The day breaks, the mind aches ...and jingles

Today
I have known
that the past
ragged, worn,
is longing
to be my friend
again
this May.

We had parted
with smiles
while sharing
open skies.
But the lesson
wasn't learnt
to this day.


And with the Beatles
it seems,
just like yesterday.

----------------

Haven't found the time to write for a while. Rather, the need hasn't arisen. Updates:
1. Wrapping up my thesis/rather resolving everyday to do so.
2. Reading "The Argumentative Indian" again but slowly and carefully, making sure I can quote at will from the book.
3. Experienced the most horrible examination in two years - Non-linear Dynamics end semester. Silly mistakes make you feel silly. Which is good once in a while.
4. Watched the "The Diving Bell and the Butterfly" - must watch french movie. Shall blog about it later if I find the time and the inclination and the need.

waters of another world
descend, trickle down
our window panes
as the sea between us
rises, and swallows
the both of us.

I wanted to say a
few last words
but they no longer
mean anything.

Even Silence,
our common friend
plays a fifth columnist.

I shall not apologize
but only stand and wait
hoping the waters
cleanse and rid me of
the only language
I know;
whose yoke I carry
upon my writing
fruitlessly.

Beseeching Motivation

My interest in my final year project has faced a slow decline during this entire semester and the previous month in particular. The absence of my guide as a source of weekly acknowledgment has perhaps significantly contributed to that feeling. Things seemed a lot more exciting four months ago. Our investigations had led to interesting results albeit the classical, purist nature of the problem we were pursuing.

Much of our earlier findings were comparatively humbler compared to this one problem that was the subject of my efforts in the last one month. The problem was to investigate the agreement/differences in predictions of the properties of a particular system using three different mathematical models or theories as you might want to call them. Refraining from getting into further details, let me say that weeks of efforts culminated in the finding that these models predict exactly the same thing about the system. I remember my guide telling me that finding a difference would be a significant result in many respects and that would lead to many more interesting threads. But that was not to be. My professor responds to my communication of this news to him in the following manner:

Dear Karthik,
These simulations establish a point either way - when they show differences and when they do not, so I would not be worried too much. These are important results nonetheless and we must plan towards communicating them.
Best,
Suresh

As a novice researcher, there are times more than one when one is compelled to question the worth of one's pursuits and efforts. And the opportunities that I encountered to make suc introspections were more than a few. I would never describe my project in too much detail to anyone who asked me; it falls short on providing either of the two kinds of joy that encourage researchers. I am well aware of the fact that my results will neither have significant practical consequences in the industry nor are the equations that I deal with and the analysis that I do even close to being a mathematician's delight. In terms of the quantum of work needed, my professor tells me that I am ready to submit my thesis but that it would be nice if I worked on a couple of other threads and got them to a 'logical' conclusion.

On another matter, I am thinking of nominating your thesis for the Indian National Academy of Engineering Award (see attached note). This might mean that you organize your work so as to complete the entire process of submission (also examination?) byJune 30. Please go through the site mentioned and see what are the requirements.

Best,
Suresh

I will work for a whole month on organizing my thesis, ensuring that my work flows logically from the premise to the hypotheses to the proofs, judiciously citing every reference and acknowledging every possible help that I received along the way, numbering each equation, table and figure; I shall organize the report in chapters nested with sections which will in turn be nested with subsections. My thesis shall be bound and the institute library will be supplemented with a copy of it. And there it shall remain till antiquity until the taste of the papers matures well enough in the musty shelves to whet the collective appetite of a community of termites.

-----

It was with this feeling of resignation that I decided to take a three day break from work :-). There was an urge to take a long walk along a rainy footpath on a hill starting midnight, to smell the wild flowers along the way, to smile at the people who come there looking for firewood before sunrise and to reach the top early enough to be able to greet the sun as it languidly but unfailingly illuminates our world. When fatigue takes over and when one lacks resolve, poetry seems less poetic and hence I decided to spend saturday night at home. Had coffee with an old acquaintance from school and kindled a (possible) friendship, let my mother relish her powers over me and my appetite and had long talks with my father after a significantly long time.

