Tuesday, June 07, 2005

Where do you work?

I ran into this woman in the elevator in my apartment building. She looked to be in her thirties, was smartly dressed, and was checking messages on her cell phone when I stepped in. Summer was in full swing in New York, and the elevator felt like a preheating oven. The woman promptly piped up: "It's hot in here." She spoke without looking at me and in a tone of soliloquy, as if talking to a phantom in the air. But I knew better and chimed in. It turned out that we lived on the same floor. She complained how she never got to know any of her neighbors. I assured her that it was not her fault since I had just moved in and would soon move out. Just as we walked out of the elevator, she asked me:

"Where do you work?"

Never had I been asked this question by a total stranger after 30 seconds of conversation. I told her my employer and reciprocated: "How about you?"

"I am a partner in Deloitte Touche." She said.

Partner, according to my knowledge of consulting, is the second highest rank one can hold in a firm. Now I understand the true meaning of her question. In the fast-paced business world in New York, it translates into:

"Are you worthy of my company?"

Friday, June 03, 2005

Dinner in Color

On the second night in my new apartment in midtown Manhattan, I prepared dinner for myself. This is my signature dish: Steak with Asparagus and Mushroom, garnished with Strawberry. I may well be a chef disguised as a chemist.

Inspection and Introspection

I am better, am I not?

Today, I took E train from Queens to Manhattan. Across the aisle from me, a woman took out an eyelash curler and a small mirror and started shaping her eyelashes. She appeared to have made the effort to look pretty, for she wore heavy make-ups and seemed to be dressed in the best fashion that she could afford. She kept pulling and curling her eyelashes for twenty minutes. First the right eye, then the left, then back to the right, for she scrutinized herself in the mirror and felt unsatisfied with the result. We got off at the same stop. That’s when she stopped eyelash-sculpting.

I thought to myself. Hmm, she just wasted twenty minutes on her vanity. She could have read a book, or a newspaper, like the respectable-looking passengers did. She could have taken a nap, which would leave her refreshed when she got off the train. Or she could have been like me – I usually pick a scientific problem and turn it in my head when I am on public transportation. Instead, she spent twenty minutes curling her eyelashes.

Maybe that is why I am well-paid in a technology firm and live on the 36th floor in a full-service apartment building, whereas she is probably a cashier in a grocery store and live in some rent-controlled building in Brooklyn.

Then I thought to myself. Wait. I just spent twenty minutes WATCHING her curling her eyelashes! I was not reading or thinking. I just wasted twenty minutes watching a woman wasting the meantime on her vanity.

Last Sunday, I had dinner with a few friends in Le Colonial, a posh French-Vietnamese restaurant in San Francisco. A man and a woman sat at an adjacent table. The woman was very pretty. The man, on the other hand, was plain looking and balding. Kings, one of my friends, made a joke when the woman and the man posed together for a picture. “That’s as close as the guy is going to get tonight.” He said. But he was wrong. When they stood up to leave, the woman kissed the man on the lips. I whispered to Kings, “Your prediction was wrong – by two miles!” My whisper was a little too loud. As soon as the couple vanished from our sight, we heard the man’s angry voice:

“Try to judge yourself, not others!”

That is exactly what I should do.

Tuesday, May 31, 2005

Encounter with Homo Soccerfanus

Tell me nothing; I don't want to know.

There are two subspecies of humans: the rest of us, and the soccer fans (homo soccerfanus). The latter resemble the former in appearance; but they can be identified by occasional peculiar behaviors, such as extreme emotions after the victory or loss of their teams, shouting and yelling at critical moments in a game, excessive consumption of beer during a match event, and, sometimes, animosity and violence toward the fans of the opposing teams.

Yu Chen is one homo soccerfanus. He roots for Liverpool, which just won the European Champions League after a dramatic comeback against AC Milan. We watched the final game in Kezar’s pub. It was not a live broadcast, but every one of us arrived without knowing the outcome. That evasion, however, was futile, for as soon as we walked in the pub the result was obvious. A group of Liverpool fans, all dressed in the red uniform, were celebrating on top of the tables. Simultaneously happy and disappointed, Yu Chen sat down to witness Liverpool’s path to triumph.

It was a game of climax and drama. Each team played one half. AC Milan scored three goals in the first half. All hope seemed to have vanished for Liverpool, then miracle happened. In the second half, within a span of five minutes, Liverpool scored three goals. Eventually, Liverpool won in the penalty shootout.

