January 2013


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This book has been one of the MOST challenging books to work through. I had tried going through this book many times in the past but could not get past the first 10 pages of the book.  The very first concept that is mentioned in the book is the extension of measure from  a semi-algebra to a sigma algebra. The proof was just beyond me for the simple reason that my fundamentals were shaky. Not wanting to give up, I had to look for an alternative path to this book.  My alternate path was to work through some of the basic fundamentals of real analysis, read around the subject , read about the historical developments behind Lebesue measure and integral, understand Lebesgue integration from a non-measure theoretical perspective,etc. I realize that I have read about dozen books in order to work through this book. Here is the list of 12 books that have helped me:

 

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Title

Summary

1

understanding_analysis

Understanding Analysis

Summary

2

metric_spaces

Metric Spaces

Summary

3

the_calculus_gallery

The Calculus Gallery

Summary

4

lebesgue_measure_integration_burke

Lebesgue Measure and Integration

Summary

5

feller

Probability Theory and its applications – I

Summary

6

Lebesgue-Stieltjes

Lebesgue Stieltjes Integration

 

Summary

7

bressoud_1

A Radical Approach to Real Analysis

Summary

8

bressoud_2

A Radical approach to Lebesgue’s theory of integration

Summary

9

capinski_0

Probability through Problems

Summary

10

protter

Probability Essentials

Summary

11

capinski_1

Measure Integral and Probability

Summary

12

inder_k_rana

Lebesgue Stieltjes Integration

Will write someday

 

I think I was extremely dumb not to follow the book at the first go/second go. There were umpteen number of mathematical concepts and ideas that I was unaware of. However spending time on these dozen books had given me confidence to go over Rosenthal’s book. I am kind of happy with myself that I have managed to get past the daunting chapters of this book and finally understand the underpinnings of axiomatic probability. Probability and Statistics go hand in hand. The better one understands axiomatic probability, the better one is in a position to understand advanced statistics. I hope understanding measure theory helps me in someway in my future work.

It is kind of difficult to review or summarize this book with out using mathematical symbols. I can give an overview of each chapter. However I will do something different .I will try to list down list of questions (top of the mind) that this book answers. If some of the questions make you curious, then this book might be worth your time. These questions are in no particular order.

  1. What do you intuitively mean by a semi-algebra of a collection of subsets of X ? Define in mathematical terms.
  2. What do you intuitively mean by an algebra of a collection of subsets of X ? Define in mathematical terms.
  3. What do you intuitively mean by sigma-algebra of a collection of subsets of X ? Define in mathematical terms.
  4. What do you understand by a Monotone class ?
  5. What is Lebesgue outer measure ?
  6. What is measurable space ?
  7. What is a measure space ?
  8. Why can’t you define a probability measure on a semi-algebra of collection of closed intervals in [0,1]? In other words why is a measure defined on an semi-algebra of intervals, not a valid triple ?
  9. Why can’t you define a probability measure on a algebra of collection of closed intervals in [0,1]? In other words why is a measure defined on an algebra of intervals, not a valid triple ?
  10. What’s the difference between Lebesgue sigma algebra and Borel sigma algebra ?
  11. Define simple measurable functions and state at least half a dozen of their properties?
  12. Define non measurable functions and state at least half a dozen of their properties?
  13. What’s the difference between measurable function on a measurable space and a measurable function on a measure space ?
  14. What you mean by a measurable function being integrable with respect to a specific measure ?
  15. Give an example of a function that is Lebesgue integrable but not Riemann integrable
  16. How do you characterize a non-negative measurable function in terms of a sequence of non-negative simple measurable functions ?
  17. How do you intrinsically characterize a non-negative measurable function?
  18. Give an example where Dominated Convergence theorem can be used.
  19. Given an example where Monotone Convergence theorem can be used
  20. Given an example where Bounded Convergence theorem can be used ?
  21. What is a metric space ? Is the space of Lebesgue integrable functions a metric space ?
  22. What are measurable sets ? How do you identify a measurable set ? What are the properties of measurable sets ?
  23. Is Cantor set measurable ?
  24. Give an example of Non-measurable function ?
  25. What is a set function ? When can a set function be called a measure ?
  26. Is conditional probability a random variable ? If so, What guarantees its existence ?
  27. What are finite measures ?
  28. What are singular measures ? Give an example
  29. If a measure is not discrete, does it necessarily have to be absolutely continuous ?
  30. What’s the relevant of Fubini’s theorem in probability ?
  31. What are the modes of convergence ?
  32. What’s the relationship between point wise, almost sure, uniform and almost uniform convergence ?
  33. Can there be a countable additive set function on intervals other than the length function?
  34. Why should the distribution function of a random variable be right continuous ? What’s the connection between right continuous and countably additivity property ?
  35. Finite additivity + Countably subadditive property of measures is equivalent to countably additive property of measures
  36. Starting from a semi-algebra of collection of intervals in [0,1], how do you construct a measure on a sigma algebra ?
  37. What’s the key result that comes from applying Borel-Cantelli Lemma ?
  38. Why does an integral crop up when talking about expected value of a random variable ?
  39. State Markov’s , Chebyshev’s, Jensen’s and Schwartz inequalities. How do they become useful in proving law of large numbers ?
  40. What’s the difference between strong law of large numbers and weak law of large numbers ?
  41. How can one restate weak law of large numbers by removing the strict condition on the boundedness of second moment ?
  42. How can one restate strong law of large numbers by removing the strict condition of finite third moment ?
  43. What are Lebesgue measurable functions and Borel measurable functions ?
  44. How do you prove the existence of Markov chain ?
  45. Definitions of transient state, recurrent state, null recurrent state, positive recurrent state, irreducible chain, aperiodic chain, ergodic chain
  46. For a  Discrete Markov chain , will the time average be always equal to the ensemble average ? If not, under what conditions do they converge ?
  47. Given an finite discrete Markov chain, How do you compute the stationary distribution ? 
  48. What’s the connection between renewal theory and stationary distribution of a finite discrete ergodic chain ?
  49. Does convergence in distribution imply convergence in probability ? Does convergence in probability imply convergence in distribution ?
  50. In a generic setting, Conditional expectation of a random variable has to be guessed. There is no clear cut formula for computing conditional expectation. So, how does one verify whether the guess is an appropriate one ?
  51. Can you relate the formula of total variance to ANOVA in statistics ?
  52. State a few important properties of Conditional Expectation
  53. How do you handle probability on events with 0 measure ?
  54. State Lebesgue decomposition theorem ?
  55. What are Hilbert Spaces ? What’s the connection between Hilbert spaces and class of Lebesgue intergrable functions ?
  56. What do you understand by product sigma algebra ? How is it relevant to multivariate distributions ?
  57. What are Lp spaces? How does one define norm on such spaces ? How do these spaces connect with the concept of “moments” for random variables ?
  58. What’s the connection between orthogonal property of Hilbert spaces and the correlation between two random variables ?
  59. Intuitively explain the difference between almost sure convergence and convergence in probability ?
  60. When you extend a measure from a semi-algebra to sigma-algebra, how do you check whether the extended measure is unique ?
  61. Is a symmetric simple random walk , a null recurrent Markov chain or a positive recurrent markov chain  ? Prove it
  62. Define a null set
  63. If a family of random variables are uniformly integrable, what does it mean ?
  64. Conditional probability is not a number. It is a random variable. Explain the intuition behind the reason for thinking in terms of random variable
  65. Define Martingale, sub Martingale and super Martingale ?
  66. What do you means by Event happening infinitely often ? What do you mean by Event happening almost always ? Can you make it precise using set notation ?
  67. Expectation operator is order preserving . Prove it
  68. Why should one not be satisfied with Riemann Integral ? What’s the intuition behind Lebesgue integral ?
  69. When you condition a variable on a sub-sigma algebra , what does it mean ? How does it relate to conditioning a variable on another variable ?
  70. What is law of total expectation ?
  71. What’s the connection between moment generating function, characteristic function, probability generating function, Laplace transformation ?
  72. Why not define measure on the outcome space rather than event space ( I guess it’s a dumb question to ask , but I never thought this aspect at all for many years !)
  73. Why can’t a countably additive measure be defined for all subsets of [0,1]
  74. What is the condition on the function to be Riemann integrable ?
  75. What is the condition on the function to be Lebesgue integrable ?
  76. State the fundamental theorem of calculus using Lebesgue integral and Lebesgue measure
  77. Convergence in pth norm need not imply convergence almost everywhere. Is it true ? If so , give an example
  78. What do you mean “ Measure A dominates Measure B” ? 
  79. What’s the connection between conditional expectation and projection ?
  80. Can a set function be countably additive and not finitely additive  ?
  81. What are some of the areas where Martingales are being used ?
  82. Convergence in measure is often a weaker result than convergence in probability ? Explain
  83. Weak convergence of distributions is equivalent to point wise convergence of characteristic functions. Prove it

