January 2010


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The author is so passionate about running that he says in the preface that

“Writing honestly about running and writing honestly about myself are one and the same thing. So I suppose its all right to read this as a kind of memoir centered on the act of running”

So, in that sense , this book is about a person who is deeply immersed in writing and running that he finds both the activities to be contemplative, meditative acts that ultimately reflects his life.Isn’t it true that whenever we do any activity over a long period of time, the process and the results reflect what we are.

From a hacker’s point of view, If you have looked at source codes of other programmers, you can easily see various personalities emerging out of the code. Inevitable personality traits like impatience , persistence, terse, boorishness, diligence, recklessness, brashness etc are evident by carefully looking at let’s say about 200 lines of code. However very few of us would however take the effort to express themselves through the work they do. It is not necessary also to always express one self through a piece of work. But somehow, the best works of art, best software written , best movies made, some of the best sportsmen in the world always leave their personality in the work they do. Well, I am way way digressing from the intent of the post.

I will try to summarize some of the points that I found interesting in the way they are written :

  • Pain is inevitable, Suffering is Optional
  • I stop everyday right at the point where I feel I can write more. Do that, and the next day’s work goes surprisingly smoothly. (Ernest Hemingway is supposed of have used this trick to be in the rhythm).
  • Most ordinary runners are motivated by an individual goal , more than anything; namely , a time they want to beat. As long as he can beat that time, a runner will feel he’s accomplished what he set out to do, and if he can’t , then he’ll feel he hasn’t. Even if he doesn’t break the time he’d hoped for, as long as he has the sense of satisfaction at having done his very best – and possibly, having made some significant discovery about himself in the process – then that itself is an accomplishment, a positive feeling he can carry over to the next race
  • A writer has a quiet, inner motivation and doesn’t seek validation in the outwardly visible
  • In long distance running, the only opponent you have to beat is yourself, the way you used to be
  • I’m the kind of person who likes to be by himself. To put a finer point on it, I’m the type of person who doesn’t find it painful to be alone. I find spending an hour or two every day running alone, not speaking to anyone, as well as four to five hours alone at my desk to be neither difficult not boring.
  • As I run , I don’t think of anything worth mentioning. (Its a kind of meditative act)
  • In certain areas of life, I actively seek solitude. Especially in my line of work , Solitude is an inevitable circumstance
  • When I’m criticized unjustly, or when someone I’m sure will understand me doesn’t, I go for running for a little longer than usual. By running longer, its like I can physically exhaust that portion of my discontent. It also makes me realize how weak I am.
  • If concentration is the process of just holding your breath, endurance is the art of slowly, quietly breathing at the same time you’re storing air in your lungs.Unless you can find a balance between both, it’ll be difficult to write novels professionally over a long time. Continuing to breathe while you hold your breath.
  • the great mystery writer Raymond Chandler once confessed that even if he didn’t write anything, he made sure he sat down at his desk every single day and concentrated. I understand the purpose behind his doing this.This is the way Chandler gave himself the physical stamina a professional writer needs, quietly strengthening his willpower. This sort of daily training was indispensable to him.
  • Most of what I know about writing I’ve learned through running every day. These are practical, physical lessons. How much can I push myself? How much rest is appropriate—and how much is too much? How far can I take something and still keep it decent and consistent? When does it become narrow-minded and inflexible? How much should I be aware of the world outside, and how much should I focus on my inner world? To what extent should I be confident in my abilities, and when should I start doubting myself? I know that if I hadn’t become a long-distance runner when I became a novelist, my work would have been vastly different. How different? Hard to say. But something would have definitely been different.
  • Exerting yourself to the fullest within your individual limits: that’s the essence of running, and a metaphor for life—and for me, for writing as well. I believe many runners would agree.
  • Muscles are hard to get and easy to lose. Fat is easy to get and hard to lose.
  • It’s pretty thin, the wall separating healthy confidence and unhealthy pride.
  • The most important thing we ever learn at school is the fact that the most important things can’t be learned at school.
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This is the first time I am struggling to write anything about the book I have read.This book explores themes in a very complex way. The author plays with opposites, heaviness and lightness, life and death , god and atheism, love and hate etc. These themes are explored from the lives of the characters in the novel , Tomas, Sabina, Teresa, Frez . Relationships with god, wife, mistress, country, animals are explored through out the novel in “opposites”.

