Slippery Slopes

But, this dictum of denying bonus to the whole firm during bad times doesn’t work quite right either, for a variety of interesting reasons. First, let’s look at the case of the AIG EVP. AIG is a big firm, with business units that operate independently of each other, almost like distinct financial institutions. If I argued that AIG guys should get no bonus because the firm performed abysmally, one could point out that the financial markets as a whole did badly as well. Does it mean that no staff in any of the banks should make any bonus even if their particular bank did okay? And why stop there? The whole economy is doing badly. So, should we even out all performance incentives? Once we start going down that road, we end up on a slippery slope toward socialism. And we all know that that idea didn’t pan out so well.

Another point about the current bonus scheme is that it already conceals in it the same time segmentation that I ridiculed in my earlier post. True, the time segmentation is by the year, rather than by the month. If a trader or an executive does well in one year, he reaps the rewards as huge bonus. If he messes up the next year, sure, he doesn’t get any bonus, but he still has his basic salary till the time he is let go. It is like a free call option implied in all high-flying banking jobs.

Such free call options exist in all our time-segmented views of life. If you are a fraudulent, Ponzi-scheme billionaire, all you have to do is to escape detection till you die. The bane of capitalism is that fraud is a sin only when discovered, and until then, you enjoy a rich life. This time element paves the way for another slippery slope towards fraud and corruption. Again, it is something like a call option with unlimited upside and a downside that is somehow floored, both in duration and intensity.

There must be a happy equilibrium between these two slippery slopes — one toward dysfunctional socialism, and the other toward cannibalistic corruption. It looks to me like the whole financial system was precariously perched on a meta-stable equilibrium between these two. It just slipped on to one of the slopes last year, and we are all trying to rope it back on to the perching point. In my romantic fancy, I imagine a happier and more stable equilibrium existed thirty or forty years ago. Was it in the opposing economic ideals of the cold war? Or was it in the welfare state concepts of Europe, where governments firmly controlled the commanding heights of their economies? If so, can we expect China (or India, or Latin America) to bring about a much needed counterweight?

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

Profit Sharing

Among all the arguments for hefty bonuses, the most convincing is the one on profit generation and sharing. Profit for the customers and stakeholders, if generated by a particular executive, should be shared with him. What is wrong with that?

The last argument for bonus incentives we will look at is this one in terms of profit (and therefore shareholder value) generation. Well, shareholder value in the current financial turmoil has taken such a beating that no sane bank executive would present it as an argument. What is left then is a rather narrow definition of profit. Here it gets tricky. The profits for most financial institutes were abysmal. The argument from the AIG executive is that he and his team had nothing to do with the loss making activities, and they should receive the promised bonus. They distance themselves from the debacle and carve out their tiny niche that didn’t contribute to it. Such segmentation, although it sounds like a logical stance, is not quite right. To see its fallacy, let’s try a time segmentation. Let’s say a trader did extremely well for a few months making huge profits, and messed up during the rest of the year ending up with an overall loss. Now, suppose he argues, “Well, I did well for January, March and August. Give me my 300% for those months.” Nobody is going to buy that argument. I think what applies to time should also apply to space (sorry, business units or asset classes, I mean). If the firm performs poorly, perhaps all bonuses should disappear.

As we will see in the last post of the series, this argument for and against hefty incentives is a tricky one with some surprising implications.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

Talent Retention

Even after we discount hard work and inherent intelligence as the basis of generous compensation packages, we are not quite done yet.

The next argument in favour of hefty bonuses presents incentives as a means of retaining the afore-mentioned talent. Looking at the state of affairs of the financial markets, the general public may understandably quip, “What talent?” and wonder why anybody would want to retain it. That implied criticism notwithstanding, talent retention is a good argument.

As a friend of mine illustrated it with an example, suppose you have a great restaurant thanks mainly to a superlative chef. Everything is going honky dory. Then, out of the blue, an idiot cook of yours burns down the whole establishment. You, of course, sack the cook’s rear end, but would perhaps like to retain the chef on your payroll so that you have a chance of making it big again once the dust settles. True, you don’t have a restaurant to run, but you don’t want your competitor to get his hands on your ace chef. Good argument. My friend further conceded that once you took public funding, the equation changed. You probably no longer had any say over payables, because the money was not yours.

I think the equation changes for another reason as well. When all the restaurants in town are pretty much burned down, where is your precious chef going to go? Perhaps it doesn’t take huge bonuses to retain him now.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

In the last post, I argued that how hard we work has nothing much to do with how much reward we should reap. After all, there are taxi drivers who work longer and harder, and even more unfortunate souls in the slums of India and other poor countries.

But, I am threading on real thin ice when I compare, however obliquely, senior executives to cabbies and slum dogs. They are (the executives, that is) clearly a lot more talented, which brings me to the famous talent argument for bonuses. What is this talent thing? Is it intelligence and articulation? I once met a taxi driver in Bangalore who was fluent in more than a dozen languages as disparate as English and Arabic. I discovered his hidden talent by accident when he cracked up at something my father said to me — a private joke in our vernacular, which I have seldom found a non-native speaker attempt. I couldn’t help thinking then — given another place and another time, this cabbie would have been a professor in linguistics or something. Talent may be a necessary condition for success (and bonus), but it certainly is not a sufficient one. Even among slum dogs, we might find ample talent, if the Oscar-winning movie is anything to go by. Although, the protagonist in the movie does make his million dollar bonus, but it was only fiction.

