The Revolution (Part 1)

My first foray into the world of writing fiction. Comments/criticism would be deeply appreciated, and help improve my writing in the future. 

(From the pen of Jaythan Kaytryn of Escavia)

Escavia was not a large planet, still isn’t. The economy thrived on Kryxium. Everyone on the planet was employed in either the mines, or the purification plants. Our life in the village was idyllic. We worked hard all day. Mining was hard work, but hardly dangerous as it used to be a hundred years ago. The invention of neutrinogentric machinery had removed any threat to human life than mining might pose. In the evening, everyone in the village would gather round a bonfire, and deliberated about the Escavia NeutroBall League, or the latest exploits of Atom – the protector of galaxies (that used to be the most popular televisor show in those days). The traders would come in their spaceships once every year. They would buy the Kryxium, and sell us whatever Escavia could not produce. Space travel used to be very expensive in those days, and nobody in my village had stepped foot on another planet. I suspect hardly twenty people on the whole of Escavia had.

Overall, life on Escavia was good. We didn’t have much, but then we didn’t need much either. And as we knew that everyone in Escavia lived pretty much the way we did, we didn’t(couldn’t) aspire for anything else either.

Till cyberportation was invented. Now, interstellar travel suddenly became cheap, and easily available. Everyone would now want to spend their holidays not on some beach somewhere on Escavia, but at some exotic snowy mountain range in a distant corner of the galaxy. Similarly Escavia too saw a large number of Litharnians, Zeelorcians and Sylverese tourists. Life had changed. As my friends traveled to distant lands, and brought stories from across the galaxy, there was a growing dissatisfaction in my heart. All Zeelorcians now had access to 3D Virtual Reality televisors in their houses, while we were still using the old ones that my grandfather used. On Chinesis, air travel was the norm while here on Escavia we were still using ancient MotorPods to travel. The galaxy had advanced, other planets were rich and had access to these luxuries. Kryxium, while an essential metal in the industry, wasn’t exactly a rare element. Thus we Escavians couldn’t really afford everything that say, the Litharnians could with their precious Neutrinogen manufacturing plants. But was this fair? I worked as hard as any old Litharnian. Why then, was their produce valued more? Why were the Litharnians richer than me and my fellow Escavians? I wasn’t alone feeling dissatisfied with the situation. True, till now we were unaware that such luxuries even existed. We were unaware and blissful in our ignorant lives. However, a child can live without a toy; but not when he knows that his brother possesses it. Can you really blame him for feeling outraged at the injustice? Now that we knew luxuries existed, we couldn’t live without them.

The Escavian youth was like a pile of dry twigs, waiting for a spark to ignite them. This spark came in the form of Gaspard von Avernus. His reputation preceded him. Apparently, he had started off as a farm hand on some agricultural planet in the galaxy, soon risen ranks and had eventually drafted some reforms that had caused the planet to prosper greatly. The day he arrived, there was a great throng of people waiting to listen to him; me amidst them. He was a thin and unimpressive man with a goatee that made him look like an old movie villain. But his eyes had a sparkle and conviction that I had never seen on any person before. And when he spoke, you had to listen to him, mesmerized. If words had force, his would move galaxies. He spoke of inequality, of injustice and how they must be done away with. His idea of a just society was one where the community owned the means of production, and thus no individual had power to subjugate another. He said that the ones that possessed the power would not relinquish it without a struggle. A revolution was needed to overthrow the current system, and install a new, fair one.

I was stirred by his words, as were many others in my village, on my planet, and indeed on several proletariat planets throughout the galaxy. I became a von Avernus disciple, as did countless others throughout the galaxy. The Revolution was about to begin.

(to be continued…..)

(Please rate, if you reached till here, so that I know how many bothered to plod through)

Non Euclidean Geometries

I wrote a few articles on Mathematics for a magazine for school kids, EducationEdge. These articles are targeted at students of classes VIII to XII. Am reproducing one of them here, hoping some of the readers of this blog might enjoy it too. 

Introduction

Science seeks to figure out how the Universe works, and tries to discover the laws which govern it. Mathematics has no such obligations. Though mathematicians and their theories generally stick to the Universe that we live in, once in a blue moon there will rise an eccentric, but genius mathematician, who will propose a radical mathematical theory, which though marvelous, has seemingly no application – at least not in this universe. In this article, we shall talk about Non-Euclidean Geometry, which is literally out-of-this-world Mathematics.

What is Geometry?

Since we have all studied some geometry in school, we have generally some intuitive idea about what lines, points, circles and planes are. The ancient Greek mathematician Euclid showed that all our intuitive notion about geometric objects can be summarized into a set of five postulates. If these postulates are assumed to be true, all the rest of geometry follows. Hence, the next time your teacher tells you to memorize some rules about circles or parallel lines, you can refuse to do so, saying that you already know Euclid’s postulates. (Disclaimer: The author is not responsible for what your teacher does to you after this!!). Euclid’s postulates are as follows:

  1. A straight line can be drawn that connects two given points
  2. A line segment can be extended in both directions to get a straight line
  3. A circle with a given center and radius can be drawn
  4. All right angles are equal to each other
  5. Given a line and a point not lying on it, exactly one line can be drawn that passes through the given point and is parallel to the given line.