For all the complexities in the book, I could not put the book down since I started reading it last evening.

One who likes exploring the opposites that come up in life would find Kundera’s book very engaging. I think this book needs to be read at least a couple of times to understand completely the author’s intent.

 

Image by Image Paul J Nahim

This is a fascinating story of i , popularly known to most of us as square root of -1 . In the first part of the book, author, Paul J Nahin , takes you through stories of various mathematicians who struggled and contributed to the understanding of sqrt(-1) . Subsequent to this historical narrative, the author provides a lens in to viewing things from a complex domain. Like they say, the easiest path from one point to another in the real world is through a complex plane, Complex numbers are used almost in every discipline you can think…

Some of the areas where I have come across usage of complex numbers in my limited exposure to things are

  • Econometrics : most of the filtering concepts in time series involves extensive use of complex numbers.
  • Algebra : Finding roots of nth order polynomial equation which usually arise from pth order auto regressive processes
  • Basic Probability : Characteristic functions extensively use complex domain
  • Fourier Transform computations become easy by taking them in to the complex space

Basically , before I read this book, my view was that complex numbers, complex theory etc..were nice tools to do quick integration, verify trigonometric identities, root finding etc. However the book changed the way I think about complex numbers . Complex domain is actually a way to see things . If one restricts its usage as a tool, well, that’s all one gets out of it. But if you use it as a lens to see a problem , as the book powerfully argues, it is going to be of considerable use to most of us. I am yet to use in that sense of the term but the book does motivate me to go in that direction.

Ok, now for the first part of the book where the author gives a superb historical narrative:


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CHAPTER 1 : The Puzzles of imaginary numbers

Image Heron of Alexandria : A Greek mathematician was one of the first persons who came very close to stumbling on square root of a negative number. In his calculations of truncated square pyramid, the slant height of the pyramid was expressed as a formula and it clearly showed that for specific values of edge lengths and volume, the slant height can throw up square root of negative number. However, as history has witnessed, Heron seemed to have fudged his formula to avoid sqrt(-1). He came so close to seeing sqrt(-1) but let it slip by

Image(c.214 – c.280) Diophantus who is kind of father of algebra, also saw sqrt(-1) in the calculations for roots but dismissed them as impossible solutions.

Image del Ferro : An Italian mathematician who was the first to solve the depressed cube equation( x^3 + p*x = q). His ingenuity in problem solving made him find a closed form solution for the depressed cube. The formula like Heron’s formula had a possibility of sqrt(-ve number) but del Ferro by imposing constraints on p and q avoided such situations. Also, mathematicians around his era were considered with only the positive root. The unique thing about this story is that delFerro did not reveal his secret until his dying moment when he told to his student Antonio Maria For.

Image Niccolo’ Fontana(Tartaglia) : A self taught mathematician who solved different versions of cubic equations. An interesting story about Antonio Maria For and Tartaglia is where the former challenges the latter on a mathematical duel ( spectator events of those times) and loses badly. Tartaglia also keeps the whole thing secret until he discloses it to Cardano

Image Girolamo Cardano(1501-76) : Cardano improvised on the del Ferro’s solution and came up with a solution for the generic cubic equation. However in the process of discovery, Cardano realized that square root of negative numbers were appearing everywhere and by working with them , instead of discarding them,he found that the combination of sqrt(-ve) numbers were actually giving out real roots.

Image Rafael Bombelli was the first person to see that if the sum of expressions which involve square root of -ve numbers is a REAL number , then each of individual elements should be conjugates of the other. A brilliant insight in the hindsight (a+i*b) + (a-i*b) = real ).