image Takeaway :

I think this is one of the best books on axiomatic probability. Stochastic processes described in the book are in the discrete setting only. However seeing something in a discrete world clearly, and understanding it, is a stepping stone for working the continuous parameter – continuous state space.

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The author starts off his book using the example of flash crash and an e-bay bidding algo wreaking havoc. He cites these examples as an indication of the extent to which multiple algos dedicated to ONE single task, i.e.bots, are being used in various domains. Obviously the start of algos and heightened excitement for it came from Wall Street. But the author tries to give a journalistic account of all the various places where bots are being used. This book is a light read. It gives examples of interesting people who are using bots to do things that were unthinkable a few years ago, thanks to the super cheap computing power and the ignition( word borrowed from Talent code) given by popular wall street quants, Page&Brin’s and Zuckerbergs of the world.

In this post, I will briefly mention the people mentioned in this book as well as the bots that they have created.

Wall Street, the First Domino

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Thomas Peterfyy

I found the first chapter of the book to be the most interesting story in the entire book. It tells the story of Thomas Peterfyy’s, a Hungarian immigrant, who lacking a full engineering degree, founded one of the most successful companies in the algo trading space, Interactive Brokers. The story is written in Michael Lewis style. where the writing is fast paced and appears like fiction, the only difference being its not. Peterfyy innovations made him a billionaire after hacking for 20 years on Wall Street.

A brief history of man and algorithms

In a space of 20 pages, this book gives a superfast recap of the developments that lead to information age. The rockstars of the story are Fibonacci, Leibniz, Gauss, Bernoulli, Pascal, Euler, George Boole, Babbage, Lovelace, and Claude Shannon.

The Bot top 40( Bots in the music industry)

I found this chapter to be second best in the entire book. It talks about four stories of how bots are making waves in the music industry.

  • Mike McCready and his Music X ray venture that is revolutionizing the way songs are chosen by various music bands and record companies.
  • Success story of Pandora.
  • David Cope creates three revolutionary bots – Emmy that recreates Bach’s music, Howell that gives successful opera concerts and Annie that composes new songs based on machine learning
  • Professor Jason Brown , a math PhD uses algos to solve some of the highly debated questions about Beatles songs and chords used in some of their hits.

The Secret Highways of Bots

This section talks about Daniel Spivey and  his venture “Spread Networks”, a firm that specializes in providing fiber-optic communication infra between NY and Chicago to Algo traders. All said and done, financial industry has been a big reason for innovation in the tech industry. Determining the next field to be invaded by bots is the sum of two simple functions: the potential to disrupt plus the reward for disruption.

For a long time, that equation yielded the largest total on Wall Street, which is why so many of our smartest people, from engineers to physicists to PhDs, began flocking there. Still, that collection of brainpower didn’t stop the industry from seeding economic disaster in 2008.That Wall Street would bring the world to the edge of anarchy and then go whistling into the night is hardly surprising. That’s a condition that may never change. But what does change, almost daily, is the hardware and technology available to grappling traders and their algorithms.

The story of how Wall Street’s technology has evolved is important because its progress eventually flowed to the rest of the economy. Even in the case of Spread Networks, a fiber-optic tunnel built for Wall Street, its effects have already leaked beyond the small world of algorithmic traders. Spivey and Barksdale’s line now carries broadband to small towns that didn’t have it. Spread is transferring large medical image files for hospitals and doctor’s offices. The company offers these non– Wall Street entities lit fiber at affordable prices— an opportunity that exists only because algorithmic traders were willing to shell out millions for exclusive strands of Spread’s dark fiber.