In real life, however, lucky accidents of circumstances play a more critical role than talent in putting us on the right side of the income divide. To me, it seems silly to claim a right to the rewards based on any perception of talent or intelligence. Heck, intelligence itself, however we define it, is nothing but a happy genetic accident.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

One argument for big bonuses is that the executives work hard for it and earn it fair and square. It is true that some of these executives spend enormous amount of time (up to 10 to 14 hours a day, according the AIG executive under the spotlight here). But, do long hours and hard work automatically make us “those who deserve the best in life,” as Tracy Chapman puts it?

I have met taxi drivers in Singapore who ply the streets hour after owl-shift hour before they can break even. Apparently the rentals the cabbies have to pay are quite high, and they end up working consistently longer than most executives. Farther beyond our moral horizon, human slum dogs forage garbage dumps for scraps they can eat or sell. Back-breaking labour, I imagine. Long hours, terrible working conditions, and hard-hard work — but no bonus.

It looks to me as though hard work has very little correlation with what one is entitled to. We have to look elsewhere to find justifications to what we consider our due.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

This philosophical clarity inspires analyses (and columns, of course) that are at times self-serving and at times soul-searching. We now worry about the moral rectitude behind the insane bonus expectations of yesteryears, for instance. The case in point is Jake DeSantis, the AIG executive vice president who resigned rather publicly on the New York Times, and donated his relatively modest bonus of a million dollars to charity. The reasons behind the resignation are interesting, and fodder to this series of posts.

Before I go any further, let me state it outright. I am going to try to shred his arguments the best I can. I am sure I would have sung a totally different tune if they had given me a million dollar bonus. Or if anybody had the temerity to suggest that I part with my own bonus, paltry as it may seem in comparison. I will keep that possibility beyond the scope of this column, ignoring the moral inconsistency others might maliciously perceive therein. I will talk only about other people’s bonuses. After all, we are best in dealing with other people’s money. And it is always easier to risk and sacrifice something that doesn’t belong to us.

Sections

• Bonus Plans of Mice and Men
• Hard Work
• Talent and Intelligence
• Talent Retention
• Profit Sharing
• Slippery Slopes

I am certain that most people will not take this job offer. In fact, there is a movie with Johnny Depp and Marlon Brando (IMDb tells me that it is The Brave) where Depp’s character actually takes up such an offer. Twenty-five thousand, I believe, was the price that he agreed upon for the rest of his life. For some of us, the price may be higher, but it is possible that there is a price that we will agree upon.

To me, my price is infinite — I wouldn’t trade the rest of my life for any amount of money. What does it help me to have all the money in the world if I don’t have the time to spend it? But, this stance of mine is neither consistent with what I do, nor fully devoid of hypocrisy. Hardly anything in real life is. If we say we won’t trade time for money, then how come we happily sell our time to our employers? Is it just that we don’t appreciate what we are doing? Or that our time is limited?

I guess the trade off between time and money is not straight forward. It is not a linear scale. If we have no money, then our time is worth nothing. We are willing to sell it for almost nothing. The reason is clear — it takes money to keep body and soul together. Without a bare minimum of money, there indeed is no time left to sell. As we make a bit of money, a bit more than the bare minimum, we begin to value time more. But as we make more money, we realize that we can make even more by selling more time, because the time is worth more now! This implicit vicious circle may be what is driving this crazy rat race that we see all around us.

Selling time is an interesting concept. We clearly do sell our time to those who pay us. Employees sell time to their employers. Entrepreneurs sell their time to the customers, and in deploying their businesses. But there is a fundamental difference between these two modes of selling. While employees sell their time once, businessmen sell their time multiple times. So do authors and actors. They spend a certain amount of time doing whatever they do, but the products they create (book, business, movies, Windows XP, songs etc.) are sold over and over again. That is why they can make their millions and billions while those who work for somebody else find it is very difficult to get really rich.

“Does it mean you will get to come home earlier?”

I was mighty pleased that he liked to have me around at home, but I said,

“No, little fellow, I may have to work much longer hours. I will make a lot more money though. Do you think I should take it?”

I was certain that he would say, no, forget money, spend time at home. After all, he is quite close to me, and tries to hang out with me as much as he can. But, faced with this choice, he was quiet for a while. So I pressed him,

“Well, what do you think?”

To my dismay, he asked,

“How late?”

I decided to play along and said,

“I would probably get home only after you go to bed.”

He still seemed to hesitate. I persisted,

“Well, what do you think?”

My six-year-old said,

“If you have more money, you can buy me more stuff!”

Crestfallen as I was at this patently materialistic line of thinking (not to say anything about the blow to my parental ego), I had to get philosophical at this point. Why would a modern child value “stuff” more than his time with his parent?

I thought back about my younger days to imagine how I would have responded. I would have probably felt the same way. But then, this comparison is not quite fair. We were a lot poorer then, and my dad bringing in more money (and “stuff”) would have been nice. But lack of money has never been a reason for my not getting my kids the much sought after stuff of theirs. I could get them anything they could possibly want and then some. It is just that I have been trying to get them off “stuff” with environmental arguments. You know, with the help of Wall-E, and my threats that they will end up living in a world full of garbage. Clearly, it did not work.