ImageFrancois Viète solved the cubic using trigonometry. His solution to the cubics was in arc cosine and cosine form. By the very definition of arc cos involved in the formula, the domain of the possible solutions is restricted to real line.

In the entire history that’s mentioned in this chapter, Bombelli stands out as he provided the critical breakthrough of WORKING with sqrt(-1).

In author’s words ” Bombelli’s insight in to the nature of Cardan formula in the irreducible case broke the mental logjam concerning sqrt(-1). With his work, it became clear that manipulating sqrt(-1) using ordinary rules of arithmetic leads to perfectly correct results”

Yes, it is not the usual way that schools teach us , sqrt(-1) is the solution for x^2 + 1 = 0 …. square equations had nothing to do with the evolution of i. It is the cubic equations that led to the development of complex numbers .

The highlight of the first chapter is a method illustrated to find the complex roots using a ruler. Read this section of the book ..It rocks!


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CHAPTER 2 : First try at Understanding the geometry of sqrt(-1)

Image Rene Descartes was a pioneer in the field of Geometry and other domains. He dismissed sqrt(-1) by saying that it was a geometrical impossibility

Image John Wallis came close to stumbling to the aspect that i could be related to a movement in the vertical direction but he did not actually develop that specific thought and explored.

Thus the geometrical world was still skeptical about sqrt(-1) as they did not any real world interpretation of the imaginary number.


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CHAPTER 3 : The Puzzles Start to Clear

Image Caspar Wessel : A cartographer by profession, his work got him involved in math and finally he discovered something which stumbled eminent mathematicians prior to his life time. What was Wessel’s contribution. He represented numbers in polar form and introduced the concept of rotation operator. He was the first person to actually organize things relating to the geometric behavior of i. However he never publicized it.

Image Jean-Robert Argand : Another person who was not trained formally in math, but gave the world a geometric representation of A+ iB

Image Hamilton : He was a mathematician who was not interested in the geometric narrative and instead developed couples (a,b) representing a+ib and formulated rules and methods revolving couples

Image Gauss : He gave the stamp of authority to Hamilton’s method and thus i became an acceptable notion in the field of mathematics.


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CHAPTER 4&5 : Using Complex Numbers

The next 2 chapters give an array of applications of complex numbers, some of which are

  • Using to solve recurrence relations
  • Applications in vector algebra by treating complex numbers in the argand plane
  • Usage in Electrical engineering
  • Astronomy , more specifically using Kepler’s laws as example
  • Transforming problems in to argand space to solve optimization problems
  • Story of sqrt(-1) in an electrical circuit was the first design for a multi billion dollar company today, HP

 


 

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CHAPTER 6 : Wizard Mathematics

This chapter is about Euler .

ImageI never knew that Euler , one of the best mathematicians that world has seen till date, was blind in the last seventeen years of his life. It is said that Euler did monstrous calculations in his head.

We all come across Euler when we see the equation exp(ix) = cos(x)+ i sin(x) . Euler’s brilliance was in connecting exponentials and complex numbers. He didn’t stop there. He published Euler’s constant gamma(nth partial sum of S1 – ln(n) as n approaches infinity) which equals 0.577215664…. , one of the universally popular constants, besides the popular pi , e, g etc. What’s the connection between this fact and complex numbers. Euler used his identity to prove the convergence of Sp where p is even. Till this date no one has ever figure out the solution for p = odd.

You can’t read this part of the book with out pen and paper as it has a lot of identities and history behind those identities that you would actually want to work them out yourselves to see the beauty of complex numbers.


 

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CHAPTER 7 : Complex Function Theory

The last chapter obviously takes the complex numbers to the next level of complexity 🙂 , functions of complex numbers. Author gives a very basic introduction to contour integration , cuchy’s theorems , greene’s theorem etc. The last chapter is very technical but contains interesting bits of historical narrative. So, one can gloss over the theorems etc to get an overall picture about complex function theory.


