June 2008 - mathfun@mailman.xmission.com

[math-fun] Salutations on COORDINATE Day
by rwg＠sdf.lonestar.org 13 Jun '08

13 Jun '08

"N. J. A. Sloane" <njas(a)research.att.com> said: >Bill said: [formulae from old MIT slides] >> I'll add them to www.tweedledum.com/rwg/idents.htm soon. >There are some pretty amazing identities there already! Wow! >Neil Well now you got me going. It's ~3 times bigger now--hopefully < 3 times diluted. There are >= 3 EIS #s in the alternate text (for which a method of viewing with Firefox still remains mysterious). --Bill

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Re: [math-fun] becoming a 21st century mathematician
by James Propp 12 Jun '08

12 Jun '08

Chris Hillman writes: >As it happens, I have recently been thinking about what math software I >have found most useful over the past year, so I guess I am well placed >to provide a lengthy answer to this query. Great! >In my response, I will assume little prior knowledge or experience with >(in particular) installing open source software I appreciate this assumption (or lack of assumption), since this very issue has often been a bottleneck for me. ("Well, first install Xtools on your laptop, and then...") >It is true that there is a widely available and easily installed open >source engine, Maxima, which is comparable to Macsyma, the system upon >which Maple is based. For this reason, Maxima syntax is very similar to >that of Maple, which is mostly helpful, although there are some annoying >differences (like subts instead of subs). Is there a simple way to install Maxima on a Mac running OS X? >Unfortunately, in my experience, the things which make Maple so useful >include Groebner basis, differential algebra, and graphics packages, plus >powerful commands like "casesplit" and "rifsimp", which at present have >no equivalent in Maxima. This is very unfortunate! Indeed, strictly >speaking "bare-bones" Maxima more closely resembles "text-based" Maple >(e.g. called with maple rather than xmaple on a linux system), although >there are open source graphical "front ends" which aim to allow users >to interact with Maxima in much the same way that they may be accustomed >to interacting with Maple. I don't use any of the Maple commands that you say "make Maple so useful", and I use it exclusively in text-based mode. So if Maxima is stable and well-documented, that might be a good choice for me. (One thing I'd like is a simple way to create an m-by-n array of small cells with specified colors. What's the right tool for that job?) >Even so, spending a few thousand on the latest version of Maple will >take you much further if you spend almost nothing on obtaining other >mathematical software (and your OS plus useful general applications like >browsers, postscript viewers, and so on, all of which are provided by any >Linux distro). I also suggest below some other "moderately big ticket" >projects you might want to consider, while you decide what to do with >your funding, such as setting up a cluster. One issue I'm facing is that Maple is not supported at Lowell. So if I have trouble installing it, and the license I get doesn't come with installation support, I'm out of luck. >2. Someone mentioned Debian as a good choice for your primary operating >system, and I'll second that (with a caveat mentioned below). I've been quite happy with my Mac OS X running shell-script windows that look like any old UNIX system. (I can think of one exception to the previous statement: I was pretty annoyed when I found out that OS X puts all the files and directories in one's Desktop into RAM at startup. Aside from the fact that it's undocumented, it's just not the sort of thing a UNIX system would do.) >And I should stress that a distro >like Mepis is specifically designed to be very easily installed along with >Windows in a "dual-boot" configuration, and in my experience installs >without fuss with one click on the icon of the installation script when >you boot off the live CD, which for Mepis and some other distros serves >the double purpose of a demo/installation disk. What's a "distro"? (Is it short for "distribution"?) >Setting up a dual-boot >system requires using a disk partioning utility and configuring a boot >loader, so this takes a bit more effort, but IIRC the Mepis instructions >are very clear and I hear good things from people who have tried this. I once had a dual-booting laptop (Debian and Windows), and I didn't like it. I think I'll use a Mac running a Mac OS that sits on top of a UNIX OS, running Parallels so that I can run Windows software. >Well, if you don't know about "live CDs" (actually, I guess you do >know!) that would probably be my first answer to the query: what else >is neat besides memory sticks? Actually, I didn't know about live CDs by that name, but I have been given a few by various people (sometimes with bootleg software). >(Some live CDs automatically >mount the disk R/W, which isn't always a good idea. "Mounting" is how >Linux makes a "file system"--- a directory tree associated with a memory >device such as a hard drive--- available to the user; this may work a >bit differently for "removable media" like pendrives and floppies under >some varieties of Linux.) One way in which a flashdrive has recently been a big help is that I've been able to mount a flashdrive with a UNIX file system on my Mac, so that it can handle directories in which two or more files or subdirectories have the same name when file/directory names are interpreted in a case insensitive way. (This matters because when I was at the University of Wisconsin and using the math department's UNIX file system, I often created directories with several files whose names differed only in that one was capitalized and one was not. When I left my job there and took all my files on a CD, I was dismayed to discover that I couldn't put them on my Mac without losing some of them! So the flashdrive is great because not only is it more compact than a CD, but it can be formatted to house a UNIX file system.) >You can also use utilities like >rsynch to keep your memory stick synchronized with the hard drive on your >primary machine. Sounds like rsynch (or is it rsync?) is also something I would find useful. How do I get it? >The Linux stand-in for Microsoft Office (spreadsheet, humdrum word >processor, etc) is Open Office, which should be bundled with any major >Linux distro (along with documentation). My Mac came with Word:mac, which unfortunately doesn't have Equation Editor. Does Open Office? I should also say that the PDF viewer that came with my Mac is not in all respects perfect. I'll probably want to spring for something better. >SciLab (open source stand-in for MatLab) That sounds like it'd be handy too. Thanks! >Of course, Mac OS has suffered some equally serious security problems >in recent years, and I need hardly mention criticism of Windows and Vista. Would the Mac OS security issue affect a user like me, who has a laptop with no fixed IP address? >If you are using Linux on laptops, probably the two most important things >you can do are to learn about wireless security issues ("factory defaults" >are likely to leave you highly vulnerable) and about encrypting your >hard drive. What about OS X on laptops? I guess I also want some sort of virus/spyware protection on my PC; any suggestions? >Hope some of this proves useful. Indeed it has been! Jim

