RK's Musings

Pricing the Future : Summary

Any book that promises a journey spanning 300 years is bound to focus on events that / people who made the maximum impact for the development of option pricing formula. If one were to pause and think about the option pricing formula, one would come up with questions like

• Pretty naïve question to start with, Why is there a need for options, in the first place? How were the traded historically? Were they precursor to some other instruments?
• What factors drive option prices? Can one mathematically pin down a few factors, assuming others are constant?
• Option by default depends on the movement of the underlying security. So , how to mathematically describe the underlying security?
  • Should one form an equation for the price?
  • Should one form an equation for price increments?
  • Should one assume a discrete process or a continuous process, after all traded price series is a discrete time series?
• Given a specific process for the underlying security, How does one go about figuring out the price of option?

This book in a way traces all the developments leading to Black Scholes equation like the Brownian motion, Ito’s calculus, Kolmogorov forward and backward equations,etc. and leading up to the most important idea of option prices, “replication”. Each of these ideas are described chapter wise. Let me summarize briefly, the chapters in this book.

Flowers and Spices

The book starts off describing Tulip mania of 1630’s and the reason it talks about Tulip mania is this : It was the first instance when government, in order to come out of a crisis, converted forward contracts to options contracts. The chapter then talks about Dutch East India company that dealt in Spices. The history of this company is closely linked to the emergence of the first formal market for options. Dutch East India company (VOC) became a powerful company in Netherlands just a few years from its inception. The shares of the company became valuable and a futures market emerged. Subsequently to cater to various kinds of demands, options market emerged for VOC shares. VOC finally got bogged down in corporate politics, corruption and became bankrupt. The period of 1680s was also the time when there was a need for communicating to general public about the ways to trade and understand options. To clarify the various terms and mechanics of options, Joseph de la Vega wrote extensively in his book,“Confusion of Confusions”. De la Vega was the first to describe in writing the workings of the stock market, in particular the trading of options. His work is held at such a high esteem that, since the year 2000, the federation of European Securities exchanges sponsor an annual prize for “outstanding research paper related to the securities markets in Europe”.

In the Beginning

This chapter contains some important developments that happened in the financial markets between 1694 and 1885.The chapter starts off in 1694 with John Law advising French king on restoring the financial stability of the country. John Law started a firm in France that printed paper money. It was the first attempt in Europe to replace metal coins with paper money as legal tender. The bank, forerunner of France central bank, guaranteed that the notes would always be worth as much as the metal coins on which they were based. Law also convinced the king to grant him powers for a natural resource trading company so that he can bring in more revenues in to the country. Law's company became very popular and there was a mad scramble amongst people to buy shares of the company. Like any bubble, the printing machine idea flopped by 1720 and France was facing an imminent financial disaster again. However the taste of trading and speculation activity that Law gave to French citizens was still in full force. Unofficial trading of various other instruments increased. So, finally in 1724, the government decided to bring some order in to this situation and an official Bourse was created. The whole system ran well until the French revolution in 1789 after which chaos ensued. There were few more developments that lead to the reopening of Paris Bourse and this time everybody was allowed to trade. Again forwards were outside the regulation but it did not stop the increasing volumes in the instruments and soon became the hub of speculators. Also with the collapse of a big investment bank, France went in to a recession. Out of all these developments, there was one positive development,legalization of forward market in 1885.

From Rags to Riches

This chapter talks about the life of Jules Regnault. It is a classic rags to riches story. Why is the story relevant to the book or options pricing ? Well, Jules Regnault was the first person at least as per the book who deduced square root of time law. He not only tried proving it using math, but also used the law in the stock markets to retire rich. He started his work life at the age of 23 as a broker assistant. His living conditions were miserable but he managed to improve his living conditions by working hard in the broker's office. Regnault was the first person to try to understand the workings of the stock exchange in mathematical terms, and his explanations had all the trappings of a scientific theory. Regnault managed this with hardly any formal education system. After a full day's work at the Bourse, he would sit in a small room under the attic and do quant. Truly inspiring life. Remember this was in 1860s and he was investigating concepts such as random walks, role of information in stock markets, useful/harmful sides of speculation, insider information, factors that drive the valuation of an instrument, ways to calculate fair value of an instrument etc. An admirable quality about Jules Regnault's life is that he never shied away from applying things in the stock market. He used all his principles at the Bourse and retired at the age of 47 after making a ton of money. In one sense, Jules Regnault can be called the first quant who made a fortune in the market.

The Banker's Secretary

In any introductory book on options theory, you are likely to see payoff diagrams for various options and option strategies. This chapter talks about the first person to use these diagrams for communicating option positions, Henri Lefevre. Lefevre was a personal secretary to business tycoon James de Rothschild. Lefevre did not participate in speculation or trading activities but was a keen observer and educator of markets. He published various books and articles, thanks to the fact that he was a secretary to Rothschild and could influence the publishers. He made two main contributions to options theory. First contribution was his mental model of comparing economy and the flows of capital and goods with the human body and its organs. In Lefevre model of economy, stock exchange is like the heart that keeps blood moving through the veins, government is like a brain that thinks, combines and regulates the flow, Speculation is like the nervous system that provides the momentum that keeps commodities and capital in continuous motion. His second contribution was in 1873 and 1874 through his books. In those books he introduced a method of analysis that we are all familiar with, the pay off diagrams. The pay off diagrams for individual options might be very simple and a use of such a diagram to explain things could be a stretch. The real power of payoff diagrams comes in to play when you are analyzing a set of option positions. The final payoff diagram for a set of option positions, at once provides the price ranges where the entire position makes or loses money. Lefevre's method and his extensive publications in the form of books , papers, articles, etc. helped the common masses understand options and options based investing in a better way.

