October 2, 2007

దేశ భాషల౦దు తెలుగు లెస్స

చిన్నప్పటి ను౦చి నాకు ఆ౦గ్లము అ౦టే వ్యామోహము ఎక్కువే. స్కూలు లో కొత్త తరగతి మొదలకుము౦దు పుస్తకాలు కొన్న పిమ్మట నా మొట్టమొదటి కార్యక్రమము ఏమనగా ఇ౦గ్లీషు టెక్స్టుబుక్కు తీసి కథలు అన్నీ చదివేయటము. పాఠాలు మొదలు పెట్టే మునుపే చదివేయటము నాకు భలే ఆన౦ద౦ కలిగి౦చేది. కాకపోతే ఇది ఇ౦గ్లషు సబ్జెక్టుకు మాత్రమే ఉన్న ప్రత్యేక స్థాయి. (తక్కిన సబ్జెక్టులకు కూడా ఇ౦త శ్రద్ధ పెట్టి చదివి ఉ౦టే ఇప్పుడు వేరే పరిస్థితులలో ఉ౦డేవాడి నేమో!) అసలు తెలుగు రమణీయత లావణ్యతల గూర్చి వివరిస్తూ శ్రీకృష్ణదేవరాయలు వారు వాడిన పదములను ఈ పోస్టుకు పేరు పెట్టి, తెలుగు భాషలోనే వ్రాస్తూ, మధ్యలో నాకీ ఆ౦గ్లమునకు ఉన్న స౦బ౦ధము పై ఎ౦దుకు ఆలోచిస్తున్నానని మీరు అడగవచ్చు. అ౦దుకు కారణము ఇది: ఆ ఇ౦గ్లీషు పుస్తకాలను పట్టిన రోజులలోనే నాకు అర్థమయ్యి౦ది ఏమిట౦టే చదవటానికి ఇ౦గ్లీషు కన్నా తెలుగు కష్టము. వ్రాయటానికి కూడా నాకు ఆ వయస్సులో ఇ౦గ్లీషుకన్నా తెలుగే కష్టమని అనిపి౦చేది. (ఈ వయస్సులో ఇ౦క టైపి౦గు అలవాటు అయ్యిన తరువాత అన్నీ ఒకటే లేన౦డి...) పైగా ఇ౦గ్లీషులో నా తోటి విద్యార్థులతో పోల్చి చూస్తే నాకు మ౦చి మార్కులే వచ్చేవి. ఈయీ కారణాల వల్ల నాకు సహజముగానే తెలుగు కన్నా ఇ౦గ్లీషు పైనే ఆసక్తి కలిగెను. ఎ౦త ఆసక్తి కలిగెన౦టే మన తెలుగు స౦స్కృతి, మన తెలుగు భాష, సాహిత్యము, సా౦ప్రదాయములను చూసి, అర్థము కాక నీరసి౦చెను. ఇ౦దుకు ఇప్పుడు బాధ పడుతున్నానా? కాబోలు. వేరేలా ఉ౦టే బాగు౦డునని అనుకు౦టున్నానా? కొ౦చె౦. మరి ఇన్నాళ్ళ తరువాత ఒకేసారి ఇ౦త అకస్మాత్తుగా ఈ మార్పు రావటానికి కారణము? మొన్న వచ్చిన నా స్నేహితులు. నాకు ఇన్నాళ్ళుగా సాహిత్యము అర్థము కాక పోయినా పాత తెలుగు పాటలు అ౦టే ఇష్టము వు౦డేది. ఐతే మొన్న వచ్చిన స్నేహితులు వివరి౦చిన తరువాత నాకు తెలిసి వచ్చి౦ది ఇన్నాళ్ళుగా సాహిత్యాన్ని అర్థము చేసుకోలేక ఎ౦త అ౦దాన్ని కోలిపోయానోనని.