Gaming the System (Bots in Sports and Entertainment)

  • Deep Blue (1997) – A bot that could analyze 200 million chess positions / second as compared to Kasparov’s 3 /second. 
  • Watson (2011) – IBM’s bot for Jeopardy game
  • Tuomas Sandholm – CMU professor’s effort to create an algorithm to play poker, using game theory. Still a long way to go to incorporate the irrational behavior and other complex human variables. Building a world-class poker bot is so hard as algorithms aren’t very good at predicting, analyzing or gaming irrational human behavior
  • Andrew Gilpin applied poker algos to stock market and has managed a hedge fund since 2010
  • Cantor Fitzgerald’s Midas algo that allows betting on sporting games
  • Bruce Bueno de Mesquita- Political science professor who uses game theory algorithms. He predicted the fall of Hosni Mubarak amidst a small group of investment managers at a Wallstreet firm. He was later asked to sign a non disclosure agreement. The Wallstreet firm then took a massive position to capture this prediction and made a ton of money.
  • Billy Beane and his stats algos for baseball– Moneyball fame
  • Prof Galen Buckwalter – The man who created the algos behind eHarmony, a dating site. The site says it now has a hand in more than 2 percent of marriages in US. , i.e. 120 marriages per day
  • Four math grads from Harvard use algos for their venture OkCupid, another popular dating site.

Paging Dr.Bot ( Bots in the medical field)

  • Al Roth uses game theory algorithms to match kidney donors and patients.
  • Dr. Brent James at Intermountain Medical Center in Utah uses data and algorithms to improve hospital performance . Managed to cut the death rate of coronary bypass surgery to 1.5% compared with 3% nationally.
  • AirStrip – Algos that provide real-time patient data straight to doctor’s iPhones, iPads
  • Nick Patterson, a Wall Street hacker , after eight years at Renaissance now writes algos to find , search and sort patterns and relationships from the DNA data. He is changing the speed at which DNA can be analyzed
  • IBM’s bot for healthcare , a modified version of Jeopardy bot, was given a job at Well point , a giant health insurer to assist doctors in their offices with diagnoses, providing a valuable and legitimate second opinion

Categorizing Humankind ( Bots in the Personality Analysis)

  • NASA’s  head psychiatrist involved in developing people-assessing algorithms to select teams for various missions
  • Taibi Kahler , a psychologist at Purdue uses algos to categorize people. These algos are used in NASA, prepping up Presidential speeches and host of other places.
  • Kelly Conway uses algos at eLoyalty, a consultancy for companies with large call centers
  • Peter Brown and Robert Mercer language and speech recognition algos are used in a lot of softwares now. In fact they were so successful that they joined Renaissance and now co-head Renaissance after Jim Simon’s retirement

Wall Street Versus Silicon Valley + Wall Street’s loss is a gain for the rest of us

These sections talk about the boom and bust of algo trading talent war. In years preceding to the financial crash, most of the talented Math and Physics Ivy league grads headed to Wall street. There was a massive need for such grads to write algos , apply math to complex derivate pricing and valuation, hft algos etc. The result of this lead to talent scarcity in many fields that were crying for algos. Soon things started to change. There are many factors that lead to grads turning down Wall Street offers. Firstly, the crisis, Secondly, the Zuckerberg-Twitter-Groupon-Dropbox-Zynga effect, i.e. technology firms were using a ton of AI, algos, bots to create apps on the internet. There is a mention of Jeffrey Hammerbacher who worked as a quant at Bear Stearns, left it to join facebook and created a ton of algos that help facebook in making the site sticky. He now heads Cloudera, another startup that uses quant stuff to manage data storage. The author cites of examples where grads have turned down offers from even Renaissance and says that they are indications that things are changing and people no longer want to end up applying math and algos for Wall Street.

The Future belongs to Algorithms and their creators

The last section of the book gives a few cues that give a sense of the ways bots are going to change and influence things in the future. What about the talent ? Are there are enough math grads and programming majors who can program these bots in various fields that are crying for algo solutions ? This question in the book leads to a discussion on the state of US education sector and the faculty at the junior school level. One of the solutions pointed out by many experts, deans, professors, tech visionaries is to expose kids at the junior school level to math and programming. Programming should be made compulsory to everyone at a high school level. The book ends with the following suggestion:

There are a lot of potentially quantitatively minded people roaming around out there who have never given their brains a proper crack at the game. Smart people aren’t in short supply. Smart people educated in quantitative fields are, however. We just need to increase the size of the funnel that gets people there. Every single student at every high school in America should be required to take at least one programming class. Most students will stop there and move on to do something else. But even if just 5 percent of those students become engaged with the power of devising their own programs and algorithms, it will change the dynamic of our education system and our economy. Imagine all of the students who never give programming or quantitative fields a thought. Math, to them, is a rote skill that must be memorized so that a test or a quiz can be passed; they never see the other side of math that’s changing our world. Or when they finally do, perhaps in college, their life vector is already set toward another field. Programming and computer science classes shouldn’t be relegated to a niche group of students— this is the skill, more than any other, that will matter during this century. All students should get their chance.

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The authors of this book run “Uncommon Schools”, a network of 32 charter public schools across Massachusetts, New Jersey, and New York. The first author, Doug Lemov , is also known for his earlier book, “Teach Like A Champion” that is exclusively geared towards teachers to improve their effectiveness. This book is also, in a way, aimed at teachers, educators, etc. though  the authors suggest that some of the techniques are more general in nature that can be be applicable to any field.

In the introduction , the authors verbalize the thought process behind the book,

What does effective practice look like? What separates true practice from repetition or performance? And what were the key design principles to ensure that practice truly made performance better? And so we arrived at the work before you: a collection of 42 rules to shape and improve how you use practice to get better.

The book, as it clear from the subtitle, talks about 42 meta rules( getting better at getting better) framed by the authors based out their years of experience in running “Uncommon Schools”.  These 42 rules are categorized in to 6 sections, i.e “Rethinking Practice”, “How to Practice?”, “Using Modeling”,”Feedback”, “Culture of Practice “ and “Post Practice”.   Let me list down a few rules that I felt were applicable in a broader context

Section I – Rethinking Practice

Rule 1 Encode Success :
The idea behind this rule is that “Practice makes permanent”. So if your method of practice is wrong and you log in a lot of hours practicing, performance is going to be mediocre. The rule says that we usually romanticize failure that lead to success. While failure may build character and tenacity, its not  good at building skills. Practice should entail working in such a way that there is a sequence of mini-successes along the path. This rule is different from what one generally gets to read where practice involves constant struggle and failures. This mindset will make one fix the problem right away, thus ensuring that there is a success element before moving on. In the context of teaching or learning math, this becomes crucial. Every concept be it an axiom or a theorem or an equation needs to be followed up by a quick test to check whether the students are getting it or not.

