Tag: apple

Ever since I’ve upgraded to Snow Leopard I’ve been having problems with the webserver.

At first there were the ‘obvious’ problems : mysql-connection lost and php-error message. These were swiftly dealt with using the excellent Snow Leopard, Apache, PHP, MySQL and WordPress! advice from ‘tady’.

Right now, access to this blog is extremely slow (and often impossible), certainly via the admin-page. The problem appears to be that most of my CPU is used by lots of pdfetex-processes owned by www. Hence the conjecture that it is a problem with either LaTeXRender or WP LaTeX.

Anyone experiencing a similar problem, or knowing a trick to resolve it? Takk.

About a year ago I did a series of posts on games associated to the Mathieu sporadic group $M_{12}$, starting with a post on Conway’s puzzle M(13), and, continuing with a discussion of mathematical blackjack. The idea at the time was to write a book for a general audience, as discussed at the start of the M(13)-post, ending with a series of new challenging mathematical games. I asked : “What kind of puzzles should we promote for mathematical thinking to have a fighting chance to survive in the near future?”

Now, Scientific American has (no doubt independently) taken up this lead. Their July 2008 issue features the article Rubik’s Cube Inspired Puzzles Demonstrate Math’s “Simple Groups” written by Igor Kriz and Paul Siegel.

By far the nicest thing about this article is that it comes with three online games based on the sporadic simple groups, the Mathieu groups $M_{12}$, $M_{24}$ and the Conway group $.0$.

the M(12) game

Scrambles to an arbitrary permutation in $M_{12}$ and need to use the two generators $INVERT=(1,12)(2,11)(3,10)(4,9)(5,8)(6,7)$ and $MERGE=(2,12,7,4,11,6,10,8,9,5,3)$ to return to starting position.

Here is the help-screen :

They promise the solution by july 27th, but a few-line GAP-program cracks the puzzle instantly.

the M(24) game

Similar in nature, again using two generators of $M_{24}$. GAP-solution as before.

This time, they offer this help-screen :

the .0 game

Their most original game is based on Conway’s $.0$ (dotto) group. Unfortunately, they offer only a Windows-executable version, so I had to install Bootcamp and struggle a bit with taking screenshots on a MacBook to show you the game’s starting position :

Dotto:

Dotto, our final puzzle, represents the Conway group Co0, published in 1968 by mathematician John H. Conway of Princeton University. Co0 contains the sporadic simple group Co1 and has exactly twice as many members as Co1. Conway is too modest to name Co0 after himself, so he denotes the group “.0” (hence the pronunciation “dotto”).

In Dotto, there are four moves. This puzzle includes the M24 puzzle. Look at the yellow/blue row in the bottom. This is, in fact, M24, but the numbers are arranged in a row instead of a circle. The R move is the “circle rotation to the right”: the column above the number 0 stays put, but the column above the number 1 moves to the column over the number 2 etc. up to the column over the number 23, which moves to the column over the number 1. You may also click on a column number and then on another column number in the bottom row, and the “circle rotation” moving the first column to the second occurs. The M move is the switch, in each group of 4 columns separated by vertical lines (called tetrads) the “yellow” columns switch and the “blue” columns switch. The sign change move (S) changes signs of the first 8 columns (first two tetrads). The tetrad move (T) is the most complicated: Subtract in each row from each tetrad 1/2 times the sum of the numbers in that tetrad. Then in addition to that, reverse the signs of the columns in the first tetrad.

Strategy hints: Notice that the sum of squares of the numbers in each row doesn’t change. (This sum of squares is 64 in the first row, 32 in every other row.) If you manage to get an “8”in the first row, you have almost reduced the game to M24 except those signs. To have the original position, signs of all numbers on the diagonal must be +. Hint on signs: if the only thing wrong are signs on the diagonal, and only 8 signs are wrong, those 8 columns can be moved to the first 8 columns by using only the M24 moves (M,R).

Below an up-till-now hidden post, written november last year, trying to explain the long blog-silence at neverendingbooks during october-november 2007…

A couple of months ago a publisher approached me, out of the blue, to consider writing a book about mathematics for the general audience (in Dutch (?!)). Okay, I brought this on myself hinting at the possibility in this post

Recently, I’ve been playing with the idea of writing a book for the general public. Its title is still unclear to me (though an idea might be “The disposable science”, better suggestions are of course wellcome) but I’ve fixed the subtitle as “Mathematics’ puzzling fall from grace”. The book’s concept is simple : I would consider the mathematical puzzles creating an hype over the last three centuries : the 14-15 puzzle for the 19th century, Rubik’s cube for the 20th century and, of course, Sudoku for the present century.

For each puzzle, I would describe its origin, the mathematics involved and how it can be used to solve the puzzle and, finally, what the differing quality of these puzzles tells us about mathematics’ changing standing in society over the period. Needless to say, the subtitle already gives away my point of view. The final part of the book would then be more optimistic. What kind of puzzles should we promote for mathematical thinking to have a fighting chance to survive in the near future?

