Book Review - Music of the Primes by Marcus du Sautoy (2003)

I can say, with some modesty, that I am familiar with the subject of mathematics more than an average person is. Despite that I hadn’t ever read a non-technical book on mathematics, so this book ended up being a very engrossing and a pleasant surprise. Marcus has done a tremendous job detailing history of search of the proof of Reimann Hypothes: interspersed with personal stories and personalities of mathematicians involved – one person at a time.

What is Reimann Hypothesis? I am not smart enough to explain, but I regurgitate what I gleaned from the book. As mathematicians are wont to do, they wanted to understand what and why certain numbers are prime and what is the distribution of prime numbers across number line. When that proved to be tad difficult of an endeavor, one of them decided to find pattern in number of prime numbers less than a certain number, say primes less than 100, prime less than 1000, and so on. There was some success in generating a formula for such counting (see later), but it wasn’t exact. Meanwhile when a mathematician B. Riemann decided to pass on complex numbers to simple looking Zeta function (1+1/2^n+1/3^n+…) in 1850s, he observed that values of  “n” for which function takes value of zero relate to counting of primes (I don’t understand how, though!). Moreover, he guessed that all such “n” have the real part of 1/2. This guess is the Riemann Hypothesis. Line passing through this point is called Reimann’s critical line.

Book gave me a fascinating glimpse into how theoretical mathematicians work and how does mathematics advance. They often work by posing ad-hoc puzzles (“what happens when kick a rotating sphere of liquid”), trying new mathematical operations on existing formulas or statistics on existing numbers (“taking moments of function”, “passing imaginary numbers to known equations”), looking for patterns and trying to find equation and explanation of those patterns, translating numbers and equations from one branch of math to another (“from numbers to graph”), trying to prove intuitions, and finally aiming for elegant, closed form solutions and formulas to problems. To an application oriented engineer, this was delightfully ridiculous – trying anything to anything and spending decades trying to make sense of it toward no immediately discernible end!

In doing so, mathematical properties sprout starting with educated guesses on observed patterns called ‘conjectures’. When supported by available data become, conjectures become ‘hypotheses’ which make a novel yet untested prediction. Hypotheses graduate to ‘theory’ when the non-trivial novel prediction comes true and proven mathematically, and eventually to ‘law’ when validated in multiple domains across time to multiple level of rigour with no scope for any further enhancement or exception.

Growth of mathematics is also, surprisingly, driven by friendly bets between prominent mathematicians. Bets, often of little material value, but taken seriously enough, are reason for many important advancements in the field. For instance, 100 million Reiman’s zeros were calculated by costing CPU processing in 1970s just to (dis)prove a bet! I wonder if this is true of other disciplines of science.

Till very recently before advent of internet, exchange of ideas through letters was usual form of brainstorming and communication among mathematicians. Yet, many also worked in isolation through their rough sketches never sharing ideas till they were comfortable of elegance of proof, or of not being challenged or ridiculed, or not wanting to share credit of their discovery too early! Consequently, the amount of knowledge, which is lost to humanity, because their family couldn’t comprehend the importance of scribbles in their papers when they died (and just threw away) is heart wrenchingly disappointing. Ramanujan’s and Reimann’s notes on having figured out proofs but couldn’t be bothered to write them out because they thought them trivial have costed mathematicians efforts of centuries.

Book underscores a unique manner of working of theoretical mathematicians – their rigorous reliance on proof. Unlike other spheres of science, where theoretical predictions are useless unless observed under experimentation, mathematicians are content with solid proof despite lack of observations, and as corollary, they still do want solid proof despite what would be overwhelming experimental observations in other sciences. And why is it so? Because math being math, incongruence with theory may occur even after trillions of observations – 10^10^10^34 is theoretical number when Gauss’sPrime Conjecture is proven false. Does it matter in practice, though? This reliance of solid theoretical proofs also means that proofs once established don’t change forever. While theory of gravity has been refined every century, mathematical proofs established from 1600s have stood test of time.

Role of computers is hinted on later parts of books, but it is aptly concluded that computer can only help in disproving a hypothesis by providing counter examples but cannot prove a hypothesis simply because any number of matching examples (evidence) don’t count and cannot constitute a proof.

Now let’s come to the personalities of mathematicians narrated in the book. If you imagine mathematicians to be hard working geniuses & nerds, you will not be wrong, on average. Like all geniuses, most of them show their signs before they turn ten. For instance, Gauss (of the Gaussian distribution) was correcting his father’s math at age of three where normal children do not know beyond counting. Most mathematicians are pacifists reveling in their own cocoon with little care or awareness of the rest of the world. Some were eccentric – for instance, G H Hardy, lived his life fighting with, tempting, and challenging God, with often comical outcome where he ended up believing in God to prove that he didn’t believe in Him.

Ramanujan’s level of genius is, of course, unfathomable. If partition number is defined as number of ways to partition N things (partition number of 3 is 3, of 4 is 5) then he literally dreamt up formula to calculate partition number of any N just in flashing insight without intermediate steps which included square root, pi, sum, mod, natural logarithm, integration, differentiation, imaginary number, and trigonometry! If not Namagiri Goddess, then how?!

Of course, there are sprinkling of revolutionaries, womanizers, and partygoers. While the book does reference tumults in the rest of world – world wars, famines, Nazi politics – and their impact on mathematicians, and hence on mathematics, they are not dwelled into more than mere mentions.