Rule 2 Practice the 20 : 
The idea behind this rule is to focus your time on 20% of things that drive 80% of the success. In a school setting this would mean that a teacher should customize the quizzes/ lessons so that each student works on his strengths and does not dissipate energy on things that will he/she might become merely good at. Being great at the most important things is more important than being good at more things that are merely useful. No wonder the online courses are a big hit amongst the students. You learn according to your strengths rather than some predetermined syllabus.

Rule 3 Let the Mind Follow the Body : 
Once you have learned a skill to automaticity, your body executes, and only afterwards does your mind catch up. This is evident in sports, music and I guess in many other domains where there is a premium placed for speed , fast innovation.

While you are executing a series of complex skills and tasks that were at one time all but incomprehensible to you, your mind is free to roam and analyze and wonder. If you use practice to build mastery of a series of skills, and if you build up skills intentionally, you can master surprisingly complex tasks and in so doing free your active cognition to engage with other important tasks.

Rule 4 Unlock Creativity . . . with Repetition : 
The more you can do something in autopilot, the more your mind can wander , analyze and make surprising connections. Once you put in a lot of practice and do some of the complex tasks in auto-pilot mode, you can learn stuff more deeply.

Rule 5 Replace Your Purpose (with an Objective) :
Quantify your work , i.e. develop your own metrics to track your practice sessions.

Rule 6 Practice “Bright Spots”  : 
Drawing from Dan and Chip Heath who coined the term “Bright Spots” (overlooked and under leveraged points that actually work), the rule says that it is crucial to keep track of what’s working for you. Let’s say you understand something well by seeing a visual, then its imperative that you look for such kind of visuals to aid your understanding. To be specific, for a long time I had difficulty understanding conditional expectation of a random variable given another random variable. Well, conditional probability is something that is intuitively easy to understand. But conditional expectation is a vastly different animal. Years ago I came across a visual that just made the concept clear and it has stuck firmly in my mind.  Since then, I have always tried to visualize any type of operator / random variable / formula in terms of pictures. Once I can associate a good visual with a definition/theorem/proposition, things stick in my mind. I guess one must keep observing ourselves, to note these “bright spots” in various contexts.
In essence , the rule says “practice strengths”

Rule 7 Differentiate Drill from Scrimmage : 
Understanding these terms are essentially to understanding this rule. A drill deliberately distorts the setting in which participants will ultimately perform in order to focus on a specific skill under maximum concentration and to refine that skill intentionally. Pick any thing you want to master, isolate one specific aspect of the process and practice. One can easily relate a “drill” in the context of playing an instrument. Suppose you are playing a set of notes on 16 beat cycle(Teentaal). Playing it on a 12 beat cycle(Ektaal) and then playing the same notes on a 10 beat cycle(Jhaptaal), would be qualify as a drill. Or keeping the same taal and increasing the tempo of the notes would also qualify as a “drill”. In a sense you are creating an artificial environment of varying taals for the same set of notes/swaras. No one does this in real performance. Usually the beat cycle remain constant for a specific rendition. But the “drill” makes you focus intensely on mastering those specific notes. A scrimmage, by contrast, is designed not to distort the game but to replicate its complexity and uncertainty.  In the context of music, this would mean giving a playing in front of your friends / a small group of people so that you are ready to face the actual audience. Both are essential but the authors say that “drill” matter more than “scrimmage”.

Rule 8 Correct Instead of Critique How to Practice
Practice is about inscribing habits on the brain through repetition with variation. What makes you execute an action in performance is having done it in practice. So critique— merely telling someone that she did it wrong— doesn’t help very much. Only correction, doing it over again right, trains people to succeed. This rule says that a mistake should be followed up by at least 4 to 5 times of doing it the right way. The rule says

It may be worth reflecting that the body’s neural circuits have very little sense of time. If you do it right once and wrong once, it’s encoded each way equally in your neural circuitry. It may matter little which one happened first. The ratio is one to one. If you are correcting, then, correct in multiples.

Section II – How to Practice?

Rule 9 Analyze the Game :
“Moneyball” is a great success story for a short period of time. Soon the model was quickly replicated by every club and it did not become a differentiating factor. The authors hypothesize that Billy Beane, the manager of Oakland A’s was in fact wrong in his thinking that skillsets are pretty much fixed and all one needs is to trade off one player against the other , much like trading stocks. The rule takes a dig at such an assumption and says that, had Billy Beane gone one step ahead and analyzed the reasons behind players’ superior performance, may be he would have turned Oakland A’s in to a talent hotbed. So, mere analysis of the game is not enough. As a coach, you have to describe those skills to others so that they are given some sort of a map.

Rule 10 Isolate the Skill  :
When teaching a technique or skill, practice the skill in isolation until the learner has mastered it.

Rule 11 Name It :
Naming a specific skill or technique becomes a powerful shorthand for talent development.

Rule 12 Integrate the Skills :
Simulate the performance environment so that you can judge how your skills work together.

Rule 13 Make a Plan :
Quantify your practice plan. The more thought you put in to preparing the plan, the better the practice session turns out to be.

Rule 14 Make Each Minute Matter :

Get a metaphorical whistle , so that you know when you are wasting time and doing something that is taking away from your valuable practice time.

Section III – Using Modeling

Most of rules in this section are too specific to teachers in a classroom environment, except possibly Rule 19.

Rule 19 Insist They “Walk This Way”  :
Sometimes replicating the action as it is, might be beneficial than trying to customize the implementation.  The various steps in activity might have a deeper meaning and you miss by customizing it. To give a specific example, let’s say you are trying to prove a theorem in a math text. You wander for while, you start out with a few definitions, lemmas but let’s say you get nowhere. It is sometimes better to follow the exact proof that is followed in the text,backtrack and then see what all paths the author has used to prove something. This way the learning is more comprehensive than “somehow” proving the theorem.