The Spurned Professor

Louis Bachelier

The study of financial markets began in earnest at the turn of twentieth century. The first underpinnings of a mathematical theory were developed in the doctoral thesis of a thirty-year-old French student , Louis Bachelier. In 1900 Bachelier defended his PhD thesis and the committee composed on Poincare, Appell and Boussinesq awarded the thesis as “somewhat better than okay”. This evaluation haunted Bachelier through out his life as he could not secure a faculty position without a “real distinction” on his PhD. One of the reasons for Bachelier's theory not getting attention was that it was incorrect. He analyzed price movements as a specific random walk ( an Arithmetic Brownian motion ) which allowed for stock prices to take negative values. So, the thesis that was probably the first step towards a mathematical treatment of financial markets lay dormant for a long time.

Botany, Physics and Chemistry

The first observation about the jiggle movement of particles was by a Dutch Scientist Jan Ingenhousz. However the credit goes to Robert Brown for the name. I find Robert Brown's life very inspiring. He made use of his free time and did all the observations and work after work hours. He never socialized or dined out. Basically he was a guy who kept to himself and did outstanding work. He observed that Brownian motion never ceases though he never knew the reason for Brownian motion. Remember this was 1827 and molecular/atomic theory was not established. Then came along Einstein , aptly named as the father of atomic theory. He hypothesized and predicted the Brownian motion behavior. He also formulated the square root law by clarifying that one must not analyze a single drunkard's walk but an ensemble of drunkard walks. In 1906 Marian Smoluchowski , another scientist made important contributions to understanding Brownian motion when he postulated that , the observed jittery motions are the displacements due to the unobservable zigzag movements that are a result of huge number of impacts. He concluded this after analyzing the speed of the particles at various resolutions. He saw that the velocity of the particles increased at higher resolutions. This made him conclude that whatever action that is seen in the microscope is basically the displacement. This book provides a fantastic analogy to Brownian motion which one will never forget after reading once. The books says it in a beautiful way:

Imagine the dance floor of a studio. Flashing strobe lights highlight the seemingly jerky movements of the dancers, Of course, even the coolest dancers do not disappear in to thin air between the flashes. They move contiguously through time and space, but their movements are hidden during the dark periods between flashes. In fact, there could be different dance steps that give rise to identical positions during the strobe flashes. This is the key point. Particles pushed around by the molecules in a liquid describe a continuous path, and the jerky motion we see under the microscope is just a sample of the entire movement.

In the next chapter, the book gives an account of Norbert Weiner's life who proved that even for the jerkiest observations, it is practically certain that continuous paths exists which give rise to them. Typically these historical developments give so much meaning to what one gets to read on a pure mathematical text on Brownian motion. Brownian motion is continuous. “Oh! ok! ” was my first reaction when I studied stochastic calculus. However books such as these give so much context to mathematical properties that learning math becomes that much more interesting.

Disco Dancers and Strobe Lights

It was in 1880 that physicist John William Strutt discovered random walk in a completely different context, super imposition of waves of equal amplitudes, equal periods but random phases ? He came to the conclusion that amplitude was proportional to the square root of number of vibrations( variant of square root rule). Thorvald Nicolai Thiele, another scientist also worked on the random walk , while developing concepts in computational techniques. He used Gauss method of least square to conclude that an ensemble of particles following random walk would have an average displacement proportional to the square root of number of steps. Some 80 years later, this was picked up by another scientist Kalman and today we know a ton of applications of Kalman filter. Karl Pearson, the famous statistician added in a bit with his article in “Nature” magazine. Despite all these efforts, Brownian motion was not on sound mathematical foundation. It was Norbert Weiner who formally defined the process, proved its existence in a 40 page paper in 1923. In 1948, Paul Levy, considered as the founding father of probability theory , defined and constructed another class of random walks called Levy processes. In the last 60 years, more and more scientists studied various classes of random walks such as reflecting random walks, loop-erased random walks, biased random walks, random walks with drifts etc. In 2006, the prestigious Fields Medal, the Nobel prize equivalent in mathematics, was awarded to a French mathematician, Wendelin Werner, for his work on random walks.

The Overlooked Thesis

Regnault had brought Statistics , Lefevre Geometry and Bachelier Calculus to understanding options. This chapter highlights some of the important elements of Bachelier's PhD thesis that shows how the thesis was so far removed from the traditional way of analyzing finance. The section mentions the following from the thesis

• The thesis referred to the efficient market hypothesis and formulates the mathematical equivalent of the same.
• It departs from the tradition of describing economic phenomenon verbally and uses mathematical equations to describe things.
• It showed that fluctuations of the stock price around true price follows Gaussian distribution.
• It showed two justifications for the square root of time law.
• It used Fourier methodology to derive heat equation in the context of price probabilities
• It showed that Options value depends on the security's volatility and time
• It used reflecting principle to reduce the complexity involving Brownian motion calculations.