అరే అసలు శ్రీశ్రీ (శ్రీర౦గ౦ శ్రీనివాస రావు) వారి పద్యాలు నాకు అర్థము కావు. సిరివెన్నెల సీతారామ శాస్త్రి వారి పాటల సాహిత్యము అర్థము కావు. వేటూరి ఎవరో తెలియదు. ఆత్రేయ ఎవరో తెలియదు. వీరేశలి౦గ౦ ప౦తులు అ౦టే ఆరవ తరగతి ను౦చే చికాకు (పెద్ద పెద్ద లెస్సన్సు ఉ౦డేవి, కష్టమైన ఆన్సర్సు బట్టీ పట్టాల్సి వచ్చేది ఈయన వల్ల). ఆ చిన్న వయస్సులో సమాజాన్ని దిద్దిన్న వారి గురి౦చి తెలుసుకుని ఏమి ప్రయోగమని అనిపి౦చదూ? గురజాడ అప్పారావు వారి నాట్యములు సరేసరి. ఏదో నా అదృష్టము బాగు౦డి బాపూ బొమ్మలు మాత్రము చూసి తరి౦చగలిగాను. ఇక గాయినీ గాయకుల౦టారా... జానకి ఎవరో తెలియదు . సుశీల ఎవరో తెలియదు. ఘ౦టసాల వారి పేరు, గొ౦తు వినక తప్పదు గాక తెలుసు. ఇది నా appreciation of telugu culture. అవును, నాకు సిగ్గు గానే వు౦ది. కాని ఏమి చేయను? ఇ౦త ఆలస్యముగా తెలుసుకున్నా, ఈ మహానుభావుల జీవిత చరిత్రలు ఎ౦దుకు ఇ౦త ప్రకాశిస్తున్నాయో కొ౦చెమైనా ఇప్పుడు అర్థమవుతు౦దని ఒక చిన్న సాటిస్ఫాక్షను.

ఇప్పటికి కూడా నా భావాలు/అభిప్రాయాలు/ఆలోచనలు/ఉద్దేశ్యములను ఇతరులకు తెలియజెప్పటానికి నాకు సులువైన భాష ఆ౦గ్లేయమే! ఎన్నో తెలుగు పదాలకు అర్థములు తెలియవు. ఎన్నో అర్థములకు తెలుగు పదాలు తెలియవు. ఉదాహరణకు spelling అన్నదానికి తెలుగు పదము ఏమిటి? ప్రాణానికి ఫ్రణవానికి భేదమేమిటి? సిరివెన్నెల చిత్రములో గాన౦ "విధాత తలపున" లో మహదేవన్ గారి మ్యూసిక్, (music కి తెలుగు పదము మర్చిపోయాను! అ౦త గతిలేని పరిస్థితి లో ఉ౦ది నా తెలుగు!) హరిప్రసాద్ చౌరాసియా గారి ఫ్లూటు, ఎ౦త అద్భుతముగా ఉన్నాయో ఒక అ౦తటకు మెచ్చుకోగలను. కాని సిరివెన్నెల గారి రచన అసల అర్థము అయితే కదా!! సర్లే౦డి... నా బాధలన్నీ చెప్పుకోవటానికి ఈ పోస్టు కాదు కదా ఈ బ్లాగు సరిపోదు! ఇక సెలవు.

August 18, 2007

Vista and Microsoft's anti-competitiveness

I'm no scholar nor historian in the age-old war between Microsoft and the Liberalists (or should I say - Librelists). But having studied and worked in decently technologically oriented college campuses, I do have an inkling about this rift. Call it adding fuel to the fire, or what you will, here I add a few observations of my own.

Recently, a friend of mine bought a laptop. Apparently, these days you do not get laptops with WinXP. More like, you cannot get laptops with WinXP. You can only get laptops (by which I mean branded ones, like HP Pavillion series or IBM Lenovo series, etc..) pre-installed with WinVista. Microsoft's first step, in pushing users towards Vista. This is not a business strategy. This is bonded labour. When you outsource Business Processing to oriental or indian trained labour markets, it is not bonded labour. That is business strategy, since on the one hand, IT companies get to reduce their costs, and Indian/Chinese/EastAsian employees are salaried in dollars, and everybody's happy. What Microsoft's pushing, though, is not a business strategy. Because the users take a hit. They have to pay extra, for something they don't need, indeed something they don't want. (Apparently, it'll cost more to even get the Vista removed from the laptop before buying it.)

Agreed, that Vista has a lot more capabilities and functional capacities than XP. But the customer bracket which includes my parents, like people who just started operating on computers just two to three years back, and would like to use computers solely for the purpose of chatting with their sons/daughters living abroad, clearly are not very adjustable to the change in operating systems. Especially when they can't really figure out the differences between a computer and an operating system, and verily, don't need to. And the customer bracket which includes those sons/daughters, who have studied in decently technologically oriented campuses, would clearly know the distinction between pests such as Microsoft Softwares and Free (both gratis and libre) Softwares. Sometimes I really am confused whether people buy Microsoft products because they like them, or because they're forced to. At other times, I'm confused whether Microsoft thinks its buyers really like its products, or perhaps it just sits smugly in the knowledge that people are forced to buy its products.

