PhD memoirs #1

I had earlier started writing a post describing in minute details an account of how I am managing to get past a hurdle that I have encountered in my research work. But after some time I realized that it probably won't be read by anyone! So I have decided to simply generalize some of my recent experiences without going into too many specifics. 

I am beginning to see how intimidating sometimes working through the PhD thesis can be. And I have not even reached the crux of it yet. I am merely trying to replicate some mathematical results of some other researcher's past work in the hope of building upon it further. But it has turned out to be quite an arduous challenge! For one, I have not been able to understand the mathematical technique described in that work and thus had to look for ones that I could. This process itself took a couple of months. Finally, I got hold of a research paper which contained one alternative technique that I could understand well. I was overflowed with joy and hope when that happened. I then set down to develop solutions to that work's problem and after finishing I found my results, worked out using a different technique, not matching with the above stated ones.

Ever since, I have been trying to tackle this problem and it has proven to be a most challenging one.  Without a systematic and logical way of handling it, this task can seem very daunting - like picking out a pebble of particular shape from a sack full of same colored and same sized ones, since theoretically there are so many possibilities where mistakes could have been made. So I had to think of a smart way to eliminate a large class of possible sources of error. I did that by checking results of a simpler (but similar) problem against some reliable reference. It took me some time to locate one such reference and after lots of efforts I finally managed to get a match between mine and those results today!

This exercise has greatly reduced the possible sources of errors of the actual results that I had originally intended to compare. I have begun to investigate the remaining possible ones and I seem to have found some! But from my past experiences I am not raising my hopes too high and have sort of prepared myself to take another blow.
Also, I haven't mentioned the full details as so to how I have been reducing the time spent on making the aforementioned comparisons since they are specific to a particular math problem.

I guess I just want to express my solidarity with other PhD students who find themselves in the same boat floating on perhaps an even wilder sea. I am not sure whether things always work out if one perseveres but certainly losing hope is not an option! Personally, in situations like these when one is thoroughly frustrated with repeated failings I find that abandoning the work for some time (hours/days - depending on the magnitude of the prevailing muddle) helps. Of course, what one does during that time also matters and in my case I try to listen to some music or watch some movies or read some articles which partially inspire me to not give up! I also draw inspiration from a fictional character (and one of my heroes!) - SHERLOCK HOLMES. This particular dialogue which is aimed at Dr. Watson has been a constant source of guidance to me in various situations including the aforementioned one :

How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?

Sometimes I also discuss it with my mother who has herself done a PhD and her suggestions, whether I find them feasible or not, do make me feel less lonely. I suppose this is where presence of good fellow researchers plays a crucial role - one doesn't feel like he/she is the only one in a limbo! [e.g. failing at repeated attempts to get the displacement fields due to a line-source double-couple elastic dislocation model of half-space obtained using Garvin's (1956) approach matched with Niazy's (1971)]! 

Talking with someone helps! 

Based on some recent experiences I would also like to mention that it is important to not lose focus (due to whatever reasons) for too long. These situations demand clarity of thought and patience in order to be tackled efficiently and it is better to keep a vigil on one's state of mind before jumping to any negative conclusions about one's inability to work things out or imagining the worst possible outcomes.

P.S. As can be seen from the time of posting, this entry has been made after an exhausting but eventually, a little hopeful day of research work.

The Agenda : Plato's Republic!

It's well past mid-night and I just finished writing what I am about to share. But first let me briefly (and vaguely, since it actually isn't very well figured out) tell what I am up to. I bought a hard-copy of Plato's Republic just before leaving my institute and heading for home. It is supposedly a well-renowned work dealing with the subject of justice(a just individual/society/state), etc. and considered to be his greatest one (at least that's what a short note on the first page of the book states). The book is divided into 10 Books (similar to Chapters) with each one approximately 30 pages long, making the book run into 311 pages. I have read Book 1 and a few pages of Book 2. Now, this is my first (of hopefully more to come) sort of deep dive into such philosophical material and don't know how objective my appreciation for its contents is, but I can't help feeling a sense of awe while holding in my hand something which contains things written so far back in time (around mid 300 BCE) and yet, after reading some of it, finding its topics of discourse not very different from what every human being today observes around and thinks about during many occasions of his/her life.