One of the offshoots of Bachelier thesis was Chapman-Kolmogorov equation that ties in the probability distribution of a variable at the end of a discrete Markov chain to its intermediate probabilities. Books such as these should be made required reading for a student before he/she gets exposed to math relating to Brownian motion. If you learn square root of time law using math and with no prior exposure to the rich history behind the development, you might learnt it but not appreciate the beauty that lies behind it. Similarly you might prove that Brownian path is nowhere differentiable but you will feel the result in a completely different way after reading Theoder Svedberg experiments about calculation of velocity of particles. All said and done, I strongly believe that historical developments about concepts/formulas are very important, sometimes more important than merely knowing a few ways to derivation of Black-Scholes equation.

Another Pioneer

Developments in science tend to be non-linear and controversy laden. Examples of plagiarism accusations are rampant. In such a context, it is but obvious that option pricing formula also has , in its history , some people whom we can only speculate that, they knew about a way to value options much before anyone else. One such individual mentioned in this chapter is Vincenz Bronzin. His work was accidentally discovered by Swiss historian Wolfgang Hafner, who later sent it to Prof Zimmermann. Both concluded that Vincenz Bronzin work in early 1920s had all the necessary math and concepts relating to pricing an option and in fact Bronzin’s work ends up deriving the same formula as Bachelier's. The fact that his work was never popular/ recognized shows that historical development of any concept is tough to attribute to individuals. You never know that some person who never published stuff might have known the concept right through. Vincenz Bronzin work on option pricing was so advanced that some of the concepts looked similar to what the final Black-Scholes formula looked like, decades later.

Measuring the Immeasurable

I loved this section where various historical figures are mentioned in the development of probability and stochastic processes. Firstly, what has a stochastic process got to do with pricing of options. What's wrong with using / trying to use a deterministic process ? Well, the basic difference between a stochastic process and deterministic process is, in the latter case you can pin point the result and in the former case, you can only get a probability distribution for the result. So, all diffusion processes, arithmetic random walks and geometric random walks are all nothing but a way to summarize the particle movement and any computations on it will likely result in a probability distribution. Ok, let me get back to summarizing this chapter. This chapter talks about Kolmogorov, the father of modern probability. Picking on one of the Hilbert's 23 problems that were announced in 1900, Kolmogorov developed a full-fledged axiomatic theory of probability in 1933. In doing so, he heavily relied on the works of Henri Lebesgue, George Cantor and Bachelier. Henri Lebesgue is credited for his revolutionary method of integration called the Lebesgue Integration that is applicable to a wide range of functions and sets of points. Lebesgue benefited from Cantor's work on real line and introduced the concept of measure. Well , the development of Lebesgue integration is  in itself is a fantastic story and “The Calculus Gallery” covers it in a splendid way. Kolmogorov also derived Fokker Planck equation in his monograph, unaware that the PDE was developed in 1913 and 1914 by two physicists Adriaan Fokker and Max Planck to describe the time evolution of a variable's probability distribution. The variable could be a particle's position in a fluid or distribution of stock price. I liked this section because of a nice analogy that gives the difference between Chapman Kolmogorov and Fokker Planck equation. I love analogies as they are the first things that come to your mind than the raw equations. I paraphrase the author's words here

The Chapman-Kolmogorov equation gives the probability of jumping from A to Z by investigating the probabilities for two consecutive jumps, say from A to P and then from P to Z, or from A to Q followed by a jump from Q to Z, and so on. It is like driving from New York in any direction and ending up in San Francisco. What are the chances of that happening ? Well, you could drive via Dallas, Texas, Via Witchita, Kansas, via Rapid City, South Dakota or via any other route. The probability of ending up in San Francisco is then computed by adding the probabilities of all possible routes. This is what the Chapman-Kolmogorov equation does. The Fokker-Planck equation goes one step further. It develops the whistle stop tours in to a distribution of probabilities of ending up anywhere on the West Coast, be it San Francisco, Santa Barabara, Los Angeles, or Tijuana, Mexico

After formulating the PDE, Kolmogorov found that the solution to the PDE was Chapman-Kolmogorov equation. He then turned the situation around: starting with a parabolic PDE, he pondered on the question whether it had a solution. If the answer was yes, then the solution could be none other than the Chapman-Kolmogorov equation. Thus he proved that Chapman-Kolmogorov equation indeed existed and was not merely a figment of imagination. Further development was needed in this area as there were strict conditions that one had to impose on Kolmogorov's PDE describing Brownian motion so that it had a solution.

Accounting for Randomness

Kiyoshi Ito

This section talks about the contribution of Kiyoshi Ito. Since the Brownian motion is jagged and jittery at any resolution, one can't calculate the velocity of the particles, as Marian Smoluchowski concluded in 1905. So how does one go about analyzing any Brownian path if the usual Riemann and Lebesgue Calculus cannot be applied ? Karl Weierstrass was the first mathematician who came up with such a nowhere differentiable function. How does one work with such functions? There is no way to slice the paths and handle it in the usual way. Whatever slice you look at , there will be jaggedness. What's the way out? Here is where Ito comes in. In 1942 Ito published a paper that contained the mathematical machinery to handle such functions or paths. He used Taylor series expansion and found that the first three terms of the expansion were all that mattered for a stochastic process and thus ignored the rest to come up a forecast of probability distributions. Today Ito's calculus is synonymous with “framework for handling Stochastic Differential equations”. Ito lived for 93 years and contributed immensely to field of Stochastics. In his Kyoto-Prize address, he says that he devised stochastic differential equations, after painstaking , solitary endeavors. For those who think that Solitude drives people crazy and must be avoided, Ito is a classic example of the tremendous possibilities of Solitude in life.