Incentives for theoretical mathematics are few and far (are they?) – most of them do this simply for the joy and, occasionally, for the fame within mathematician community. There is no Nobel Prize in math. The highest award, the Field Medal is given only once in four years for living mathematics under forty years of age and accompanies just CAD 15,000. Opportunities for commercialization are rare – though of course, cryptography and encryptions are important exceptions. Makes you wonder how cheap and easy to sponsor a prize in math and yet why hasn’t anyone done so?

While reading the book, I also realized that my level of thinking as commoner, despite my admissions in the opening line of this review, is closer to what mathematicians were doing 400 years ago. Hence, what mathematicians are doing today, reflected in the later chapters of the book, went completely over my head! Marcus has done excellent job in talking about mathematics without using mathematics, but I do feel that book can be slightly better by exposing readers to real math – say equations or screenshots of seminal papers – even with clear expectations that reader won’t understand. Else there is risk of getting too lost in analogies!

Search for Reimann Hypothesis has led to multiple discoveries and developments on the way, and in recent years even found a connection to Quantum Physics, where distance between consecutive Reimann Zeros is found to mimic distance between energy levels in atoms! Was this coincidence or some universal pattern? Being able to predict next number in moments of Reimann Zeta function by observed energy level of atoms confirmed this as a tangible connection. Not only is the universe stranger than we imagine, but it is also stranger than we can imagine!

Longevity of Reimann Hypothesis has given it an enigmatic status. Some mathematicians take this as challenge of ultimate proportion. Others shy away knowing that it may as well be the end of their careers. Many proofs in other areas of mathematics depend on Reimann Hypothesis being true. Will we ever prove this almost 200 hundred year old hypothesis? There were 300 million zeros discovered which follow Reimann Hypothesis – as of book’s writing in 2003 – and 10 trillion as of writing of this review, giving overwhelming evidence about its truth, but alas no solid conceptual proof exists yet (how Reimann Zeros look?). It’s even proved that there are many more zeros within an arbitrarily small band around critical line than outside, but that doesn’t prove that all zeros are on that line. It’s even proved that there are infinite zeros on the Reimann’s critical line, but that still doesn’t prove that all zeros are on that line.

Godel’s incompleteness theorem says that we cannot prove that same set of math axioms won’t lead to two different answers (contradictions), and there are going to be some true statements which cannot be proven. It’s amazing how mathematical logic can even prove such abstract generalized statements! A possible consequence of this is that Reimann’s Hypothesis may be one of those statements which cannot be proven. But mathematicians believe in elegance of solution and haven’t yet surrendered that such important hypothesis won’t have a proof.

A person like me who doesn't understand Reimaan Hypothesis, has no comprehension of its importance or role in the world, cannot even being to understand even after trying - and I did try, during and after this book, and still ended the book feeling the sadness one feels when one departs from a lovable character at the end of the book: feeling of parting the long journey and deep melancholic awareness that next chapter of that story may never come within my lifetime. This is the power of well told story written by Marcus du Sautoy.

***

Below are some noteworthy facts about Prime numbers and Reimann hypotheses which have nothing to do with the book review but elicited aha for me and documented just for fun.

• Number of primes up to number N is approximately 1/ln(2) + 1/ln(3) + … + 1/ln(N)
• Harmonic series, 1/n, is called so because pot filled with water up to 1, 1/2, 1/3, … levels produce harmonious sound but not at other levels!
• Mathematicians have created a 26 variable equation to generate all primes. This works when results are positive numbers, but most often, they are not.
• AT&T played key role in mathematical research, even as telephone company they had little applications for mathematics, but it was not purely altruistic behaviour towards science & humanity, but a commercial and public relation consideration since they had restrictions on how much profit to absorb because they were a monopoly.
• How to test if a number is Prime, without necessarily trying out all divisors? X^p=X(modulo p) only if p is Prime for any X. This is important to find keys for Public Key Cryptography.

Are four billion years not enough?

Concept of evolution of specie is really as complex to truly understand as easy it appears to understand. No wonders myths abound. I didn’t know, for example, that evolution doesn’t favour survival of the fittest specie but of the fittest gene. Or that, evolution neither guarantees nor ensures improvement in quality of life or quality of specie. Evolution doesn’t necessarily mean increase in complexity as well, despite what appears to be the case as we human see ourselves at bottom of tree of biological evolution. Evolutionary outcomes are also not necessarily global optima for its members. In language of Prisoner's Dilemma, while best strategy to ‘cooperate’ for both, evolutionary stable strategy would be to ‘defect’ for both.

Yet, theory of evolution is invoked many a times in explaining natural behaviour of any animal. Why do giraffes have long neck? Why do turtles have hard shell? Why did birds learn to fly? Why are human omnivore? Strange markings on the fish? Sounds of whale? Speed of tiger? And so on. You can think of, might have heard about, or can imagine evolutionary reason behind all this. Sometimes theory to so stretched so as to appear force-fitted. But most of the times, experts will confidently claim that the reasons giraffes have long necks is that, by chance of genetic mutation, those who ended up with longer necks had advantage in foraging leaves from tall trees, and hence could survive longer, and are able to pass on their genes ([1],[2],[3]). Such explanation is offered for any and every type of behaviour. I wonder, naturally.

Given enough time, if theory of evolution in current form is correct, any tiniest of difference can provide one gene higher survival than other, to the extent that other gene is no longer part of genetic pool of that specie. Given enough time, then, it seems natural that there should ultimately be only very-very few species that would prevail. If human have genetic advantage over gorilla, over time, only homo-sapiens should remain surviving specie. That’s how we are explained non-existent of pink tiger i.e. reason tiger have stripes. Yet, number and variety of species in existence has only been growing with time.