I know it's difficult to find any kind of reconcilation when you're dissatisfied with work. Acknowledgment works to an extent to satisfy the deluded man. He/She who is satisfied by mere acknowledgment is in all probabilities someone who doesn't have a passion to pursue anything in this world dedicatedly. I have often seen the following question pop up during conversations that I have been a part of, especially if the persons involved are feeding on each other's dissatisfaction with the world as to which pill must Alice take, happy delusion or her unhappy self?

Something that partially inspired me was a letter by Richard Feynman to one of his former students who was unhappy with his life and research. The student had sent a congratulatory mail to Feynman on the latter's winning the 1965 Physics Nobel but had sublimely expressed his unhappiness. The student wrote that he was a 'nameless man' working on 'a humble and down-to-earth type problem' somewhere in oblivion. Feynman writes,

Dear Koichi,

I was very happy to hear from you, and that you have such a position in the Research Laboratories. Unfortunately your letter made me unhappy for you seem to be truly sad. It seems that the influence of your teacher has been to give you a false idea of what are worthwhile problems. The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. A problem is grand in science if it lies before us unsolved and we see some way for us to make some headway into it. I would advise you to take even simpler, or as you say, humbler, problems until you find some you can really solve easily, no matter how trivial. You will get the pleasure of success, and of helping your fellow man, even if it is only to answer a question in the mind of a colleague less able than you. You must not take away from yourself these pleasures because you have some erroneous idea of what is worthwhile.

To Koichi Mano (the student) referring to himself as a nameless man, Feynman wrote the following words. In the past two days, I have forwarded the entire letter to many of my friends. One among them said that she read the following lines 'over and over again'; they are indeed moving:

You say you are a nameless man. You are not to your wife and to your child. You will not long remain so to your immediate colleagues if you can answer their simple questions when they come into your office. You are not nameless to me. Do not remain nameless to yourself - it is too sad a way to be. Know your place in the world and evaluate yourself fairly, not in terms of your naïve ideals of your own youth, nor in terms of what you erroneously imagine your teacher's ideals are.

Best of Luck and Happiness,

Sincerely,

Richard P. Feynman

This letter carries a lot of meaning for me and as luck would have it, I encountered it at the most appropriate time.

Mars and Venus

Benedick: That a woman conceived me, I thank her; that she brought me up, I likewise give her most humble thanks: but that I will have a recheat winded in my forhead, or hang my bugle in an invisible baldrick, all women shall pardon me. Because I will not do then the wrong to mistrust any, I will do myself the right to trust none; and the fine is, for the which I may go the finer, I will live a bachelor.

Beatrice: What should I do with him? dress him in my apparel, and make him my waiting-gentlewoman? He that hath a beard is more than a youth; and he that hath no beard is less than a man: and he that is more than a youth is not for me; and he that is less than a man, I am not for him: therefore I will even take sixpence in earnest of the bear-ward, and lead his apes into hell.

- Much Ado About Nothing

As I gradually burrow my way through this fantastic comedy, I enjoy being witness to the amazingly crafted sexual tension between the first MCP and the first feminist in literature (feminist is probably a wrong word but I don't know of the female equivalent of an MCP and I don't want to call her a b**** for Beatrice is much too adorable for that).

Taking a break from non-fiction. Will struggle and get past the comedies of Shakespeare in the next few months :-).

A final example

Understandably, I have been subjected to some criticism for my previous post. I do not wish to prolong the dialectic but I quote in this post a specific example of how a mind capable of producing brilliant images through poetry on one instance can seem seriously deluded on another. I quote the example of Samuel Taylor Coleridge, who was one of the prolific romantic poets in late eighteenth century England. He is known to have written very little poetry but all of his works are regarded for their sheer brilliance. E. T. Bell states in "Men of Mathematics" that the German mathematician Riemann is to mathematics what Coleridge is to English poetry.

Coleridge is best known for 'The Rime of the Ancient Mariner', some verses of which I happened to read as a kid in school. I distinctly remember following lines; perhaps the stern manner in which my English teacher enunciated these lines facilitated in their being imprinted in my memory,

Day after day, day after day,
We stuck, nor breath nor motion;
As idle as a painted ship
Upon a painted ocean.

Water, water, everywhere,
And all the boards did shrink;
Water, water, everywhere,
Nor any drop to drink.