 

ImageTakeaways:

The book starts off with a good narrative and becomes progressively more technical. So, one really can’t describe it as a non-fiction book nor can one describe this book as a textbook. I guess its a good primer for people who want to know about complex numbers. Yes, this definitely falls under “reading around the subject” category which will motivate a person to dig deeper in to the concepts , workings and the application of complex number theory in their respective domains. Personally I loved the narrative part described in the first part of the book. Applications of Complex numbers in finance which is immediately relevant to my job, well , it is a looooong way to go , before I can connect things from different domains and implement something useful out of it.

Another takeaway from reading the historical narrative is that, one can’t miss the point that most path breaking discoveries and techniques came from people who were not formally trained in mathematics ,but by people who had a passion for math. It will be interesting to compare these developments in today’s context , where formally trained Math PhDs are spreading their wings and working on areas in various disciplines, finance, biotech, nanotech, internet search technologies, analytics etc. What developments will we see in the next 25 years ?

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Non-technical books by doctors are rare , and amongst them, “hard to put down” books , are extremely rare.

A view on performance by a doctor is always a nice read, for you would want to know, the variables that a doc attributes to the success. For whatever I have known about doctors, mainly anecdotal, I have the following impression :

  • Doctors need to have excellent PR to succeed , besides the skill sets which are kind of default in any doc
  • Its more touchy feely thing that makes you choose a specific doctor. You need not always judge a doc by the medicine he/she gives.
  • Doctors need to constantly update their knowledge about whatever domain they are working in.
  • Doctors make a ton of money, at least in US.They slog till early 30’s , establish a practice by late 30’s and early 40’s and then its heaven
  • Doctors in US have to deal with a truck load of insurance problems . One of my friend who is a doc in US thinks that insurance knowledge is sometimes the key between a successful and an ordinary doc
  • Doctors are usually health conscious , cleanliness focused people .

What’s this book about ? This book is by Dr. Atul Gawande, a endocrine tumor surgeon , who talks about performance. Well, to begin with, I imagined this book to fall in either of the following categories, A book which cribs and brings out the darker aspects of medicine OR A book which would talks as though docs are next to god etc.

THANKFULLY, this book did not fall in to any of those categories and it was a pleasant surprise to read

3 paragraphs in the introduction made the connection while I was browsing in book section at a crossword store in Mumbai.

Author , in the intro says the following :

The three core requirements for success in medicine are :

1. Diligence , the necessity of giving sufficient attention to detail to avoid error and prevail against obstacles. It seems easy and minor virtue( just pay attention!!) But it is most central to performance and fiendishly hard.

2. To do Right : Medicine is fundamentally human profession. It is therefore , forever troubled with human failings, failings like avarice, arrogance, insecurity , misunderstanding. So , the solutions / problems / issues are interwoven with human traits

3. Ingenuity : It is not a matter of superior intelligence , but of character. It demands more than anything, a willingness to recognize failure, to not paper over the cracks , and to change it. It arises from deliberate , even obsessive reflection on failure and a constant searching for new solutions.

If one thinks about the three requirements mentioned above, one can apply this to trading too. Ask a successful trader the reason behind his most successful trades, most often, he attributes it some personal characteristic and not to intellectual technical prowess or some PR skills. Reread the three characteristics mentioned above by the author again and you will agree that the three traits are infact the traits for a successful trader too.

Actually the mention of errors in various parts of the books is what pulled me to read this book. The author highlights various facets of errors, like error causality, error quantification and error reduction. The author clearly has a statistical bent of mind and is definitely a numbers guy . Obviously I can never recreate the experience of reading the book, but I will attempt to summarize this book so that it might motivate a reader who likes numbers to read this book and find his/her aha moments

As mentioned earlier, there are 3 themes in the book which are


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Diligence : The constant and earnest effort to accomplish what is undertaken

Image Ignac Semmelweis

A story about “Washing Hands” brings out the devilish difficulty of compliance to a simple rule. There is a story is about Ignac Semmelweis, who was vociferous in his opinion about hand washing in hospitals , which he rightly believed to be the cause of maternal deaths. Though everyone came to realize this after 150 years , story till this day is that doctors do not strictly adhere to this policy. Who says, ensuring compliance is easy ?