May be we are not doing it right. We cannot expect our kids to do as we say, and not as we do. What is the use of telling them to value “stuff” less when we cannot stop dreaming of bigger houses and fancier cars? Perhaps the message of Wall-E loses a bit of its authenticity when played on the seventh DVD player and watched on the second big screen TV.

It is our materialism that is reflected in our kids’ priorities.

Long version now. Recently, I had this problem with my PC that it wouldn’t wake up from hibernation or sleep mode properly. The PC itself would be on and churning, but the screen would switch to power save mode, staying blank. The only thing to do at that point would be to restart the computer.

Like the good netizen that I am, I trawled the Internet for a solution. But didn’t find any. Some suggested upgrading the BIOS, replacing the graphics card and so on. Then I saw this mentioned in a Linux group, saying that the size of the swap file should be more than the physical memory, and decided to try it on my Windows XP machine. And it solved the problem!

So the solution to this issue of blank screen after waking up is to set the size of the virtual memory to something larger than the memory in your system. If you need more information, here is how, in step-by-step form. These instructions apply to a Windows XP machine.

1. Right-click on “My Computer” and hit “Properties.”

   

2. Take a look at the RAM size, and click on the “Advanced” tab.

   

3. Click on the “Setting” button under the “Performance” group box.

   

4. In the “Performance Options” window that comes up, select the “Advanced” tab.

   

5. In the “Virtual Memory” group box near the bottom, click on the “Change” button.

   

6. In the “Virtual Memory” window that pops up, set the “Custom Size” to something more than your RAM size (that you saw in step 2). You can set it on any hard disk partition that you have, but if you are going through all these instructions, chances are you have only “C:”. In my case, I chose to put it on “M:”.

   

Although my skepticism renders me susceptible to seeing the darker side of these modern day saints, I do have a counterbalancing respect for our heritage and culture, and the associated wisdom and knowledge. It is always with thrill of awe and pride that I listen to Swami Vivekananda’s century-old Chicago speeches, for instance.

The speeches of the modern yogis, on the other hand, fill me with bewilderment and amused confusion. And when I hear of their billion dollar stashes, bevies of Rolls-Royces, and claims of divinity, I balk. When I see the yogis and their entourage jet-setting in first class to exotic holiday destinations with the money extracted in the name of thinly disguised charities, I feel a bit outraged. Still, I am all for live-and-let-live. If there are willing suckers eager to part with their dough and sponsor their guru’s lifestyle, it is their lookout. After all, there are those who financed Madoffs and Stanfords of the greedy era we live in, where fraud is a sin only when discovered.

Now I wonder if it is time that the skeptics among us started speaking out. I feel that the spiritual frauds are of a particularly disturbing kind. Whether we see it that way or not, we are all trying to find a purpose and meaning to our existence on this planet through our various pursuits. We may find the elusive purpose in fame, glory, money, charity, philanthropy, knowledge, wisdom and in any of the hundreds of paths. All these pursuits have their associated perils of excess. If you get greedy, for instance, there is always a Madoff waiting in the wings to rip you off. If you become too charitable, there are other characters eager to separate you from your money, as my Singaporean readers will understand.

Of all these pursuits, spirituality is of a special kind; it is a shortcut. It gives you a direct path to a sense of belonging, and a higher purpose right away. Smelling blood in the carefully cultivated need for spirituality (whatever spirituality means), the yogis and maharishis of our time have started packaging and selling instant nirvana in neat three or five day courses that fit your schedule, while demanding vast sums of “not-for-profit” money. Even this duplicity would be fine by me. Who am I to sit in judgment of people throwing money at their inner needs, and gurus picking it up? But, of late, I am beginning to feel that I should try to spread a bit of rationality around.

I decided to come of out my passive mode for two reasons. One is that the gurus engage their victims in their subtle multi-level marketing schemes, ensnaring more victims. A pupil today is a teacher tomorrow, fueling an explosive growth of self-serving organizations. The second reason is that the gurus demand that the followers donate their time. I think the victims do not appreciate the enormity of this unfair demand. You see, you have only a limited time to live, to do whatever it is that you think will lead to fulfillment. Don’t spend it on wrong pursuits because there is always something that you are sacrificing in the process, be it your quality time with your loved ones, opportunity to learn or travel, or enjoy life or whatever. Time is a scarce resource, and you have to spend it wisely, or you will regret it more than anything else in life.

So don’t be blind. Don’t mistake group dynamics for salvation. Or charisma for integrity. Or obscurity for wisdom. If you do, the latter day gurus, masters of manipulation that they are, will take you for a ride. A long and unpleasant one.

The binomial tree pricing model works by assuming that the price of an underlying asset can only move up or down by constant factors $$u$$ and $$d$$ during a small time interval $$\delta t$$. Stringing together many such time intervals, we make up the expiration time of the derivative instrument we are trying to price. The derivative defined as a function of the price of the underlying at any point in time.

Figure 1. Binomial tree pricing model. On the X axis, labeled i, we have the time steps. The Y axis represents the price of the underlying, labeled j. The only difference from the standard binomial tree is that we have let j be both positive and negative, which is mathematically natural, and hence simplifies the notation in a functional language.

