second time puzzled.

Git is fast becoming a scm tool of choice for most online development projects( Linux kernel uses it!). There are some excellent screencasts (pity, some require you to pay) that teach you how to work with it. I recently got hooked to git myself and was charmed immensely with the functionality it provided, esp the ability to have your github on web. But getting git (msysgit in my case ) to work behind proxy proved somewhat nightmarish in my home computer running windows. There are some links scattered to help you with it. After struggling for about 4 hours, I got it working using the steps outlined in link .

start msys_git.sh

$ mkdir ~/.ssh

$ chmod 700 ~/.ssh

Create public key/private key pairs using ssh-keygen

$ ssh-keygen -q -f ~/.ssh/id_rsa -t rsa

id_rsa.pub contains the public key. Copy this to git hub creation page.

Steps below are from here


start puttygen ( which should be in same folder as putty ): import the file id_rsa and convert it to create a .ppk file in the same directory.

Start putty.exe
Set the host to ssh.github.com, port 443.

Under Connection / SSH / Auth, select your private key file (.ppk file) for SSH authentication.

Under Connection / Proxy, select HTTP and enter appropriate information for the host and port.

Save your session with a name such as “gitproxy”.

Click “Open” - you should receive a login prompt. Close this.

Start pageant, the putty authentication agent. It appears on sys-tray. Rightclick and load the private key used above (.ppk file).

Back on msys_git command prompt run:


$ git remote add github git@gitproxy:svark/notes.git

$ git config --global user.name "Your Name"

$ git config --global user.email "youremail@gmail.com"

$ mkdir notes

$ cd notes

$ git init

$ touch README

$ git add README

$ git clone http://github.com/svark/notes.git

put plink in the path and make sure we have pagent still running.

$ declare -x GET_SSH="plink".

$ git commit -m 'first commit'

$ git remote add github gitproxy:svark/notes.git

$ git push github master


This pic of an eclipse taken in 1992 and available at nasa's site, I recently saw, struck me with some awe. It is one of those moments when Nature beckons for us, almost shyly, to leave our quibbles aside for a moment and appreciate its majestic presence. The Sun in horizon is on this occasion shrouded by a disc. Yes, it is the moon playing a little trick on us, but we can not help but feel a sense of disbelief as we behold this spectacle. Certainty of events like the sun's appearance on horizon which we take so much for granted is called into question, if only temporarily, reminding us of our own impermanence, of our vulnerability among other things.

But that cluster of palm trees also standing against Suns path seems to have a different story to tell. Life in this painfully lonely planet in an indifferent universe, is fragile and prone to destruction by cosmic elements and yet, it has kept its flag flying, defying nature and has stood tall like the cluster of palm trees in picture. The pic seemed to me a perfect ode to life on our planet, though a mute one. It mocks us at our shattered lives with its unreasonable grit to survive, taking on natures apathy in its own way. Sentimental wish-wash aside, it definitely feels good to forget all for a brief while and gaze at this celestial wonder.

Bhupinders long sonorous droning. Talks and laughter in between to relax the notes, flexing rules of rendition. A deft handling of a harkat, leaving a trailing drone. I almost succumb to the drone were it not for the sharp upping of the tempo and pitch, as the sweet, almost cloying, voice of sulakshana pandit asserts itself. Notes gather momentum, but his resonant voice intervenes to pull it back:
गूँज रहे हैं दुब्द्ते सायें, शाम की खुशन्न्न्बू हात न आये..
Kushboo becomes Kkusshhhnnnbooo as if rendering with a nasal tinge this way would make it smell better. Then continues

गूंज्थी आन्खों की नशीली बोलियाँ. कट्टी मीठी आन्खोँ की रसीली बोलियान्न्न।

I close my eyes and imagine what the synesthetic experience of tasting intoxicating words from salty eyes would sound like.

Labels: music

Rudin's text on mathematical analysis provides a proof that √2 is irrational by showing that the set of rational numbers A consisting of all rational numbers whose square is greater than 2 has no least element and the set B of all rational numbers whose square is lesser than 2 has no greatest element. He considers A first and shows that for any p in A, we can find
a number q that is lesser than p and yet in A. He conjures up from apparently nowhere the rational number

q = p – (p^2 - 2)/(p + 2) ……….(1)

The number q is immediately seen to satisfy the needs of the proof for the set A.

How did he arrive at (1)? Some algebra shows that it does not matter what denominator is chosen in (1) as long as it is a rational greater than p + √2. So this could have been 2p for example. This it turns out is sufficient for us to work up a number such as q in (1) ourselves.

Since p > √2, we expect 2/p < √2. So √2 and hence the rational q we are searching for lies between p and 2/p, and of course q should be greater than √2. But first let us find out by what ratio the number √2 divides the segment (2/p,p). Let us say the ratio is µ. Then

√2 = μ 2/p + (1 - μ) p = μ (2/p-p) + p……….(2)

From which, we get = p / (√2 + p). The above equation suggests that as μ varies between 0 and p / (√2 + p), the number μ 2/p + (1 - μ) p spans the segment (√2,p), which is exactly the interval in which we are looking for rational numbers q. We now can find q, by choosing a appropriate value for μ. Now since p >
√n, we can choose μ = p / (p + p) < p/(√2 + p), so we have q = p/2 + 2/2p = p/2 + 1/p.