By the way, its online version is available for free on the internet: http://classics.mit.edu/Plato/republic.html This makes it rather difficult to justify my intent for sharing what I am about to share but I will nevertheless state it honestly : As of now (since I don't know whether I would like to continue with it in the future) I wish to, in the least, share my own translations of the important discussions that I find in that text in a simplified and orderly form and with as much accuracy as possible. I may give my critical comments in the process (in whatever details) or may simply refrain from doing it. There are chiefly 2 reasons that motivate me to do it: (1) I am currently finding it an interesting and yet not too much taxing (probably not for long) exercise which presents to me the opportunity to understand the book's text thoroughly if I persevere till the end and thus, something that I might feel happy about and claim with little pride afterwards. And it seems possible to do it at a convenient pace of my own (2) Some readers who might not feel comfortable with reading the original text or who might be curious to know what its contents are before committing themselves to read the full text, might benefit from these translational notes which I will try to make quite understandable for a reasonably good English reader.

The book that I have has an interesting introduction by an Indian academician, Dr. Dhananjay Singh, which instantly excited me to start reading it. I do not wish to write that here (feeling too sleepy) and the readers will have to take my word that at least Book 1 contains interesting stuff. 

Plato was a student of Socrates and Republic's text is written as a first person account of Socrates.  However, my notes are in the form of a third person account of it. I found the text quite enjoyable since its mostly in the form of dialogues which take place between Socrates and his acquaintances and friends. 

So, here are my notes of Book 1 that I finished writing and editing just before making this entry (the end of these notes will mark the end of this post since I am feeling sleepy and can't cause myself to give it a more suitable ending):

Book 1

The interesting arguments are between those of Thrasymachus and Socrates. Thrasymachus makes 2 claims: (1.1) Justice is the interest of the stronger (1.2) Justice is much less advantageous than injustice. Socrates first contradicts (1.1) by claiming that the ruling class (stronger class) is fallible and thus may falsely conceive certain provisions as serving their own interest when in fact it’s the opposite and thus, wrongly ask the subjects to obey them. The subjects, being just in obeying the rulers, would thus not be serving the interest of the rulers. To this Thrasymachus essentially adds the clarification that in as much as the rulers are astute in discerning their own interest and commanding the subjects to do their bid in favor of those interests, the subjects are just in doing what they are commanded to do. To this Socrates, by a series of dubious arguments, shows that a ruler, in the true and strictest sense of the word ‘ruler’, will actually never care for his interests but rather those of his subjects. He does this in following steps

1.  Every art has one and only one subject of its interest (e.g. the art of horsemanship is concerned with taking care of horses, art of medicine is concerned with taking care of body ailments, etc.) and it doesn’t care for itself (a little strange statement to make).

2.  Thus all arts are concerned with catering to needs of their respective objects which they serve and to no one else. In this sense the arts are superiors and their subjects of interest are weaker.

3.  The professionals of each art, in the strictest sense, thus serve only the subject of their arts. E.g. ‘no physician, in so far as he is a physician, considers his own good in what he prescribes, but the good of his patient; for the true physician is also a ruler having the human body as a subject, and is not a mere money-maker’

4.  By extending this trait to a ruler, it thus follows that a ruler cannot consider his own interest but only that of his subjects in order to be a true ruler.

Thrasymachus ridicules Socrates for getting to this conclusion and points out how rulers actually behave in reality. He then also gives many examples of (1.2) which I will cover later. To Thrasymachus’ retort, Socrates essentially points to him the inconsistency in his definition of the term ‘true ruler’ and ‘true artist’, and again claims that a true ruler, just like the true artist, is concerned only with the interest of its subject. But he makes the admission that in reality, the artist or the ruler does require remuneration for his work but the remuneration doesn’t change the fact that the job of the ruler/artist is that of caring for his subject. So, while the artist does receive some benefit for his work, his work produces benefits solely related to the functionality of his art and exclusive of the benefits he receives. The same is applicable to a true ruler. In fact, since people who take up work related to governing others are unwilling to do so without some form of payment, it shows that they are doing a service for others for which they demand that payment. Socrates then digresses from the argument at hand and talks of three incentives that may lead someone to take up work which involves ruling over others: (1) money, (2) honor and (3) penalty for refusing to do so. He then claims that the 3^rd incentive actually drives the ‘best of men’, for a good man will not like to do service for others for monetary gain or for ambitious motives like earning honor. He will do so only from the fear of experiencing some punishment. I think this excerpt best describes his point which interestingly makes much sense:

‘Now the worst part of the punishment is that he who refuses to rule is liable to be ruled by one who is worse than himself. And the fear of this, as I conceive, induces the good to take office, not because they would but because they cannot help – not under the idea that they are going to have any benefit or enjoy themselves, but as a necessity, and because they are not able to commit the task of ruling to anyone who is better than themselves, or indeed as good. For there is reason to think that if a city were composed entirely of good men, then to avoid office would be as much an object of contention as to obtain office is at present; then we should have plain proof that the true ruler is not meant by nature to regard his own interest, but that of his subjects; and everyone who knew this would choose rather to receive a benefit from another than to have the trouble of conferring one.’

I find the last line of the above excerpt quite interesting. It implies that Socrates considers a good man to have at least the following attributes: (1) he does exactly what his job requires him to do – here, being a true ruler - to not care for his own interests but those of his subjects (2) he need not necessarily be charitable, since he can make the choice of not serving others by not taking up office.

Before responding to Thrasymachus’ claim (1.2), he enquires his general view about justice and after a series of questions he gets Thrasymachus’ opinion of

• An unjust person as being ‘wise’ and ‘good’
• Injustice as ‘discretion’, ‘honorable’, ‘strong’, ‘wisdom’ and ‘virtue’
• Justice as ‘sublime simplicity’ and having other qualities opposite to that of injustice. 

First, he disproves Thrasymachus’ claim of the unjust person as being ‘good’ and ‘wise’ using the following dubious arguments and getting Thrasymachus’ approval at each step of the deductive process:

1.  A just man doesn’t try to gain any advantage over another just man but considers it just to gain advantage over the unjust (but won’t be able to, Thrasymachus adds). Whereas, the unjust man will strive and struggle to obtain more than the unjust [as well as the just] in order that he may have more than all.

2.  Rephrasing (1): the just does not desire more than his like but more than his unlike, whereas the unjust desires more than his like and his unlike.

3.  Socrates then takes examples of arts for illustrating something - a musician, when adjusting the strings of a musical instrument, will not desire or claim to do it better than another musician whereas he will than a non-musician. Similarly, a physician, while prescribing treatment to his patients will not wish to go beyond another physician in the practice of medicine but will certainly claim to go beyond a non-physician in doing so. Just like the cases of musician and physician, a knowledgeable person will not desire or claim to know or say more than another knowledgeable person but will definitely desire or claim to know more than an ignorant person. But the ignorant person will desire to have more than either the knowing or the ignorant.

4.   The knowing is wise. The wise is good. So, from (3) it follows that the wise and good will not desire to gain more than his like, but more than his unlike and opposite. Whereas the bad and ignorant will desire to gain more than both.

5.  Comparing the characteristics of a just and unjust person with those of knowledgeable and ignorant person, Socrates concludes that the just is like the wise and good, and the unjust is like the evil and ignorant and subsequently claims that it thus follows that the just is wise and good and the unjust is evil and ignorant.

Second, he deduces that since wisdom is stronger than ignorance so justice (being wisdom and virtue) is stronger than injustice (being ignorance) and thereby disproves another of Thrasymachus’ claim that justice is weaker than injustice.

Third, he further elucidates other consequences of injustice and its connection to Thrasymachus’ claim that the unjust have many more advantages than the just. He takes the case of a hypothetical State which dominates and enslaves other states in an unjust manner and examines whether that State would be able to exert that power with or without justice. To answer this, he points out that a State, or an army, or a band of robbers and thieves or any other gang of evil-doers cannot act in unity if they injure one another. He further points out that injustice has a tendency to create divisions and provoke hatred wherever it is present, whereas justice imparts harmony and friendship. This view is captured well in the following excerpt:

‘Yet is not the power which injustice exercises of such a nature that wherever she takes up her abode, whether in a city, in an army, in a family, or in any other body, that body is, to begin with, rendered incapable of united action by reason of sedition and distraction; and does it not become its own enemy and at variance with all that opposes it, and with the just?’