We can visualize the binomial tree as shown in Fig. 1. At time $$t = 0$$, we have the asset price $$S(0) = S_0$$. At $$t = \delta t$$ (with the maturity $$T = N\delta t$$). we have two possible asset values $$S_0 u$$ and $$S_0 d = S_0 / u$$, where we have chosen $$d = 1/u$$. In general, at time $$i\delta t$$, at the asset price node level $$j$$, we have

$$S_{ij} = S_0 u^j$$

By choosing the sizes of the up and down price movements the same, we have created a recombinant binomial tree, which is why we have only $$2i+1$$ price nodes at any time step $$i\delta t$$. In order to price the derivative, we have to assign risk-neutral probabilities to the up and down price movements. The risk-neutral probability for an upward movement of $$u$$ is denoted by $$p$$. With these notations, we can write down the fair value of an American call option (of expiry $$T$$, underlying asset price $$S_0$$, strike price $$K$$, risk free interest rate $$r$$, asset price volatility $$\sigma$$ and number of time steps in the binomial tree $$N$$) using the binomial tree pricing model as follows:

$$\textrm{OptionPrice}(T, S_0, K, r, \sigma, N) = f_{00}$$

where $$f_{ij}$$ denotes the fair value of the option at any the node $$i$$ in time and $$j$$ in price (referring to Fig. 1).

$$f_{ij} = \left\{
\begin{array}{ll}
\textrm{Max}(S_{ij} – K, 0) & \textrm{if } i = N \\
\textrm{Max}(S_{ij} – 0, e^{-\delta tr}\left(p f_{i+1\, j+1} + (1-p)
f_{i+1\, j-1}\right)) & \textrm {otherwise}
\end{array}
\right.$$

At maturity, $$i = N$$ and $$i\delta t = T$$, where we exercise the option if it is in the money, which is what the first Max function denotes. The last term in the express above represents the risk neutral backward propagation of the option price from the time layer at $$(i+1)\delta t$$ to $$i\delta t$$. At each node, if the option price is less than the intrinsic value, we exercise the option, which is the second Max function.

The common choice for the upward price movement depends on the volatility of the underlying asset. $$u = e^{\sigma\sqrt{\delta t}}$$ and the downward movement is chosen to be the same $$d = 1/u$$ to ensure that we have a recombinant tree. For risk neutrality, we have the probability defined as:

$$p = \frac{ e^{r\delta t} – d}{u – d}$$

For the purpose of illustrating how it translates to the functional programming language of Haskell, let us put all these equations together once more.

$$\textrm{OptionPrice}(T, S_0, K, r, \sigma, N) = f_{00}
$$
where
$$f_{ij} = \left\{
\begin{array}{ll}
\textrm{Max}(S_{ij} – K, 0) & \textrm{if } i = N \\
\textrm{Max}(S_{ij} – 0, e^{-\delta tr}\left(p f_{i+1\, j+1} + (1-p) f_{i+1\, j-1}\right)) & \textrm {otherwise}
\end{array}
\right.$$
$$
S_{ij} = S_0 u^j
$$
$$u = e^{\sigma\sqrt{\delta t}}$$
$$
d = 1/u
$$
$$
\delta t = T/N
$$
$$
p = \frac{ e^{r\delta t} – d}{u – d}
$$

Now, let us look at the code in Haskell.

optionPrice t s0 k r sigma n = f 0 0
    where
      f i j =
          if i == n
          then max ((s i j) - k) 0
          else max ((s i j) - k)
                    (exp(-r*dt) * (p * f(i+1)(j+1) +
                    (1-p) * f(i+1)(j-1)))
      s i j = s0 * u**j
      u = exp(sigma * sqrt dt)
      d = 1 / u
      dt = t / n
      p = (exp(r*dt)-d) / (u-d)

As we can see, it is a near-verbatim rendition of the mathematical statements, nothing more. This code snippet actually runs as it is, and produces the result.

*Main> optionPrice 1 100 110 0.05 0.3 20
10.10369526959085

Looking at the remarkable similarity between the mathematical equations and the code in Haskell, we can understand why mathematicians love the idea of functional programming. This particular implementation of the binomial pricing model may not be the most computationally efficient, but it certainly is one of great elegance and brevity.

While a functional programming language may not be appropriate for a full-fledged implementation of a trading platform, many of its underlying principles, such as type abstractions and strict purity, may prove invaluable in programs we use in quantitative finance where heavy mathematics and number crunching are involved. The mathematical rigor enables us to employ complex functional manipulations at the program level. The religious adherence to the notion of statelessness in functional programming has another great benefit. It helps in parallel and grid enabling the computations with almost no extra work.

Sections

• Zeros and Ones
• Paradigms All the Way
• Magic of Object Oriented Languages
• Functional Programming
• A New Kind of Binomial Tree

Adapting this notion of functional programming may sound like regressing back to the pre-object-oriented age, and sacrificing all the advantages thereof. But there are practitioners, both in academia and in the industry, who strongly believe that functional languages are the only approach that ensures stability and robustness in financial and number crunching applications.

Functional languages, by definition, are stateless. They do everything through functions, which return results that are, well, functions of their arguments. This statelessness immediately makes the functions behave like their mathematical counterparts. Similarly, in a functional language, variable behave like mathematical variables rather than labels for memory locations. And a statement like x = x + 1 would make no sense. After all, it makes no sense in real life either.

This strong mathematical underpinning makes functional programming the darling of mathematicians. A piece of code written in a functional programming language is a set of declarations quite unlike a standard computer language such as C or C++, where the code represents a series of instructions for the computer. In other words, a functional language is declarative — its statements are mathematical declarations of facts and relationships, which is another reason why a statement like x = x + 1 would be illegal.

