November 2014 - mathfun@mailman.xmission.com

[math-fun] Grothendieck
by Warren D Smith 16 Nov '14

16 Nov '14

>Here are readable sources concerning biography and work: >Pierre Cartier 2001, "A mad day's work: from Grothendieck to ..." > http://www.ams.org/journals/bull/2001-38-04/S0273-0979-01-00913-2/home.html --is there anybody who claims to understand that? You know, R.P.Feynman once was unable to communicate his excellent ideas about path integrals and the foundations of QED, even though Schwinger apparently was able to communicate his (considerably harder to use) ideas... which RPF explained by remarking that "his machines came from too far away." Well, looks to me like Grothendieck's machines come from still further away. The Cartier piece does not mention a single application, and apparently neither do any of the sources in his bibliography. But there is a lot of handwaving about how maybe this is somehow floating around in a lot of places that might have something to do with applications someday. That are really really profound, so profound as to be unable to connect to anything concrete; that would merely diminish its profundity. In particular (just to issue a random provocation) Simon Plouffe, who started all this about Grothendieck and speaks his language, strikes me as a far more concrete guy and I'd guess that therefore he's unable to comprehend Grothendieck. And in my case, perhaps it is a defect of my mind, but in order to motivate me to put in the work to understand an area, I need to have some evidence it does something I'll find useful. Where is that evidence?

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Re: [math-fun] Alexander Grothendieck
by Axel Vogt 15 Nov '14

15 Nov '14

Here are readable sources concerning biography and work: Pierre Cartier 2001, "A mad day's work: from Grothendieck to ..." http://www.ams.org/journals/bull/2001-38-04/S0273-0979-01-00913-2/home.html and W. Scharlau (mainly his family and biography, in German)

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[math-fun] Fwd: Alexander Grothendieck
by Fred Lunnon 15 Nov '14

15 Nov '14

Even more than you thought! WFL ---------- Forwarded message ---------- From: Axel Vogt <mail(a)axelvogt.de> Date: Sat, 15 Nov 2014 23:24:34 +0100 Subject: Re: [math-fun] Alexander Grothendieck To: Fred Lunnon <fred.lunnon(a)gmail.com> I was a bit too hasty http://www.scharlau-online.de/ag_1.html The AMS notices are in English at least, http://www.ihes.fr/document?id=1723&id_attribute=48 Best regards, Axel On 15.11.2014 23:14, Fred Lunnon wrote: > Fascinating --- the paradisical picture of unification of apparently > disparate areas > of mathematics this tantalising review painted kept me from my dinner > for an hour! > It even offered a glimmer of hope that one day I might understand the > purpose of > category theory ... WFL > > > > On 11/15/14, Axel Vogt <mail(a)axelvogt.de> wrote: >> Here are readable sources concerning biography and work: >> >> Pierre Cartier 2001, "A mad day's work: from Grothendieck to ..." >> http://www.ams.org/journals/bull/2001-38-04/S0273-0979-01-00913-2/home.html >> >> and W. Scharlau (mainly his family and biography, in German) >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> >

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[math-fun] Alexander Grothendieck : 1928-2014
by Simon Plouffe 15 Nov '14

15 Nov '14

this just came out, http://www.lemonde.fr/disparitions/article/2014/11/14/le-mathematicien-alex… I did not find any other source in english, the article is in french. Considered to be one of the greatest mathematician. Simon Plouffe

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[math-fun] Games of no strategy
by James Propp 14 Nov '14

14 Nov '14

What are fun examples of combinatorial games that (like Conway and Paterson's game of Brussels Sprouts) appear to be games of strategy but whose outcome doesn't depend on what either player does? One of my favorites is Impartial Cutcake, aka the Candy Bar Game. The initial state is a chocolate rectangle, scored into unit squares. On any given turn, a player may take any rectangular piece bigger than a 1-by-1 square and divide it along a horizontal or vertical scoring-line into two smaller rectangular pieces. The two players alternate. When no further divisions are possible, the game ends, and the player who made the last move wins (and, if you like, gets to eat all the pieces). Jim Propp

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[math-fun] global warming ==> more lightning -- could this save us all?
by Warren D Smith 13 Nov '14

13 Nov '14

David M. Romps, Jacob T. Seeley, David Vollaro, John Molinari: Projected increase in lightning strikes in the United States due to global warming, Science 14 November 2014: Vol. 346 no. 6211 pp. 851-854 DOI: 10.1126/science.1259100 These authors predict global warming will cause more water vapor which will cause 50% more lightning strikes by end of this century. It is probably too much to hope for -- but could this effect SAVE us? To explain, it is believed that a substantial part of fixed nitrogen comes from lightning generating NOx which rain washes down to the ground. This is why rainwater is better for agriculture than tap water. The other main ways nitrogen is fixed are by microbes and by human activity making fertilizers. It would be good to know what percentages are contributed by these 3 causes. I have seen quite widely differing unsourced claims about that. It is well known nitrogen shortage is one of the biggest limiting factors for plant growth. Anyhow, my point is, with more lightning there will be more nitrogen available for plants hence more plant growth. This will use up CO2. Thus this whole effect is a negative feedback "thermostat" which, to the extent it works, helps stabilize global temperature. I am somewhat skeptical this will be enough to save us from global warming, but it's an interesting idea which might be new. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Drawing pictures with an iMac
by Steve Witham 13 Nov '14