Does this mean that it’s merely matter of time? That four billion years of life on earth is insufficient for evolution of THE ONE specie? Perhaps. But what’s more important to understand if we are even moving in that direction? I don’t think so. Where lies my misunderstanding of evolution?

Edit 02/09/2011: Please read comments for discussion/clarification.

Used or pirated books

Last month I visited Churchgate in Mumbai and bought over 15 second-hand books from famous vendors at Flora Fountain. Around same time, I saw vendors selling pirated copies of popular books at Andheri station. Last week I found myself with a question to which I could find no answer. While I am stumped at stupidity of not realizing this earlier, answer has profound implication for me.

What is the difference when one buys second-hand books or pirated books? Aren’t they same to all relevant parties?

In both cases, neither publisher nor author gets any fee. In both cases, both publisher and author get credit and fame (since pirated books are printed exactly like original). In both cases, buyer pays less than original price of the book — which, of course, is not single number because retailers have different discount schemes. In both cases, middleman benefits from the sale — either a vendor of used books or publisher and seller of pirated books.

Yes, technically, there is a difference. A new book buyer buys book under proper license and credit. Once book becomes his property, he can sell it to anyone he deem fits. This buyer can re-sell it and so on. A publisher of pirated books steals the copyrighted content and sells to buyer. Yet, practically, if I have to chose between buying a second-hand and a pirated book, there is no difference. In both cases, creative talent is not rewarded and only middle facilitator benefits. Why should I be partial to profits of used book vendors while desisting profits of pirated books vendor? True that one stole and another legally purchased but they are but mere nuances since material impact to all concerned parties is exactly the same. It might be said that one is making an honest living while another is stealing (but who is the victim? Original author but only if only alternative is to buy new book, not used book).

This gets further compounded by the fact that used book vendors themselves are lot which don’t get much sympathy from buyers because of obsessive margins maintained by them (my guess, don’t jump on me for this). While buying second-hand books is perfectly acceptable commercial transaction in all societies of world, buying pirated is considered immoral and unethical. But if there is no difference between both, does buyer of pirated books need to feel guilty (if he does at all)?

This, of course, assumes that choice is between buying pirated and used books. Buying fresh new books is always better move, without doubt. This also assumes that feeling of reading original (without typos and poor print that typically occur in stolen material, though, it appears that quality of pirated books is increasing rapidly) book is not an issue with the reader.

I end this post with one plausible weak reason where buying pirated books could be worse than buying used books: people buy new books only to be able to sell them later. If this is plausible, then buying pirated reduces market for used books thus reducing re-selling ability of vendors and plummeting the sell price of original buyer. This disincentives the original buyer from buying new books and thus original author and publisher also suffer material loss and financial damage. This argument is weak because most book lovers who buy new books don’t buy because they intend to sell them (they might as well sell them but that is not reason of buying in the first place). They buy new books because they like the feeling of fresh crisp pages and smell of printed paper. They buy new books because they want to own and re-read the books and maintain a library. How many of first time buyers sell their books (not talking of textbooks in this post) anyway?

Unless I receive satisfactory response to my conundrum, I will be become more immune to guilt of buying pirated book (unless, of course, I plan to buy original one).

Hindi count approximation number pair

This post is based on Hindi colloquial/conversational number pairs used in approximating a quantity. Knowledge of colloquial Hindi is requisite.

Hindi conversational numbering follows Hindu-Arabic Decimal Number System with Hindi pronunciations. One (1) becomes Ek, Two (2) becomes Do, Three (3) becomes Teen and so on. When asked to approximate a quantifiable noun viz. in response to “how many minutes before the dad comes home?”, Hindi speakers often speak in number pairs such as Ek-Do (1-2). Not all pairs are acceptable and feel “right” when you say them aloud. This post will try to discern if there is a mathematical pattern in acceptable set of pairings.

Table: List (partial) of acceptable pairs

Pair	Type
1-2	Next
2-1	One
2-3	Next
2-4	Double, Next 2x
2-5	Plus 3
3-1	One
3-4	Next
4-1	One
4-5	Next
4-6	Next 2x
5-1	One
5-6	Next
5-10	Double, Next 5x
6-1	One
6-7	Next
7-1	One
7-8	Next
8-1	One
8-9	Next
8-10	Next 2x
9-1	One
9-10	Next
10-1	One
10-11	Next
10-12	Next 2x
10-15	Next 5x
10-20	Double, Next 10x
11-1	One
11-12	Next
12-1	One
12-13	Next
12-15	Plus 3
13-1	One
13-14	Next
14-1	One
14-15	Next
15-1	One
15-16	Next
15-20	Next 5x
16-1	One
16-17	Next
17-1	One
17-18	Next
18-1	One
18-19	Next
18-20	Next 2x
19-1	One
19-20	Next
20-1	One
20-21	Next
20-22	Next 2x
20-25	Next 5x
20-30	Next 10x
21-1	One
21-22	Next
22-1	One
22-23	Next
22-25	Plus 3
23-1	One
23-24	Next
24-1	One
24-25	Next
25-1	One
25-26	Next
25-30	Next 5x
25-50	Double
26-1	One
26-27	Next
27-1	One
27-28	Next
28-1	One
28-29	Next
28-30	Next 2x
29-1	One
29-30	Next
30-1	One
30-31	Next
30-32	Next 2x
30-35	Next 5x
30-40	Next 10x
31-1	One
31-32	Next
32-1	One
32-33	Next
32-35	Plus 3
33-1	One
33-34	Next
34-1	One
34-35	Next
35-1	One
35-36	Next
35-40	Next 5x
36-1	One
36-37	Next
37-1	One
37-38	Next
38-1	One
38-39	Next
39-1	One
39-40	Next
40-1	One
40-41	Next
40-42	Next 2x
40-45	Next 5x
40-50	Next 10x