This leads him to conclude that evil men, who work together to commit great crimes of injustice, are in reality not perfectly evil men since then they would not have been able to act in unison, but it is evident that there must have been some remnant of justice in them, which enabled them to combine.

Finally Socrates proceeds with properly refuting Thrasymachus’ claim (1.2) that ‘Justice is much less advantageous than injustice’. He does this by first stating (and getting Thrasymachus to understand and agree) that anything to which an end is appointed has an excellence. For illustration, he gives examples of an eye and an ear. One cannot see without an eye or hear without an ear. Thus, to see and to hear are the respective ends (or functions) of an eye and an ear. If the eyes do not maintain their excellence (i.e. they do not function well) and have some defect, then they do not meet their ends which is to provide sight. Similarly, ears which are devoid of their excellence won’t meet their ends of making it possible to hear. Socrates claims this applies to every other thing which has an end, including a person’s soul. Here, Socrates doesn’t explicitly state the definition of soul but he regards the ends of a person’s soul as giving life to a person and causing him to superintend and command and deliberate and the like (as a side point, he concludes that because soul causes one to superintend, an evil soul must necessarily be an evil ruler and superintendent and the good soul a good ruler). And similar to the eyes and ears, a soul will not fulfill her own ends when deprived of her excellence. Socrates then asserts (with Thrasymachus agreeing) that justice is the excellence of the soul and injustice is the defect of the soul. Since life is one of the ends of the soul, a just soul (and thus, a just person) will have that end met completely because a just soul retains its excellence, which means that he will live well. On the other hand, by same reasoning an unjust man will live ill. This is the subsequent conversation between Socrates and Thrasymachus 

S: And he who lives well is blessed and happy, and he who lives ill the reverse of happy?

T: Certainly.

S: Then the just is happy, and the unjust miserable?

T: So be it.

S: But happiness and not misery is profitable.

T: Of course.

S: Then, my blessed Thrasymachus, injustice can never be more profitable than justice.

At the end of these arguments Socrates laments that his original intent of finding the nature of justice has still not been fulfilled despite all these discussions:

‘I left that enquiry and turned away to consider whether justice is virtue and wisdom or evil and folly; and when there arose a further question about the comparative advantages of justice and injustice, I could not refrain from passing on to that. And the result of the whole discussion has been that I know nothing at all. For I know not what justice is, and therefore I am not likely to know whether it is or is not a virtue, nor can I say whether the just man is happy or unhappy.’

 

Life as a tutor#2

It's been more than a month since my previous (and the only other) blog entry on my experiences as a tutor at IIT Kanpur. It's less than my anticipated periodicity of making the entries but not entirely unexpected. During this gap I sometimes did feel like penning some my thoughts but couldn't gather enough motivation or didn't have the peace of mind to do it. Moreover, from my past experiences I have observed that one often has sudden intellectual discoveries or abstract realizations in such  strange situations or unexpected places that unless one has sufficient time and resources (or perhaps some kind of skill/practice) to preserve those thoughts in their pristine form, it becomes very difficult to recollect them later on in their entirety or for them to have the same effect as they did originally. Probably that has also been the case with me. 

I am currently at my home in Chandigarh - there's a week long mid-semester recess at my institute - after nearly 3 months since my last visit and with no particular agenda (except one, which I will mention later) on my mind. I have had a decent start today by normal standards (e.g. not waking up at noon time which has usually been the case on previous such visits) and feel quite at ease to make this entry.

... I spent a few minutes just now thinking of some interesting experiences worth mentioning but couldn't find any despite having taken 4 more tutorials.. I mean, of course, from an academic point of view I have had the opportunity to solve and discuss some interesting problems in the class which also allowed me to (1) gain more insights and (2) treat them in a way which is less mathematical and more intuitive, but I don't think the readers would be interested in knowing those technicalities (in case you do, feel free to get in touch with me!) and it will take a considerable time to explain them here. However, let me go ahead and illustrate an example of one such problem that I discussed in the previous tutorial class (#8):

Try to image a long wooden plank of dimensions, say 2 m length, 30 cm width  and 5 mm height (phatta, as they call it in Hindi/Punjabi).... Wait, I just found the exact problem on the internet! Just take a look at the below picture. Its caption is the problem statement. And don't worry, I won't go solving the problem here. I just want to highlight a few interesting features of this problem.