The declarative nature of the language makes it “lazy,” meaning that it computes a result only when we ask for it. (At least, that is the principle. In real life, full computational laziness may be difficult to achieve.) Computational laziness makes a functional programming language capable of handling many situations that would be impossible or exceedingly difficult for procedural languages. Users of Mathematica, which is a functional language for symbolic manipulation of mathematical equations, would immediately appreciate the advantages of computational laziness and other functional features such as its declarative nature. In Mathematica, we can carry out an operation like solving an equation for instance. Once that is done, we can add a few more constraints at the bottom of our notebook, scroll up to the command to solve the original equation and re-execute it, fully expecting the later constraints to be respected. They will be, because a statement appearing at a later part in the program listing is not some instruction to be carried out at a later point in a sequence. It is merely a mathematical declaration of truism, no matter where it appears.

This affinity of functional languages toward mathematics may appeal to quants as well, who are, after all, mathematicians of the applied kind. To see where the appeal stems from, let us consider a simple example of computing the factorial of an integer. In C or C++, we can write a factorial function either using a loop or making use of recursion. In a functional language, on the other hand, we merely restate the mathematical definition, using the syntax of the language we are working with. In mathematics, we define factorial as:

$$n! = \left\{
\begin{array}{ll}
1 & n=1 \\
n \times (n-1)! & \textrm{Otherwise}
\end{array}
\right.$$

And in Haskell (a well known functional programming language), we can write:

bang 1 = 1
bang n = n * bang (n-1)

And expect to make the call bang 12 to get the factorial of 12.

This example may look artificially simple. But we can port even more complicated problems from mathematics directly to a functional language. For an example closer to home, let us consider a binomial pricing model, illustrating that the ease and elegance with which Haskell handles factorial do indeed extend to real-life quantitative finance problems as well.

Sections

• Zeros and Ones
• Paradigms All the Way
• Magic of Object Oriented Languages
• Functional Programming
• A New Kind of Binomial Tree

We do see the abstraction process running a bit wild in design patterns. When a pattern calls itself a visitor or a factory, it takes a geekily forgiving heart to grant the poetic license silently usurped. Design patterns, despite the liberties they take with our sensitivities, add enormous power to object oriented programming, which is already very powerful, with all the built in features like polymorphism, inheritance, overloading etc.

To someone with an exclusive background in sequential programming, all these features of object oriented languages may seem like pure magic. But most of the features are really extensions or variations on their sequential programming equivalents. A class is merely a structure, and can even be declared as such in C++. When you add a method in a class, you can imagine that the compiler is secretly adding a global function with an extra argument (the reference to the object) and a unique identifier (say, a hash value of the class name). Polymorphic functions also can be implemented by adding a hash value of the function signature to the function names, and putting them in the global scope.

The real value of the object oriented methodology is that it encourages good design. But good programming discipline goes beyond mere adaptation of an object oriented language, which is why my first C++ teacher said, “You can write bad Fortran in C++ if you really want. Just that you have to work a little harder to do it.”

For all their magical powers, the object oriented programming languages all suffer from some common weaknesses. One of their major disadvantages is, in fact, one of the basic design features of object oriented programming. Objects are memory locations containing data as laid down by the programmer (and the computer). Memory locations remember the state of the object — by design. What state an object is in determines what it does when a method is invoked. So object oriented approach is inherently stateful, if we can agree on what “state” means in the object oriented context.

But in a user interface, where we do not have much control over the sequence in which various steps are executed, we might get erroneous results in stateful programming depending on what step gets executed at a what point in time. Such considerations are especially important when we work with parallel computers in complex situations. One desirable property in such cases is that the functions return a number solely based on their arguments. This property, termed “purity,” is the basic design goal of most functional languages, although their architects will concede that most of them are not strictly “pure.”

Sections

• Zeros and Ones
• Paradigms All the Way
• Magic of Object Oriented Languages
• Functional Programming
• A New Kind of Binomial Tree

Some paradigms have faded into the background although the terminology evolved from them lingers. The original paradigm for computer networks (and of the Internet) was a mesh of interconnections residing in the sky above. This view is more or less replaced by the World Wide Web residing on the ground at our level. But we still use the original paradigm whenever we say “download” or “upload.” The World Wide Web, by the way, is represented by the acronym WWW that figures in the name of all web sites. It is an acronym with the dubious distinction of being about the only one that takes us longer to say than what it stands for. But, getting back to our topic, paradigms are powerful and useful means to guide our interactions with unfamiliar systems and environments, especially in computers, which are strange and complicated beasts to begin with.

A basic computer processor is deceptively simple. It is a string of gates. A gate is a switch (more or less) made up of a small group of transistors. A 32 bit processor has 32 switches in an array. Each switch can be either off representing a zero, or on (one). And a processor can do only one function — add the contents of another array of gates (called a register) to itself. In other words, it can only “accumulate.”

In writing this last sentence, I have already started a process of abstraction. I wrote “contents,” thinking of the register as a container holding numbers. It is the power of multiple levels of abstraction, each of which is simple and obvious, but building on whatever comes before it, that makes a computer enormously powerful.

We can see abstractions, followed by the modularization of the abstracted concept, in every aspect of computing, both hardware and software. Groups of transistors become arrays of gates, and then processors, registers, cache or memory. Accumulations (additions) become all arithmetic operations, string manipulations, user interfaces, image and video editing and so on.

