EDX

It is 9.30 AM and I know that there are a hundred things I should be working on right now. But sometimes you feel inspired, and then those hundred things wait and you write a blog. EDX is the newest online teaching website.  A couple of months back, I registered for a course in Physics taught by a professor at MIT. It was a 5 week course, with new course material released every week and a problem set to be submitted weekly. I struggled to keep up the pace. Missed a few deadlines. Managed a few. Then we had the final exam. I got 80% and that took my aggregate grade to 63%. Just above 60% and I passed! That's not the point. The point is the elegant manner in which the professor taught the course. The beauty of how he developed a complicated theory for the students bit by bit. And, it is all available for free. The best thing about EDX is the software which allows you to submit answers even when they are as long equations. Online learning has come a long way. EDX has emerged as the leader. It's the future.

Orange

Everytime I eat an orange, I get fascinated by its amazing design. To start with, there is the skin. It is porous, hydrophobic, squishy, and sticks to the fruit with a mesh of fibers. The inside has spherically arranged packets holding liquid and covered with a thin fibrous layer. If we open a packet, we find small spheroid bulbs filled with beautifully colored liquid and covered with a delicate layer. Orange grows symmetrically out from a small bud, becoming enlarged as it adds cells in a defined structure, it is not assembled piece by piece like the way we manufacture items. And, if left alone, it seamlessly mixes into the ground. An amazing beauty, an intricate balance, a piece of art, and zero pollution. It is produced by a small plant not more than 6-7 feet in height, 3 feet in diameter. No raw materials to be shipped in, no workers doing 3 shifts - just an un-disturbing existence. Humans are in the stone-age of manufacturing. We lack the intellect to design. We are struggling.

"Parallel lines meet at infinity"

"Parallel lines meet at infinity", my cousin in class 10 told me, and also that his teacher had mentioned that if one cannot understand this apparently simple concept then one can never hope to understand mathematics. I was in class 8 at that time. I wonder why did the  teacher say so. The concept is still not obvious to me. By linking an obscure statement to the ability to understand mathematics, the teacher very effectively killed any uncomfortable questions about it from the students.

Suppose I am standing near a  set of parallel lines, say a railroad. I look towards positive infinity - the lines meet at some point. We will never reach that point and the point is not a well-defined point, but the lines do meet as per the statement. Now, let me gaze towards minus infinity. Again, the parallel lines meet at minus infinity. Now if two lines meet at two distinct points, then they are nothing but the same line. So, we arrive at a contradiction, and parallel lines do not meet at infinity.

My mathematician friends tell me that this line of reasoning is not quite correct, as one cannot have a well defined point at infinity and that the statement that "parallel lines meet at infinity" is only valid in projective geometry.