Coming to the motivation for this post, I noticed that once you install gtalk on Vista, all the browser links from gtalk open in IE, eventhough you've selected Firefox as your default browser. Investigating this issue a little more closely, I found that Vista has a different concept of a default browser. Infact, it has a different view of default programs. What used to be the "File Types" tab in the Tools->Folder Options dialog box, no longer exists in Vista. What used to be the "Set Program and Access defaults" has also been slightly changed. All this is now included in the Default Programs tool in the Control Panel, in Vista. With a twist. This twist being, even though Firefox is the default browser, it is not allowed to open files of type .mht, .mhtml, or .url. Why? Firstly, Firefox 2.0+ does not support mhtml. I really don't understand/know why. I'm illiterate in this area. So when i google it up, i come across an article on Wikipedia (where else?) saying that MHTML has something to do with internet mail extensions, and what i learnt in my fleetingly small attention span is that none of the current browsers are any good at supporting this thing. But the issue still remains. IE has the sole rights to .mht and .mhtml files, and you can't even remove it. You cannot even change the program associated with the .url files! I mean c'mon! they're just text files!! What is the sense in preventing, infact disabling the user from doing whatever he means to do? Isn't there the Vista's system restore and HP's backup files or restore schema to overcome any damage that the user might inadvertently do? I dunno. Call me uneducated and cavemanish, but all I see is Microsoft's monopoly. Coz when I tried to change the default program associated with each filetype, the Windows Explorer all of a sudden started acting up, and had to restart itself (thereby exiting Default Programs tool of the Control Panel). It might have been a bug, but does it really have to be activated only when one uses the Default Programs tool? That too to ensure IE is maintained the default program for three filetypes? As I've said before, sometimes I keep wondering...

August 17, 2007

Of n-dimensions and Euclidean distances

This is more of an excercise in writing formulae on my blog than actually doing some math. But then again, who needs a reason to write equations?

Well anyway, there was this doubt that a friend asked me, which was put to the students by a prof in his class. We know that the Euclidean distance, between two points and in n-dimensions, is given by:
We also know that for any three points in 2-dimensional space, , , and , the Triangle Inequality holds, namely,
This is a well known result in Euclidean Geometry, and I'm loathe to go into the proof of this here. Now the question, was to find three points , and in 3-dimensional space, which violate the Triangle Inequality!

At first glance, one will easily see that even in 3-dimensional space, the three points will still form a triangle, and so the Triangle Inequality should hold. But how do we prove it? This is where geometric visualization aided me.

You see, in 3-d space, one has a lot more freedom to twist and turn shapes. Maybe it has to do with the degrees of freedom, which I never understood clearly. In 2-d, all that one can do with a shape, say a square, is to translate, rotate, or scale it. Put it in more layman terms, you can put the square at any place on the paper, turn the paper whichever way, and even shrink or expand the paper. Translation is possible in two directions, and rotation in only one ('coz , which basically says that rotating anticlockwise is the same as rotating clockwise through a larger angle). All this, while still retaining the properties of the square. In 3-d, on the other hand, all that one can do is still essentially the same, translate, rotate, or scale it. But here, you can translate or rotate in 3 different directions (unlike 2-d, rotation is possible in 3 directions, since rotations in different directions are not commutative).

I'm pretty sure all this previous paragraph would give a sore headache, to any layman. What I've put forward, in not-so-informal terms, is the justification for the following transformations:

Translate the origin to , thus making , and .
Rotate the axes, such that lies on the x-axis, thus making , and .
Rotate the axes, such that lies on the xy-plane, thus making .

All these transformations are perfectly legitimate, in the sense that the relative positions of the three points do not change. But by doing this, we notice that we've transformed our axes such that all three points now lie on the same plane (the xy-plane here). The truth is that the three points always lay on the same plane, ('coz any three points in 3-d lie on a plane) but we've shifted our axes such that this plane became our xy-plane. In any case, I claim that these three points are the same as three points in 2-d space, since I've reduced the component of all of them to zero. And we know that the Triangle Inequality will hold for any three points in 2-d space.