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Re: [math-fun] Missing Catalan identity
by Dan Asimov 11 Jun '08

11 Jun '08

Steve Gray wrote: << <<< James Buddenhagen wrote: . . . something that has been bothering me for a long time: when should I accept that something is true? . . . >>> You raise interesting points. Like it or not, mathematics is partly a matter of consensus. This is dismaying because we were educated, explicitly or implicitly, to think of math as absolute. Instead, it's only the most absolute thing we humans are allowed. There being no "god," the limitation to our possible knowledge (also evident in physics for several reasons) is built into the universe at a very deep level. The most complex proofs must be accepted provisionally, since all advanced science and math is accepted on the basis of approval by experts. As much as I dislike it, even mathematics is therefore subject to authority. But I, for one, plug along, continuing to find and prove some of these maximally absolute things (in my case, rather minor ones) knowing that a theorem once established will very likely never be disestablished. >> I would distinguish between mathematics per se, on the one hand, which I think of as the absolute body of things that can be proved (and being a Platonist, I also include facts that may be undecidable, possibly including things like the Twin Prime Conjecture) . . . . . . and the *sociology of mathematics*, on the other hand, which includes the vague hierarchy of authority that determines what each individual mathematician believes to be proved, and the consensi whomof. (It is indeed rare, but there are striking examples of putative proofs of valid theorems that were debunked many years later, like Kempe's 1879 putative proof of the four-color theorem (about 15 years), Lucas's 1875 putative proof that 70^2 is the unique square > 1 that equals 1^1 + 2^2 + . . . + n^2 (43 years?), and Dulac's 1923 putative proof that a polynomial vector field V(x,y) = (P(x,y),Q(x,y)) in the plane has at most a finite number of limit cycles (65 years?).) --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] NYTimes: Game Over: Sudoku Spoils a Trial in Australia
by Henry Baker 10 Jun '08