The Sealed Envelope

Wolfgang Doblin

This section talks about Wolfgang Doblin, a young mathematician who commits suicide while serving in the army to avoid getting killed by Germans. Before his death, he sends a sealed envelope to Academy of Paris. There is a big history behind the sealed envelopes that one can read from this section. The sealed envelope was supposed to be opened in 2040 but thankfully it gets opened in 2000. The math that Doblin sent to the academy had a framework to deal with Stochastic PDEs in such a way that one could lessen the restrictions imposed on it. Mathematicians wonder that if Doblin had not served in the army and had not met the fatal outcome, option pricing would have developed much earlier. In any case, a reader gets a glimpse in to this young genius,thanks to this book. Doblin's life revolved around math and it served as a way to get him out of his gloomy and depressing environment. Though he only had the rare hour to focus entirely on math, usually during the night shifts hidden away in the telephone station that he was guarding and that provided some heat, his preoccupation with mathematical problems alleviated the dreariness and kept him from falling in to depression In one of his letter to his professor he writes,

Fortunately, my mathematical work helps me fight despair. As I am not interested in alcohol, I do not have the luxury of getting drunk like others.

The Utility of Logarithms

Paul Samuelson

This chapter talks about Paul Samuelson who relooked at Bachelier's thesis and improvised on it. Instead of considering plain vanilla Brownian motion, Samuelson insisted on geometric brownian motion because of couple of reasons

• Share values are always positive in GBM scenario
• Price jumps, in percent, are equally distributed
• Model is in accordance with human nature, as displayed by Weber and Fechner's psychology
• Data observed on stock exchanges fit GBM than Arithmetic Brownian motion

The chapter also mentions M.F.M.Osborne, a Physicist, who claimed in 1958, that log values and not the changes in stock prices are normally distributed. He was motivated to analyze the behavior after reading the works of psychologists Weber and Fechner. This observation is the same utility argument made by Daniel Bernoulli in 1713 while solving St.Petersburg Paradox.

The Nobelists -  The Three Musketeers

  

Fischer Black – Myron Scholes – Robert Merton

The next two chapters talk about Fischer Black, Myron Scholes and Robert Merton. MIT was one of the common denominators for all the three people. Fischer Black and Myron Scholes worked together on consulting projects for financial firms and thus were aware of markets and the places where quant techniques could be applied. They developed a good working rapport as Black's forte was theory and Scholes was good at implementation. Robert Merton had worked on pricing warrants along with his MIT professor Samuelson. Warrants were similar to Options but for some technical differences. Before the trio cracked the formula, there were quite a number of scholars who came close to cracking it. In 1961, a graduate student in economics, Case Sprenkle made some headway. He assumed GBM for prices and allowed drift. But his approach was faulty as he posited that investor's utility function would be revealed in prices. Also he ignored time value of money. In 1962, James Boness another student from Chicago also attempted and improvised on Sprenkle's model by incorporating time value of money. However there were some problems with his theory as he assumed, all stocks on which the options are traded are defined to be of the same risk class and all investors are indifferent to risk. So, all attempts of Thorp, Case Sprenkle, James Boness, Robert Merton and Samuelson had shortcomings. But they all carried seeds of the eventual solution.

Somewhere in 1968 Fischer Black tried formulating the option price as PDE but faced a tough time solving the PDE. So, he filed it in his cabinet and went on with his work. However in 1969 , while conversing with his sole associate of his company, Myron Scholes, Black got a chance to start the work again. The key idea that was used in cracking the formula was “Portfolio hedging and replication” . If the option is deep in the money, then delta or the hedge ratio is 1. This means you can perfectly hedge a long call option by shorting one share of the underlying contract. If the option is not deep in the money but near ATM, then the hedge ratio is definitely not 1. It must be less than 1. If you represent the hedge ratio as x, then the combination of call and hedge position is basically a risk free portfolio growing at risk free rate. With the unknown hedge ratio as a variable, Black and Scholes wrote an equation describing option pricing.

With the PDE in hand, Black-Scholes made an educated guess that turned out to be the solution for option pricing formula. The solution to Black-Scholes PDE surprisingly did not have stock return component at all. This was totally unexpected from the prevailing notion that option price should somehow contain the return of the underlying instrument as one of its components. But Black-Scholes proved it otherwise. Robert Merton arrived at the same solution using Ito's calculus. Initially Black had a lot of difficult publishing the paper in academic journals. It was only in 1973 that Black and Scholes managed to publish it under the title,”The Pricing of Options and Corporate Liabilities”, in Journal of Finance and Journal of Political Economy. According to a study undertaken in 2006, the paper garnered 2589 citations, making it the sixth most cited paper in all of economics. In the paper they acknowledged the fact that Merton had worked out a different approach and arrived at the same solution, thus kind of validating their final solution to option pricing.

The Higher They Climb ...

This section highlights the lives of the three musketeers before the Nobel Prize award in recognition to the work. There are some people who believe that Texas Instruments was solely responsible for the tremendous marketing of Black Scholes formula by incorporating it in the module in its calculator. Traders did not need to know anything about the formula except the inputs. So, they happily traded away the options at CBOE that is today one of the biggest derivative exchanges in the world. Black joins Goldman at the age of 46 , becomes a partner with in two years and dies at the age of 56 (1995) because of cancer. Scholes and Merton land up at LTCM a fund using quant stuff to manage money. The principals get their recognition in the form of a Nobel Prize in 1997.