After manual enumeration of all such pairs where first number is up to 40, we can observe following seven type of pairings:

1. Next: This is the most common type of pair in which each number is paired with next whole number following it.
2. One: This is the second most common type of pair in which each number is paired with number One, except, of course, number One itself.
3. Next 2x: Numbers 2, 4, 8, 10, 18, 20, 28, 30 and 40 pair with next number which is multiple of 2 i.e. next even number. Primarily, numbers ending in 0 seem to follow this pairing. There is temporary pairing of this type for numbers ending in 8 but this doesn’t continue long since after 38 this doesn’t work. 2 and 4 are obvious exceptions.
4. Plus 3: 2, 12, 22 and 32 seem to follow this type of pairing. Projecting further, it appears that all numbers ending in 2 would following this pairing.
5. Next 5x: 5, 10, 15, 20, 35 and 40 predictably follow pattern of paring with next number which is multiple of 5. These numbers themselves are multiple of 5 clearly following a pattern.
6. Next 10x: 10, 20, 30 and 40 again following pattern of pairing with next number which is multiple of 10 while themselves being multiple of 10.
7. Double: Numbers 2, 5, 10 and 25 pair with numbers twice them though 2, 5 and 10 be also be categorized to other pairing types which makes more sense. Projecting beyond 40, we see that while 50 doesn’t follow this pairing, 100, 150, 200, 500 do so. There doesn’t seem to be any identifiable pattern here.

I also tried to find pattern in sum, product and ratio of numbers in these pairs and in ratio of consecutive sums and consecutive products without success. Possibly, enumerating pairs after 40 may identify more types of pairings. What are your thoughts and observations?

(Peculiarity of such pairings have been in mind for quite many years but this post on Futility Closet — which, by the way, is a recommended read blog — propelled me to write this post.)

Thank-o-meter

Cultural differences between oriental and occidental societies are well known and expressing gratitude through explicit thanking is one such area of difference.

European and North American societies exhibit an all pervasive tendency to thank family, friends and strangers for the most trivial of the matters which grates Indians — or at least me — in two ways. One, it reduces act of thanking to mere perfunctory ritual rather than heartfelt recognition of gratitude received because it becomes difficult to recognize true thanking to courtesy thanking. Two, it embarrasses me to receive profuse thanking for task which I don’t consider worthy of gushing praise bestowed on me. One English colleague at my firm, for instance, once asked me for “a very very big favour” by asking me to explain her how many thousands were in a lakh. I am often at loss to even respond to such overwhelmed dose of expressed thanking.

Asian societies, on the contrary, are more cautious in thanking and when done, it is almost always to strangers. In fact, a good yardstick to measure how close one is in personal circle of thank-er is to notice for what and how often one is thanked. A close friend or family member never expects to be thanked and some even take offence at thanking. Even strangers are thanked for things more substantial than mere getting out of the way on footpath. This, naturally, comes out to West as rude and ungrateful behaviour.

Those of us educated and exposed to Western culture are pushing thanking in Indian social interaction to same extent. While thanking someone for efforts he put into helping you is desirable social mannerism, anything done in excess loses its meaning as happens on the other side of the Earth. What we need is moderate amount of thanking and thanking from heart for things for which thank-er is really thankful about. What we need is thank-o-meter™!

Thank-o-meter is each individual’s personal cumulative counter of thanks he received and thanks he gave throughout his life. Because thanking someone will decrement thank-o-meter reading, one would do so only when meant genuinely and when other’s effort are substantial enough and worthy of a thank. This will obviously increase value of thank to receiver as well. Because one will be able to thank only when he has positive balance of thanks, he will have to earn thanks through efforts before he can spend them.

Implementation of this scheme can only be undertaken by God for He only has such scalability and omniscience required for this project. Implementation details such as initial stock of thanks can be worked out. What may happen is that some miser may stop handing out thanks or some other start hoarding them. Thanking in return of cash gift would be equivalent to selling thank-o-meter readings. Humankind may end up deciding price of a efforts in units of thanks which will be function of demand (low during natural disaster) and supply (high during charity event) and may work much like today’s forex market (and can possibly be traded).

Rupees ten thousand per life, only

There was a news couple of days ago about a couple committing suicide along with two children and a neighbour because they couldn’t pay 50,000/- fine imposed by caste panchayat. While such locally imposed caste laws are bane of the society, what had me thinking was the meagre sum involved. Naturally, half-a-lakh rupees was not meagre for people concerned who couldn’t think of anything else but to kill themselves, but this is not large amount for many people like us. Well, not trivial enough to throw away, but trivial enough to save five human lives. I wondered if somehow one would have known about it before they decided to die, he could have saved them — and he need not be doing any charity.

What if I pay off their loan and in return they work for me for free for one full year? I will be paying 60,000 (+lodging+boarding) for five members (and three working adults) for 12 months thereby effectively paying 1700/- per month per person which is less than market rate for full time servant. This, of course, is win-win for both since however substandard their life would have been with me at subsistence wages, it is still better than alternative of death. Two questions come to my mind: how would have I known about it, and whether they would have accepted this proposal?