Non-Euclidean Geometry

As you can see, the postulates seem simple and obviously true. However, mathematicians are not simple and obvious creatures. A few mischievous mathematicians thought, “What if we assume one of these postulates to be false? What if we assume something that is contrary to one of these postulates to be true?” They did so, and came up with several different kinds of geometries, all of which are inconsistent with our normal notion of Geometry, but nonetheless, consistent within themselves. “But what is the use of all this?”, you may ask, “If these geometries are not real, and don’t work in our Universe at all, why do mathematicians want to study them?” These are very valid questions, but mathematicians are a crazy bunch of people, and often do mathematics just for the sake of it, even if it seems to have absolutely no utility anywhere in the real world.

Elliptical Geometry

One of the non-Euclidean geometries, that is relatively easy to understand is called Elliptical Geometry. In this geometry, the fifth postulate in Euclid’s postulates is changed.

  • Given a line and a point not lying on it, no line can be drawn that passes through the given point and is parallel to the given line.

In order to understand this, you must suspend your usual notions about what a point, line, etc are. In our new universe, these are entirely different things than what we usually think of them. We shall hence redefine them in our new universe. To avoid confusion, we shall write point when we wish to refer to constructs in the new universe, and point when we wish to refer to our usual notion. Imagine a sphere. A plane is defined as the surface of this sphere. A point is defined as a pair of diametrically opposite points on this sphere. A line is a great circle on the sphere(A great circle is a circle, like the equator, whose plane contains the center of the sphere). Notice that two lines always intersect in exactly two diametrically opposite points, that is exactly one point.

Observe that in this elliptical geometry, the first four of Euclid’s postulates still hold. (Keep down this article and think about the first two postulates now. I assure you that you will find it a rewarding exercise). Though we have not formally defined circles and angles due to lack of space, it can be proved that the third and fourth postulates also hold true in elliptical geometry. Notice also, that the new fifth postulate is now true in this system. Given a line and a point lying outside it, it is impossible to construct a line parallel to the one given. Remember that a line must lie on the plane and since, in this case a plane is the surface of the sphere, the plane of any line through a given point must pass through the centre of the sphere and thus must intersect the given line at some point (see Figure). This makes it impossible, in Elliptical Geometry, to draw a pair of parallel lines! Many other interesting and non-intuitive facts also emerge in this system. For example, the sum of the angles of a triangle is greater than 180 degrees. Mindboggling, but true.

Conclusion

We saw that even a simple subject like geometry is a subject of deep mathematical study. The essence of mathematics is to question. Mathematicians ask questions like, “What is a number?” or “What is a point?” Though they seem silly, finding the answers to these questions involves much thought, and a journey full of adventure into the dark and mysterious land of mathematics.

 

Salakhen

उस हरी दूब पर बारिश की बूँदें

उस ठंडी हवा से पत्तों का सरसराना

और पानी की बूंदों का यूँ गिरना

मानो नदी से नहा कर निकली सुंदरी

सर हिला कर बाल सुखा रही हो

फिर इन्ही बूंदों को सूरज की एक किरण

जब छू कर निकलती है

जी करता है मेरा भी उस बूँद को पकड़ लूँ

सूरज की मंद रौशनी को मुट्ठी में भर लूँ

उस पत्ते की तरह बारिश में नाचूं

पर ये सलाखें

जो नज़ारे दिखाती भी हैं

और उन तक पहुँचने नहीं देती

ये सलाखें

यही मेरा दायरा है

यही मेरी दुनिया है

A question on morality

One of the arguments that we vegetarians, animal lovers, and human beings in general like to give is that we do not support killing, as long as it is avoidable. That we are pro-life in some sense of the word (NOT the abortion sense). Now, suppose there is a problem of stray dogs in a city. We would probably not support indiscriminate culling of stray dogs. We would, however, probably not be too opposed to catching hold of male dogs and performing vasectomies on them – soon the existing population would die out, and the problem would be solved. Elegant solution, eh? Not cruel at all. What we are disregarding here is that we are still culling potential future life. So then we are not really pro-life in the real sense. More like pro-present-life or more simply anti-death or anti-pain. 

Incidentally, Islam says that it is pro-(human)-life and it goes all the way, including potential future life. Hence very conservative Muslims frown upon masturbation and condoms.

But coming back from the digression. The anti-pain policy explains why we oppose poultry farming. It is true that those chickens would not exist, or ever come to life, if not for the fondness that human beings have for the taste of their flesh. However, what good is life without physical comfort, no freedom – no meaning? Not existing at all is probably preferable.

But octopii and squids do not have a central nervous system. They can’t really feel pain in the conventional sense of the term. Why oppose eating them? One argument could be that when fishermen go to catch them, they try to flee. Hence, clearly they do not like getting caught. Therefore, even if they can’t feel pain the way human beings do,  they do ‘feel’, if I may use the term, some sort of discomfort or resentment at getting caught. Discomfort is bad, hence catching octopii and eating them is bad.

But now suppose tomorrow scientist develop a new breed of chickens that do not have a central nervous system. Suddenly the pain argument goes for a toss. Also, consider that scientists manage to ensure that all these chickens are born brain-dead. Hence, they can’t feel pain and can’t even fail discomfort. Heck, they can’t feel at all! They’re born a vegetable, live as a vegetable, die as a vegetable, but still taste like chicken! I can hear a voice inside my head screaming, “This is wrong!” “This is immoral!” “This is unethical”. But why? There is no pain. No discomfort even. The very purpose of existence of these chickens(if I may call them that) is to provide human beings with the soft, tender, succulent taste of chicken that they so love. “But its wrong!”, the little voice still says. Why, though? I don’t know. Do you?