Unfortunately, this dramatic twist was lost amidst the premature celebration of the Liverpool fans in the bar. It was outrageous. Each time Milan scored, Liverpool fans cheered. When Liverpool was three goals behind, its fans danced and laughed and toasted to their team and gulped down their beers. Yu Chen talked to us in a slightly patronizing tone.



Exhibit 1. The Liverpool fans in the bar cheered when their team was 0:3 behind AC Milan.

I took my camera with me, hoping to capture Yu Chen’s reactions in the course of the game. There was, of course, no emotional reaction at all. No intense pleasure or sorrow can come from certainty. Only at one moment was Yu Chen surprised, when Liverpool scored its equalizer. It was a penalty shot. Yu Chen’s reactions were recorded in the following sequence of photos.



Exhibit 2. The penalty shot by Liverpool's Alonso was blocked by Milan's goal keeper Dida. Stefan, sitting next to Yu Chen, was a Milan fan.



Exhibit 3. The ball bounced off Dida. Alonso on the second attempt kicked the ball into the net.


Exhibit 4. Now the score was 3:3. The Liverpool fans would smile to the last.

Simply Free

It has everything, and nothing more.

Nike just introduced a new running shoe, Nike Free. I tried it on in Nike Town. It was the most comfortable running shoe my feet had worn.

Holding Free in the hands, one will immediately notice its light weight. The upper of the shoe is extremely thin. It also has numerous tiny slit openings to enhance ventilation. The sole is flexible, so flexible that the shoe can almost fold in half. Running in Free is an exhilarating experience. I did it on the treadmill in Nike Town. My feet felt light and free, just as the shoe’s name suggests.

I also watched the TV spot for the shoe in Nike Town. It must be one of the most effective commercials ever made. A group of runners, all wearing white T-shirts and shorts, run barefoot on a wet sand beach. Yet it is no ordinary beach. The runners step over a manhole; they zoom past by parking meters, fire escape ladders, newspaper venders, mailboxes, and fire hydrants. A yellow cab drives by. Pedestrians. Then a bus crosses the screen. When it is gone, the scene has changed to a street corner in New York City. Only one runner remains. The camera switches to his feet. He is wearing Nike Free. The scene blurs, and a message appears on the screen: “Run barefoot”.

The music used in the commercial? Chariots of Fire. The tune, repeated twice, imprints in anybody’s mind.

What makes a great product? Invariably, a great product is built around a simple concept. It is conceived with a clear vision of how it will be marketed. Run barefoot, run free. Nothing can be simpler than that. Everything about Free revolves around this simple concept, from the choice of fabric to the shape of the shoe. It has not an ounce of extra weight. It flexes to conform to the shape of the foot. It is probably the most plain-looking sneaker that Nike has ever made. Once the simple concept is established, no effort is spared to realize that concept in the product.

Apple also makes great products. iPod Shuffle, for instance, took the flash player market by storm. The simple concept here? Life is random, so give chance a chance. So goes the tiny LCD screens, so goes the cluttered buttons of controls. All the fat is stripped off the Shuffle, and the result is a lean flash player that the market has never seen.

The technology that goes into Nike Free or Ipod Shuffle must be enormous. Yet Nike and Apple mention none in their commercials. They sell the concept, not the technology. Ever watch the infomercials? “Our product is made of materials used in spacecraft.” Hello! Anybody interested in buying a spacecraft?

So what makes Nike Free, or iPod Shuffle, a great product? In short, it has everything, and nothing more.

Monday, May 16, 2005

Hand versus Penis

We humans are obsessed with sex. Whereas other animals copulate only when they come into heat, which happens once or twice in a year for most mammals, we humans screw all year round. We enjoy sex; we view it as a recreation as much as the means for procreation. We seek sex when we are not having any. We seek more sex when we are having some. The proverbial wisdom has it that a man thinks about sex every three seconds. A woman thinks about sex not much less, if we believe Sex and the City.

Sex sells. Most magazines in any newsstand have on their covers some beautiful women in revealing clothes and suggestive postures. Nudity and strong sexual contents boost box office for movies and promote ratings for cable TV programs. Viagra has annual sales in the billions and has prompted a number of me-too drugs from competitors. Experts tell us: sex is important for relationships, marriages, and health.