Coleridge was also known for his masterful prose. In the following paragraph (which I reproduce from "Unweaving the Rainbow"), Coleridge notes his exhilaration on seeing a rainbow in the sky (Anima Poetae, published 1895):

The steadfast rainbow in the fast-moving, fast-hurrying hail-mist. What a congregation of images and feelings, of fantastic permanence amidst the rapid change of tempest- quietness the daughter of storm.

Coleridge is known to have tried his hand at science too. He attempted to dissect the light spectrum and is known to have nourished a sincere aim at some point of time in his life to write a treatise on the subject. The following is an excerpt of his 'analyses'. This was written almost a century and a half after Newton had published his authoritative 'Optiks' which had laid the foundation of the corpuscular theory of light spectra and lenses until the wave theory superseded it in many respects. In Dawkins' words, 'Coleridge's heart must have been in the right place with respect to science.....but he failed to live up to his own ideals to "unfold and arrange" his ideas in "distinct, clear and communicable conceptions"'. The following is a critique of Newton that Coleridge penned in 1817:

To me, I confess, Newton's positions, first, of a Ray of Light, as a physical synodical Individuum, secondly, that seven specific individua are co-existent (by what copula?) in this complex yet indivisible Ray; thirdly that the Prism is a mere mechanic Dissector of this Ray; and lastly, that Light, as the common result, is = confusion.

For those who find the above paragraph out of context, Coleridge was essentially opposed to Netwon's thesis that white light consists of seven component lights (which are essentially frequencies corresponding to violet, indigo, blue, green, yellow, orange and red) respectively and they are resolved on passing a ray through a prism. Coleridge had more radical ideas about the nature of colour,

So again, Colour is Gravitation under the power of Light, Yellow being the positive, blue the negative Pole, and Red the culmination or Equator; while Sound on the other hand is Light under the power or paramountcy of Gravitation.

Coleridge and Newton lived more than two hundred years ago. Perhaps, science and poetry were then luxuries that only the elite could afford. But as an individual who perpetually enjoys a healthy confluence between the two domains, I truly feel that obscurantism should be criticized. Romantics who choose science as a subject to write about should judiciously try to keep their language simple and avoid ambiguities. Mathematics and physics do not need to be exoticized to concoct poetry. The poetry is already there.

Pseudo-science and cosmic energy

I had read an article in TOI half a year ago in the "Speaking Tree" column which appears on the bottom right of the editorial page. Prior to that I never dispensed anything more than a perfunctory glance towards the column on usual days. There were a couple of times, however, when I had read the articles on my father's recommendation. They were personal accounts/anecdotes narrating spiritual awakening and I remember liking whatever I read. So when I was recommended this article by my father (who had been apprised of it by his uncle), I immediately got myself a copy of the paper and read it.

The article was titled, "In Divine Mathematics, Zero = One = Infinity" and I was naturally intrigued by the title. More importantly, I wanted to find out what 'divine mathematics' was in the first place; I was of the prior opinion that the queen of the sciences revealed herself in the same light, be it earth or heaven. The author of the article played around with some mathematical notions and arrived at some supposedly 'startling' conclusions that commensurated, he claimed, with the modern theory of numbers. With all humility, he acknowledged the genesis of these notions to Vedic scriptures towards the end of his essay. His writing was fluent and I found myself appreciating his ability to churn a sparkling prose. The mathematical reasoning, however, was completely flawed and I could not help but wonder how misinformed the author had been. I remember mentioning this to a friend but he chided me for my nitpicking, "Why does one have to read these things objectively. Why can you not regard them as pure contemplative exercises which seek to evoke existing notions in a different light?".

Sure, the pursuit of art and science have one thing in common. Both seek to rid our collective consciousness of the anesthetic of familiarity. The process is not sharp but extremely gradual where a wall is shattered brick by brick and a cubicle is slowly illuminated. This is especially true for poetry, which possesses a masterful capability to evoke and de-familiarize like few forms of art can. There exist so many emotions and thoughts that fail to find expression in our vocabulary and can be stimulated only through media like music and poetry. The following lines by William Blake have, for a long time, been my favorite and never fail to fill me with a sense of wonder whenever I read them:

To see a world in a grain of sand
And a heaven in a wild flower,
Hold infinity in the palm of your hand
And eternity in an hour.
- Auguries of Innocence (1803)