Another feature of computing that aids in the seemingly endless march of the Moore’s Law (which states that computers will double in their power every 18 months) is that each advance seems to fuel further advances, generating an explosive growth. The first compiler, for instance, was written in the primitive assembler level language. The second one was written using the first one and so on. Even in hardware development, one generation of computers become the tools in designing the next generation, stoking a seemingly inexorable cycle of development.

While this positive feedback in hardware and software is a good thing, the explosive nature of growth may take us in wrong directions, much like the strong grown in the credit market led to the banking collapses of 2008. Many computing experts now wonder whether the object oriented technology has been overplayed.

Sections

• Zeros and Ones
• Paradigms All the Way
• Magic of Object Oriented Languages
• Functional Programming
• A New Kind of Binomial Tree

Rich in paradigms, the field of computing has a strong influence in the way we think and view the world. If you don’t believe me, just look at the way we learn things these days. Do we learn anything now, or do we merely learn how to access information through browsing and searching? Even our arithmetic abilities have eroded along with the advent of calculators and spreadsheets. I remember the legends of great minds like Enrico Fermi, who estimated the power output of the first nuclear blast by floating a few pieces of scrap paper, and like Richard Feynman, who beat an abacus expert by doing binomial expansion. I wonder if the Fermis and Feynmans of our age would be able to pull those stunts without pulling out their pocket calculators.

Procedural programming, through its unwarranted reuse of mathematical symbols and patterns, has shaped the way we interact with our computers. The paradigm that has evolved is distinctly unmathematical. Functional programming represents a counter attack, a campaign to win our minds back from the damaging influences of the mathematical monstrosities of procedural languages. The success of this battle may depend more on might and momentum rather than truth and beauty. In our neck of the woods, this statement translates to a simple question: Can we find enough developers who can do functional programming? Or is it cheaper and more efficient to stick to procedural and object oriented methodologies?

Sections

• Zeros and Ones
• Paradigms All the Way
• Magic of Object Oriented Languages
• Functional Programming
• A New Kind of Binomial Tree

The beauty and perfection I’m thinking about are of a different kind — those of ideas and concepts. At times, you may get an idea so perfect and beautiful that you know it has to be true. This conviction of truth arising from beauty may be what made Einstein declare:

But this conviction about the veracity of a theory based on its perfection is hardly enough. Einstein’s genius really is in his philosophical tenacity, his willingness to push the idea beyond what is considered logical.

Let’s take an example. Let’s say you are in a cruising airplane. If you close the windows and somehow block out the engine noise, it will be impossible for you to tell whether you are moving or not. This inability, when translated to physics jargon, becomes a principle stating, “Physical laws are independent of the state of motion of the experimental system.”

The physical laws Einstein chose to look at were Maxwell’s equations of electromagnetism, which had the speed of light appearing in them. For them to be independent of (or covariant with, to be more precise) motion, Einstein postulated that the speed of light had to be a constant regardless of whether you were going toward it or away from it.

Now, I don’t know if you find that postulate particularly beautiful. But Einstein did, and decided to push it through all its illogical consequences. For it to be true, space has to contract and time had to dilate, and nothing could go faster than light. Einstein said, well, so be it. That is the philosophical conviction and tenacity that I wanted to talk about — the kind that gave us Special Relativity about a one hundred years ago.

Want to get to General Relativity from here? Simple, just find another beautiful truth. Here is one… If you have gone to Magic Mountain, you would know that you are weightless during a free fall (best tried on an empty stomach). Free fall is acceleration at 9.8 m/s/s (or 32 ft/s/s), and it nullifies gravity. So gravity is the same as acceleration — voila, another beautiful principle.

In order to make use of this principle, Einstein perhaps thought of it in pictures. What does acceleration mean? It is how fast the speed of something is changing. And what is speed? Think of something moving in a straight line — our cruising airplane, for instance, and call the line of flight the X-axis. We can visualize its speed by thinking of a time T-axis at right angles with the X-axis so that at time = 0, the airplane is at x = 0. At time t, it is at a point x = v.t, if it is moving with a speed v. So a line in the X-T plane (called the world line) represents the motion of the airplane. A faster airplane would have a shallower world line. An accelerating airplane, therefore, will have a curved world line, running from the slow world line to the fast one.

So acceleration is curvature in space-time. And so is gravity, being nothing but acceleration. (I can see my physicist friends cringe a bit, but it is essentially true — just that you straighten the world-line calling it a geodesic and attribute the curvature to space-time instead.)

The exact nature of the curvature and how to compute it, though beautiful in their own right, are mere details, as Einstein himself would have put it. After all, he wanted to know God’s thoughts, not the details.

The topic of conversation on that day was a bit philosophical, and we were eagerly absorbing the words of wisdom emanating from Lee. He was describing to us how the Earth could be considered a living organism. Using insightful arguments and precisely modulated glib articulation (no doubt, forged by years of intellectual duels in world’s best universities), Lee made a compelling case that the Earth, in fact, satisfied all the conditions of being an organism.

Lee Smolin, by the way, lived up to our great expectations in later years, publishing highly acclaimed books and generally leaving a glorious imprint in the world of modern physics. He now talks to global audiences through prestigious programmes such as the BBC Hardtalk, much to our pride and joy.

The point in Lee’s view was not so much whether or the Earth was literally alive, but that thinking of it as an organism was a viable intellectual model to represent the Earth. Such intellectual acrobatics was not uncommon among us physics students.

