rants

daddy wasn’t impressed

Dec 19th

Posted by lievenlb in general

1 comment

A first year-first semester course on group theory has its hilarious moments. Whereas they can relate the two other pure math courses (linear algebra and analysis) somewhat to what they’ve learned before, with group theory they appear to enter an entirely new and strange world. So, it is best to give them concrete examples : symmetry groups of regular polygons and Platonic solids, the symmetric group etc. One of the lesser traditional examples I like to give is Nim addition and its relation to combinatorial games.

For their first test they had (among other things) to find a winning move for the position below in the Lenstra’s turtle turning game. At each move a player must put one turtle on its back and may also turn over any single turtle to the left of it. This second turtle, unlike the first, may be turned either onto its feet or onto its back. The player wins who turns the last turtle upside-down.

So, all they needed to see was that one turtle on its feet at place n is equivalent to a Nim-heap of height n and use the fact that all elements have order two to show that any zero-move in the sum game can indeed be played by using the second-turtle alternative.1

A week later, one of the girls asked at the start of the lecture :

Are there real-life applications of group-theory? I mean, my father asked me what I was learning at school and I told him we were playing games turning turtles. I have to say that he was not impressed at all!.

She may have had an hidden agenda to slow me down because I spend an hour talking about a lot of things ranging from codes to cryptography and from representations to elementary particles…

For test three (on group-actions) I asked them to prove (among other things) Wilson’s theorem that is

~(p-1)! \equiv -1~\text{mod}~p

for any prime number p. The hint being : take the trivial action of S_p on a one-element set and use the orbit theorem. (they know the number of elements in an S_n-conjugacy class)

Fingers crossed, hopefully daddy approved…

  1. for the curious : the answer is turning both 9 and 4 on their back [↩]
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first things first : jailbreak

Dec 10th

Posted by lievenlb in iMath

11 comments

iTouch

  1. NeB on Leopard and iPhone
  2. first things first : jailbreak
  3. Wiki on iTouch
  4. top iTouch hacks
  5. IF on iTouch
  6. overloaded iTouch
  7. yahoo pipes on iTouch
  8. iTouch as network sniffer

You may have surmised it from reading this post : Santa brought me an iPod Touch!1 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.2 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 pod3, dare to void the guarantee and risk your new gadget being bricked4 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…

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  1. or rather : Santa brought PD2 an iTouch and knowing his jealous nature ordered one for him as well… [↩]
  2. rumours are that Apple will enable DiskUse in firmware 1.1.3, coming up next februari… [↩]
  3. and frankly there’s not much else Apple allows you to put on it [↩]
  4. but, if I can pull if off you certainly can.. [↩]
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Segal’s formal neighbourhood result

Dec 8th

Posted by lievenlb in geometry

1 comment

Yesterday, Ed Segal gave a talk at the Arts. His title “Superpotential algebras from 3-fold singularities” didnt look too promising to me. And sure enough it was all there again : stringtheory, D-branes, Calabi-Yaus, superpotentials, all the pseudo-physics babble that spreads virally among the youngest generation of algebraists and geometers.

Fortunately, his talk did contain a general ringtheoretic gem. After a bit of polishing up this gem, contained in his paper The A-infinity Deformation Theory of a Point and the Derived Categories of Local Calabi-Yaus, can be stated as follows.

Let A be a \mathbb{C}-algebra and let M = S_1 \oplus \hdots \oplus S_k be a finite dimensional semi-simple representation with distinct simple components. Let \mathfrak{m} be the kernel of the algebra epimorphism A \rightarrow S to the semi-simple algebra S=End(M). Then, the \mathfrak{m}-adic completion of A is Morita-equivalent to the completion of a quiver-algebra with relations. The nice thing is that both the quiver and relations come in a canonical way from the A_{\infty}-structure on the Ext-algebra Ext^{\bullet}_A(M,M). More precisely, there is an isomorphism

\hat{A}_{\mathfrak{m}} \simeq \frac{\hat{T}_S(Ext^1_A(M,M)^{\ast})}{(Im(HMC)^{\ast})}

where the homotopy Maurer-Cartan map comes from the A_{\infty} structure maps

HMC = \oplus_i m_i~:~T_S(Ext_A^1(M,M)) \rightarrow Ext^2_A(M,M)

and hence the defining relations of the completion are given by the image of the dual of this map.

For ages, Ive known this result in the trivial case of formally smooth algebras (where Ext^2_A(M,M)=0 and hence there are no relations to divide out) and where it is a consequence of a special case of the Cuntz-Quillen “tubular neighborhood” result. Completions of formally smooth algebras at semi-simples are Morita equivalent to completions of path algebras. This fact motivated all the local-quiver technology that was developed here in Antwerp over the last decade (see my book if you want to know the details).

Also for 3-dimensional Calabi-Yau algebras it states that the completions at semi-simples are Morita equivalent to completions of quotients of path algebras by the relations coming from a superpotential (aka a necklace) by taking partial noncommutative derivatives. Here the essential ingredient is that Ext^2_A(M,M)^{\ast} \simeq Ext^1_A(M,M) in this case.