Second question is a tricky one. From my point of view, proposal is bargain for them because I’d be willing to work for free and easily for more than one year if alternative is suicide. However, once I pay the sum, there is no incentive for them to stick to their commitment however great generosity I might have bestowed upon them, except moral obligation and gratitude to the benefactor. Unfortunately, humans have horrible track record in honouring their commitments. Ideally, I’d expect them to be forever thankful to me, but practically, I’d have fears that they will rob my house and run away very next day I kept them. Somehow, that is all possible. This possibility, real in my mind, could be reason enough for me not to make that proposal in the first place, unless I am willing to forego the money without expecting any return. Such situations are not uncommon in Indian society where people dying of cold or hunger or inability to repay loans is regular news. A donation of 50/- could have saved that life, if only, donor and sufferer had known in advance.

Am I being paranoid? Do you think proposal would have been accepted? What are the risks?

Strange connections

When I tinker with my eyes, as in when I am trying to put on contact lenses, specially when it takes longer than usual and my eyes become watery, why does my nose start running too?

Why do I cough when digging in my ear using an ear stick?

Why does sneezing makes me momentarily deaf?

Why are there such strange connections between two unrelated parts of the body? What are other examples?

Edit 30/04/2010: See comments for some asnwers.

A classic love story

Like any love story, boy and girl are passionately in love with each other. Like any classic love story, their parents don’t approve of this.

I’ve seen it happen at least three times and I’ve heard about it about double the number of times and story is always the same. Parents do come around and accept the proposed nuptial after rounds of persuasion, cajoling and threatening — assuming that the couple didn’t choose to go ahead anyway, not at least right away. And Indian couple do attempt to bring families together for marriage because despite choosing to find their partner themselves, they still believe in marriage as relationship between two families. There is a catch, of course. One parent is the most difficult one to please: he is (almost) always father of the groom. Question is, why?

I don’t wonder why parents oppose love based or inter-caste unions. Answer is obvious, even if conservative and prejudiced. I do wonder, however, among four parents, why must it be father of the groom?

We can rule out two women quickly, because, as mothers they usually don't care for social rules over happiness of their wards. They might not like it — in fact, they might feel cheated of their right and dream to choose their daughter- or son-in-law — but they accept anyway. They might need to be persuaded but gentle stream of tears is enough to melt their hearts. They might be angry but that doesn’t stop them from blessing the couple.

Among the two gentlemen, though, debate becomes tougher. Girl’s father has many reasons to be angry. He is going to lose his reputation in the community if he gives away his daughter to another community. There is larger tag of shame on his name as his daughter rescinds his caste and joins another. There is a danger that his way of life may not prevail, that traditions will not be continued and that daughter might change her name and her habits to something despicable in his caste (viz. may cook, or worse, eat meat). Boy’s father, on the other hand, has less reasons to be antagonized. He is gaining a member to his community and symbolically winning over other caste by stealing its woman. His way of life and traditions are guaranteed to prevail. New member of the household may not be conversant with the traditions of his house but can be taught and moulded accordingly. So far, we’ve listed reasons to be affronted and found that girl’s father has more and hence must be more outraged. Why, then, the anomaly?

If we turn around and question who can afford to be angry we obtain different answer. This, clearly, must weigh more for we observe this. If couple elopes, then girl’s family suffers much more social dishonour than boy’s family. This risk defines who can afford to be offended and not who has reasons to be offended.

In all three cases, wedding was organized only by girl’s family and boy’s family boycotted it completely. Couple, after months and years of cajolery, had to give up trying to join two families. Some still hope: some day. Your take?

60 hours without food

More because I was bored and because I wanted to do something exciting with my body — I’d always imagined that I’d want to subject my body to limits such as starvation, thirst and exhaustion (not simultaneously) just to see what happens and whether I can do it, particularly after reading days long hunger strikes of popular leaders — than really intending to lose weight, I decided to go on crash diet for three days. I chose a simple one: only warm water with honey and lemon for three days and nothing more. I eventually didn’t continue third days but not because I was feeling hungry or weak. In fact, my experiment surprised myself so much that I didn’t feel any particularly different that I delayed writing about it so far, because, there wasn’t anything to write about.

After a moderate dinner night before, I went through first day on 4-5 helpings of water+honey combos without feeling much twist in my stomach. After momentary hunger pang at lunch time, which I would have felt any other day as well when I delayed my lunch, I was perfectly okay well up to the night. That night, I did feel little difficulty in falling asleep and my stomach kept me awake for one hour before letting me slip in to land of dreams. Next day, surprisingly, was better. I went through whole day without as much as pang of hunger and had a peaceful sleep the next night too. I could have easily continued for the third day, or even longer, before my body starts giving hints of starvation, but I didn’t. Particularly because I knew getting back to routine would take time and I didn’t want my first meal to be on work day (Monday) where my luncheon menu is less healthy and beyond my control. My break-fast was light, as required, and by the dinner time I was back to my original routine. My physical activities during past two days were normal and didn’t include huge acts of physical exertion.

Only thing this experiment has taught me is that I feel no difficulty in not eating for two days straight and that I should try even longer time frame next time if I really wanted to stretch limits of my body.

Gazillion Pillows

Room I was staying in Holiday Inn in London had to undergo renovation. So I was upgraded — so I was told — to better room. This room was exactly same as the one before, except that now I had eight pillows on my double bed rather than two. When I went to sleep, I just threw down seven of them on the floor. Why would anyone need so many of them was perplexing. I was reminded of this the other day when reading this article:

One might think that beds are made for sleeping in, but they’d be wrong. Apparently, unbeknownst to men everywhere, beds are in fact made to hold as many pillows as possible. Only a fraction of the pillows present are actually functional at any given point in time, while the rest are there for some unstated purpose. Sleeping on the bed requires several minutes of relocating pillows to suitable locations, which of course will be designated by the woman who placed them to begin with.