Just how important is sex to us? We may glean some idea from how much we value our sexual organs.

The following is an excerpt of the schedule that the state of Connecticut uses to compensate for work-related injuries, in descending order of value.

Lost or Damaged Body Part and Corresponding Compensated Weeks of Pay

Heart 520
Pancreas 416
Liver 347
Arm (master) 208
Arm (other) 194
Hand (master) 168
Eye 157
Hand (other) 155
Foot 125
Penis 35-104
Vagina 35-104
Thumb (master hand) 63
Thumb (other hand) 54
Finger (first) 36

The most valuable organs are apparently the vital organs. We cannot live without a heart, a pancreas or a liver. The second most valuable organs are the ones that we rely on in everyday life and work: master arm and hand, and eyes. But the surprise is that penis and vagina – our reproductive and pleasure organs – are valued much less than the subordinate hand and arm, and foot. Sometimes, they even rank below the thumbs and the first finger.

So maybe we do not value sex THAT much after all. As the Chinese saying goes, he who is fed and warm desires sex. Foremost we want our arms and hands intact to fend for ourselves. Sex is a thought after that.

Friday, May 13, 2005

Price Index

What do you measure money in?

Purchasing power is an important concept in macroeconomics. Defined loosely as how much goods a unit of currency can buy, it is a measure of the worth of money. The most careful analysis of purchasing power usually looks at the average price of a basket of essential goods. But there is a simplification. The price of Big Mac turns out to be a good indicator of the purchasing power; therefore the famous Big Mac index.

Also important in macroeconomics is the consumer's price index, which can reflect the living expenses in a region. It is again measured by the average price of many things. But I accidentally discovered a simpler way.

I was talking to Johannes the other day, who was complaining how expensive it was to live in Milan. Exactly how expensive? A pint of beer cost 10 Euros! "How much does a pint of beer cost in New York City?" Johannes wanted to know. That was how he assessed the living expenses in a city.

Of course, Johannes is German. So the living expense will be different for a French, an Italian, and a Chinese. We all have our own essentials in life, and we measure money accordingly.

Wednesday, May 11, 2005

Time to Leave

When things start to break, it is time to leave.

I have lived in San Francisco for twenty months by now. Things started to break. About a month ago, I dropped the lid of my Brita water filter, and it broke. That was the first of a chain of incidents. The handle on my Dell laptop bag gave way two weeks ago, and I had to use the shoulder strap since, until last Friday when the strap also came off the hook. I lost my keys. Even my eyesights seem to have deteriorated.

Maybe it is a sign. When things start to break, I probably have stayed in a place for too long. Time to leave. I am moving to New York City in June.

Friday, April 29, 2005

What’s Wrong with the Force Field?

If people don’t understand it, they won’t trust it.

“I sense a great disturbance in the Force”, Darth Vader says as Obi-Wan Kenobi boards the Super Star Destroyer. I am a believer in the force field that Jedi knights manipulate with miraculous effects. But I have grown wary of the force fields that computational biologists use in their simulations.

To simulate on computers the behavior of a molecular system, say, the binding of a drug to a protein, or the conformational changes in a signaling molecule, it is crucial to calculate the interactions between the atoms accurately. Although quantum mechanics can compute these interactions in principle, in practice empirical energy functions have to be used due to limited computing power. Many empirical energy functions have been developed and affectionately referred to as force fields. In the beginning, there were only simple interaction parameters for inert gases, then carbon monoxide, then water. Then there was the need to simulate proteins, and complex force fields were developed. Many different force fields emerged independently, each christened with its acronym. There are Amber, Charmm, Gromos. There are OPLS-AA and MMFF. There are many more. Each is a cult with followers and they are constantly at war.

After decades of development, however, computer simulation is still greeted with skepticism by biologists. Compared to experimental technologies of similar age, this is a curious exception. True, almost everybody uses simulation now. But whenever there is a disagreement between the simulation and the experiment, the simulation result becomes the primary suspect. The Journal of Molecular Biology recently rejected a computational paper with the comment that it “will only accept computational works that AGREE with experimental results.” This reflects the general attitude toward computer simulation: it is only good for verifying experiments, but not good enough to generate independent hypothesis.