Thus we see, that the Triangle Inequality should indeed hold for any set of three points in 3-d space as well. And so the original question now takes a further leap: Will the Triangle Inequality hold for any set of three points in n-dimensional space? With the help of reasoning similar to the one above, I claim yes!

Key concept used: Any set of n points in n-dimensional space lie on the same (n-1)-dimensional hyperplane. Is this really true? you tell me :P

June 29, 2007

Locked and Loaded!!

First of all, it should be loaded and locked. Seriously, how can you load it once it is locked? But then again, English is as weird as a language can get, so I won't mind. Now here's the scenario: I have to shift my room, luggage and everything else from the fourth floor to the ground floor. And this is what happens, when there are too many locks. The story of three locks:

Lock 1: Owned by the hostel management, for the room no. 40, which was allotted to me newly.
Lock 2: Owned by me, for the room no. 396, the room which i was occupying.
Lock 3: Owned by Mahesh, for the room no. 44, of which a copy I was given. Coz let's face it, I lived in that room more than Mahesh.

Now the problem is to shift all the luggage from room 396, to room 40, using room 44 as a buffer, all by yourself, while ensuring that every room is locked when you are not in it. And of course, the end result should be that Lock 1 is given back to the hostel management, Lock 2 is now on room 40, and Lock 3 is still safe with you during all this ruckus. Oh and I forgot to mention, the luggage consisted of 7 fully loaded containers, ranging from as small as a dust bin to as big as a mountaineer's haversack. So you need to also ensure that you don't get too worn out while running up and down the stairs (yes stairs, you won't find lifts in Universities here...) while still having enough energy to carry that load.

So yes, i finally was able to juggle mattresses and buckets all the way down four floors, through cramped staircases, only to realise I forgot the keys to Lock 1 somewhere. :D typical me. Easy solution, use room 44 as the buffer, coz I wouldn't be losing the keys to Locks 2 and 3 in a hurry. And then retrace my steps to find that missing key, and resume the algorithm. I guess this is what they call a lock-step process. How I wish these transactions (or atleast the luggage) were atomic!

By the end, I had to whip out yet another lock, coz I had to lock room 4o, while handing over Lock 1. If everybody was as crazy as me, I guess we'd all be automatons, devoid of feelings and consideration for the poor readers of such nonsensical blogs. But then where's the fun, if you knew they didn't have feelings either?

June 28, 2007

My latest obsession

ViManga (link: http://www.vimanga.ru ) is a huge online collection of many mangas. Some of them pretty good, but then again, they might not interest everybody... (<_<) Do visit this site, if you're interested in manga at all...

Regret

I've done a lot of things till now that i'm not exactly proud of. But given a second chance, I'd probably have done the exact same things over again. Which gets me thinking about the choices a person makes. And the choices that make the person. Are my choices a direct consequence of who I am, my inner self, the Jungian psyche (more on Jungian stereotypes later...)? Or am I the result of the decisions that I have made? Do we have a choice in all this at all? It gets very confusing sometimes, when people talk about destiny. It's all very romantic to think that there's this superpower that governs your life, and that you'll eventually end up becoming the same thing no matter what you do. But that would defeat the purpose of living, doesn't it? On the other hand, what about things that happen in which you have no choice at all? Like natural disasters. Or or bolts out of the blue. Is there an answer to all this? We do make decisions and stick to our choices without thinking about all this stuff, and of course it's all a lot easier to do it that way. But what if you do realize one day, that beyond all doubt, there is this destiny or fate which governs your entire life. Will that stop you from making choices? On the other hand, there you go, a normal person thinking about normal things, making decisions and choices based on rationale and the current circumstances, and you actually end up becoming nothing. Will that give you as much satisfaction, of being safe and secure, as opposed to what you would have become if you were an irrational impulsive freak obsessively following your own passions? And what if you don't end up safe and secure after all, even though you've made the correct (according to you) decisions all your life?

Should we be even thinking about all this stuff? The Vedas give an easy solution to all this:
कर्मण्यॆवाधिकारस्ते माफलॆषु कदाचन
karmaNyEvaadhikaaraste maa phalEShu kadaacana

basically saying that one should not think about the consequences of the action, but should perform one's duty. Then what is our duty? Oh no.. don't start that now. Go read the Bhagavad Gita (also available in your local language by now) and see if you understand the concept of कर्म, loosely put, "duty" in English.

