# Tag: OSX

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).

Four years ago I had a brief fling with wardriving. It went only as far as getting Ethereal to crack the security of our house-network. I simply couldn’t picture myself walking around the neighborhood with my laptop under my arm… However, jogging around with an iPod will attract far less attention.

Starting an iTouch in a network-rich environment you will be asked which network you want to connect to (see for example this wardriving video). However, if you need more information on the networks, there is a port of the OSX-tool iStumbler for the iPhone/iTouch : Stumbler (available also from the Install.app under Network). This morning I flipped open my iTouch in a generic street near the University and was surrounded by 12 wireless networks, 6 of them wide open…

One may then ask : what about less innocent wardriving tools such as Kismet or Ethereal itself? The problem with porting those seems to be that no-one knows whether the iTouch wireless driver can be put into ‘promiscuous mode’ (see for example this thread).

Once you have collected open networks at your favourite places or have passwords to closed networks, it would be nice if the iTouch would auto-detect these and connect to them without you having to remember the particular name or having to type in username/password combinations. Surprisingly, this is possible thanks to the people at devicescape.com. Create a free login, then get Devicescape Connect (available under Network) run it and write down the pincode you are given and follow the instructions to complete the installation. You can then edit your Wi-Fi list of desired hotspot or personal networks, together with all login-data. There is a nice TidBit article describing devicescape in full detail.

You may have surmised it from reading this post : Santa brought me an iPod Touch! (( or rather : Santa brought PD2 an iTouch and knowing his jealous nature ordered one for him as well… )) Ive used an iPodClassic to transfer huge files between home (MacBook) and office (iMac) as well as for backup purposes. I wanted to find out what new tricks this trio could play now that iPod can go online. Major disillusion : one cannot even enable DiskUse via iTunes at the moment. (( rumours are that Apple will enable DiskUse in firmware 1.1.3, coming up next februari… )) What’s wrong with Apple? They make this marvelous piece of technology and then do a Golem-act preventing anyone else from using their precious thing. I understand their business plan, but soon it will make more sense to buy Apple shares than to buy their computers…

Enters the 13-year old AriX writing iJailbreak to free the iTouch. So, before you put any music or video on your pod (( and frankly there’s not much else Apple allows you to put on it )), dare to void the guarantee and risk your new gadget being bricked (( but, if I can pull if off you certainly can.. )) by Jailbreaking it! There are plenty of good guides around, both for Windows and Mac, but most of them can be slightly improved. I’ve followed Let’s Jailbreak the iPod touch 1.1.2 with OS X but shortened his downgrade to 1.1.1 procedure which is the first (and hardest) step in the whole procedure. The moment PD2 will see I can use Maps and Weather she’ll want me to jailbreak her iTouch too, so mainly for myself I list here the procedure before I forget it.

Jailbreak 1.1.2 with Leopard on Intel, use at your own risk.

Get a decent browser such as Firefox or Flock (to prevent the download to selfexpand, so when given the choice to open it with iTunes or save it to Disk, save!) and download Firmware1.1.1 and place it somewhere (why not create a Folder called Jailbreak).

Connect your iTouch and fire up iTunes and select your iTouch in the left column. Hold down the option key and click in the summary pane the Check for Update button. This will open a Finder window allowing you to navigate to the downloaded file and open it. The iTouch will downgrade itself to 1.1.1. Just wait until it reappears in iTunes and disconnect it.

With Safari on the iTouch go to jailbreakme.com and scroll to the bottom and click on the InstallAppSnap button. Let it do its magic and afterwards there is a new Installer-icon on your ‘springboard’ (the opening iTouch page). Open it and refrain from installing all the goodies now, just scroll down to Tweaks (1.1.1) open and select “OktoPrep” and install it (button top right-hand corner).

Connect iTouch to mac, start iTunes and select your iTouch. Click on the update button and now iTunes will bring you back to Firmware 1.1.2. After finishing wait until your iPod reappears in the left column. (Do not panic if you fail to see the Installer-icon on springboard, it will reappear later on). Then, close iTunes (your iPod stays connected via USB to the Mac). Use any browser on your mac to download Jailbreak 1.1.2 and place it somewhere.

Find the Java-applet jailbreak.jar in the folder and double click it. Again, magical things are happening ending with the iTouch booting up several times and you performed the Jailbreak.

Let’s open up the iTouch to the world

So, what was the point of all this? We still have no DiskUse enabled nor can we speak to the iTouch directly. But all of this is going to change rapidly. Let’s make it available to our DeskTop.

With “install package xxx” I will mean : fire up Installer from your springboard, donate as quickly as you can to the guys making this available, then click on the “install” icon lower-left. This will open up lists of packages, scroll down to package xxx, click on it to read more about it, and then hit the “install” button top-right. That’s it. (If you ever want to unistall a package, do the same process now starting from the “uninstall” icon lower-right).

Install first BSD Subsystem (under System packages) and the AFPd (under Network). This will turn your iTouch into an AFP-server. By clicking on its icon in the Springboard you can turn the server on and off (remember to turn it off when not needed!) and turn on Broadcast if you want the iTouch to show up on your Desktop (in the Leopard-Finder under ‘Shared’). You can now connect to the iTouch by clicking on its icon in the Finder and hitting connect. The default user/password combination for a Jailbroken iTouch are
root/alpine. Change this as soon as you figure out how to do it. ‘Alpine’ must be the most popular password right now… The AFPd-page also contains the Wi-Fi IP Address of the iTouch and you will need it soon, so write it down.

For we are going to connect via ssh and sftp to and from iTouch/Mac. Install the OpenSSH package (under System) and the Term-vt100 package (also under System). From the Mac to iTouch you can connect via something like

ssh root@10.0.1.197

(change the number to the IP-Address of the iTouch) and login with the alpine password. You’re in! Conversely, open up the Term-vt100 icon in the springboard which give you a genuine *nix-Terminal. You can connect via ssh to your mac provided you know its IP and your login. That’s all.

Btw. you can also use your favourite file-transport program (mine is Transmit to connect to and from your iTouch via SFTP. Right, now that the iTouch is under control we might as well give it a voice of his/her own.

Install Apache (under System) and PHP (under Development) and follow the instructions from the iTouch Fans Forum (you will need to register, but if you’re not an iTouch-fan there’s little point in you reading this post anyway) and you will have turned your iTouch into a PHP-enabled webserver! On the left is a screenshot of the proof via the php-info testpage.

Finally, we can turn the world upside down completely. Before all of this we had no way to get control of the iTouch, now we can use the iTouch to take control of all our Macs serving VNC (Leopard comes with it, enable the password in System Preferences/Sharing/Screen Sharing/Computer Settings and you’re under iTouch control). To pull this off, just install the VNsea package (under Network). It really works well!

Oh, you’re only here to install the iPhone Apps…

Well, that’s easy enough. Just follow the instructions of the Install and use iPhone Apps in iPod touch from the excellent blog by Rupert Gee. The most difficult part is to get hold of the iPhone Apps if you don’t own an iPhone… Well, I’m happy to provide you with this secret information