1. Okay.. but what does it mean??: Those who are not familiar with the concept of 'bending moment' won't be able to make out what the problem statement actually means. Here's what it means:

Where should the two bricks be placed so that the risk that the plank will collapse under the weight of the books is minimum?

And my guess is that even those who know the concept of 'bending moment' won't be able to make this interpretation without putting in a little extra mental effort. I think the above translated problem statement is likely to be understood by a layman - as a thought exercise imagine two extreme cases: (1) the bricks are placed at the ends of the plank (2) the bricks are placed very close to the plank's center. Can you intuitively feel these two cases presenting a high risk for the plank to collapse? Thus, there might be a case, somewhere in the middle of (1) and (2) (i.e., when 'a' is nearly half of the plank's length) when that risk is minimum. In fact, this is how I presented the problem to the students. Only afterwards I described the problem in terms of the 'bending moment' concept. If you are curious, the answer is: a=0.586L, obtained under certain idealizations (a jargon employed whenever engineers wish to acknowledge that their mathematical model adopted for solving the problem, despite their best efforts, does not exactly match the real one!), which is interestingly not very far from what one might expect intuitively.


2. Other possibilities: Another interesting thing about this problem is that once the logic behind the solution method is understood, one can solve for other interesting variations of the problems (e.g. given some finite number of books of different weights, what is/are (1) the best way(s) to arrange them on the plank and (2) best way(s) to place the two brick supports, such that the risk that the plank will collapse is minimum). I was able to illustrate these possibilities in the class.


3. Optimization technique: A further interesting feature of the problem was regarding the approach to be adopted for optimization (a term associated with any problem which involves estimating values of certain parameters which maximize/minimize some quanti(ty/es) of interest, e.g. length 'a' in this case). I won't explain the details here but I would like to mention that the approach that I discussed in the class was less mathematical and more intuitive (mathematical, nevertheless) which I thought the students will be able to geometrically visualize. At one stage, I asked the students to come forth and mark the answer on a graph that I had drawn on the blackboard and one student did volunteer and marked it correctly, to which I gave my commendations generously!

I hope the above brief discussion will lend some concreteness to (a)-(e) exercises that I mentioned in the previous blog entry under 'New discoveries' sub-heading. 

So, I have had the opportunity to solve such interesting problems in the class. I think I will end this entry here since its now lunch time here and I am feeling hungry. Also I believe the readers would probably want it to end. Hopefully, I will share the rest of the things tomorrow. Oh, and I will also probably mention the agenda that I have on my mind these days!

Life as a tutor #1

I had been thinking of making this type of entry for some time during this month but, as is generally the case, I didn't gather enough enthusiasm and motivation till now.

This semester I am a tutor of a course taught to many 2nd year undergraduate students of IIT Kanpur. Its titled 'ESO202A : Mechanics of Solids'. I myself did this course in 2007 under the tutorship of Dr. S. N. Tripathi of Civil Engineering Dept. It would have been impossible then to imagine myself taking up his role sometime in the future. I probably would have quickly dismissed even a slight hinting at that scenario by someone. But here I am, today, in this unforeseen situation. And in the ensuing few blogs (hopefully) I intend to share some of my feelings, experiences and observations. Part of the reason for doing so is that I think the readers will find some of these experiences funny and interesting. Another reason is that I like the idea of revisiting these entries in some distant future.

For readers’ information who are unfamiliar with the academic duties of a tutor of a theoretical course at IIT Kanpur (brackets correspond to the present case): 

The student body (273 students) crediting the course is divided into certain number of sections (9). A tutor is assigned to each section. The tutor is either a faculty member or a graduate student. Once a week (Thursday) there is a 50-minutes tutorial class(in addition to the regular lectures taken by the course instructor). The tutor is supposed to solve certain problems, the problems being suggested by the course instructor and illustrative of theory discussed in regular lectures. In the present case we are not provided with the solutions to those problems by the instructor which isn't a big deal if you are (well, you should be!) well-familiar with the subject. And we are supposedly required to do a good job at that and answer students’ questions.