So why am I quoting Scriptures here? Because I'd like to believe that age-old wisdom has been passed down to us, in the form of Scriptures (not only the Gita, Scriptures in all religions...), and that if you know how to search for it, all the answers lie in these Scriptures. Hell, even Schrodinger's concept of Quantum Mechanics is supposed to be influenced by them. In the meanwhile, before we understand what it means to read the Scriptures, we better do whatever we need to survive. It's a shame that Humanity, is simultaneously the cause and the effect of such wisdom. Or abstract thought. Call it whatever you wish. Humans will be humans, they will breed evil and seek evil for all time, until the fear of Final Judgement looms really large and inevitable. Until then, that's all folks!

June 23, 2007

Three cheers for the Trinity!!!

Abso-i'm so awed i don't have the words to put it right-lutely awesome!

the Trinity:

Scorcese, DeNiro, and Pesci.
Raging Bull, Goodfellas, and Casino.

Just thought i'd mention them again, coz i just finished seeing Casino. You'd think you know how a typical Scorcese movie would look like, especially one that stars DeNiro and Pesci. And then you see one of these movies, and you get amazed all over again! The three movies are in three different eras: 1980, 1990, and 1995 respectively, and you'd think that should account for something. I mean maintaining that sort of chemistry over 15 years? No words.

June 11, 2007

The Fountain

"Darren Aronofsky is a genius" seems to be the general opinion, from what few reviews i've read on the net. When I saw the movie "The Fountain", I couldn't get past the first few minutes without interruption. I couldn't understand what the movie was about, although I was certainly awed. And intrigued. I had to look up imdb to see what the movie was about, to convince myself to sit through the movie. And that was when I realized Darren Aronofsky, the director, was also the one who wrote and directed Requiem for a Dream. And Pi. That in itself was enough to convince me.

Yggdrasil, the Tree of Life, Fountain of Youth, eternal life, Mayan creation legends, cancer, disease, death, fight for survival, medical experiments on monkeys, animal rights, space travel, bubbles, reincarnation, schizophrenia, yoga, the Lotus Position, Spanish Inquisition, treasure hunt, astronomy, the Xibulba nebula, yeast cultures, co-dependence, eternal quest. Some of the things that figure in the movie. And oh, by the way, there were no computer-based CG effects used, the awesome depiction of stars and nebulae was done by micro-photography of yeast cultures. And this is only what you see. What is meant to be understood, after seeing it, is still a mystery. Even after seeing the whole movie I still couldn't understand what the movie was about, except that it ended. And somehow, I was fulfilled. In Aronofsky's own words, "it's very much like a Rubik's cube, where you can solve it in several different ways, but ultimately there's only one solution at the end".

Open to interpretation. That's what I like about some movies, like the hindi one I saw the other day, "Life in a Metro". Seems to me that involving the audience, in the movie and its interpretations rather than in creating plot twists and story arcs, (such as taking online polls of what kind of story the public wants --- ouch!) is an integral part of critical success.

April 12, 2007

The rains are here!

How they dance in the courtyard, sweet summer sweat
Some dance to remember, some dance to forget


As you run out into the street, droplets of rain lashing at you from every direction, you just can't help the smile that forms. You can't get rid of that innocent blissful grin on your face, even though you know it makes you look even stupider (if that was ever possible). You forget for a moment what you learnt was possible, and start to leap to a plane that is above everything. Petty comparisons, differences of opinions, little insecurities all vanish for a moment from your conscious thought, as you give up your hold on your body to those little wet needles that tingle you everywhere. You wish you could fly higher, so that no tree would be able to block the rain. You wish you could fly higher, so that you can see the thunder cloud much closer, and play with the lightning. You settle for something equally pleasing and equally stimulating, a walk in the rain. You think of all your friends who are missing out on these little joys in life, and pray for them. You think of all your friends elsewhere, who would be out dancing in the rain too, and wish that you were with them. You think of how rare it is to see the sun up and shining bright, when it is raining hard on your face. And then you search for the ever-elusive rainbow. And the pot-o'-gold at the end of the rainbow.

And when the rain leaves you alone, and the sun glaringly points this out to you, all you do is bask in the knowledge and hope that all is well with the world.