Section IV- Feedback

Rule 23 Practice Using Feedback (Not Just Getting It)  : 
The authors quote Joshua Foer’s book “ Moonwalking with Einstein”, that says “People often arrive at an “OK Plateau,” a point at which they stop improving at something despite the fact that they continue to do it regularly. The secret to improving at a skill is to retain some degree of conscious control over it while practicing  is to force oneself to stay out of autopilot.” The process of intentionally implementing feedback is likely to keep people in a practice state of increased consciousness and thus steeper improvement. The Rule says that we all get feedback but few of us use it to improve themselves.

Rule 24 Apply First, Then Reflect :
Once you get a feedback, try to work on it asap, instead of discussing and debating about the feedback. The sequence that practice should generally follow is 1. Practice 2. Feedback 3. Do over (repractice using the feedback) 4. Possibly do this multiple times 5. Reflect. This is different from the sequence that most people are naturally inclined to follow: 1. Practice 2. Feedback 3. Reflect and discuss 4. Possibly do over

Rule 25 Shorten the Feedback Loop : 
Speed of consequence beats strength of consequence pretty much every time. Give feedback rightaway even if its imperfect.Remember that a simple and small change, implemented right away, can be more effective than a complex rewiring of a skill.

Section V – Culture of Practice

Rule 31 Normalize Error :

The book mentions a skier’s story to point out that importance of the attitude that we take toward failure. In this context, the book mentions Joshua Foer’s (Moonwalking with Einstein) illustration of the OK plateau

When first learning, we initially improve and improve until we ultimately reach a peak of accuracy and speed. Even though many of us spend countless hours typing in our professional and personal lives, however, we don’t continue to improve. Researchers discovered that when subjects were challenged to their limits by trying to type 10– 20 percent faster and were allowed to make mistakes, their speed improved. They made mistakes, fixed them, then encountered success.

The authors give specific examples of classroom situations where teachers use specific words and body language. They are relentless in ensuring that errors don’t go unaddressed and become more inscribed. They correct warmly and firmly. They prefer the rigor that self-corrections provide (as by having a student reread a challenging passage and fix her own mistake) but are direct when necessary (“ That word is pronounced ‘diagram’”).What is the relationship between the need to practice success and the need to normalize error? What you do in practice is practice succeeding. But when practice is well designed, you can also use it to isolate failure. This allows people to take calculated risks in order to improve at a particular skill. When failure happens in your organization, you want to have built a culture that embraces it. When you effectively normalize error, what starts with failure reliably ends in success. The process of encoding success is what makes failure safe.

Rule 32 Break Down the Barriers to Practice :

Practicing what we already know is sometimes boring to our mind that craves novelty. The chapter describes a few ways to overcome it

Rule 33 Make It Fun to Practice :
I think this is a very important aspect of practice. Unless you have this mindset, it is difficult to sustain practice for a long time.

Rule 37 Praise the Work Post-Practice :
Carol Dweck has studied the impact of praise on student achievement. Her work has demonstrated that when you praise children for a particular trait (for example, being smart) instead of a replicable action (for example, working diligently on a challenging set of math problems), students may actually underperform because they don’t see their achievement as being within their control. Praising traits leads students to believe either “I’m smart” or “I’m not,” whereas praising actions leads them to believe they can change their behavior to influence outcomes. We should learn from Dweck’s work when working with both children and adults in practice. Praise the actions that you want to see from your players, your children, or your employees, and these actions will multiply.

There are a ton of examples used in the book like,

  • Lionel Messi and his way of practicing that involves isolating a specific aspect of the game and just working on that aspect for hours together. Even if one does not understand the game, one can seek out the same kind of mindset in one’s work
  • Xavi Hernandez ,one of the top soccer midfielders in the world practices “rondos”, a specific soccer activity every single day. This example bluntly asks the reader , “Are you doing something every single day ?”. If not, may be you need to reevaluate your practice sessions.

Conclusion

The authors end the book with a section called “ The Monday Morning Test” . It talks about concrete actions and approaches that can be applied in an array of settings and that one can start using as early as Monday morning. In one of the scenarios, they reemphasize specific rules that suggest how one might use these rules as an individual in the quest for success in any endeavor.

Rule 17: Make Models Believable Seek Believable Models
As an individual you need to seek out believable models, people who are doing the same work you are doing, in a similar context. Don’t just go to the symphony to hear the greats perform; go behind the scenes and watch how they practice— the process by which they get better. You don’t have to live near a concert hall to be able to do this. YouTube is an amazing tool for practice. Use it to see how the greats practice.

Here’s a link mentioned in the book that emphasizes practicing slowly and practicing for about 5hrs max in a day.

Rule 23: [Seek and] Practice Using Feedback
Learn from Atul Gawande and seek out a coach. It doesn’t have to cost you anything. Ask someone, even a peer or colleague in your field, to be your “extra ear.” Practice using the feedback you receive from your coach. Don’t just nod your head in acceptance; immediately try out your coach’s suggestions to incorporate them into your practice.

Rule 4: Unlock Creativity
Identify those skills in your profession or hobby that are weak, thus preventing you from being more creative. Practice these skills again and again until they are committed to your muscle memory. This will allow you to free up more creative space and reach new heights, whether you are sitting at a piano, delivering a speech in a boardroom, or teaching math to 30 sixth-graders.

Rule 31: Normalize Error
Be willing to push yourself a little bit harder, out of your comfort zone, and take calculated risks in the name of improvement. Maybe that means practicing a difficult conversation that you never thought you could have with your boss about your career development, speaking with conviction and persuasion. Or perhaps it means practicing your violin solo with the metronome four ticks higher than you normally would. Push yourself to make mistakes in the name of improvement.

 

image_thumb2 Takeaway :

It should come as no surprise that most of the situations mentioned in the book are from a class room environment , as the authors run academic institutions.  Having said that, a persistent reader will find a few gems in the book that will help him/her in improving her practice, be it practicing an instrument, learning a new language , playing a game etc.