I can imagine need for second pillow for those who like to cuddle with pillow when sleeping or need an extra prop support when sitting. My creativity runs out when envisaging need for third pillow or more.

On airline safety

Perhaps the most embarrassing part of the job of a flight attendant is safety announcements. If a well draped, polished executive who is about to deliver keynote speech at podium is asked to recite ‘twinkle-twinkle’ before he can begin, that is how he would feel. This awkwardness multiplies because, one, nobody in audience pays attention, and second, they have to do it twice in Hindi and English, both. Their lackadaisical gestures are far too easily noticeable when drained steward or stewardess mechanically goes through the motions. I often dream about final exam of flight attendant’s school necessarily having a question on steps of safety demonstration. From what I’ve observed, stewards are more uninterested than stewardesses in moving their hands more than a foot away from their bodies. So routine this routine has become that process has lost its very purpose — for I believe that first time flyer will find these instructions too fast and too limited. It’s another matter that even after numerous flying miles, I am still not sure if I can find my safety jacket beneath my seat.

This brings me to the second point. Why must these instructions be relayed live? Most airlines, even those who have personal entertainment screen for every seat, conduct these announcements live: narrated by an on-board attendant and demonstrated by other attendants. I would imagine that having a tape recorder with instructions to be played could be simplest thing to have. If inbuilt tape recorder is expensive proposition requiring rewiring of aircraft’s public announcement system, I can imagine a steward playing a pocket tape into the microphone. Of course, alternative thought suggests that once in-flight crew is on board, they might as well do something to keep themselves busy.

Third point on this topic is about requirement of doing so at all. Surely, Government of India guidelines specify wording of instructions and usage of two languages*, but must those be followed to the letter? Could their be an AAI or DGCA official sitting in plainclothes among traveller who’d report the violation? Or perhaps the penalty of violation is large enough to dissuade airlines from taking any chances at all. Then there is something-to-do reasoning, again.

*God bless them for continued Hindi usage, for if left to airline and airport staff only, Hindi would completely disappear as it did from shopping complexes — richness often being irrevocably associated with usage of English and abandonment of National language. Note that any announcement which is not part of required announcement is only relayed in English, chief among them being Captain’s mid-air flight summary.

Riding on a moving platform

Sometimes I have to ride standing up. Short travel from airport departure gate to airplane and in local bus and train journey necessitates me to ride on a moving platform standing up. Such rides are not always smooth, even after ignoring the bumps on the road, force of acceleration, deceleration and curvature throws off the person with weak support. Hence, to stabilize myself, I need to hold on to handrails or handlebars. One point support at top end of my body frame doesn’t provide me full steadiness and unless I have something to hold on to at my waist level by other hand, my posture is not firm. Such horizontal support is not easy to come by, particularly if there is paucity of handrails compared to people, if I am holding some piece of luggage with my other hand, or if I am lodged in the middle of crowded vehicle away from walled boundaries of said platform.

At such moments, which are far too common, I must brace myself using my feet. Knowing that bending moment of a cross section is function of cube of the height and of only width, I position my both feet in L shape so as to provide me maximum moment of inertia on two perpendicular direction. Any force of jolt from any direction can be adequately born by two mutually perpendicular frames of my leg by splitting the component of force along two axis defined by L shape. At least, this is hoped. On many such occasions, I observe position of feet of co-passengers and find no apparent logic or system to buttress against the swing of turning or stopping.

Irony of the matter is that despite my posture based on solid grounds of physics and dynamics, I’ve found myself more vulnerable to jerks compared to other people who exhibit no visible support better than me.

Unimpressed by magic

I’ve seen magic shows (live, on TV, on web) and I’ve read about them. Because they are magic shows, they are, well, magical and unbelievable. Some stuff just seems impossible, but being magical, is shown to be possible. I’ve read about people being handcuffed and locked in multiple iron boxes and thrown in sea and come out free as a bird few hours later. This is quite unbelievable and more magical than tricks on stage because you don’t have access to equipment and stage itself. I’ve seen people in audience dropping their jaw and going ‘wow’ over magic. I’ve found myself interestingly amused but not blown over. Why?

For first, I am convinced that there is some trick to magic so it’s not real magic but merely an illusion. It’s not a momentous insight but this knowledge doesn’t let me really get into magic because part of being blown over is to believe it as real. Second, being aware that trickery is being performed, and being aware that I don’t know what is it, implies ignorance on my part which is not something I am impressed by. Magic, thus, is thrown in category of things-unexplained-yet-but-there-is-explanation-somewhere-that-i-don’t-know-yet along with God, black holes and what women want. These are the things I am fascinated by but not awestruck by.

What gets me going is though the explanation behind magical tricks. That, of course, is not easy to come by. I’ve read workings of trivial magical tricks in books and on web and seen some of those in movie The Prestige (which is a must watch movie, by the way). A double layered milk bottle which when turned upside down drains its little quantity of milk into oversized bottle stopper thus creating a illusion of whole bottle worth of milk disappearing is simple yet impressive trick for me.

Genius which creates illusion which blows over masses and confuses prowess of brain is worthy of my true admiration, and not it’s creation.