Mathematics and Physics are poetic in many respects. I remember being awestruck on being told as a little boy that the medians and altitudes of any triangle intersect in a single point. I remember being fascinated when I read quantum mechanics, whose notions are so perversely orthogonal to common sense (Richard Feynman is known to have said that someone who claims to understand quantum mechanics does not know it at all) but whose predictions have been vindicated in the real world to astonishing orders of accuracy. I am still coming to terms with whatever I learned in the Non-linear dynamics class I took this semester (The notion that a completely deterministic system can produce long term 'random' behaviour still puzzles me and I know of no philosophical reconciliation to this). Something is 'poetic' because it has this ability to illuminate the unknown even though it might not be able to 'explain' it. Nonetheless, be it the four lines of Blake or the consequences of a scientific theory like relativity, the feeling that one gets on confronting these is that of an unparalleled excitement.

For a extremely masterful exposition on how science can be poetic, I recommend Richard Dawkins', "Unweaving the Rainbow", a book that I shall finish reading by tonight (Unfortunately, many people who are known to me disliked Dawkins immensely after reading his recent book, "The God Delusion. However, polemical though he may be, I stress that this is a man who is worth listening to purely for his forthright honesty accompanied with a rare erudition in the things that he talks about).

My aim in this article, however, is different. The TOI article that I mentioned earlier is an example of what Dawkins refers to as 'bad poetic science'. In fact I would not even go as far as calling it by that name. The article did not contain a modicum of originality that could illuminate the reader; its style was systematically obscurantist like many other exotic commentaries on Hindu philosophy with a startling lack of concern for consistency and sensibility.

In heated wave of excitement, I drafted a critique of the article and promptly mailed it to TOI. A part of it appeared the next week in the newspaper. On retrospection I wasn't very happy with the tone of my mail. On hindsight I feel I was extremely caustic and irreverent even if my thesis was reasonable. When I happened to find it while clearing my mailbox today, some thoughts resurfaced. I have copy pasted the mail below.

I still believe that pseudo-science should be severely criticized. A vocation of precision leaves room for intuition but not hand waving incoherence. But the tone of the critique needs humility. Can one be a benevolent extremist? Some of my friends would disagree. The others would laugh and look the other way.

----------------------------------------------
Dear Sirs,

I do not regularly subscribe to your paper but I happened to lay my hands on the daily issue last Wednesday. I read the article “In Divine Mathematics, Zero = One = Infinity” and by the end of it, was not sure whether I was more amused or more irritated. The article seemed to me a second rate attempt to appeal to the puerile fantasies of many of us (educated) Indians who are infatuated with our scriptures to the point of delusion. As Arundhati Roy remarked in the ‘End of Imagination’, “One can find whatever one wants in the Vedas and the Puranas, so long as one knows what one’s looking for”. As a student of mathematics, who in all humility does not claim authority on the subject beyond the capacity of his limited intelligence, I was shaken by the masterpieces of illogical reasoning that the author puts forward in so facile a manner, perhaps because indiscreet reasoning is the only way one can arrive at some of the fantastic conclusions that he has arrived at. While it is certain that the author needs to retake his primary classes in elementary mathematics, I believe he can be absolved of the act of having his substandard logic published in the editorial section of a national newspaper. Before making an attempt at the English readers of this country, he has successfully mastered the art of self-deception. My knowledge of metaphysics is extremely limited but I know my math well and if I were to possibly imagine a healthy confluence between the two, this article would be the exact antithesis of the same. Though it is beyond my time and inclination to attempt a part-by-part dissection of the article, I shall mention 2-3 instances of extremely bad mathematical reasoning.

The first and foremost thing the author needs to read up is the classification of numbers on the line. Integers and fractions are not all. While I must remark that no student beyond her/his fourth grade would use the word ‘fractions’ (the term is ‘rational numbers’), there is another class of numbers on the number line beyond integers and ‘fractions’ called irrational numbers, which, certainly cannot be interpreted as ‘fractions’. The author is correct in mentioning that a ‘fraction’ is as good a nodal point on the number line as an ‘integer’ but where he errs is to deduce from this that every fraction is an integer! That every imaginable number is a nodal point on the number line does not make all numbers fall in the same class. Integers, rational and irrational numbers are subsets of a bigger class called real numbers. Then there is the class of complex numbers which along with real numbers form the set of all numbers that occur as solutions to algebraic equations. Integers, for instance, have their genesis in elementary counting. While all integers are expressible as fractions (20 = 20/1), all fractions are definitely not integers!