How close is this number to the in (1)?. As I said earlier in the post this would be the same number if we replaced the denominator in (1) by (p+p) instead of p + 2.

 

Daybreak was not a regular event in planet mersus. As it charts along its orbit through heavenly space-time, the event marks a departure in the evolutionary progress of many life-forms and for a good many others the event brings sudden extinction. As the star rays shine across dark side side of the planet, the light of a thousand suns brings a protozimmer back to its animated self; the glow all but managing to pierce its vestigial eyes long blinded by the dark ages. Yet, those eyes could feel the glow that turned the tangible to the visible. It fritters about sensing danger anticipating the unthinkable, seeking the safety of darkness, again. In an instant all hell breaks lose. Breathing in all the atmospheric helium, it emits a shriek that splits helium to puffs of hydrogen and I awake, sneezing, to find myself on a monday morning again- my mother dusting the bed.

Labels: the surreal.

The recent Heathrow bomb scare reminded me of my flight to the U.K in march this year and a minor scare we had then. In Dubai, as I waited for the plane to take off for Heathrow, I tried to occupy myself by reading a book. Minutes before the flight took off, a 30-ish South-Asian looking guy got on board and walked to my seat. I couldnt help notice that his newish jacket was too big for his arms and his pants were short enough to make his shins visible above the socks. He had neither removed his sunglasses nor the "jim courier" cap, whilst looking around intently around my seat comparing the seat number on his boarding pass with the confusing array of A B C's and digits printed on the baggage shelf. A while later he mustered courage to ask for help in solving this number puzzle and it didnt take long before we managed to get him seated. He thanked me profusely in an accent that was distinctly British and introduced himself as Mr Latif. ( that explains why arrived so late) and said he was going back to London after his long stay at his village near Lahore. Before I could introduce myself, he began his rant about the ill-treatment he received from the crew in P. Intl. Airways when he asked for a drink and proceeded to asked me, the frequent flier with a history of 2 flights in 28yrs, of my informed opinion on Emirates. He was visibly pleased when I told him that I thought highly of Emirates and mumbled that the steward's and stewards were very friendly.

His next question didnt surprise me: Will drinks be served now? Do they serve liquer? Where was I from, India?. What do I think of the resistance in the U.S senate to the ongoing nuclear deal with India -- surprising me with his command over Indian current affairs. India and Pakistan are like brothers split apart, he proclaimed, and started addressing me as his "brother". He spoke of his 6-month long stay in native village where he committed the crime of owning a piece of land which almost cost him his life, the bloody family feuds, corrupt customs officials at the airport in Pakistan, and confided in me, his brother of 10-minutes, how sad he was when he left behind his child and wife crying at the airport. The mention of his child & wife brought liquer to his mind and he asked the inevitable question: When will drinks be served?. When told to be patient, he amused himself by pressing the buttons in front of his seat. His prayers were answered soon. The stewardess arrived with her drinks trolley and asked us, assuming her usual business-like sweet voice- what we gentlemen would like. He asked her in an equally sweet voice what her name was, played a guessing game on her nationality (singaporean,nobody guessed) and finally also asked her with all his munna-bhai charm to choose a liquer for him that she best liked. I guess, she would have handed the trolley to him that moment, but she refrained and gave him some brandy. Little did she realize what the aftermath of her indiscretion would be. Drink after drink followed. His stories became repetitive and tears rushed to his eyes as he told of his wife and his child. He also spoke of his Sikh friends in London and even invited me for a `davat` at their place.

I had never met a guy with Pakistani background but already I was seeing the traits of the archetypal Punjabi which extends across border and religion: Prone to fits of laughter and fits of sadness, and always threatening to hug the next person. Everytime he wanted a drink he would compose himself removed seat belts and sashayed to the stewardess and somehow managed to get more. When asked how he managed this, he told me this: the trick is not to slur in your speech and assume the smoothest tight-lipped brit accent while asking "May I have a drink, please". I still dont believe he managed to trick them this way.

By evening, no tightlippedness could prevent him from the slur. He turned completely silly and defied all attempts to get him back to his seat. A lady in the plane had her chappal stolen and he was later found wearing it and refused to give it back. The cabin crew became wary of him and arranged to forcibly get him back to his seat and tie him with his seat belt. They probably also informed police in Heathrow by then. Poor thing kept shouting "Ki hoi, Choudui ##@$$$&*&" and spent the rest of the time in a half-conscious state drooling like a dog on my lap while I pretended as if everything was alright.

Heathrow arrived. Everybody was asked to be seated and the captain announced -- Mr Latif, please show up at the door first. He didnt as he was still with his "Choudui" in his native village. The police arrived and asked him questions, he answered in Punjabi first and after some prodding and pushing he realized was in Heathrow, got his accent and senses back and chatted amiably with them and even asked jokingly --what did they think? that he was the o s a m a? That was the last I saw of this little 'o s a m a'.

Heres an interesting linear algebra problem: Let F be a field and let V be a finite dimensional vector space over F. If α₁ , ... , α_m are finitely many vectors in V, each different from zero vector, prove that there is a linear functional f on V such that


     f(α_i) ≠ 0 , i = 1 , .., m

My attempts at proving this lead to this problem: Can a union of finitely many sub spaces of dimension N-1 (hyperplanes) cover a vector space of dimension N.? Which seems an interesting problem in itself.