Edit 20/03/2010: Explanation of one of truely amazing tricks:

Anticipatory pleasures

Among the things I like to eat, there are some things I start missing if I’ve not had them for many days. Rich chocolate cake, pizza, turai sabzi, daal-baati and Subway™ sandwich are some such examples. When faced with opportunity of consuming them, I develop irresistible urge to savour the object of desire. I often succumb to my urge. What is surprising to me is the fact that I end up enjoying them mere okay and not become as ecstatic as I thought I would be after eating them. Even more surprising fact that despite my less than extraordinary experience this time, I will once again start missing same things and cycle will continue.

Why does my mind plays such tricks on me? Do my expectations always overshadow my real experiences? If so, why don’t my expectations decrease next time? Am I tough nut to please? Am I subconsciously enjoying them? Is there such thing as subconscious enjoyment of eatables?

It seems that only way for me to enjoy what I enjoy is not to really enjoy it but only anticipate the enjoyment the enjoyable object will bring.

Lovers are, Love isn’t

Different, that is.

Each person is unique in the world. Each has a life story to tell which, in hands of good writer, has potential to engage other humans emotionally. It is too bad that world doesn’t have enough storytellers to tell about experiences, feelings, fears and ambitions of every person on earth*. My belief is that however intellectual we may be, we, as humans, love to read about personal lives of others. Personal life in sense of personal triumphs and misfortunes, escapades and coincidences, and not just dirty laundry of others.

Two individuals in love are, however compatible, very distinct entities. Each love affair in the world has a unique story, driven by uniqueness of both of their characters and circumstances. Starting from the “how did they meet” to “till death do them apart”, each couple has potential to tell a mesmerizing tale. Yet, love that binds them is not all that different. Feelings of love are uncannily similar across the world. Actions based on those feelings may differ based on individual persona and means but desires and wants are surprisingly universal. Why else would otherwise every romantic poem seems to appear to a forlorn lover written exclusive for him? Hindi music, with it predominantly romantic musicals, has ample melodies to suit every occasion of lovers’ relationship, and it appeals to them at very personal level. It would be natural to expect something unique between them but they will probably find that hormones which run (or ruin?) their lives aren’t all that much different from other people.

We all are puppets of our genetics.

*Though, one can question that who will read trillions of books?

Accounting disposition

A set of roommates often find need for a system to keep accounts of their common expenses*. That much is no news. What, however, I’ve found interesting in my journey across different sets is that manners of doing that, and how much it relates to their mental disposition.

At MIT, a hard core technocrat institution, me and my roommates had developed a cross-platform programming language based tool residing on intranet which would read input from text files or command line and produce outputs on text file or screen. Any of us could use that independently.

At, Los Angeles, where my roommates were of eclectic background, a simple Excel based model would serve the purpose. On the other hand, my brother tells me that they — bunch of software and hardware engineers — use an web-based utility which supports multiple login to same account to collaborate their expenses online.

In my dormitory at IIM, partially because of recently undergone course of Excel and VBA, I introduced an Excel based binary matrix system, which would let one person collate and distribute expenses in transparent manner.

My current roommates, most from IIMs, most from engineering background, however, use a simple pen on paper system to keep account, largely driven by one economist’s resistance to move to more automated and transparent versions such as Google Docs.

It is surprising that, while in India student hardly ever choose their career because of real disposition to any particular field, their temperament is irreversibly altered after having gone through years of study in their field.

*For those unfamiliar with this: input of system is collection of expenses distributable across roommates and output is netted required transfer amount. For example, if A paid Rs.10 for supplies of common use between A and B but not C, then system should tell net transfer of Rs.5 from B to A.

Looking for a blogger who is…

Blogs are the windows to the world of people of the world. Despite how many persons you have met, each new one has an amazing story to tell. Each new one is unique character. Each has something to teach you. Yet, not many know the way to tell this story and hence most blogs become uninteresting. Blogs have opened my world to people I could never have dreamt of knowing thoughts of: celebrities, scientists, journalists, politicians, expatriates and students of various backgrounds and interest. More importantly though, blogs have introduced me to minds of as unreachable people as a porn store clerk, a call girl, a barista, a teacher and a custom officer. Yet, there is no doubt that blogosphere doesn’t represent all the variety in the world and is overwhelmed by software engineers and students. Sometime I wish I could read what goes on in mind of…

• A postman
• A soldier
• A policeman
• A bus conductor
• A retail shopkeeper
• A chef
• A traffic constable
• An airhostess
• A pilot
• A sailor
• A PSU clerk
• A train driver
• …

List could be endless because idea is to peek in minds of people of interesting and varying occupation. I would like to know about their feelings, their world and their opinion of their interaction with others. Do you know any blogger who has uncommon profession and interesting blog?

Why do we like Music?

I am surprised at myself that it took me so long to ask this question. While attending a instrumental performance the other day, it occurred to me that I don’t know what makes people like music? Turns out, as it should be, I am not alone in asking the question. No one, though, knows the answer.

Primitive human must have heard music in his environment in form of songs of birds, fall of waterfall, running of horses, and so on. A rhythmic repetitive sound is considered music. Early human must have liked it and sometime would have started making his own music using stones and woods. Some speculate that rhythmic heartbeat of mother’s heart initiates association of pleasure with music. Here is a very detailed speculative argument for it, which, in essence, says that faster heartbeat during rage and excitement and smoother heart beat during rest and peace are beginning of our association of music with those kinds of emotions. Modern science has proven that listening music affects our emotions and moods though release of various hormones. Could that be the reason for our love of music, that we want to feel emotional? Perhaps we intentionally prefer a music which psychologically alters our physiological state of mind.