As is evident from this structure, the tutor is given a lot of freedom as to how he/she wishes to perform his/her task. I do not know how things are done in other IITs or other engineering colleges but I really like this feature of my institute!

I have presently tutored in 4 classes with the last class being held just yesterday morning. I will highlight some of my thoughts and experiences in the form of points

1. What I most want: If someone asks me what matters the most to me, that I tend to always keep in mind while preparing for the tutorial classes, my answer is this: I wish the students think they have learned something interesting during those 50 minutes and that they consider it to be a nice experience.

2. New discoveries: To get some assurances of (1) I have been trying to find ways of presenting the material and explaining things which generate some interest in the students. Fortunately, the current course is more of an applied physics course so that almost everything they study can be made to relate to what they see in the physical world. This is where things get interesting - you see, when I did this course in 2007 I actually almost didn't bother to (a) think beyond things mentioned in my class-notes, like possible real life applications of the abstract concepts, (b) pause and rigorously question all the assumptions on which a theory/solution is based, (c) verify whether the solution to a problem is in line with common experience or intuitively makes sense, (d) think of alternative approaches to solving a given problem and (e) reconcile two or more different explanations of the same result with each other/themselves. In short, I let my imagination starve and used the analytical tool kit sparingly. My guess is that this is typically the case with most undergraduate students. And I don't think its because the students are incapable of using their imagination. I think it’s got to do with the practical reasons of time constraints and it being a reflection of the way things are actually taught in the lectures and the way they have been trained to think about what they have been studying since school days. Anyway… what has been very interesting is that in order to be successful in (1) I am inevitably resorting to (a)-(e) exercises, and its turning out to be a pleasurable experience! I find it a little sad that the academic schedule of the students often doesn't allow them to experience this feeling but on a bright side, I am, in my own little way, trying to open for them a door to some exciting possibilities which they probably aren't conceiving on their own. In the process I am also benefiting by gaining new insights into the concepts, an example of which is mentioned below in (3)!

3. Mohr Circle: The tutorial h­­eld yesterday was different from the rest. In most cases, the theory on which the discussion problems are based is already taught to the students beforehand in their regular lectures. This time the problems were based on a concept that had been introduced only briefly to the students and the tutors were requested to familiarize the students with that concept while solving the problems. The concept is called 'Mohr Circle'. Put plainly, it is a geometric representation of a mathematical relationship between some physical quantities. During my undergraduate days I used to find this concept a little irritating since I often forget its construction. Later on, while doing some graduate courses I gained much more confidence, but it wasn’t till the past couple of days that I realized how little I had explored it. This time while going through the concept I came up with alternative possible constructions of the concept and made guesses so as to why they were not in mainstream use and eventually shared them yesterday ­with the students. Then, while solving the discussion problems I thought of developing an animation in MATLAB to help students visualize the concept and to highlight some results. This last activity proved to be fun as I discovered some more interesting things that can be done in MATLAB which I hadn’t tried before! And finally, I was able to illustrate that animation in yesterday’s tutorial to my satisfaction. I have uploaded it on YouTube:

4. Being a teacher: As a student I have sat through many lectures with a dull expression on my face. I have sometimes presented an indifferent disposition when the teacher asked questions to the entire class. I have many a times not tried to conceal a yawn. I have sometimes arrived a little late in the classroom. I have sometimes started discussions with the neighboring students in an ongoing lecture some of which were a bit too noisy. And yet I had given no thought as to what impact these behaviors make on the teacher. Well, I think I am becoming a little more knowledgeable in that regard! Yesterday, many students were not on time for the class and I found it a bit irritating to see them stand at the door entrance while I was teaching and to give them a nod to grant entry into the classroom. Then, while I was not lecturing and instead writing something on the blackboard (oh, and writing with chalk on a blackboard sucks!!) I could hear some conversations behind my back which also irritated me. After about half-an-hour I found many of the students sitting at the far-end of the classroom sleeping peacefully, which was a bit disappointing. Sometimes, when I posed questions to the class I was a little taken aback by some blank stares in response. I hope any student reading this will be able to empathize with me and reflect on his/her behavior. Certainly I would, from now on!

