Don Quixote: an inspiration?

Old days should have been much better to live, I hope. Meanwhile, I know that this is a foolish hope. Yet, why I hope so is because of the kind of art that was produced in those lost times. Currently, this thought is inspired in me by the story of Don Quixote. I remember, as a small boy, as small as ten years old or so, reading an abridged comic book illustrating the story of Don Quixote, a person, thin and fragile, in his fifties, who, after reading so many heroic stories of knights, becomes insane and deluded to think that he was a knight, too. Perhaps, he must have been bored of the ordinary country life he used to be going through. He sets forth to travel around the world and foolishly reacts to everything he comes across. And, in all his thoughtless endeavours, he fails. But he believes that he succeeded in every situation and defeated everyone who fought with him. I am trying to recollect how my mind was reacting to this fabulous story. Interestingly, I was very confused; at that age, I was unable to make out why a person should behave like that. In the story, he sets forth to many heroic actions but ends up as a fool. I was confused if he was a hero or a comic character. Hero should not fail, right?

The following picture was included in the comic book I read. It illustrates Don Quixote, going mad, while reading a book. Look at the characters his imagination creates around him! In my childhood, my mind was stuck with it. Even now, looking at it, I feel some mystic sensation within.

Don Quixote going insane, by Gustave Doré. (The photo is from wikimedia
resources and is in the public domain.)

As a grown up, I understand what the author, Cervantes, was trying to tell us. Besides, particularly after joining for Ph.D., I feel like Don Quixote! Have I set myself to a task, without much thinking and preparation? Is this true in the case of my decision to get married before finishing my Ph.D.? Truly speaking, I want to find out if Don Quixote had inspired me and, if yes, how. I had procured the unabridged version (of course, translated to English from Spanish) of the book five years ago, but haven't started reading yet. It is very big, probably with 600 pages or more. I think I must read it in the near future.

Mathematics -- Pure and Applied -- and Engineering

I was trying to understand "what is mathematics" and how it differs from engineering (indeed, a stupid question to ask). I love mathematics, and I am fascinated by it, though I have no good mathematical talents. Furthermore, I know that engineering problems demand so much mathematical skills and knowledge. And many a time, my mind digress from  the simplicity of engineering to the wilderness of mathematics without my knowledge. This creates confusion as to what I am doing. A confused mind needs clarity. That is how I began to ask the above question.

I had heard that there is a difference between pure mathematics and applied mathematics. A notable mathematician of the last century, Paul R. Halmos gives clear distinction between them in his talks, interviews and books. According to him, mathematics is an intellectual discipline, done for its own sake. Though it is influenced by nature -- in the sense that a mathematician is a human being, who is a product of nature -- its objective is not the study of nature. In other words, its objective does not have to deal with any natural phenomena, or control of nature, or use of natural forces for humanity. Its objective is to play around clearly defined axioms -- which are often motivated by nature but generalized and expressed as abstract ideas so that its connection with nature has become irrelevant and invisible -- and to understand their implications completely. That is, mathematicians are after  the complete knowledge of an axiomatic system. Research in mathematics is to discover (note this: discover, not invent) any hidden knowledge in the abstract system, generated by axioms. And axioms are gods -- no questioning them, as long as they are clearly defined (there are debated axioms, too, e.g., axiom of choice -- if I am wrong tell me). On the contrary, the objective of applied mathematics is, using the Halmos' term, action; he implies physical action, or manipulating nature and its forces for some use. In other words, applied mathematics solves mathematical problems, which arise exclusively from applications. For example, suppose we arrive at a weird and so far unheard type of differential equation (I don't know if such an equation exists, but I contrive this as an illustrative example from my limited imagination) while trying to design a system. Finding out a method to solve such a problem means research in applied mathematics. Or else, it can be trying to find an efficient (fast or computationally light) method from the existing ones. Hence, applied mathematics heavily appears in physics, engineering and other applied sciences -- wherever there is action. To summarise, the pure mathematicians are after knowledge, whereas the applied mathematicians are after action.

Of course, an engineer can solve the kind of problems that an applied mathematician works on, but one must be very talented, having a good hold on mathematics. Rather, engineering is probably different. By and large, people say that an engineer is a problem solver. So, he may not really develop the mathematics required to solve a problem, but, rather, he may borrow the most appropriate concepts from mathematics to develop an efficient and practically realizable solution. This is my current thought on this.  However, I know that it is not complete. I am trying to understand this more. I guess that I should look into what the "engineers" have done in the past, especially, the greatest ones.

In the above effort, which was just an errand from my normal studies, I found a few interesting facts. I list them above, without organizing them well and without any purpose.

1. Paul R. Halmos is the first to use "iff" in the place of "if and only if" in mathematics literature (at least he claims so).
2. Paul Halmos is the first to use the small square to indicate the end of a proof in mathematics.
3. Josiaph Willard Gibbs is the first person who was awarded the first Ph.D. in the United States in engineering (strictly speaking, applied science and engineering); this happened in 1863, and he got the degree from Yale University. Why it is interesting to me is just because I, as a signal processing engineer, know Gibbs through Gibbs phenomenon. He is not a signal processing engineer, though.

When I leave this post, a few problems are lingering in my mind: What is engineering? What is a "fundamental" problem in engineering like? What can be considered as a seminal contribution in engineering:  solving a "problem" or inventing "something" new?

Stupid AMMA

Shameful, they call it AMMA -- a word that symbolizes love and unselfish service. By AMMA, I mean the "Association of Malayalam Movie Artists".  They embarrassed all the Malayalis by keeping themselves away from the ONAM celebration function organized by the Govt. of Kerala to honor the great actor Kamal Hassan [1].  AMMA says that Kamal is not a Malayali, and the Govt. of Kerala should choose a Malayali actor to honor rather than a Tamil actor.  This is a blunder -- a Himalayan blunder.  Fortunately, other associations in the Malayalam film industry did not subscribe to AMMA's views but actively participated in the program.

Kerala Chief Minister V.S. Achuthananthan honoring Kamal Hassan on 22 Aug, 2010, at Thiruvananthapuram. (Photo courtesy Mathrubhumi Malayalam daily)

In a larger perspective, the AMMA's argument caters to nothing less but the narrow-minded regionalism, which is otherwise unheard in Kerala.  This attitude is always destructive.  The Chief Minister V.S. Achuthananthan may be right to say that the Malayali actors are coveting only fame and recognition; they have no respect for the true art.  We know this from the recent experience.  The golden age of Malayalam cinema was in the 80's and 90's.  Those days are gone.  To save Malayalam cinema from the grave peril of forgetfulness, new talents are to rise.  Then, the old, sterile idiots will be wiped out forever.  For the sake of the art I wish this happens soon.

[1] Mathrubhumi news -- 23/08/2010