...The Harder They Fall

This section talks about the fall of LTCM. The LTCM bust is basically a `leverage' lesson for all money managers.If one needs to read in detail about the demise of LTCM, the book by Roger Lowenstein is spot on. This section does not fit the flow of the book.

The Long Tail

The last chapter talks about the problems behind Black-Scholes formula such as assuming volatility constant, assuming GBM that has normal distribution at it's core. The books ends by saying

So, there are pitfalls and they can and do lead to spectacular failures like the LTCM crash, crisis of 2007, demise of Lehman Brothers. But to fault Black, Scholes and Merton and their equations for such aberrations would be utterly wrong. This would be like accusing Issac Newton and the laws of motion for fatal traffic accidents.

 

Takeaway

”What risk premium should be used for option pricing” was a stumbling block for developing the option pricing formula. The answers given by Black-Scholes-Merton surprised everyone : no risk premium at all. This book traces the historical developments leading to option pricing formula and in doing so, weaves an entertaining and a gripping narration of all the mathematical developments that were a precursor to Black-Scholes formula.

Moonwalking with Einstein : Summary

“Moonwalking with Einstein” is a book recounting the experiences of US Memory Championship winner Joshua Foer, whose day job is NY Times journalist. The book is easy on eyes and can be read in a few hours time. One might shy away from books that deal with memory assuming they are of “self-help” type books . But that's not the case with this book. This book is a result of curious journalist who happens to cover National and International Memory championships for a couple of times and starts wondering about the participants. He starts pondering over a few questions:

• Passive questions like (When I say passive, any memory championship event spectator would have these questions)
• How do people memorize a long list of random numbers ?
• How do people memorize a deck of cards ?
• How does one memorize a poem ?
• Curiosity driven questions like
• Are the participants’ brains wired differently?
• Are they gifted people and average Joe can never perform such feats ?
• How does brain remember things? Memory competitions definitely check on working memory. So, Is long term memory involved at all in improving short term memory ?
• Does memorizing some arbitrary collection of random things be useful at all ?
• How do the mathletes practice for these memory events ? Is there something that one can learn from these people so that we can apply to anything that we want to become good at.

In fact all the people whom the author interviews say that their feats are achievable by anybody. All it takes is to learn the right technique and master it. This makes the author very curious and so begins his quest for learning about memory, memory techniques, deliberate practice, exploring the common myths surrounding memory etc. Well, the first question that any reader gets by reading a few pages in the book is : There are so many devices/gadgets/services that help us remember things. Basically our culture is an edifice built on external memories. So, Why develop internal memories ? Is there any point in developing them?

I have listed down a few points against the various sections of this book that I found interesting.

• There is something about mastering a specific field that breeds a better memory for the details of the field
• Experts process enormous information flowing through their senses in more sophisticated ways.
• Chunking is key to remembering and learning better. Chunking is key step in memorization techniques.
• At the root of chess master's skill is that he or she has a richer vocabulary of chunks to recognize
• Expertise is vast amounts of knowledge, pattern-based retrieval, and planning mechanisms acquired over many years of experience in the associated domain.
• You need a stockpile of images / places to form visual images of words. You sequence these images to remember better.
• We are exceptional at remembering visuals and pathetic at remembering words, numbers,etc. and this is key aspect driving all the memory techniques. The author describes his learning process with his mentor Ed. He learns about a technique called memory place, a method where you represent the content you want to remember using images and then populate the images in a familiar location.Humans are amazingly good at gobbling spatial information.So, instead of our memory that is non linear in nature, you are making an effort to linearize, put a pattern, put a sequence to these images. By laying down elaborate, engaging, vivid images in your mind, it more or less guarantees that your brain is going to end up storing a robust, dependable memory.
• We read, read and read, then we forget, forget and forget. Frankly most of us read a lot of stuff and forget almost instantly. So, why read at all ? is a valid question as so much of info is readily externalized. You want any fact about any thing, you get it on net. You want to keep track of things, there are to-do list reminders The rate of externalizing memories has become faster. Anything you would want to commit to memory ,there are devices/gadgets/tools to make the memorization unnecessary. So, is there going to me a need for memorization at all ? This question I guess has to be answered by each one of us individually. As for me, I think there is a value in memorization as it instantly helps you connect the new material you are reading with the stuff that is already in your brain.

In the entire book, I found two sections particularly interesting.

First one is where deliberate practice is tied to memorization techniques. The author hits a plateau in his preparation for the US memory championships and this leads him to explore  `deliberate practice', a concept popularized by Dr. K. Anders Ericsson.

What's deliberate practice ? Well, we all go thorough various stages of learning, right from Cognitive stage where we are intellectualizing the task, to Associative stage where we are concentrating less, making fewer errors , to Autonomous stage where we operate in autopilot mode. It’s fine if we are in autopilot mode for some mundane stuff but it is not ok when we are want to gain expertise in something.