Diligence , as defined above seems simple. You just keep doing things. However there are tons of things that resist / deviate you from the diligent efforts that you would like to put in. Think of any task which you wanted to do on a regular basis but couldn’t and you will see why diligence which seems so easy is SO DIFFICULT. A story about polio eradication in India brings to light the extraordinary achievement of doctors whose diligent efforts can perform things which WHO finds it difficult to execute.

The story of US Military doctors is probably my favorite in this part of the book. This story brings out the importance of hidden variable, a well known concept in stats. When Iraq war casualties were rising, there was a realization that it was the trauma care that was the hidden variable behind these numbers. Improve the trauma care and you drastically reduce casualties. Not waiting for the new technologies to develop, diligent efforts in injury quantification, injury data analysis resulted in wonderful and effective solutions in trauma care. All these improvements came from the doctors focus on quantification of the patient condition, patient progress etc. This story is my personal favorite because the improvements came from studying the system carefully and making improvements. I tend to believe that most of the problems of any domain can be solved by studying the system and quantifying it. Well, my thinking has been shaped more from my black belt experience at GE , many years ago where I learn ways to solve system related issues by error quantification and analysis. That’s exactly, in a grand scale,is what I see in this story of medical doctors . A story of quantification of the problem, trauma care , brought down the casualty rate in the IRAQ war.


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Author talks about one of the most sensitive and costly aspects of medical profession, Mal practice suits. Some of the numbers mentioned in here brings out the severity of the problem. In US, about 55000 patients sue the doctors and out of which 1 in 100 get money and usually the money is a windfall amount. Malpractice lawyers charge a ton of money . Look at these numbers. There is a mention of Barry Lang, an independent malpractice suit lawyer who manages to get 5 cases to trial ever year out of which 4 cases are given compensation. Attorneys get about 40% for <$150k, 33% for>$150K and <$500k and 25 % for >$500K. So, on a average the lawyer makes about $50K per case , earning him a total of about $200K . We are talking about an independent lawyer with no attachment to a specific branded agency. So you see that system is similar to a lottery , of course the outcomes involve human lives in this case..Nevertheless, the system is highly skewed. A doc gets sued atleast once in 6 years and pays about 1/2 million to 1 million as insurance premium in his life( may be I am underestimating here, but definitely not overestimating). So, the whole system is designed not to provide relief to a majority of people . Docs are humans after all, they make mistakes too . Operating under uncertainty is almost a daily exercise. However when things go wrong, inspite of the docs reputation, one mistake could cost his/ her license. Strange are the ways in which the whole system is designed. After going through the numbers and sad story of the system, the author presents a remarkable case of a system which works, “Vaccines” . Vaccines are given to children and obviously any mistake by the manufacturer led to law suits. This had a great effect on the availability of vaccines, shortages , artificial price hikes etc. To deal with this situation , American vaccine association came up with a nice idea. Price the vaccines in such a way that a part of the price goes to a fund which then allocates money to the cases where vaccines have caused harmful effects. Well ,vaccines carry 75% surcharge (15% of the total costs) , the money generated is then used to deal with cases. Well, it is not a windfall amount but at the same time the affected parties are usually satisfied with the amount. A great case which shows tinkering with crucial elements of the system make the system efficient. It reminds me of Critical Chain , a Goldratt’s book which talks about the same thing . A few critical elements and tinkering with them changes the whole game!!. A project management principle, however, has a wide range of applications to a lot of systems!

Author then goes about writing things more specific to medical domain like the hazy compensation structure, the ethical dilemmas of the doctors who are sought help to give lethal doses to criminals in prisons, etc.