13 Nov '14

This page http://stackoverflow.com/questions/2350167/basic-skeleton-for-a-c-opengl-pr… contains a ~70 line C program to put up a window and draw a triangle using Open GL. It looks like a good starting point for someone like Dan who already knows Open GL and C. It compiles on my Mac with this command: cc oglexample.c -o oglexample -framework OpenGL -framework GLUT I was surprised to find it. It's as if the whole industry wants to steer people away from simple solutions, and yet the right question, "opengl headers mac", Google, and those Stack Overflow users, had one. --Steve

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Re: [math-fun] More 4th Grade Science
by Steve Witham 12 Nov '14

12 Nov '14

> From: Bill Gosper <billgosper(a)gmail.com> > <Photo of Apollo astronaut about about 1ft above the lunar surface, > resembling those bad photoshops of Chinese officials floating above > recently opened highways> I assume everyone's seen SG Collins' "Moon Hoax Not"? I remember movies of an astronaut sort of skip-hopping over the surface with both feet leaving the ground at some points. > "On the moon, an astronaut can jump higher than on Earth. Is this fact or > opinion?" > Assuming that cumbersome spacesuits and safety concerns prevented anyone > from actually trying this, how can we call it fact? "Fact" means "done". > So isn't it > still simply a very believable opinion? Hah! But can you jump higher *in the suit* on the Moon than you can on Earth? That may have been demonstrated. --Steve

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Re: [math-fun] Drawing pictures with an iMac
by Steve Witham 12 Nov '14

12 Nov '14

> From: Dan Asimov <dasimov(a)earthlink.net> Dan, a couple clarifications would help ... > I have a nice iMac Do you mean an Intel iMac? Do you want to o Just use Mac OS , o Throw away Mac OS and run Linux, o Dual-boot Mac OS and Linux (one at a time), o Run Linux under something like virtualbox or Parallels, inside Mac OS? > I used to have GL (what gave rise to openGL) under Unix, and could just > write a program to do pretty much anything I wanted. > > (The key is having the command "Paint pixel (K,L) the color (R,G,B).") I really understand the desire for that operation. Do you want to o see the individual pixels show up as they are computed, o draw frames and have them flip as you finish each frame, o just see one finished picture when it's done, o produce a picture file in a standard format, o produce an executable for other people to run? I second Mike Stay's endorsement of Processing. It's a simplified dialect of Java. The native form of it has very simple IDE (text editor with a run button, basically) and runs your program locally, or you can export a program as a combination web page and .jar file for the web. Processing's paradigm is that you write a procedure called "draw" that calls functions like draw-a-pixel. Draw gets called n times a second to draw frames. I think the default is that you draw over a copy of the previous frame, so you can incrementally build up a drawing. Processing also has interaction on the model "Is the mouse down, and if so at what x and y?" Do you want to program in o C or C++? o Python o Java o Other? For C, basically all of the APIs for graphics in Unix are available in their standard Unix forms. Mac package managers (for downloading/building/installing standard software) with their repositories of ports are different from the Linux ones. o MacPorts a.k.a. the BSD "port" command. Sponsored by Apple. I use it. o Homebrew. Some people use this for Mac. o Fink. has gone stale. But, when MacPorts doesn't have it, often download/untar/configure/make/make install works. I have not used openGL through C. For Python, there is o the pyglet library to do openGL, o PyProcessing, which is surprisingly similar-seeming to (Java-) processing. o Reportlab pdfgen, I find it very easy to write simple vector graphics with text in it. (Basically the postscript drawing model only you program in Python instead of FORTH.) o PIL, the Python Image Library, for producing image files. > Is that really necessary? After all, there's a form of Linux > on the iMac and I'd be happy to program with that. > ) From: Jon Ziegler <jonz(a)alumni.caltech.edu> > No, it isn't necessary. No, there's no Linux on the iMac. The basic thing to keep in mind is that an Intel Mac is just a standard Intel PC. Ordinary Intel Linuxes run on the Mac. As I mentioned above, many people keep Mac OS around also, either by dual-booting or running Linux in some virtualizer. > What's on the iMac is Mac OS X, which is Unix. Officially certified (see here<http://www.opengroup.org/openbrand/register/apple.htm>). Anything that works on a real Unix should work on the Mac. This part is true. For instance, Motif got installed on my Mac just because it was a dependency of some LateX renderer I wanted. > Of course if you want it to run using the Mac's regular user interface, which has nothing to do with Unix, then you'll need to program all sorts of stuff for that. Or use something compatible. But if you're clear about what you want there are good places to ask for help. In a lot of approaches there's some window or GUI system (e.g. Qt or Tk) consciously involved just because your program needs to ask for a window for your graphics to show up in. Likewise if you want to have "Quit" in the menu or handle more interaction. This is true in Linux, too. But it's not true for the native Processing, that is, having a window appear when you run the program just happens. --Steve

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[math-fun] More 4th Grade Science
by Bill Gosper 12 Nov '14

12 Nov '14

<Photo of Apollo astronaut about about 1ft above the lunar surface, resembling those bad photoshops of Chinese officials floating above recently opened highways> "On the moon, an astronaut can jump higher than on Earth. Is this fact or opinion?" Assuming that cumbersome spacesuits and safety concerns prevented anyone from actually trying this, how can we call it fact? "Fact" means "done". So isn't it still simply a very believable opinion? --rwg

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