Then comes the experiment that he asks the reader to perform- I quote it verbatim here so as to facilitate a better analysis:

Take a sheet of paper. It is a whole: it is 1. Tear it in two halves. Each half is ½. This is only relative. Otherwise, each half is an independent whole, a one. How do you know that your original sheet of paper was not one half of something else? Likewise, if you tear the half sheets again into two, you get a total of four ones. This process can go on ad infinitum. In effect, you have created an infinite number of integers between 0 and 1. Your original sheet of paper – your original 1- is now infinity. Eka is Ananta!

Applause. Any person of average intelligence armed with a handful of logic would be able to discern that what author has demonstrated in the above ‘experiment’, as he likes to call it, is that any number is infinitely divisible. And certainly not “one=Infinity”, as the author glibly concludes. The total amount of paper (volume, mass however you may refer to it) is conserved (Personally I’d love to read the authors thoughts on Physics) and all subsequent divisions of the paper contain a fraction of the amount of paper in the original sheet. Yes, if you like, you may count these divisions as one, two, three,…ad infinitum. All this says that our notion of numbers is not dependent on the attributes of the physical object that they refer to. But that the whole is infinitely divisible is not equivalent to saying that the whole itself is infinity.

The first sentence of the next paragraph is my personal favourite in the monograph.

Likewise, zero can be understood as being one. How? 1=1/1 = 1/infinity=0. Inversely, 1/0 = infinity. This validates the equation we began with, 0 = 1 = infinity.

The great French mathematician, Fermat stated his last theorem but could not find place for his proof. It took mathematicians nearly 400 years to crack his problem. Personally I don’t think even eternity is enough to come to terms with the level of mathematical erudition that our author displays. What the author has done in 600 words is to make an attempt at thwarting the foundation of mathematical formalism and logic developed by minds certainly more judicious than his over a period of 2000 years. But what disturbs me is another associated fact. If he author would have published his masterpiece minus the references and allusions to the Vishnu Sahasranamam, he would have most certainly been classified a lunatic and been universally ridiculed. And my personal belief is that there is nothing wrong in that because our standards morals, ethics, logic and reasoning should be based on years of experience and not derived in a literalist manner from an antiquated text. These are historical texts which should be preserved and cherished as a part of our cultural heritage but most certainly should not be used as a source of legitimation of our whims and fancies. Let us explore our principles, values and ethics in a world where there is no heaven, hell, redemption, perdition or immortality to look forward to and that would be the highest form of vindication for the atman, if there is some such all pervasive being.

As a message to the editors, I would request them to follow discretion while publishing articles in this column, lest one year down the line “The Best of Speaking Tree” becomes a nationwide bestseller in the humour section of all bookstores.

Sincerely,
Karthik Shekhar

A sense of magnitude

" ...Fling your arms wide in an expansive gesture to span all of evolution from its origin at your left fingertip to today at your right fingertip. All the way across your midline to well past your right shoulder, life consists of nothing but bacteria. Many-celled, invertebrate life flowers somewhere around your right elbow. The dinosaurs originate at the middle of your right palm and go extinct around your last finger joint. The whole story of Homo erectus and our ancestors the Homo sapiens is contained in the thickness of one nail clipping. As for recorded history; as for the Sumerians, the Babylonians, the Jewish patriarchs, the dynasties of Pharaohs, the legions of Rome, the Christian Fathers, the Laws of Medes and Persians which never change; as for Troy and Greeks, Helen and Achilles and Agamemnon dead; as for Napolean and Hitler, the Beatles and Bill Clinton, they and everyone that new them are blown away in the dust from one light stroke of a nail file."

- From Richard Dawkins' "Unweaving the Rainbow"

Unmoved by those who suffer,
Unaffected by the chirping sparrow,
Inconsiderate of those below,
Oblivious to the plaintive roar
pleading its way through extinction.
We lead a life of characteristic immoderation,
with an anesthetic imperviousness,
an inability to notice and wonder.

-Anonymous