Sadly for the computational biologists, this dismissal of their work is largely justified. Currently, computer simulations are riddled with problems, and many a simulation have produced results far from well-established experimental observations. The force fields bear much blame. Everyone agrees that they are not good enough. (At the same time everyone contends that his or her force field is BETTER than others.) Everyone agrees that something has to be done about them. But what is wrong with the force field?

The common opinion in the computational community is that the force field needs to be more accurate. The definition of accuracy, of course, is tricky, and depends on the specific problems to which simulation is applied. So although everyone is talking about improving the force field, most people are doing just that, talking.

I think that the force field has a much more crippling problem than its inaccuracy. That is it is too complicated! Way too complicated! In the quest of accuracy, increasing number of parameters have been shoved into the energy functions, so that all present force fields are messy compilations of thousands of parameters. I doubt anyone, including the folks who parameterized the force fields, can correctly remember a tenth of the parameters, or even to recollect why these parameters are chosen over others. For example, in most of the force fields, there are many subtypes for each atomic element. Take OPLS-AA force field. It contains 329 subtypes for carbon atoms, 165 for hydrogen, 76 for nitrogen, and 47 for oxygen. Mendeleev would have turned in his grave.

The complexity of the force field is really the cause of its plight. Worse, it is the complexity without underlying order or reason. In the blind pursuit of accuracy, parameters are fitted ad hoc, without justification. The consequence of the Machiavellian philosophy – “the end justifies the means” – is that only the end remains meaningful. The only useful result from the force field calculation is the total energy. The components, such as van der Waals, hydrogen bond, or electrostatic energies, are only believed by the most faithful.

I was once in a group meeting where a graduate student talked about his calculations of the stability of a structural motif in proteins. He used his results to argue that hydrogen bonds were responsible for the stability. Yet the force field used had nothing to describe hydrogen bonds. I proposed that the stability could come from pure electrostatic interactions and asked him about the charges on the atoms as assigned by the force field. Unsurprisingly he had no clue. He was forgivable. How can someone be expected to know these numbers when there are so many?

Most people use the force field as a black box. Unfortunately, people tend to abuse black boxes. When the simulation works, people over-interpret the results. When it fails, people simply sweep it under the rug. Few try to understand the reason behind the success or failure. To do so one has to open the black box. But it is too messy inside.

Contrast that to experimental techniques. An NMR spectroscopist usually has a good knowledge of the chemical shifts of protons in different environments, and a biologist doing fluorescence experiments knows the absorption band and photon efficiency of the labeling dye. NMR spectroscopy and fluorescence labeling are respectable experimental techniques not because they always give correct results. It is because when they go wrong, the experimenters can understand why.

That is the problem with the force field. People do not know why their simulations succeed or fail. It is like a blind cat trying to catch a dead mouse. The cat may stumble upon the mouse, but the cat does not know why and how to do it again.

In science, the simple always supercedes the complicated. The clear is preferable to the confusing. Inaccuracy in the force field is tolerable as long as the applicability and limitations of the force field are understood and predictable. So instead of pushing for better accuracy by adding atom types and parameters, we should simplify the force fields first. Reduce the number of atom types, reduce the number of independent parameters, and minimize the set of standard data to which to fit the parameters. Make it simple, make it comprehensible, and it will be respectable.

May the force be with us.

Monday, April 18, 2005

Subterranean Magic

Saturday, Yang and I took subway from Queens into Manhattan. New York City subway got its weekend relief from its workday congestions, and there were only a handful of passengers in our car. Our ride was roomy and long, so I took the opportunity to show off my card tricks.

It is a challenge to do the tricks for Yang, for she is more interested in catching my sleights than being entertained. This is true for most of my friends. It is the amateur magician’s adversity. When a professional magician performs his art, the audience assumes that his technique is beyond detection, and gives up the attempt to catch his maneuvers. Besides, no one buys the ticket just to shout “wait, he just palmed my card!” Amateur magicians do not have the luxury of a lenient audience. Amateurs beg to perform for their friends, and they delight in any “well done” from the audience. My friends do not watch my tricks for entertaining magic – they go to Vegas or watch television for that – they watch me to catch me. They take it as a puzzle that can be solved. They take me as the weakest and breakable link in the ring of magic.