10 Jun '08

FYI -- The jurors should be thankful that they didn't meet Archimedes's end. June 10, 2008, 4:40 pm Game Over: Sudoku Spoils a Trial in Australia By Mike Nizza Say what you will about the performance of the airline industry Â it was first to identify a threat in sudoku. In one of the first major signs that the game had grown into a phenomenon, British Airways told its 13,000-strong force of flight attendants in 2006 that they were forbidden to play sudoku during takeoffs and landings. Two years later, the number puzzle, which has its own section on NYTimes.com, has succeeded in spoiling a federal criminal case in Australia, wasting almost $1 million in the process. Judge Peter Zahra made the decision to abort the trial and discharge the jury after the forewoman admitted to a prodigious amount of puzzle solving during the proceedings, according to The Sydney Morning Herald: She said four or five jurors had brought in the sudoku sheets and photocopied them to play during the trial and then compare their results during meal breaks. She admitted to having spent more than half of her time in court playing the game. The judge was apparently less than persuaded by her assurances that Âit helps me keep my mind busy paying more attention.Â After all, Âsome of the evidence is rather drawn out and I find it difficult to maintain my attention the whole time,Â she explained, according to The Associated Press. Some jurors worked crossword puzzles as well, she added. To be sure, the trial was a complicated one, the product of what was apparently a lengthy, complex investigation that yielded drug and conspiracy charges against two men. The court heard evidence in the case for 66 days, including testimony from more than 100 witnesses, 20 of them police officers. At the same time, the game can be more engrossing than the juror acknowledged. Back in 2006, Edward Rothstein of The New York Times offered a much different characterization of SodokuÂs power to command attention: When it comes to sudoku, there is no escape. The grids of these puzzles seem to shut down the mental apparatus, enclosing oneÂs faculties in a tightly constrained universe Â a 9 by 9 array that must be carefully filled up with the numbers 1 to 9, following certain rules. That enclosure is hypnotic. Not so the testimony in the Australian drug case, it would seem. The jury forewoman said the sodoku-playing commenced early on in the trial, Âprobably when the surveillance evidence was on.Â But something other than boredom may account for the puzzle-mad Australian jury. In an essay on sodoku that seemed especially relevant to todayÂs news, Will Shortz, The New York TimesÂs crossword editor, wondered whether it was all really about control: Most of lifeÂs challenges donÂt have black-and-white solutions, and many have no resolution at all. We jump into the middle of problems and muddle through as best we can. With sudoku Â or any other human-made puzzle Â carrying it through from start to finish, and finding the perfect solution in the end, can produce a feeling of great pride. Is the no-sodoku-in-court rule one of those black-and-white solutions? The jurors didnÂt violate Australian law, media reports said. But the next panel selected to try the case, which is supposed to begin anew within weeks, would be wise to avoid being seen writing vertically Â the telltale sign that gave away the last crew.

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Re: [math-fun] becoming a 21st century mathematician
by James Propp 09 Jun '08

09 Jun '08

I wrote: > (I can think of one exception >to the previous statement: I was pretty annoyed when I found out that >OS X puts all the files and directories in one's Desktop into RAM at >startup. Aside from the fact that it's undocumented, it's just not >the sort of thing a UNIX system would do.) here is a link about this: http://www.macosxhints.com/article.php?story=20051117154624368&lsrc=osxh Jim

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Re: [math-fun] becoming a 21st century mathematician
by James Propp 09 Jun '08

09 Jun '08

>A (good) alternative is pdflatex, which creates a pdf directly from you >LaTeX file (if you use figures you have to take care). My problem is that I am using pstricks these days, which pdflatex doesn't seem to understand. I have to use latex to create the dvi file and then use dvipdf to create the pdf file. The results are acceptable, but it'd be nice to have a single program that does this. In fact, what would be better still would be an environment that lets me edit the source file in one window and hit an "update .pdf file" button so that the PDF file in the other window gets updated. (Right now, I basically have to restart the viewer each time I change the source file and want to see what the resulting PDF file looks like.) >I use DataViz PDF To Go, part of Documents To Go. From something the >Mac application says, it looks like I paid for this version, although >at least a demo came with the Treo? It's called "Documents" on mine. I have this too. It's good for most things, but TERRIBLE for equations. (Though maybe the problem is that I haven't paid for an upgrade to the latest version.) Can anyone suggest anything better? Jim

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[math-fun] PDF on Treo
by Steve Witham 09 Jun '08

09 Jun '08

>From: James Propp <jpropp(a)cs.uml.edu> >Then there's a whole bunch of Treo software I'd like, such as: >* Good way to view PDF files I use DataViz PDF To Go, part of Documents To Go. From something the Mac application says, it looks like I paid for this version, although at least a demo came with the Treo? It's called "Documents" on mine. I turn Google maps, campus maps, scanned restaurant menus and train schedules into PDFs and keep them on my Treo. But then, that's probably because I'm too cheap to get internet service for it. I also have EasyCalc, a free scientific graphing calculator. And Numerus, a Roman numeral calculator. --Steve

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[math-fun] Analytic continuation software?
by Dan Asimov 09 Jun '08