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Laplace Transformation is a useful tool in problem solving. From the probabilistic theory perspective, Moment generating function is nothing but a linear combination of two Laplace transforms. In fact moment generating function has a more direct relationship with Laplace-Stieltjes transform. Most of the calculations involving MGF and convolutions become easy with the use of Laplace Transform.   I think one of the most powerful ways to use Laplace transforms is solving Partial Differential equations.  Having the basic Laplace transforms and Inverse Laplace transforms at your fingertips is good for solving Toy PDEs. But in real life, most of the Inverse Laplace transformations have no closed form solutions. They have to be solved numerically. Coding up an Inverse Laplace transform in whatever language you are comfortable is a nice learning experience. My Laplace transform fundas were rusty, so decided to go over this book quickly.  The author P.P.G Dyke, being an applied mathematician, makes the book interesting by giving a range of problem domains where Laplace and Fourier transforms can be used. This book is ideal for those who want a quick recap of Laplace and Fourier transforms.

Inverting a Laplace transform has some bit of math of behind it. Here is a paper by Joseph Abate and Ward Whitt that gives the details behind numerically inverting Laplace transform. The nice thing about the paper is that the pseudo code for the algorithm is given so that one can go ahead, code up the algo and subsequently write at least a dozen unit test cases for each of well known closed form Inverse Laplace transforms.

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Use of Fourier and Laplace transform and such analytical methods have been surpassed by computers that solve a PDE using numerical methods. However analytical methods give the intuition behind the solution that is not so obvious from the numerical solution.

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Reading this book was like revisiting an old services marketing course. This book is written by Terry Green, a guy who has been in to Queue management  business for over 20 years. So, it is more a practitioner’s book written to help supermarket chains, banks, or any establishment that deals with customers who form a Queue to get serviced. This book does not have a single mathematical formula but intuitively covers many aspects of the math behind Queueing.

Let me mention briefly the kind of math that is used in analyzing Queues. A Queueing system is generally denoted by “A/B/X/Y/Z”, where A describes the arrival pattern for a system, B stands for the service pattern, X stands for the number of parallel service channels, Y the restriction of system capacity and Z , the queue discipline.  If you want to analyze any system, you need to classify the system accordingly. Broadly the classification could be :

  • A – Arrivals can be Exponential, Deterministic, Erlang, Mixture of k exponentials, Phase type or Generic distribution
  • B – Servicing can be Exponential, Deterministic, Erlang, Mixture of k exponentials, Phase type or Generic distribution
  • X – # of parallel servers can be finite or infinite
  • Y – System capacity can be finite or infinite
  • Z – Queue discipline  First come- First served , Last come – First Served , Random Selection for service, Priority Queue, General

Given these broad categories ,the number of queueing models can be as high as (6 arrival types*6 service types*2 types of servers *2 types of System capacity *5 types of Q discipline)  as 720 different stochastic models. Add to this, customer behavior like Balking, Reneging, Jockeying, the number of models can actually explode. Well, the number 720 that I have mentioned here is an exaggeration. All queueing systems can be analyzed as a continuous time birth-death Markov process. If you understand let’s say G/G/1 queueing system, the rest of the systems are basically tweaks as far as problem formulation is concerned.The structure is more or less same but the way to solve the steady state equations differ. Generating functions/ Differential operators / Iterative methods/ Linear Algebra / Simulation are some of the various ways to find the steady state probabilities of the system.  The more you assume exponential distribution for various components, the more your life become easy and most of the times you can derive closed form solutions. Beyond exponential arrival and exponential servicing, the math becomes fairly complicated.

I think that doing ONLY the math behind the queueing system creates a bias. Let me give an example.Imagine you are a graduate student and you are moonlighting at a cafeteria to earn some extra bucks. Let’s say , the inter arrivals of customers in to the cafeteria is an exponential distribution with average of 15 customers/ hr. The time you take to service each customer follows a Generic distribution , let’s say on an average you are able to serve a coffee in 3 minutes  with a standard deviation of 1 minute. What’s the average Q size that might form in the cafeteria? Not to make things complicated, assume that the cafeteria has the capacity to accommodate infinite Queue length. Answering this simple question  needs a fair amount of math (PollaczekKhintchine formula).But once one gets past the math and derives an expression, it is easy to think that everything is neat and water tight and that’s all there is to it. However even for this simple model, there are multiple real life aspects that need to be incorporated. Is it first of all M/G/1 queue ? Is there reneging or balking ? What if there are bulk arrivals(Usually a group of friends decide to have something and then head to the cafeteria).  You can try to incorporate these things, but there are so many soft factors involved in the Queue formation that modeling the process and coming up with an implementable solution seems mind boggling. Extend this to supermarkets, hospitals, banks, call centers where there are multiple people servicing customer who do not behave as a standardized Poisson process or for that matter any stable generic distribution.

Books like these are valuable for two kinds of readers. First kind are those who believe that developing a right model is all that is there to Queue management. Second type are those who might not be using data/ statistics AT ALL to solve queueing problems in their service environments. This book is a bridge between the totally subjective way and totally scientific and objective way of handling queueing and service environments.

The author Terry Green is the founder of Qmatic system, a Queue management system that has been widely adopted in UK. Qmatic,  has around 55,000 systems in 120 countries across the world. Roughly, a quarter of the world’s population benefit from fairer, faster service every year as a result. When the first installation of Qmatic was done, it so happened that, the cashier number 3 was available to be served for the customer waiting in the Q and hence the title of the book,”Cashier number 3 please”. Also the voice in Qmatic system is that of Terry Green.

The book starts off with emphasizing the perception of managing waiting times with an example from Disney theme parks.

Theme parks are about fun. People go there to experience the thrill of the attractions. And yet how much of the day is spent on the actual rides? Probably no more than 30%. The rest of the time is spent moving between rides, taking refreshment breaks, and queueing for the next ride. Theme parks have thus become the stars of the waiting game – and Disney indisputably the masters. Their work on managing the perception of waiting customers has been an integral part of the success of their parks.

Most of the businesses now care about the customer waiting times and try to systematically manage it. The author gives his first experience in Queue management at UK post offices

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If you look at the above Queueing situations, the traditional multiple queue is still the one used in supermarkets and many other places. The book talks about the situation of Post offices in 1990 when the traditional multiple queue system was followed. Since there was no categorization of counters, some Qs moved very fast, some Qs took ages to move. Customers did all sorts of things like jockeying, balking, reneging etc. Obviously one had to come up with a better solution. Intuitively the Single linear queue is a better alternative as the effect of one guy taking a lot of time is not felt by others in the Q as they find other servers free.

