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.

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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