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bloomsday end

Jun 9th

Posted by lievenlb in rants

1 comment

From time to time you may see here a message that NeverEndingBooks ends on Bloomsday (June 16th). Soon after, I hope to restart with another blog at the same URL. For starters, Neverendingbooks refers to my never-ending bookproject on noncommutative geometry started in 1999, a millenium ago… Today I\’m correcting the proofs and have even seen the cover-design of the book, supposed to be published in the fall. So, it should be really EndingBook(s), finally. From time to time it is good to start afresh. The next project is still pretty vague to me but it will be a lot more focussed and center around topics like Moonshine, the Monster, the Mathieu groups, Modular forms and group etc. Suggestions for a blogtitle are welcome (M-theory is already taken…). Besides there are technical problems with the machine running the blog, a new one is expected around June 16th. As I will not be able to clone between the two (one PPC, the new one Intel) I decided to start again from scratch. Anyway, Ive made a database-dump of NeverEndingBooks and will make it available to anyone interested in reading old posts (even the ones with a private-status). Finally, there are other reasons, better kept private. Give me a couple of weeks to resurface. For now, all the best.

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kvraagetaan

May 29th

Posted by lievenlb in rants

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Sorry, this is categorified (sic) as ‘off’, but believe me, it’s way, way, off… Still, it’s my best shot at getting the Nobel Peace Prize. Here’s my proposal : in whathever country you live, search for an unemployed band (cant be that hard), convince them to write 20something oneliners about their childhood memories (assuming they’re 30somethings or worse (or even better for that matter)), we will provide the easy-listening music (hear below). If they are into a specific dialect, please dialectizise as much as possible (will only add to the hype). The remaining step to stardom : download the song to YouTube, sit back and see the world change around you… (btw. the clip shouldnt be a problem either, we propose the format : a 20a30 years old suburban living room in the main frame (in which the band will perform their song), on top : two smaller frames giving ample hints to decode the dialect-lyrics (see below). Before we go any further, I think it’s best if you click the play button below in order to get at least an idea (in Belgium : an all time record of weeks number one in the charts…). You will not understand a word (and you better stop when the song stops, about half of the videoclip-time) but if you don’t, you won’t understand a word of what comes next


Right, now you know at least a bit of the Fixkes’ craze in Flandres(belgium). It’s a simple and therefore ingenious idea : sing about the childhood-memories of 35-50something people (okay, probably they aimed at a 30-40yrs. public, but I’m just trying dramatically to squeeze myself in…), but do it encrypted (that is, in dialect, or rather, let the public decrypt your phrases), fun assured… For weeks now they play this song around 18hrs when we are having dinner, and each and every time, ThePartner and me try to decode another line of the lyrics, and do this so vehemently that PD2 feels uncertain whether we’ll be all there the next morning… I’d better admit, sometimes I was plain wrong. When they sing “er was nog gene gsm gene vtm
en niemand die a hannibal of murdock wilde zen ”
(translated into something like: ‘there was still no GSM nor VTM(commercial TV), and no-one wanted to be Hannibal or Murdock’) i was thinking : they are talking about commercial TV, so they must be talking about Murdoch (NOT Murdock…). I’m just too old to know about the bloody A-team (I’m more of a Starsky&Hutch or Dempsey&Makepeace person). ThePartner, laughing and rolling all over the carpet… Today was a better day (for me). We were decoding the lines “showen in de boksauto’s
outrun in plaats van onze commodore”
(translated into something like “to show off in our boxing cars, outrun instead of our commodore”. ThePartner believes that “Outrun” and “Commodore” are names for places where you could drive ‘boxing-cars’ (or whathever they’re called in proper AngloAmerican, driving cars on a fair)… but for me it was plain clear that Commodore meant THE Commodore64-console! A heated debate followed until we thought something like ‘wouldn’t they have a clip on YouTube by now?’ and sure enough the clip proved me right…). But now that I’ve seen the clip, I dread the forthcoming decoding of “en buurman wa doet u nu
veur ons allereerste tetjes”
(translated as “Neighbour what are you doing now? Our very first tits”) The pervert I am, I know perfectly well what they are singing about (alas, the video-clip doesnt provide proof. probably due to exaggerated rights for a section of the Flodders movie (parental-warning-signs-flashing-all-over-the-screen). I’m not sure whether I will enter a fight on this one or just feign ignorance… Btw. the title of the track is “Kvraagetaan” which is a perfect Flemish sentence to anyone of my generation, (or younger by at most 20 yrs.) When we were at primary school the whole bizness of relationships was pretty easy either something was ‘on’ or it was ‘off’. So, if you’d fancied a girl (or conversely) all needed was the question ‘I ask it on’ (Kvraagetaan). When my daugthers were the same age, romance had dropped quite a bit. They had to ask something like “Wilde gij op mij zijn?” which translates into “Do you want to be ontop of me?” which leaves much less to the imagination… Still, looking around in my circle of acquaintances, I feel that most of them really enjoy a popular song, full of old-time-memories, to start a heated debate with their loved ones. If only all nations would follow Flandres-path in this, the world would be a lot more fun and peaceful. Thank you!

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