It was thus no surprise that after I made a card vanish, Yang held my hand and tried to see if I had anything up in my sleeves. I ignored her and continued my routine. Taking out the four aces and placing the rest of the deck into my pocket, I was getting ready for my favorite trick of twisting the aces. Then I heard a man’s voice next to me:

“Oh, that is the end of my fun.”

I turned my head and saw a man with dark curly hair and a strongly contoured face, looking to be in his thirties. Sitting next to him was an attractive young Asian woman, with rather pale complexion and short hair reaching the back of her shoulders. I vaguely remembered this couple sitting across the aisle and a few seats away from us. They must have moved to the adjacent seat after I started my magic.

It was not often that I got a voluntary spectator who enjoyed my magic. I was flattered. I reassured the man: “There is more.”

I did my twisting the aces. When I finish, Yang tried to guess, incorrectly, how I turned the cards between the cards. I looked at the man. He was quite amused with the trick. But he did not show any sign of puzzlement normally expected from a spectator of magic.

I did a few more tricks. Failing to catch my sleights, Yang lost her interest. It was almost our stop. I was about to put the cards away, when the man asked me:

“Who taught you this?”

I did not hear him very well in the clanking noise of the train, and he had to repeat the question twice. Then I told him that I learned card manipulation from McBride’s DVDs. On hearing the name, the woman casually turned her head to the man and asked:

“McBride. Do you know him?”

The man said:

“Yes, I know him.”

I felt something was not right. I managed to say how great a card manipulator McBride was.

The man took out a card, his business card, and handed it to me.

“You give me a call.”

I did not have to look at the card to guess its content. Printed on the card in plain Ariel font was

Richard D. Prestia
Magician

Saturday, April 09, 2005

My Operating System

I took a personality test to determine the most fitting OS for me. Not a surprising result.

Saturday, March 19, 2005

Lessons from the Acquired Immunity

Evolution has no foresight. Neither do we.

This is an age of insecurity. Hijacked planes, suicide bombs, weapons of mass destruction, phishing emails, computer viruses. We are under attack everywhere and everyday.

But this is also an age of protection. National security advisory code, airport shoe check, National Missile Defense system, liberation of Iraq, sophisticated message encryption, antivirus software, firewalls, deadbolts on the doors. We live behind the shields of better and better defense.

But are we protected? A recent commentary published in the journal Immunity should make us thinking again.

In his article, Stephen Hedrick re-exams the usefulness of the acquired immune system. The acquired immune system is vertebrates' second line of defense against pathogens, and it is activated when the first barrier against infection, the innate immune system, is breached. The acquired immunity employs a sophisticated mechanism -- somatic hypermutations combined with thymus or germinal center selections -- to generate pathogen-specific T-cells and B-cells to search and destroy the invaders. These T-cells and B-cells then remember their specific targets, and become a fast response force against any recurring infection. Thanks to the acquired immunity, we do not get many diseases twice, and we can be vaccinated against these diseases before they strike. In contrast, the innate immunity, which is universal to vertebrates and invertebrates alike, uses seemingly mundane mechanisms: cell membranes and coagulation to deny pathogen's access into host, defensins and lysozymes to destroy the parasites before their entry, and other brute force measures.

Until now, the majority of immunologists view the acquired immunity as an optimal defense system, a superior weapon that confers great health advantage onto vertebrates over invertebrates. Hedrick's commentary overturns this conventional view. He argues that the acquired immunity overall does not benefit vertebrates as a kind. Comparisons between insects and vertebrates have yielded several surprises. For example, the morbidity and mortality of insects due to infection are not higher than that of vertebrates. Compared to the pathogens for invertebrates, the pathogens that infect vertebrates have developed more adaptive strategies to evade the acquired immune system. Influenza is one best known example of this adaptability. Not only the acquired immunity can be easily rendered useless by the evasive pathogens, it can also be exploited by the viruses for their replication, as in the case of AIDS, or backfire on the host and cause autoimmune diseases such as arthritis and lupus.

Instead, the acquired immunity appeared to be an evolutionary misstep. The strain that first developed the acquired immunity had a temporary advantage over the rest of the animal kingdom, so it multiplied, eventually developing into the vertebrate subphylum. Unfortunately, it underestimated the infinite resourcefulness of the pathogens. The fateful genetic mutation that gave rise to the acquired immunity inadvertently escalated the war between the pathogens and the vertebrate hosts, one that had inflicted heavy costs and casualties on both sides for the past four hundred million years. Meanwhile, the acquired immunity becomes an absolute necessity for vertebrates, because any deficiency in it will make the individual defenseless against the highly evolved pathogens.