The trick is to get out of autopilot mode as much as possible by practicing hard. Practicing hard need not be practicing for long hours. It means to design the work in such a way that it stretches you and there is a possibility of learning from failures that ensue. So, according to Ericsson,the way to achieve expertise in any field is to practice failing so that there is a constant feedback for your work. In one word, we need to be attentive and choose hard tasks to become damn good at something. The author finds that mathletes apply these same scientific principles for memorization too. They develop hypotheses about their limitations, conduct experiments and track them. This reminds me of Atul Gawande's book, “Better” , where he makes a strong case for tracking something, whatever be your interest.Tracking gives you an instant internal feedback. 

The other section of the book I liked was about a particular school in NY.The author visits a school in South Bronx, more specifically a class taught by a teacher who trains 43 kids in the class in developing memory. Whenever we hear memory development, there are only negative images that come in to our minds, like rote learning, creativity crushing etc. However this teacher at this school firmly believes that memory needs to taught at school level like any other skill. These memory techniques involve methods where kids are inculcated ways to visualize things. Every fact is turned in to an image. Well, do these techniques help ?The class is a case in point where all the 43 kids do extremely well in the school and in the entire region of South Bronx.

The author also manages to meet Tony Buzan. Though the author is extremely sarcastic about Buzan's goals, he does seem to agree one of Buzan’s core principle that, memory and intelligence go hand in hand.

There is a nice little fact mentioned in this book : “Inventio” is the root word for the words “Inventory” and “Invention”. So in one sense , until one does not have some inventory of thoughts, invention seems unlikely, as more often than not, invention is nothing but clever combination of seemingly unrelated ideas/facts.

Takeaway :

Memory is like a spider web that catches new info. The more it catches the bigger it grows. If you are curious about `memory' and its role in every day learning / awareness, you will find this book very interesting.

Dawkins Theory

 

I never had a chance to read Dawkins work and the following 5 lectures have motivated me immensely to read at least a couple of his famous books like “The Selfish gene” and “ Blind Watchmaker”.

Ep 1: Waking Up in the Universe - Growing Up in the Universe - Richard Dawkins
Ep2: Designed and Designoid Objects - Growing Up in the Universe - Richard Dawkins
Ep3: Climbing Mount Improbable - Growing Up in the Universe - Richard Dawkins
Ep4: The Ultraviolet Garden - Growing Up in the Universe - Richard Dawkins
Ep5: The Genesis of Purpose - Growing Up in the Universe - Richard Dawkins

Measuring the World : Summary

This book is more an historical account of two scientists (Alexander von Humboldt, Carl Friedrich Gauss) than a work of fiction.Daniel Kehlmann weaves interesting fiction around these two brilliant scientists exploring their lives, their view points, their personalities that seem to be completely opposite. Alexander von Humboldt believed that knowledge comes from exploring the world, while Gauss pretty much developed everything sitting in an observatory.

Alexander von Humboldt 1769- 1859	Carl Friedrich Gauss 1777- 1855

I will try to summarize the contrasting lives that the book that this book brings out.

Background

Humboldt came from a wealthy family and he used a part of the wealth to explore the world. In modern day parlance he never needed any VC funding. He funded his explorations all by himself. Gauss on the other hand always skirted with poverty in the process of living in the “Numbers” world. He takes up a surveying job to take care of his bread and butter. He remarries second time so that there is someone to take care of his children as he could not afford a nurse. The scientists thus have a contrasting financial background.

Belief

Humboldt’s vision was that of a unified science of earth, vegetation, animals, human beings , a science that integrated everything. He self taught every branch of science. This is really unbelievable stuff if you look at the range of contributions that Humboldt made. He self taught everything be it measurement types, instruments, instrument design, design of experiments, etc. Humboldt believed that “Whenever things were frightening, it was a good idea to measure them”. I am reminded of Robert Almgren from NYU who said a similar thing about intra-day volatility. If intra-day volatility is frightening, all the more reason to measure it.

Humboldt also knew that there is no easy way out for knowledge. An incident described in the book strikingly makes this point. Humboldt orders his servant to place two hot cupping glasses on his back so that it produces blisters on his back. He wanted to test some hypothesis about the flow of current. If a person can subject himself to such a torture to understand stuff, his motivation must have been completely different. Somewhere in the book he says,”A great deal of knowledge escapes man because he is afraid of the pain. The man who deliberately undergoes pain learns things that he didn’t. One wanted to know because one wanted to know.”

Gauss on the other hand had markedly different beliefs. For him learning was effortless. He could see things instantly and formed conjectures and theories very easily. A brief balloon ride made him realize that space was curved and parallel lines can meet based on the type of assumptions one made. For Gauss, everything was obvious. He could add up numbers from 1 to 100 with in no time. He could count primes like one counts numbers. He disparaged people who could not match his intellect which included his son too. His looked down upon people who could not think as fast as he could. He sometimes felt that “People wanted Peace. Most People wanted to eat and sleep and have other people be nice to them. What they didn’t want to do was think”. Needless to say with this kind of personality he was a loner and most of his work was result of singular brilliance. Contrast to this, Humboldt was a classic collaborator. His contributions grew by the kind of associations he formed with various scientists, philosophers, mathematicians etc.

Deliberate Practice

Humboldt spent his time practicing stuff before he could make his contribution. For about one year, he took daily measurements of the air pressure, he mapped the magnetic field, tested the air, the water, the earth and color of the sky. He practiced dismantling and reassembling every instrument until he could do it blind, standing on one leg, in rain, surrounded by a herd of fly-tormented cows. He believed that “A hill whose height remained unknown was an insult to his intelligence” and hence spent an enormous time measuring things. The measurements and the travel helped him become universalist. Direct experience through the senses of world, but measured experience made Humboldt a true quantitative researcher.

