximation to the curve 1/x, 1<x<2, whose integral is log2. >> Yes. Also, unvarnished H(2n) - H(n) is a very good approximation to log(2n) - log(n) = log(2). --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] King walk on a square grid to write 0 to 100
by Eric Angelini 21 Jul '10

21 Jul '10

Hello Math-Fun, (from Gardner's "Incredible Dr. Matrix") . . . U . . C O X S A H I N . . R L M . . . D . . This is a "spelling matrix" which shows "RICHARD.MILHOUS.NIXON" when moving from cell to cell like a king in the game of chess (start with R, 4th row). What would be a "minimal king's-tour spelling matrix" showing all integers from 0 to 100? Double digits can be accomodated by the rule that a cell may be counted twice. The attempt below is for sure not minimal (minimal = quantity of cells = 24, here): 9 2 3 4 7 8 9 4 7 8 0 5 3 . 0 6 1 2 9 1 . . 5 4 3 6 4 . Best, É. (sorry if this is old hat)

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[math-fun] Nicole Oresme in the year 1350 and Zeta[1]
by wouter meeussen 21 Jul '10

21 Jul '10

remember the days when Nicholas O. showed elegantly that 1+1/2+1/3+1/4+1/5+... is unbounded? he stated, according to http://en.wikipedia.org/wiki/Nicole_Oresme that 1+1/2+(1/3+1/4)+(1/5+1/6+1/7+1/8)+ ... must be greater than 1+1/2+(1/4+/4)+(1/8+1/8+1/8+1/8)+... and so must be greater than 1+1/2+1/2+1/2+... a nice tidbit given by eric's http://mathworld.wolfram.com/HarmonicSeries.html My surprise: good old Mathematica 4.0 gives no solace for each of those cool brackets: Limit[Sum[1./k,{k,2^n+1,2^(n+1)}], n->Infinity] aka limit of HarmonicNumber[2^(n+1)]-HarmonicNumber[2^n] aka limit of -PolyGamma[0, 1 + 2^n] + PolyGamma[0, 1 + 2^(1 + n)] but, numerically, it looks a lot like Log[2]. The question "why?" is sometimes translated as "proof?" Wouter.

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[math-fun] Re Tour de France
by Guy Haworth 21 Jul '10

21 Jul '10

The cyclists in the TdF are not independent entities but are paid to be members of a team (of about 10). Live commentaries on the web (Eurosport, ITV4 etc) make this clear. Teams which lose riders along the way (injury, fatigue, timed-out or disqualification) are at a disadvantage, as are teams where members are not proving to be up to doing their job. The 'domestiques' give moral and geographical support, protecting their (relative) 'lead riders' from headwinds and also cross-winds, acting as 'wing men', fetching water from the team cars, 'leading out' in sprints, shepherding riders to the front, ... making things happen for their team or preventing things happening for another team. It's chess on wheels. The team with the strongest strategical reason to be at the front - exercising control - tends to be there in obvious numbers. There is an initial gameplan and a running strategy, conveyed by radio link. At the front, it's easier to form a line and keep in the optimal formation: work is not shared on an even basis as riders like O'Grady sacrifice themselves in 'Grand Classification' or 'overall time' terms for the sake of their lead rider. This year's Tour will effectively be decided on the slopes of the Tourmalet tomorrow or in the final time-trial (when there is no 'team effect'). Contador remains favourite because of his apparent superiority in time-trials over Schleck. G

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Re: [math-fun] Less is more, inverse graffiti for math fun
by James Propp 21 Jul '10

21 Jul '10

Hilarie writes: >For the mathematician vandal: consider removing the "n" from street >signs for "Pine". Going in the other direction, I attended a conference in honor of Ramanujan a couple of decades ago; most of the talks were held in room 314. One morning before the talks I added a decimal point. And while we're discussing mathematical vandalism: while visiting MIT about fifteen years ago, Ron Graham suggested to me that someone should write L(η) on the glass door of the service elevator. (In case that Greek letter doesn't come through, it's an eta.) I never got around to doing it, but I hope someone does this at MIT (or at some other Boston-area school). Jim Propp

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[math-fun] Less is more, inverse graffiti for math fun
by Hilarie Orman 21 Jul '10

21 Jul '10

For the mathematician vandal: consider removing the "n" from street signs for "Pine". Hilarie

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Re: [math-fun] A Scientist Takes On Gravity
by Henry Baker 21 Jul '10

21 Jul '10

Read the paper, then Google the physics blogs for "Verlinde" & download Verlinde's (~1 hour) audio & PDF slides from a lecture that he gave. In the audio file, there are questions from the audience that are interesting. I've listened to it once & will listen to it several more times. Apparently, he does handle Lorentz & GR & even provides some explanation of dark matter (!). I didn't follow much of this, but apparently much of what you're asking about is the "easy" part, as it has already been done before for other models, including holographic & string theory models. At 07:34 AM 7/17/2010, Fred lunnon wrote: >I've always found cosmology intriguing --- though not alas enough to actually >learn any properly. Much out there in the field seems solidly based >(if too detailed for a casual enquirer to grasp properly), and I'm >pretty sure I >could get to grips with it if sufficiently motivated --- the Standard >Model being >a case in point. Much else is patently crank, generated by individuals with >impaired judgement --- we might not always agree about individual cases here >--- String Theory, anyone? > >Very occasionally though I encounter something genuinely shocking --- so >improbable and outrageous that I become aware of an emotional reaction, >attempting to suppress it from consciousness --- general relativity and >quantum mechanics come to mind here, when first met long ago. >And perhaps more recently, the original (quaternion) formulation of the >Maxwell equations. > >But now Jacobson, Verlinde & Co. are rattling the bars of my comfortable >worldview again, and folks, I'm reeling somewhat. > >Tell me it ain't so --- space just the grin on another Cheshire cat? > >How can Lorentz transformations occur --- space and time axes finally >interchanging in the proximity of the Schwarzschild radius --- if spacetime >is asymmetrical? > >Do these ideas explain why space has just three dimensions --- never >mind about a single time? > >Have they any relevance to the missing mass problem? > >Somebody, help! Fred Lunnon > >On 7/16/10, Henry Baker <hbaker1(a)pipeline.com> wrote: >> The paper: http://arxiv.org/abs/1001.0785 >> >> I read over the paper, and it is surprisingly readable for mere mortals. >> >> I don't know enough physics to comment on its accuracy as a model of the "real" world, but even as an abstract model it is very beautiful. >> >> Basically, Verlinde turns Bekenstein on his head. Verlinde rearranges the world so that gravity falls out of information/entropy instead of the other way around. >> >> Bekenstein showed that the universe is "holographic", meaning that _all_ the information about what is going on within a simple region of space is encoded in bits on its surface, and the _amount_ of such information is proportional to its surface area. >> >> Verlinde goes backwards and shows that gravity is an emergent concept from the statistics of microstates. The closest high school physics analog is an osmotic force across a membrane: the force arises because it is far more probable that the more concentrated fluid becomes less concentrated than the other way around. >> >> Interestingly, the Heisenberg constant h plays very little part in Verlinde's derivation, which treats entropy, temperature, etc. as continuous variables. This makes a lot of sense, as gravity itself is a macroscopic phenomenon. >> >> From a blog about Verlinde's paper: >> >> http://motls.blogspot.com/2010/01/erik-verlinde-comments-about-entropic.html >> ...

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