Docs are elevated to the status of gods and we like docs who fight and fight for patient’s illness . From the perspective of most of the successful docs, the element of fight is a little differently viewed. It is very easy to let the ego do the talking / working. When you bring your egos to the surgery table , then there is a huge danger of putting the patient at risk. I cannot equate a noble field of medicine to rather mundane domain of arbitrage trading. But in a way, a novice trader can learn that it is sensible to know when to let go of the egos for the various trading situations. When stoploss / risk limits are breached, it is always better to get out rather than let the ego do the talking. It is similar to the host of examples mentioned in this essay. When to fight and When to let go is a crucial decision that doctors take . These decisions are taken keeping in mind the patient. It is not about doctor’s expertise, doctor’s credentials or past performance..Its always always about the patient in front of them. Most of the successful docs stop when they realize that it is not worth trying or when they realize that it is better to let the patient die.

It is a stretch to find this situation analogous to trading but I tend to think it is. In the world of fin modeling, you cant be wedded to models. They are just a form of representing reality. If a trade goes right, good for you. But if the trade starts going wrong, its time to cut the losses, tweak the parameters etc than thinking that you have power over every trade. Sometimes the best of best trading signals turn out be phantom signals. As a trader, you have got to be sensible enough to keep things in perspective. It should never ever be EGO thing . Every trade is specific, time bound and needs action. You diagnose the numbers, check for signals , get in or get out based on the patterns that evolve. I have a looooooong way to go in terms of understanding these things in a detailed way….


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This is the best part of the book as it reveals the quant thinking that lead to solutions for some of the vexing problems in the medical domain.

Image Virginia Apgar

Till late 1930’s childbirth was considered to be one of the most dangerous events in a woman’s life as the mortality rates of woman was very high. Most of the solutions sought were aimed at stricter rules, technological improvements, smart techniques etc. However there was one Ms. Virginia Apgar who attacked the problem from a numbers perspective. A Columbia grad who , while working as an anesthesiologist came up with a score to measure the child health immediately after the birth. Apgar score had a few critical variables, which could be easily measured and reported at the end of the child birth. This metric was a great contribution from her that became instrumental in looking at the whole delivery process. Thousands of improvements like prenatal care, obstetrics techniques and post natal care were developing by focusing on the apgar scores across a lot of operations. In this context, I remember the words of Dr.Robert Almgren at NYU, who, in his talk on volatility said , ” I don’t know whether volatility is good or bad in financial markets. All I want is to measure it“. This approach is a killer approach as some of the finest high frequency algorithms and related work has been done by Robert Almgren at NYU.

Quantifying changes the way you look at things and there could be totally surprising and pleasant consequences of the quantification!

There is also a story about Don Berwick who uses quant and diligent care to fight Cystic Fibrosis, a deadly genetic disease. I guess one needs to always keep in mind , the bell curve in our work. There will be times when we end up doing average work and there will be times when we do brilliant work. One needs to carefully introspect at the kinds of work that brings out the best in oneself and keep at it. I guess that’s the central message from Cystic Fibrosis Story.

Author’s final thoughts are from his experiences from a visit to India. He sees the range of operations and procedures being conducted by doctors using textbook knowledge, shared knowledge . He is totally stunned by the sheer amount of people being handled by doctors. He concludes by saying , “Arriving at Meaningful solutions is an inevitably slow and difficult process. Nonetheless, what I saw was: better is possible. It does not take a genius . It takes diligence. It takes moral clarity. It takes ingenuity. And above all, it takes a willingness to try”

Author’s Suggestions for becoming a Positive Deviant:

  • Ask an Unscripted Question. Ours is a job of talking to stranger, Why not learn something from them ?
  • Don’t complain. Its boring. It doesn’t solve anything and it will get you down.
  • Count something. If you count something you find interesting, you will learn something interesting
  • Write something. Published word is a declaration of membership to a community and also a willingness to contribute something meaningful to it.
  • Change.Find something new to try and something to change


ImageTakeaway :

Betterment is Perpetual labor

Diligence , Doing the right thing and Ingenuity are the critical elements that will make you better