Hedrick’s insight should reach beyond immunologists.

So much as our sophisticated acquired immunity cannot make us impermeable to germs, any defense that we can mount against foreign or domestic attacks can be defeated by a clever enemy. It is an arms race that no one wins in the end. The National Missile Defense system will not protect us, because it will be easily overwhelmed by inexhaustible possibilities of countermeasures. Hundreds of billions of dollars will only buy the Americans a false sense of protection, and will prompt the Russians and the Chinese into a race to develop missile technologies capable of circumventing NMD.

Neither will the antivirus software make our PCs virus-free. After all, it can only recognize a known virus and is useless against any new strain. It seems that the real defense against computer viruses is plain caution: do not visit suspicious websites, do not download programs without a proper certificate, do not open emails from unknown senders. It is just like the innate immunity, mundane but effective.

Yet all is too late. The acquired immunity is here to stay. So is the National Missile Defense, so is the antivirus software, so is the spam email filter. They have all become the cause of their own necessity. We pay for their existence because they protect us from all known forms of attack. But by the force of the unknown future, we remain in the shadow of menace.

Monday, March 14, 2005

Gender Equality with Wheelchair Access

To promote women, we must demote men.

When I first went to Columbia University, the Department of Chemistry had one female professor. A year later, the department hired a young woman as an assistant professor, doubling the size of its female faculty. The department had a total of twenty faculty members at that time.

In University of California, San Francisco, on the floor that I currently work, there are twenty one faculty members. Three are women.

When I interviewed in the Department of Chemistry in University of Washington, Seattle, I met 16 professors, out of whom only one was a woman. She was newly tenured in the department, along with four male junior professors.

Why are there so few female professors?

According to some people, including Lawrence Summers, the president of Harvard University, women lag in science partially because they are biologically different from men. Perhaps testosterone stimulates mathematical genius; estrogen suppresses it. Perhaps women are innately more susceptible to beauty in a flower bouquet than beauty in a mathematical formula, more adept at counting inventories than counting neutrons, more disposed to mixing cooking recipes than doing chemical synthesis.

Wait a minute. As I remember, from primary school all the way to college, the top-scoring student in my class had always been a girl. In the College Entrance Exam administered by the Chinese Bureau of Education, girls do just as well as boys.

Anticipating such retorts, Dr. Summers contends that although average math aptitude may be analogous between the sexes, more men tend to occupy the tails of the distribution. In other words, the dumbest and the most ingenious are male. Women can surely do calculus, but only men can prove Fermat’s Last Theorem.

But that argument does not hold water either. Once appointed, female professors are as successful in contending for research grants and career fellowships as male professors. The McArthur fellowship, widely dubbed as the genius award, has been awarded to many outstanding women in the past decade. I have personally met many women who are absolutely the top-tier scientists in their field.

Well, if estrogen does not poison the brain, what hinders women’s advance in science?

In a different way, women are shackled professionally by their own biology. The optimal child bearing age of a woman coincides with that of the critical stage of her career. A twenty-two year old woman, just out of college, faces the tough choice between rearing children and pursuing a career. If she wants to go into academia, she will have to postpone having children indefinitely. Five years of graduate school, three years of postdoctoral study, six years of untenured junior professorship, that is fourteen intense years almost impossible for her to have a baby. Even fourteen is the most conservative estimate. Finally, at thirty-six, way past the optimal child bearing age, she is ready to have a baby, if she is fortunate to have a man who is willing to be patient for so long.

In a recent op-ed in New York Times, David Brooks advocated a rounded alternative: the sequential life style. In a nutshell, the sequential life style suggests that a woman out of college spend five years at home, rearing a child. She will then reenter the work force and pursue her career uninterruptedly like her male colleagues.

Superficially, Mr. Brooks laid out a perfect plan. But at closer scrutiny, this sequential life style does not hold up. Not only does it outright bereave women five years of their professional lives, it takes away five of their best career years, the years when they are mint with skills, knowledge and connections acquired in college, the years when a person’s drive to succeed is the strongest. Not to mention that these women will be competing at a disadvantage with men five years younger.