In the last few years, Lee has actually taken this mode of thinking much farther in one of his books, picturing the universe in the light of evolution. Again, the argument is not to be taken literally, imagining a bunch of parallel universes vying for survival. The idea is to let the mode of thinking carry us forward and guide our thoughts, and see what conclusions we can draw from the thought exercise.

A similar mode of thinking was introduced in the movie Matrix. In fact, several profound models were introduced in that movie, which probably fuelled its wild box-office success. One misanthropic model that the computer agent Smith proposes is that human beings are a virus on our planet.

It is okay for the bad guy in a movie to suggest it, but an entirely different matter for newspaper columnist to do so. But bear with me as I combine Lee’s notion of the Earth being an organism and Agent Smith’s suggestion of us being a virus on it. Let’s see where it takes us.

The first thing a virus does when it invades an organism is to flourish using the genetic material of the host body. The virus does it with little regard for the well-being of the host. On our part, we humans plunder the raw material from our host planet with such abandon that the similarity is hard to miss.

But the similarity doesn’t end there. What are the typical symptoms of a viral infection on the host? One symptom is a bout of fever. Similarly, due to our activities on our host planet, we are going through a bout of global warming. Eerily similar, in my view.

The viral symptoms could extend to sores and blisters as well. Comparing the cities and other eye sores that we proudly create to pristine forests and natural landscapes, it is not hard to imagine that we are indeed inflicting fetid atrocities to our host Earth. Can’t we see the city sewers and the polluted air as the stinking, oozing ulcers on its body?

Going one step further, could we also imagine that natural calamities such as Katrina and the Asian tsunami are the planet’s natural immune systems kicking into high gear?

I know that it is supremely cynical to push this comparison to these extreme limits. Looking at the innocent faces of your loved ones, you may feel rightfully angry at this comparison. How dare I call them an evil virus? Then again, if a virus could think, would it think of its activities on a host body as evil?

If that doesn’t assuage your sense of indignation, remember that this virus analogy is a mode of thinking rather than a literal indictment. Such a mode of thinking is only useful if it can yield some conclusions. What are the conclusions from this human-viral comparison?

The end result of a viral infection is always gloomy. Either the host succumbs or the virus gets beaten by the host’s immune systems. If we are the virus, both these eventualities are unpalatable. We don’t want to kill the Earth. And we certainly don’t want to be exterminated by the Earth. But those are the only possible outcomes of our viral-like activity here. It is unlikely that we will get exterminated; we are far too sophisticated for that. In all likelihood, we will make our planet uninhabitable. We may, by then, have our technological means of migrating to other planetary systems. In other words, if we are lucky, we may be contagious! This is the inescapable conclusion of this intellectual exercise.

There is a less likely scenario — a symbiotic viral existence in a host body. It is the kind of benign life style that Al Gore and others recommend for us. But, taking stock of our activities on the planet, my doomsday view is that it is too late for a peaceful symbiosis. What do you think?

In high school, I used logarithm tables to work out results in physics and chemistry experiments. Calculators were not allowed. Though inconvenient, this practice honed my arithmetic skills — skills that calculators and spreadsheets have eroded by now.

Similar erosion is taking place in our reading skills as well. We don’t read to retain information or knowledge any more. We search, scan, locate keywords, browse and bookmark. The Internet is doing to our reading habits what the calculator did to our arithmetic abilities.

Easy access to information is transforming our notion of (dare I say, respect for?) knowledge in a fundamental way. In a knowledge economy, knowledge is fast becoming a cheap commodity. We don’t need to know stuff any more; we just need to know how to find it.

I was talking to a lecturer the other day. According to him, a good lecturer is not the one who knows most and has a deep understanding of the subject, but the one that can locate the answer the fastest.

The power of instant information came with the Internet, which made experts of all of us. We can now make intelligent comments and informed decisions on anything.

Suppose, for instance, your child’s doctor recommends the procedure “myringotomy,” quite possibly something you have never heard of before. But you can Google it, read (sorry, browse) the first couple of search results, and you will know the rationale behind the doctor’s advice, the exact procedure, its risk factors and benefits, and so on. In ten minutes, you will know what took the doctor years of hard work to learn.

This easy access to knowledge may, quite mistakenly, diminish your respect for the medical degree. This diminished reverence for knowledge is unwise; a little knowledge is a dangerous thing. A doctor’s expertise is not so much in memorizing a webpage worth of information, but also in knowing all the special circumstances where that information doesn’t apply. Besides, the webpage you happened to read may be just plain wrong. We should be careful not to mistake easy information for deep knowledge. Let’s guard our respect for true knowledge and wisdom despite our access to ready information.

Such misguided lack of respect is evident in the workplace as well, where managers think they can always hire specialized knowledge at will. I had a friend who was planning to roll out a product using Bluetooth, back when it was an emerging technology. I pointed out the obvious flaw in his proposal — he didn’t know much about Bluetooth. His reply was, “No big deal! I’ll just hire somebody who does!”

My worry is, when everybody wants to hire a Bluetooth expert and nobody wants to know how it works, there won’t be an expert any longer.

Knowledge is not cheap, although our easy access to it through the Internet may indicate otherwise. When we all become users of information, our knowledge will stop at its current level, because nobody will be creating it any more.

We are not there yet, but I worry that we are heading that way. I worry about the support structure of our knowledge base. How will our knowledge empire stand when all its foundations are gone?