5. Managing time: This is one aspect that I am having difficulty handling. Except for the 1^st tutorial class I have failed to cover all the intended material in the allocated 50 minutes (usually, I am able to extract about 5 additional minutes). Yesterday, I was not able to discuss two problems although I can justify it by the fact that a lot of well-deserved time was spent on explaining the concept of Mohr circle which is usually not the case. However, I also spent time explaining some basic preliminary concepts which the students ought to be quite familiar with in order to understand Mohr circle. Indeed, while preparing for the tutorial I anticipated this problem and was faced with the dilemma of whether to or not to explain those basic preliminary concepts – on the one hand, those concepts had already been taught in regular lectures and ideally it’s the responsibility of students to make sure they understand it well which, if they did, would save me the trouble of spending time on that and thus increase my available time window; on the other hand, if the students are not familiar with those concepts then I don’t see much point in explaining further advanced concepts built upon those, but then explaining those basic concepts would decrease my available time window. I have come up with one strategy for handling this problem. I have created an online discussion forum using Google groups and have invited the students to join it. I plan to post any missed out things (e.g. answers to the two problems that I missed) or some ideas that I failed to discuss in the tutorial class due to lack of time or my own neglect. Of course, I have invited students to post their other doubts on the forum which I will be glad to answer! I have also invited them to share their own insights/discoveries with the rest of the group members. I will also keep posting interesting/important things. I hope this venture proves successful! However, I do hope that as the course progresses the students devote sufficient time on learning and understanding the things being taught in their class, otherwise it will become a hassle for me..

I guess that’s all I want to share for the time being. I will share other interesting experiences as they come along in the subsequent entries which I hope won’t be as lengthy as this one! Phew!

On Appreciation

24 April

2:10 A.M.

Yup, you read it correctly, I am making this unexpected entry at this seemingly odd hour. Its unexpected since, as will become clearer by the end of it, the motivation behind this entry doesn't come from a strong conviction to express something substantial related to critiquing human behaviors and current socioeconomic system. Its also different from the rest since I have not endeavored to spend some time to properly organize my thoughts before expressing them here. I have a train to catch at 5:50 A.M. from Kanpur to New Delhi (I am going home for a short visit... finally) and have booked a taxi which will pick me up at 4:45 A.M. and I am beginning to feel sleepy. And I know that if I do not write it now, I probably won't be writing it afterwards. 

As for my reasons for consideration of it being worthy of a blog post - just a while back, sitting in a toilet (Indian style - to make the already gruesome imagery more vivid :D ), my thoughts, while flying randomly, somehow began to hover over a point of view about a topic which I had discussed with a friend some time back and I was able to make its connection to some of my recent experiences, the result of which seemed pretty neat. I can not recall having seen this point of view being expressed elsewhere explicitly and I suspect it will be seldom prevalent. So, in the spirit of this blog's title I thought of writing it. 

Once, sometime during the late summers of last year, while me and my friend were sitting in our hostel canteen and watching football on television, we started having a discussion about the biased sense of Indian people's interest in cricket. Then, as I can now recall, after thinking about it for sometime I proposed two reasons (1) its a cultural phenomenon which gets propagated down the generations with significant contribution from the media (2) most of the people haven't played a sport other than cricket or haven't played it to the extent of learning it as technically as one learns to, say, play some musical instrument.

Its point (2) that I intend to elaborate here and, if it has elements of truths in it, sketch its broad consequences and significance. My rationale for (2) came from my own personal experience. A few years back, I was reasonably good at playing table tennis. And when I say 'reasonably' I am comparing it with national level players' competence, so that, obviously, I was much more skilled at it than majority of Indian people. I am now, as I was at the time when the discussion with my friend took place, pretty much out of touch with it. However, this (had/has)n't prevented me from not enjoying watching a match between two good T.T. players. And the reason is that I am able to very much appreciate all the great strokes that a player makes. To me, every great stroke is an indication of the amount of time and energy that has gone into mastering it with such a perfection. The difficult the stroke the harder the labor has gone in. And to behold it in this light is a thing of beauty ! Clearly, a person who hasn't played T.T. even once or has not tried to master its difficult techniques would be far less able to appreciate an ongoing T.T. match between two good players in the sense that I have explained than a person like me would. So, I thought (and still do maintain) that there was a sufficient reason to believe that (2) is a good explanation.