As for Gauss, he spent a lot of time silently watching the various planets, making measurements of various heavenly bodies. His deliberate practice involved sitting hours , observing and noting measurements diligently. So, this is one commonality of the two geniuses. Malcolm Gladwell’s theory of “10k hours to become a genius” seems to holding water in many cases.

Work

Humboldt begins working at mining academy. Unlike today’s mining world, a lot of new theories were put forth by mining experts. He would have learnt a lot of math/ earth science. Biology / geology were just being created around the time of Humboldt. This initial exposure to the mining world made him believe that “Whole world as a lab”. Gauss on the other hand, theorized effortlessly.

Family & Social Life

Gauss contemplated suicide incase his love was to be rejected. To his biggest surprise his love was accepted and he aborted the suicide attempt. Humboldt never married and remained a solitary individual throughout his life. Gauss had a mistress whom he loved more than his second wife. After the death of his first wife, he even considers marrying his mistress but finally doesn’t after being dissuaded by one of his friends. He remarries so that there could be someone to take care of his children as employing a nurse was expensive for him. He hated his children as none could match up his expectations. Gauss spent an enormous time seeing through his telescope in the observatory to take the measurement of the planets, heavenly bodies etc. He practically never had to move to work. His work was entirely sedentary. This is in marked contrast with Humboldt who formed instant connections with strangers who sometimes were part of his major explorations. Humboldt loved travel and hated home. He disliked his mother and never cried when mom died. Gauss on the other hand loved his mother more than anybody else in the world. For him mother came first and only then came others.

Work & Key Achievements

Gauss shot to prominence after he accurately predicted the precise date and time of the appearance of a planet. Subsequently he started studying and working in the field of astronomy.

Humboldt believed that data had to be presented well in order to get insights. He was the first person who was pivotal in making science more visual. During his explorations, he was actively charting stuff, creating new kind of maps( ISO Maps). He was first person who analyzed the world geographically and not historically ( new world vs old world kind of stuff). He was the first person to discover the Natural canal that connects Orinico and Amazon.

His work inspired Darwin who went on to create an outstanding piece of scientific literature – “Origin of Species”. Darwin described him as 'the greatest scientific traveler who ever lived'. Goethe declared that one learned more from an hour in Humboldt’s company than eight days of studying books and even Napoleon was reputed to be envious of his celebrity.

Humboldt spent 5 years in exploring the world and wrote profusely for the next 30 years. One wonders whether this prolific output is one of the main reasons for him becoming a household name by the turn of century. Most of his written text romanticizes his expedition and findings. The 30 odd volumes describing his measurements and adventures shows that he was totally passionate about his measurements, his explorations etc.

Takeaway

The book is a clever play on contrasting narrative. Humboldt firmly believed that to become the scientist, you have to travel. Gauss philosophy, on the other hand, can be understood by the following statement from the book:

Gauss observed the moment of the magnetic needle by the light of an oil lamp for hour after hour. No sound penetrated to him. Just as the balloon flight showed him what space was, at some point he would understand the restlessness in the heart of NATURE. One didn’t need to clamber up mountains or torment oneself in the jungle. Whosoever observed the needle was looking in to the interior of the world.

Despite these contrasting life styles and beliefs, both the scientists made ground breaking discoveries. This book delves in to their personalities and provides a fantastic narrative which makes it a worthwhile read.

Complications : Summary

I stumbled on to “Better” at a crossword store in Mumbai. Picked it up immediately after spending a minute browsing through the book... The book turned out to a great read. Had blogged about it here a month back.

So, with that experience behind, I ordered the other two books written by the author Dr. Atul Gawande. His first book which is extremely popular is “Complications”. “Better” is his second book and recently he came out with a book titled “Checklist Manifesto” . With very high expectations, I began reading “Complications” and by the end of it , the book did not disappoint me.

This book talks various incidents in the medical field under three themes which are Fallibility, Mystery and Uncertainity . 

                 
Fallibility 

The image of bad doctors ,for most of us  , are doctors who do evil things with their patients. However the author recounts a different experience. There are lot of good doctors who become bad doctors, and what he means by bad, is that they unknowingly do harm to the patient , more so because of their personal problems. Be it divorce , alcohol, burnout , or plain neglect to be constantly aware of the patient needs drives some of the doctors to do more harm than the status quo of the patient. Some doctors , as it seems, forget the nature of human fallibility and the consequences of dealing with such doctors becomes rather tricky for the hospital and the supporting staff.

For people like me, who have no clue what goes on in the medical world, it was interesting to read about the way doctors learn from their mistakes, individually & collectively.  The author mentions about M&M, Morbidity and Mortality conference where the docs talk about their mistakes. The purpose of such meeting is to discuss faults, failures in various surgeries that were undertaken by the respective hospitals.

Another interesting aspect mentioned about the field of anesthesiology is the way the docs are prepared and trained. A life size computer driven mannequin is used to to train anesthesiologists. It reminds me of the book Talent Code , where there are umpteen number of examples where learning was accelerated when there was an environment to make errors and quickly learn from them. The computer driven mannequin served the same purpose. With out harming any real human being, the docs learnt about various errors and hence they could deliver superior performance in the real world. 