One can prove that single linear queue is superior to traditional multiple queue by making a few assumptions( however some of the assumptions are questionable as we have noted in the cafeteria example).  In the first case it is 5 independent M/M/1 systems.In the second case, the Queueing system is an M/M/5 system since there are 5 servers.  The difference is that arrival rate for each server in the first system is 1/5th of the arrival rate of the second system. In fact it can be shown that any M/M/X system is better than X independent M/M/1 systems under certain assumptions(service rate is constant). One can easily show that the expected waiting time in the Q for traditional multiple Q is greater than Single linear Q.The math also concurs with our intuition that single linear queue system localizes the customers who have heavy server requirements.

After convincing the post office to convert single linear Q , there were subsequent problems to be solved. How does one tell the head of the Q member to proceed to the counter that is free. Since we are all used to Qing systems, we automatically think that there should be announcement and digital display for Queue management. However things did not evolve in such a straightforward manner. The author talks about various failed solutions before which the electronic counter + announcement made way to the post offices.

Around the same time, virtual Queueing was being adopted in European countries, where you book a place in the queue and then reach the server at the allotted time. There is a great debate on the question ,”Which Queueing system is better ?”. The author describes multiple cases where it is more a matter of convenience than anything else that differentiates between two systems. Even though the author starts off with analyzing the math and statistical aspects of Queueing systems, he realizes that managing perceptions of the customers was critical, i.e. behavioral models were far more important than statistical data models. The entire book contains a ton of cases where math aspects of Queueing had to combined with customer’s perception and customer’s expectation of the waiting time and service time.

You are certain to end up in a Queue somewhere or the other in your daily life, be it a supermarket store / bank / book store/ mall /waiting for a phone service rep. In all of these cases, the system is common. You have arrivals, you have queues and you have servers.  This book at minimum will give you new eyes to look at a Queue. So, instead of getting frustrated in Queues and tiring yourself, you can quietly watch the queue dynamics and think about the things that are done well, the things that are being sidelined, the things that can be improved..After all, books you read,  should make you curious about the world you live in and this book does a nice job of giving an intuitive reasoning for the Queueing systems that you encounter.

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Little is known about Annapurna Devi in the media and amongst sitar lovers. Some people know her as the wife of the Pt. Ravi Shankar, some  know her as an expert in Surbahar ( an instrument that is technically superior to Sitar) , some know her as a recipient of Padma Bhushan award. However nothing much is known about her personal life except that her marriage with Ravi Shankar was a disaster. Annapurna Devi has chosen to make herself almost inaccessible. She has stopped performing in public / stopped giving concerts, stopped recording her music. She has shunned public life to an extent that she hardly steps out of her house. She does not welcome any visitors. She teaches sitar and music to a selected few. In a sense, she has almost no contact with the outside world.

Here is an artist who has not given a public performance for the last 50 years and yet music stalwarts like Nikhil Banerjee, Hari Prasad Chaurasia consult her before their concerts. What is it in her that draws various artists to take suggestions?. Why has she stuck to playing Surbahar and not Sitar ? What motivates her to get up each day with the single motto of playing and teaching Sitar and nothing else? All these questions and many more are answered through this book. This book is indeed quite an achievement by Swapan Kumar Bondyopadhay, who manages to get to her , in the first place(as she does not meet any outsiders), knows about her life’s journey first hand, interviews her siblings and disciples and writes her story.

Annapurna was the third child  of Baba Allauddin Khan and Madina Begum. She was born at Maihar, Madhya Pradesh in 1927. Her father Baba Allauddin Khan is the Sarod Maestro and a mentor to a host of Indian music legends like Pandit Ravi Shankar, Ustad Ali Akbar Khan, Nikhil Banerjee, Panna lal Ghosh, etc. Baba Allauddin Khan was a court musician and lead a life that was solely dedicated to music. Incidentally, the name, Annapurna, for her daughter was suggested by the local King where he rendered his services.  Baba’s elder son Ali Akbar Khan and his eldest daughter Jahan Ara were both introduced to the world of music at a very early age. Baba was afraid to teach Annapurna Devi as her eldest daughter Jahan Ara’s passion towards music lead to her eventual death. Jahan Ara’s in-laws were against any form of music and hence made her life miserable. Baba having seen her eldest daughter die in front of his eyes needed all the courage in the world to teach music to her second daughter. Naturally , he resisted his urge to teach Annapurna for quite some time. But then it all changed one day when he heard Annapurna sing and correct her brother’s composition. He might have thought that he would be doing a great mistake by not allowing this latent music talent to flourish. So, he started teaching Sitar to Annapurna.  During her initial learning years from Baba, she meets Ravi Shankar. It so happens that Baba accompanies Uday Shankar’s troupe and gives many performances all over Europe and that’s when he meets Ravi Shankar. He  teaches a few music lessons to Ravi Shankar while in Uday Shankar’s troupe, but gives a word of caution to the fidgety Ravi Shankar that,

ek sadhe sab sadhe, sab sadhe sab jaaye

One who concentrates on one thing gets it, One who runs after too many things loses all

Even though Ravi Shankar is attracted to the western life and is mesmerized by all the things he gets to see and do as a part of Uday Shankar’s troupe, he decides to give it up all, for the talim under Baba. That was a life changing decision. He leaves his brother’s troupe and comes to Maihar to learn Sitar from Baba. Ravi Shankar starts living next door to Baba to learn Sitar from him. The strict focus on riyaz under Baba’s talim gives the much needed direction to Ravi Shankar’s life. During his stay at Maihar and learning music, he  marries Annapurna Devi  when she was  just 14 years old. They have a son , Subhendra Sankar with in a year. So for a while it looks like the entire family was having a great time. With Baba’s talim, Ravi Shankar and Annapurna’s musical abilities were growing exponentially. With Subhendra’s arrival in to the family, there was happiness all around.  Alas! these happy times came to an abrupt end as Ravi Shankar started having an affair with Kamala, the sister of one of the Baba’s disciples. In fact Ravi Shankar comes home one day and confesses to Annapurna that she is totally in love with Kamala. Hearing this, Annapurna’s life is shattered and heads back to Maihar with her son. Those were the initial signs of a life long bitter relationship between the two. Ravi Shankar continues to practice Sitar. But at the same time, he had his affair going.