By extension it has interesting consequences in many spheres of human activities which demand a specialized skill and which, indeed, need not be physical in nature. It may well be possible that many of the great scientists derive their source of pleasure from research work because of their tremendous appreciation for the work done by previous great scientists, which probably won't be appreciated by someone who's not into mathematics and science. This can be extended to arts and literature as well.

Very recently, I watched some excerpts of a short documentary on Richard Feynman. In that he's asked whether he finds it easier to have a good conversation with people from scientific background like him than with people who do not have such kind of background, for example, artists or musicians. His immediate reaction is an affirmation and he starts justifying it, only to stop in the middle, and after reflecting on it again, says "I take all of my words back". Then he cites an example of a well-renowned artist with whom he had a great conversation and concludes that provided the person has excelled immensely in his field, regardless of the field, he would be able to have a scintillating conversation with him. 

I think the above view of Richard Feynman, when taken in conjunction with point (2), may possibly provide certain clues as to what attracts someone's attention and whether its possible to make something interesting enough for someone, and if so, how to do so. In a more subtle way, this possible knowledge also behooves us to be more tolerant for other people's likings and interests and have more rational reasons for appreciating or criticizing some skill other than that resulting from complete or partial ignorance about it.

A letter to Body Waves

Dear P-Wave and S-Wave,

I hope you both are enjoying your trips traveling beneath earth's crust while occasionally giving seismologists a chance to observe you at the ground surface. In this letter I would kindly request you to answer some of my questions.

I will be honest. I am not a seismologist. I am just a PhD student who happens to be working on your biography. Even though you are quite famous among many seismologists and I see a lot of academicians referring to you in research papers in a manner which suggests a good deal of intimacy between you and them, your origins during an earthquake still elude me. Quite frankly, I am tired of being in this state of perpetual ignorance. 

I have tried searching for your origins and travel plans in journals and books. I have come to understand the basics: the relationship between your speed and earth's properties; the motion-pattern followed by the neighboring medium particles upon your arrival; your appearance through the Helmholtz Decomposition method when applied to the governing equations of motion. But what perplexes me is that how to extract you from a seismic record in a fool-proof way! 

Some people like Castellani and Bofi have suggested a plane-wave model to (1) trace the time spent by you at a particular location and (2) compute the amplitudes generated in the medium particles. But these knowledgeable people, who I in no manner wish to offend, have failed to provide justification for the underlying assumptions of the model and have left me with a lot of unanswered questions, for e.g. (1) what is the nature of the source that is generating you (2) why should this method be so heavily relied upon when it can offer no scope for attenuation of particle amplitudes with increasing epicentral distances (3) how can the assumed angle of incidence proposed for you be trusted. 

Some people have even suggested that you do not like to travel alone at large epicentral distances, and charitably, give your cousins, Rayleigh Wave and Love Wave, a chance to become famous. These astute people, in a similar fashion, have proposed models to extract you and your cousins from a seismogram without addressing my above doubts.

I have now turned my attention to works of some other seismologists and academicians like Lamb, Knopoff, Burridge, Sato, Kanamori, Kawasaki, Aki, Richards, etc. who have used the Green's reciprocal theorem in modeling the expected motion resulting from a discontinuity (they give it a fancy name : dislocation) in the displacement field across the fault plane. Unfortunately, their work is substantially more mathematical than previously briefly discussed methods. And sadly, due to my past experience, I have lost some faith as to whether this pursuit will lead me to what I am looking for. 

Hence this letter.

I would be much grateful if you could spare some time from your busy travel schedule and answer this: what criteria do you use to prepare your travel itinerary under different faulting conditions? I wish I could directly ask you the details of your future travel plans but we all know it’s something you don’t share with anyone. In your view, things will get very mundane for us humans if it were known. On that note, allow me to clarify that I do not hold any negative opinion of you. Some humans are quite afraid of the prospect of your arrival. I think it’s simply because they are not adequately prepared to receive you. And it is because of this reason that I wish to learn more about you so as to help my fellow human beings to become less secluded and more ready to welcome you.

Yours humbly,

Varun