I can related one thing I have been doing for the past few years ONLY, though I should have done this much much earlier. Whenever I learn something , I try to simulate data and examine the results, rework and get the formula / estimate being talked about. Simulating data and then working on this data has given me an idea about the things that could go wrong in an analysis. I can test all sorts of bias and see whether my analysis holds good.  I have increasingly started living, examining, testing in this artificial simulated world for the real world offers very few data points and the mistakes , if they happen, you pay a heavy price.

The book talks about Shouldice hospital, a case in point of specialization and focus. In most of hospitals 10-15% of hernia operations fail. But not at Shouldice hospital. Why ? What’s so special about this hospital ? Well, it turns out that Shouldice hospital employs about dozen surgeons who don’t do anything but hernia operations. They do about 680 hernia operations per year , more than a surgeon would do in a life time. So, this repetition of the same type of operation day in day out, changes the way the docs at Shouldice hospital think about their problems. In Gladwell’s words, may be the sheer # hrs logged by the docs performing hernia operations makes them outliers. In Gawande’s words, Repetition changes the way the docs think. Most of the activities are done automatically with doctor’s mind focused on those little nuances of the patient’s health which are crucial to the make or break of an hernia operation.  This is a beautiful case which shatters the myth that doctors should dish out individual customized treatment. Well it sounds good in theory, but as far as stats are concerned, systems , error induced learning, # of hrs logged in doing that activity play a far more important role in the overall success rate of a hospital , in the context of a specific surgery.

“The key then to perfection is routinization and repetition”

So, to think of it, if a job at a company is routine and repetition, then probably there is a chance for you to master something. If you are working on multiple projects in a year, ya , you might know a lot of things , but it is unlikely that you will master something!! . When you hear your friend / coworker saying “ My job sucks because it is routine..”.. Well,  I guess you can sympathize with them not because of the situation they are facing, but because they are not utilizing the situation that something is routine and repetitive , to master it.

The author mentions another interesting point about high performance surgeons versus the rest. He quotes a few research studies which bring out the point that , highly successful surgeons are those who are willing to engage in sustained training. Skill and Confidence in surgery is learnt through experience, haltingly and humiliatingly. So, one’s willingness to practice is all that matters. High performers are clearly those who put in a greater amount of deliberate practice. This means that,

“The most important talent may be the talent for practice itself”

    Mystery

This part of the book deals with various mysteries surrounding the field of medicine, which we outsiders think that docs have all the solutions in the world. The author takes the reader through a few essays that deal with issues that doctors consider it a mystery . Some of the mysteries explored are the mystery of pain in a human body, mystery of nausea , mystery of blushing in a person, mystery of overeating. With specific instances for each of these above mentioned issues, the author drives home the point that science has no clear cut answers to identify symptoms and offer remedies to the patients.

 

 

Uncertainty

In the world of stats, there is a term called “ Aggregation Bias” . This basically means that if you observe an effect at a global level, you cannot generalize at a local level. For example, if you think have data from all the major cities in India about 2 variables, Y being income levels, X being % educated population . Lets say you make a model out of these two variable only. You might see some effect of education on the income levels. Can you generalize it to every person in every city..No ..This effect is valid at a city level. By applying it to an individual, you are assuming that the city and % educated population are independent. Are they ? They need not be and in most cases they are not. So, this aggregation bias is a killer for most of the social sciences papers that have been published..You see some effect at a macro level but you cant say anything at a local level.

Ok, why is the above stuff relevant to the book? Well, doctors are trained on general rules and general symptoms etc. Basically you can think of it as imparting education at a macro level. However when they work with the patients, do those rules, heuristics, education etc help ? Well , to some extent says the author. More likely it is not going to help . Author gives an analogy of ice cubes. If you study the properties of a set of ice cubes, you can be reasonably sure about the property of an individual  ice cube..Alas!! humans are complex species. So, the doctors always face uncertainty in dealing with their patients and this part explores a few uncertainties that are part of everyday life of docs.

  Takeaway :

The book is a real page turner which gives one , an insider’s look in to the medical field. Your understanding about Fallibility, Mystery and Uncertainty will definitely be more richer after reading this book.

Scientific Illusion

Here is a nice paper that I have stumbled on, "The Scientific Illusion in Empirical Macroeconomics" by Lawrence Summers.

Basic argument of the paper is :

Formal econometric work where elaborate technique is used to either apply theory to data or to isolate the direction of causal relationships where they are not obvious a priori virtually always fails. If this argument is accepted it suggest that in evaluating empirical work we should begin by asking different questions than the ones usually posed.Instead of considering the methods employed, we should ask whether the fact reported is an interesting one that affects our view of how the economy operates. Does it affect our belief about a substantive question?

Good empirical evidence tells its story regardless of the precise way in which it is analyzed. In large part, it is its simplicity that makes it persuasive. Physicists do not compete to find more and more elaborate ways to observe falling apples.Instead they have made so much progress because theory has sought inspiration from a wide range of empirical phenomena.

Macroeconomics could progress in the same way. But progress is unlikely as long as macroeconomists require the armor of a stochastic pseudo-world before doing battle with evidence from the real one.

Books such as freakonomics , frequels, undercover economist etc are a hit in the non-fiction world, precisely because there is a dearth of literature in "doing and articulating empirical research work". Deep structural parameters, structural models give a sense of scientific jazz to economics...but at the end of the day, one must realize that economics / finance is SOCIAL science.