You can find enough research on why brain likes music: it does because it makes brain feel good. None of it answers the fundamental question that why music makes brain feel good. Why do pleasurable hormones secrete when listening to favourite melody? Why did we became such that we like music? Whales and Dolphins are known to sing but do they really sing or their communication is interpreted as singing by humans? There is some evidence that other animals and even plants enjoy music. Plants are thought to grow faster when exposed to pleasing music everyday. Is definition of music universal in that do animal consider music what humans consider music? Clearly there are cultural differences among humans themselves in their preferences, but question is not whether one likes a music but whether one understands a series of sounds as music. Or perhaps it is mere perfunctory to classify some sounds as music and all sound is music some of which we, as humans, like and some we don’t. Was there evolutionary advantage to type of human who could appreciate and enjoy music, or is it mere side effect of some other evolutionary useful trait?

Some sounds are considered pleasing while others are not. Origin of some is perhaps related to environment around us. Screeching of crows in irritating while singing of cuckoo is soothing, and hence our music grew to incorporate later. But not all tunes can be traced back to nature, so what makes one set of sounds pleasing than others? Here is another blogger asking the very question and his thoughts parallel mine very much (recommended read). I leave you with this paper which goes a little deep but still fails to answer the basic question. Natural extension of this question is why do we like art (picture, dance, painting…) in general?

Temporarily dead aka asleep

It doesn’t incite concern for it’s part of daily life. Yet, if one were to think about it, sleep is a very strange phenomenon. Being asleep is closest one could get to experiencing death and being able to wake up to tell about it. Is it not strange that every day we are overcome by stupor which necessitates us to stop doing whatever we do and just fall unconscious: vulnerably and helplessly? Is it not terrifying that we completely lose passage of time and awareness of our surrounding when we are sleeping? How long eight hours pass in a instant and we don’t even have a clue where our life went then? Would you not be paranoid if you didn’t know what happened with you for those odd hours beyond your own control? This Onion articles tells it as it is. We’d be petrified if not for the fact that it is talking about night and sleeping. Yet, we don’t really think about it at all. Except, when an stranger from alien land displays shock about this strange habits of humans (and other species) and our nonchalance about it, as it did in a small story by Isaac Asimov.

Science has been proving that sleep is very useful for our body. It is so important, in fact, that you would die earlier if you didn’t sleep than if you didn’t eat. It helps us relax our body machine. It helps us digest (notice sour burps after long sleeplessness). It helps process and organize memories (lack of sleep results in loss of memory). It helps repair and maintain our body cells damaged during the day. Sleep occurs in roughly 90 minutes cycles of regular sleep and Rapid Eye Movement (REM) sleep. Brain repairs body in regular cycle and itself in REM cycle, where we are in very deep sleep. An opinion on internet suggests that if we sleep in multiples of 90 minutes, we may be able to avoid groggy eyes and wake up cheerful even after shorter sleep. There is no scientific confirmation of this. We know what sleep does, but we still don’t know why and how.

Why would sleep evolve through Darwinian evolution? What advantage could an being immovable, unaware and vulnerable over hours  had over those who didn’t sleep? Intuitively, it fails logic. An specie which learned to sleep will soon be devoured by predators even if other which didn’t is slow or stupid (some links* on the topic). Yet, most animal species sleep, indicating that development of sleep must have occurred long ago in evolution tree.

What science hasn’t understood completely, and what has huge implication of our society, is the frequency of sleep. It somehow came to be understood that sleeping once a day during night is the right way. Modern biology has even told us about the required length for good sleep. Most of it is driven by industrial revolution and non-agrarian societies. However, what remains unexplored, is if sleeping twice a day for equal duration or any other combination of duration might work better. People have different personal experience on this one but I find that an hour nap in afternoon increases productivity of rest of day significantly. On a fanciful note, I had always wished that we had capacity to store sleep upfront when there is much time for later when there isn’t enough.

Next time when you hit the sack do ponder over our very little understanding of such an important and obscure phenomenon.

*This argument seems invalid to me because as Richard Dawkins tells in The Selfish Gene, it’s not survival of the fittest specie that is aimed towards by evolution but survival of the fittest gene.

Concept of Nation State

Increasingly, we all are tolerant of differences within our country. A person from whichever corner of India finds welcome, at least in theory, in any other corner of India. Laws make it easy to move, to work and to settle wherever one wants. Such intra-country freedom is common in most other countries. What we are still fiercely protective about are our national borders. Somehow, barbed wire fences there attach so much meaning that killing and dying for them is considered laudatory whereas doing same for borders within the nation is considered ridiculous and dangerously divisive.

Will there come a time where concept of nation state will dissolve to permit real global citizenship? It seems impossible. Despite our acceptance of different cultures, nationalities and races, country still gets number one priority spot in our loyalties (after family and clan, for some). One would rather save one life in his own country than ten in other. Yet, this distinction stops within different states in a country. A geography under highest government is expected to be inclusive. Will it be possible to have one government for the world in future? This is mere hypothetical question but it will mean that policies will be designed for overall welfare of humankind rather than that of citizens of a particular nation at any cost to other people in the world. Will it ever be understood that all lives are really equal? What will it do to idea of patriotism which will be a defunct concept then.

These are thoughts I never harboured or had inkling about until that day about four years ago when I happened to meet this women at AID’s picnic. She strongly championed elimination of concept of nation state and questioned my views on patriotism. I am not really sure where I stand but idea has been fascinating enough to stick with me this long.