While I still like the idea and am considering the proposal, chances are low this book ever materializes : the blog-title says it all…

Then, about a month ago I got some incoming links from a variety of Flemish blogs. From their posts I learned that the leading Science-magazine for the low countries, Natuur, Wetenschap & Techniek (Nature, Science & Technology), featured an article on Flemish science-blogs and that this blog might be among the ones covered. It sure would explain the publisher’s sudden interest. Of course, by that time the relevant volume of NW&T was out of circulation so I had to order a backcopy to find out what was going on. Here’s the relevant section, written by their editor Erick Vermeulen (as well as an attempt to translate it)

Sliding puzzle For those who want more scientific depth (( their interpretation, not mine )), there is the English blog by Antwerp professor algebra & geometry Lieven Le Bruyn, MoonshineMath (( indicates when the article was written… )). Le Bruyn offers a number of mathematical descriptions, most of them relating to group theory and in particular the so called monster-group and monstrous moonshine. He mentions some puzzles in passing such as the well known sliding puzzle with 15 pieces sliding horizontally and vertically in a 4 by 4 matrix. Le Bruyn argues that this ’15-puzzle (( The 15-puzzle groupoid ))’ was the hype of the 19th century as was the Rubik cube for the 20th and is Sudoku for the 21st century.
Interesting is Le Bruyn’s mathematical description of the M(13)-puzzle (( Conway’s M(13)-puzzle )) developed by John Conway. It has 13 points on a circle, twelve of them carrying a numbered counter. Every point is connected via lines to all others (( a slight simplification )). Whenever a counter jumps to the empty spot, two others exchange places. Le Bruyn promises the blog-visitor new variants to come (( did I? )). We are curious.
Of course, the genuine puzzler can leave all this theory for what it is, use the Java-applet (( Egner’s M(13)-applet )) and painfully try to move the counters around the circle according to the rules of the game.

Some people crave for this kind of media-attention. On me it merely has a blocking-effect. Still, as the end of my first-semester courses comes within sight, I might try to shake it off…

MacBookAir? Is this really the best Apple could come up with? A laptop you can slide under the door or put in an envelop? Yeez… Probably the hot-air-book is about as thick as an iTouch. The first thing I did was to buy a leather case to protect the vulnerable thing, making it as thick as a first generation iPod… (needless to say, when my MacBookPro breaks down, ill replace it with a MacBookAir, clearly!)

Ranting about MacWorlds : Wired has a great article on last year’s event. Steve Job’s iPhone presentation is something that will be part of the collective memory when it comes to 2007-recollections. Few people will have realized that the Apple-team didnt have a working prototype a few weeks before… Here’s The Untold Story: How the iPhone Blew Up the Wireless Industry. A good read!

If you plug in your jailbroken iTouch, you will be asked wether you want to upgrade to 1.1.3, something we all feared for a long time and so it takes just nanoseconds to hit the cancel-button. But, there is good news! Rupert Gee reports that you can downgrade to 1.1.1 and redo jailbreak. I won’t try it for some time, but still…

In the unlikely event that you come here being a mathematician, here’s what I did with my iTouch today. Ive downloaded the Connes-Marcolli talks on Renormalization and Motives part 1, part 2, part 3, part 4, part 5, part 6, part 7 and part 8 at work. They are in mp4-format so you can load them into iTunes and onto your iTouch!!! Weather is not favorable for outdoor-cycling at the moment, so I used the home-trainer, put the iTouch in front of me and, boy, was I educated…

So, you did jailbreak your iTouch and did install some fun or useful stuff via the Install.app … but then, suddenly, the next program on your wish-list fails to install ??!! I know you hate to do drastic things to your iTouch, but sooner or later you’ll have to do it, so why not NOW?

Move the Applications Folder

The problem is that there are two disk partitions (a small one, meant only to host the apple-software and a large one to contain all your music, videos and stuff) and Install.app installs programs in the /Apllications folder on the smaller partition. So, we want to move it to the other partition using a symbolic link trick (as in the wiki-hack post). Here a walkthrough, more details can be found on Koos Kasper’s site.

• Have BSDsubsystem and OpenSSH installed, so that you can ssh into the iTouch.
• verify that the second line of the /etc/fstab file reads as below (or edit it if necessary, in my case it was already ok, perhaps this is done during jailbreak?) and reboot the iTouch (if you had to change it)

/dev/disk0s2 /private/var hfs rw 0 2

• ssh into the iTouch and type in the following commands (to move the folder and make the symbolic link)

cd /
cp -pr Applications /var/root
mv Applications Applications.old
ln -s private/var/root/Applications /Applications

• reboot the iTouch, ssh into it and remove the old Application-folder to free space

cd /
rm -rf Applications.old

From now on, all (most) new programs are installed on the larger partition. If you reinstall the OpenSSH application (as suggested) make sure to remove on your computer the old key for iTouch.