The life at Maihar changed Annapurna to a large extent. As she went through suffering her heart grew stronger. The long hours of introspection in Maihar helped her to detach and gain a mature outlook on life and its frustrations. It was in this period that she grew intellectually very rapidly. For a while Annapurna tried reconciling to this fact and thought about somehow getting back Ravi Shankar.

So, despite Ravi Shankar’s affair, she decided to go and stay with him at Delhi. Their personalities were poles apart. Annapurna played sitar for the soul and there was no need for unnecessary embellishments. For her music was an outlet for the expression of joys and sorrows one one’s life. It was independent of the externalities of a stage appearance.  Ravi Shankar wanted to change according to the times. He knew that people were no longer going to sit and enjoy a two hour long aalap. He wanted to bring in speed, beats, tabla, and novelty in to Sitar. For a brief period of time, things went well professionally. But soon, he hit a bad patch.

Nothing worked for Ravi Shankar and his life in Delhi was miserable. He tries committing suicide but just in time, a guru whom he calls tatbaba comes to his rescue and gives a new lease of life. He encourages Ravi Shankar and restores his self-esteem. From then on Ravi Shankar treats tatbaba as a god. This is again one of the reasons for the rift between Annapurna and Ravi Shankar. Annapurna did not believe in such type of gurus and idol worships. For her, music gave all the inner strength and purpose to live. Someone trying to end his life because of his inability to get by in life , was something unthinkable for Annapurna. But that’s exactly what her husband was up to.

During her stay with Ravi Shankar, they disagreed on the many aspects of music, for example, the tempo of the compositions that they were to play at concerts. Annapurna liked the slow soulful surbahar instrument(technically far more superior than Sitar), Ravi Shankar preferred Sitar. Both gave a few performances in Delhi and for which the book says anecdotally that Annapurna was better appreciated than Ravi Shankar.  The book says after a few concerts , Annapurna never played in public with Ravi Shankar. Some say that Ravi Shankar made her take a vow that she would not give a concert in public. But the book makes it clear that there was some other reason for Annapurna deciding never to share a stage with Ravi Shankar. The author says that he was unable to get the actual reason out of Annapurna.So, I guess the answer to the question, “Why did Annapurna stop giving public performances with Ravi Shankar?” will remain a mystery forever.

In any case, the couple could not live together in Delhi as they were constant quarrels. The quarrels in fact were one sided as Annapurna would always maintain silence for any accusation.Most of the accusations by Ravi Shankar were trivial as compared to the reason for her stony silence, i.e. Ravi Shankar’s affairs. So, soon, the logical thing happened. Annapurna left Delhi and returned to Maihar with her son. She wanted to dedicate her life to two tasks. Firstly, carry on the tradition of Baba’s musical inheritance and secondly , teach her son so that he becomes a great Sitar player.  A wonderful thing happened then. Her sibling Ustad Ali Akbar Khan started a music college in Calcutta and recruited her as the vice-principal. Annapurna’s got a second life in Calcutta. She immersed herself in hours of riyaz and teaching Sitar.

When any relationship goes sour, there are repercussions felt by people around. In this case, it was their son, Subhendra’s life became a tragedy. He struggled to find meaning in his life, given that his parents were diametrically opposite in their thinking styles and ways of life. He didn’t know the right path to follow. There are some instances mentioned in the book that point to Subhendra’s superior sitar talent than his father. Under her mother’s talim, he learnt a ton of stuff and was getting groomed to become a great musican. But destiny had something else planned for him. He craved for the razzle-dazzle of his father’s  life. So,in a way he was torn between the stoic, soulful artist, his mother, and the performer,  his ever glamorous father.

One doesn’t know how much to believe, but the book says that Ravi Shankar deliberately had arranged for a lesser volume speaker for his son’s sitar whereas a higher and better quality speaker for his own sitar, when they performed together on the stage. The book mentions many a people claiming that Subhendra was on par and superior to Ravi Shankar. In any case, the fact remains that Subhendra, the son of the two of the greatest sitar players , inheritor of Maihar parampara met with a tragic death.

Since the last 40 years, Annapurna has been living in Mumbai and teaching Sitar to a selected few. Some of her disciples are the stalwarts of Indian music , i.e. Nikhil banerjee, Hariprasad Chaurasia, Aamit Bhattacharya, Nityanand Haldipur, Suresh Vyas, Basant Kabra.  The author of this book, Swapan Kumar Bondyopadhay, meets all these musicians and tries to cull information about Annapurna. The narrative given by each of the disciples gives a little more idea about the kind of life Annapurna lived.

Here are some assorted statements about Annapurna and music, mentioned at various places in the book:

  • What’s the approach to a raga ? There is nothing like approach to a particular raga. It is approach to the music total. For her music is like an act of worship. When she surrenders to it, it just happens.
  • In the Zen sense. The Zen master archer does not aim and shoot. He shoots and the target is there. Same is the case with Annapurna with Sitar.
  • She is one of the most insightful persons I have ever met. I think living alone has done her a lot of good.
  • When asked, Why do you shun company ? Annapurna replies, “I have found out that it is much more peaceful not to meet people. That helps me focus and immerse myself in music”.
  • One should always practice as if the teacher was sitting in the next room listening.
  • I realized that the secret of her strength resided in the fact that she was all by herself shunning the outside world. I think all this, being a recluse and living alone , works in her favor. If you are in a excited state or angry , you cannot judge the situation. You have to calm down and focus. And she is in that state all the time.
  • Music of for that matter any form of art, is a spiritual quest. Knowledge per se, we divide in to two. Intellectual and Experimental. Intellectual knowledge covers normal education and collection of data and information. Experiential knowledge is concerned with spiritual things where your holistic being is used. Your mind, body and spirit are all focused to experience something and the attempt is always to bring oneself to a certain level. In that your mind does not come in the way. Your experience and and your mind do not match.

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By bringing out Annapurna’s life in to the media, the author has done a world of good because this book is a testimony to the superlative experience that one gets by playing an instrument slowly. The aalap, the slow soulful playing of notes and experiencing each note is the essence of playing Sitar. The book cautions against becoming a speed demon.