One of my secret tactics is to develop a sense of proportion, harmless as it may sound. Proportion can be in terms of numbers. Let’s start with the number of individuals, for instance. Every morning, when we come to work, we see thousands of faces floating by, almost all going to their respective jobs. Take a moment to look at them — each with their own personal thoughts and cares, worries and stresses.

To each of them, the only real stress is their own. Once we know that, why would we hold our own stress any more important than anybody else’s? The appreciation of the sheer number of personal stresses all around us, if we stop to think about it, will put our worries in perspective.

Proportion in terms of our size also is something to ponder over. We occupy a tiny fraction of a large building that is our workplace. (Statistically speaking, the reader of this column is not likely to occupy a large corner office!) The building occupies a tiny fraction of the space that is our beloved city. All cities are so tiny that a dot on the world map is usually an overstatement of their size.

Our world, the earth, is a mere speck of dust a few miles from a fireball, if we think of the sun as a fireball of any conceivable size. The sun and its solar system are so tiny that if you were to put the picture of our galaxy as the wallpaper on your PC, they would be sharing a pixel with a few thousand local stars! And our galaxy — don’t get me started on that! We have countless billions of them. Our existence (with all our worries and stresses) is almost incompressibly small.

The insignificance of our existence is not limited to space; it extends to time as well. Time is tricky when it comes to a sense of proportion. Let’s think of the universe as 45 years old. How long do you think our existence is in that scale? A few seconds!

We are created out of star dust, last for a mere cosmological instant, and then turn back into star dust. DNA machines during this time, we run unknown genetic algorithms, which we mistake for our aspirations and achievements, or stresses and frustrations. Relax! Don’t worry, be happy!

Sure, you may get reprimanded if that report doesn’t go out tomorrow. Or, your supplier may get upset that your payment is delayed again. Or, your colleague may send out that backstabbing email (and Bcc your boss) if you displease them. But, don’t you see, in this mind-numbingly humongous universe, it doesn’t matter an iota. In the big scheme of things, your stress is not even static noise!

Arguments for maintaining a level of stress all hinge on an ill-conceived notion that stress aids productivity. It does not. The key to productivity is an attitude of joy at work. When you stop worrying about reprimands and backstabs and accolades, and start enjoying what you do, productivity just happens. I know it sounds a bit idealistic, but my most productive pieces of work happened that way. Enjoying what I do is an ideal I will shoot for any day.

In the unforgiving, dog-eat-dog corporate jungle, you need to be sure of the welcome. More importantly, you need to prove yourself worthy of it. Fear not, I’m here to help you through it. And I will gladly accept all credit for your survival, if you care to make it public. But I regret that we (this newspaper, me, our family members, our dogs, lawyers and so on) cannot be held responsible for any untoward consequence of applying my suggestions. Come on, you should know better than to base your career on a newspaper column!

This disclaimer brings me naturally to the first principle I wanted to present to you. Your best bet for corporate success is to take credit for all accidental successes around you. For instance, if you accidentally spilled coffee on your computer and it miraculously resulted in fixing the CD-ROM that hadn’t stirred in the last quarter, present it as your innate curiosity and inherent problem solving skills that prompted you to seek an unorthodox solution.

But resist all temptation to own up to your mistakes. Integrity is a great personality trait and it may improve your karma. But, take my word for it, it doesn’t work miracles on your next bonus. Nor does it improve your chances of becoming the boss in the corner office.

If your coffee debacle, for instance, resulted in a computer that would never again see the light of day (which, you would concede, is a more likely outcome), your task is to assign blame for it. Did your colleague in the next cubicle snore, or sneeze, or burp? Could that have caused a resonant vibration on your desk? Was the cup poorly designed with a higher than normal center of gravity? You see, a science degree comes in handy when assigning blame.

But seriously, your first task in surviving in a new corporate setting is to find quick wins, for the honeymoon will soon be over. In today’s workplace, who you know is more important than what you know. So start networking — start with your boss who, presumably, is already impressed. He wouldn’t have hired you otherwise, would he?

Once you reach the critical mass in networking, switch gears and give an impression that you are making a difference. I know a couple of colleagues who kept networking for ever. Nice, gregarious folks, they are ex-colleagues now. All talk and no work is not going to get them far. Well, it may, but you can get farther by identifying avenues where you can make a difference. And by actually making a bit of that darned difference.

Concentrate on your core skills. Be positive, and develop a can-do attitude. Find your place in the corporate big picture. What does the company do, how is your role important in it? At times, people may underestimate you. No offense, but I find that some expats are more guilty of underestimating us than fellow Singaporeans. Our alleged gracelessness may have something to do with it, but that is a topic for another day.

You can prove the doubters wrong through actions rather than words. If you are assigned a task that you consider below your level of expertise, don’t fret, look at the silver lining. After all, it is something you can do in practically no time and with considerable success. I have a couple of amazingly gifted friends at my work place. I know that they find the tasks assigned to them ridiculously simple. But it only means that they can impress the heck out of everybody.

Corporate success is the end result of an all out war. You have to use everything you have in your arsenal to succeed. All skills, however unrelated, can be roped in to help. Play golf? Invite the CEO for a friendly. Play chess? Present it as the underlying reason for your natural problem solving skills. Sing haunting melodies in Chinese? Organize a karaoke. Be known. Be recognized. Be appreciated. Be remembered. Be missed when you are gone. At the end of the day, what else is there in life?