09 Jun '08

Speaking of math software, can anyone tell me if there exists analytic continuation software? In particular, given a subroutine f_0 to evaluate an analytic function f on a disk D_0 in C centered at z_0 and of radius R_0, and a curve a: [0,L] -> C with a(0) = z_0 . . . . . . then -- the software would output a set of curve parameters 0 = t_0 < t_1 < t_2 < . . . < t_n = L and radii R_k, 1 <= k <= n such that the original function f_0 element can be successively continued along curve a(t) to the function elements f_k, via the disks D_k of radius R_k about z_k = a(t_k), for 1 <= k <= n (where of course f_(k-1) must agree with f_k on the overlap of D_(k-1) and D_k). The software would also output a routine that will evaluate the function f_k inside the disk D_k. (Or a statement that the function cannot be continued along a(t), 0 <= t <= L.) . . . . . . and all this to a pre-specified level of numerical accuracy. NOTE: The hardest part here is probably ensuring the numerical accuracy of the f_k's. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] becoming a 21st century mathematician
by Steve Witham 09 Jun '08

09 Jun '08

>From: James Propp <jpropp(a)cs.uml.edu> > >Chris Hillman writes: > > >In my response, I will assume little prior knowledge or experience with >>(in particular) installing open source software > >I appreciate this assumption (or lack of assumption), since this very >issue has often been a bottleneck for me. ("Well, first install Xtools >on your laptop, and then...") >... > on a Mac running OS X? If you are maybe thinking of "XCode" instead of "Xtools," XCode is something you almost have to have on your Mac if you're going to use open source stuff. If you have a /Developer directory, you do have XCode. If not, XCode is a disk that comes in the OS X box. (Yes I know Xtools too, this just reminded me.) >I've been quite happy with my Mac OS X running shell-script windows >that look like any old UNIX system. Which it is. The question is why it keeps seeming...in a different class, heh. > (I can think of one exception >to the previous statement: I was pretty annoyed when I found out that >OS X puts all the files and directories in one's Desktop into RAM at >startup. Aside from the fact that it's undocumented, it's just not >the sort of thing a UNIX system would do.) I am not familiar with the phenomenon to which you refer... unless someone configured your computer with some serious evil magic I don't understand. >Sounds like rsynch (or is it rsync?) is also something I would find >useful. How do I get it? Erm, $ which rsync /usr/bin/rsync $ Yes, I'm pretty sure it comes with OS X. I know the OS X rsync handles the weirdnesses of Mac files. >I should also say that the PDF viewer that came with my Mac is not in >all respects perfect. I'll probably want to spring for something better. As far as I know, Adobe reader (free), (although it's the most annoying about blasting you with ads for itself and extra icons on the display) is the best PDF viewer (in particular the best at displaying papers with bitmapped fonts). This is a big mystery to me. According to legend, Knuth produced TeX and later MetaFont (caps?) because he was disappointed with the state of math typesetting and wanted to see beautifully typeset math. DVI, the output format of TeX, supports outline fonts. So why is it that math papers, produced through LATEX, always have the WORST fonts!? I have seen comments that this is because some people haven't updated to the 1998 version of LATEX or something, but it KEEPS HAPPENING. What is the exact deal? > >Of course, Mac OS has suffered some equally serious security problems The seriousness of security problems is a subjective thing. I mean, maybe Debian had a lapse and Mac OS has needed to patch potential vulnerabilities and these are "serious," but then there's Windows serious. >Would the Mac OS security issue affect a user like me, who has a laptop >with no fixed IP address? If you say "yes" to install the security updates it reminds you about, then probably not. --Steve

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Re: [math-fun] Analytic continuation software?
by Dan Asimov 09 Jun '08

09 Jun '08

Gareth wrote: << On Monday 09 June 2008, Andy Latto wrote: > On Sun, Jun 8, 2008 at 5:05 PM, Dan Asimov <dasimov(a)earthlink.net> wrote: > > Speaking of math software, can anyone tell me if there exists analytic continuation software? ... > > . . . and all this to a pre-specified level of numerical accuracy. > > I don't think this is possible. In finite time the software can only > . . . The same argument proves that numerical integration and differentiation are impossible. And yet, if you pick a function you're interested in and ask Maple or Mathematica or whatever to integrate it for you over a given range to a given level of accuracy, they can generally do it pretty well. >> Yes, though usually Maple or Mathematica has more than just the ability to evaluate the function at a given point, but an algorithm to do so -- whose details must go into determining the accuracy of the calculation of the function's derivative or integral. In fact, I can provide an algorithm for the initial function (for what I need) . . . but it would be somewhat tricky for it to work backward through a sequence of n power series to be sure that the final answer is of a given accuracy. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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