April 1, 2007

Theory

What is a bit? Where did the notion of a bit come from? To understand such essential concepts one should truly understand Shannon's Information Theory. What is to be understood, is that a bit is nothing but a measure of information. Weight (mass?) is measured in kilograms, length in metres, and information (data?) in bits. The minimum amount of information that can exist is a bit. A bit contains information about a certain flag, as to in which of these states it lies: TRUE (1, high, on) or FALSE (0,low, off). How is this information sufficient enough to do anything with it? Because we already know what that flag was intended for. We only needed to store the current state of the flag, and hence the bit.

Notice, that a flag can exist in only one of two states, T or F. Nothing intermediary. This is the basis of Binary Logic, Binary arithmetic and etc.. Arithmetic to the base 2. Why do we use only base 2 arithmetic? If we could store states 0, 1, 2, ... 9 in a "dit" (a decimal bit), we would obviously need a lot less number of dits to store the same information than the number of bits. So why is the number 2 sacred? Why does every computer use Binary logic instead of Decimal logic? The answer to that lies in material sciences. We have transistors that can work in between two electrical levels. Each of these electrical levels (, , VDD/VCC, etc.. ) can represent only one state, so there can be only two states represented by the transistor. And besides, arithmetic that can be done with any base can also be done with base 2. In other words, Decimal logic, is no more powerful (in terms of calculational possibilities) than Binary Logic. Hence the whole idea of Flip-Flops, etc.

Why am i talking about bits and pieces? What is the whole picture here? Basically i wanted to talk about "Qubits". Quantum Theoretic equivalents, of the Information theoretic bit. When we said any dits or other-its are as powerful as bits, why are we talking about these qubits? coz they come under a wholly different category. A qubit can exist in infinitely many states!

eh? what does that mean?

Think of an electron. It has spin angular momentum, according to our highschool physics text books, of either or . Let us represent the spin with say 0 and spin with 1. These states are mutually exclusive, in that no electron can exist in both these states at once. But what is interesting, and what is not taught in high school text books, is that an electron can exist in a combination of these two states! But hey! Didn't we learn that spin angular momentum of an electron was only either ? Now what's this about combination of states? Ahha. There in, lies the secret of the principle of Superposition.

What is not apparent at the first glance, is that outcomes of an experiment may not indeed tell you everything about the state of the system before the experiment. What I'm trying to say, is that we (meaning most computer scientists and almost all engineers) are so used to the black box approach, that we assume we know everything about a system and the states it might have been in, once we know the inputs and outputs through that black box. Maybe, this is not true in the Quantum world. Or is it? I really don't know. What I do know, is that we can never really say that an electron was in such a place in such a time (remember? Heisenberg's uncertainty principle?). When you can't even say that, or the direction in which it is spinning, how can we say whether it had a positive or a negative spin angular momentum? What in fact happens, or is theorized to happen, is that electrons might be spinning in a mixed state. Meaning they have a little of and a little of spin. But the moment we try to measure which of these it has, the state "collapses" to either one of them. Imagine a vector , which is neither completely a real number, nor completely a non-real number. But the moment you take a projection of this vector along one of the axes, the vector "collapses" to its component along that axis. This is how I understood what happens, when an experiment is done. The state of the system collapses to the observed state. But there is a difference to be noted, which might be the difference between a classical system and a quantum system. In the case of the vector, we knew a priori the axis that we were going to project the vector upon. This is not the case with a quantum experiment. You do indeed observe either a or a spin only for an electron, but you can never tell which value the result of the experiment will be. So essentially, an electron before measuring its spin angular momentum is in a state that is neither of the observable states, but in fact, a mixture of both and a lot more. Which is what I mean when I say a qubit exists in infinitely many states!


Now having said all of this, I still am not really sure whether what I've written is anywhere even remotely near to the physical/mathematical/scientific reality that I proclaim to study! (What is it that I proclaim to study? Please... )

Is it really true? LaTeX??

Well, there's only one way to find out, isn't there? let's try this for instance:



This just adds a whole new dimension to my blogging! :D let's see if this works out now, after publishing....


OK, it works after publishing toO! but why don't LaTeX equations on other blogs show up? Anyway, interested people might find out more (instructions, prerequisites, etc..) from here, all credit due to this person.

January 22, 2007

Rings, Cycles, and Circles.

Lost
Desperation
Confusion
Hope
Resolve
Ambition
Success
Complacence
Lust
Failure
Lost
Desperation
.
.
.