Some women chose to sacrifice their procreative rights for a fair game in their careers. But a great sacrifice it is. In science, quite a few successful female professors over forty are single and childless. Sadly, the highly successful but childless professional women will be out of the gene pool in just one generation.

Up to this day, the effort to promote gender equality is focused on creating more opportunities for women in the professional world. This emphasis is epitomized by the affirmative action – should a woman and a man equally qualify for a professional opportunity, be it a job or a promotion, the opportunity will be preferentially awarded to the woman.

Unfortunately, affirmative action, or many other similar measures, does not address a more fundamental problem rising out of the inherent biological difference between women and men. Only women can carry children, and breast-feed them. Most women still view maternity a responsibility and a joy. Yet it conflicts with their careers.

Therefore it is not enough to give women jobs. It is equally important to create an environment where women can excel professionally without sacrificing their personal, especially maternal, needs.

When I first came to the United States, I was surprised by the number of handicapped people I saw on the street and at work. In China, I rarely met a handicapped person. Was it because there were more handicapped people in the States than in China? Not likely. The true reason is that more convenience is extended to the handicapped population in the States than in China. From designated parking to the wheelchair accessible bathrooms, the American society has created an environment where the handicapped enjoy as much mobility as the otherwise privileged population. In contrast, China, until recently, has not provided the same facilities for its handicapped population, who are consequently confined in a narrower living space.

Similarly, if we want to foster women’s professional success, we must not only give them the initial access to an opportunity, but more importantly, we must create an environment where they can excel with as much ease and freedom from biological burdens as men. This is especially important for women with babies. A firm that provides wheelchair access to its handicapped employees should similarly allow new mothers to bring their babies to work and provide the necessary breast-feeding stations. It should provide daycare centers so that young mothers can go to business meetings without worrying about their children.

Significant changes must also be wrought upon social conventions. Feminists have long been arguing that men should share the burden of rearing children. Yet this is difficult to practice as long as the society exercise the conventional pressure on a man’s professional success. Just like women, men cannot simultaneously shoulder the responsibility of rearing children and pursuing their careers. Something has to give. The society must relent on its obsessive value set on men’s professional success. Women should cease to select mates based on their career success. Only when men can proudly declare themselves house-makers, can true professional gender equality be achieved. A single, childless woman should arouse no more pity than a single, childless man. Neither should a jobless househusband receive more frown than a housewife. Only then is gender equality a reality.

In Sex and the City, Miranda marries Steve. Samantha falls in love with Jared Smith. That should be a heartening ending for the professional women.

Life on the Crutches

Seeing the bus leaving the stop, I ran after it. My life changed for the next three weeks.

Exhibit 1. The swelling was still visible a week after I sprained my left ankle.


The accident

When I was thirty years old, I went on crutches for the first time. The accident happened on a Thursday night, when I severely sprained my left ankle as I ran to catch a departing bus. That night, Bosco and I were heading to Chinatown to get some authentic Cantonese noodles with beef tripes. Bosco, a chronic procrastinator, took his time in the men’s room. By the time we came to the bus stop, the bus was already leaving. I ran toward it, waving my hand. As the bus was stopping for us, the accident happened. My left foot twisted, the ankle bent sharply inward, and I started to fall. Yet my obstinate body resisted it, exerting a strong torque on my ill-positioned left ankle. The pain shot up my left leg and tore my brain. I wanted to lie down and wait for help. But I knew that the passengers on the bus must have seen my amusing accident, and I fear of being laughed at. Driven by that fear, I limped forward onto the waiting bus.

“Are you okay?” Bosco followed behind me, taking a seat.

In the next hour, we had our authentic Cantonese food. I ate the entire meal with my left hand pressing a bag of ice against my left ankle. Yet the ice was not enough to suppress the swelling. By the end of the meal, my left ankle doubled in size and looked like an orange wrapped in a sock. Clearly I needed to go to an emergency room.

“You want to come with me?” I asked Bosco as I stepped into a taxicab.

“No, I think I will just take the Muni home.” Bosco thought it inappropriate to share a cab with someone needing emergency care.

Emergency room

I had seen quite a few advertising posters for some hospital’s ER service. The posters generally showed some hapless yet jolly souls getting into an accident, such as falling over a banana skin, and a big “Whoops”. The text at the right corner said emergency care under 30 minutes in Blah-Blah hospital.

After a full hour of waiting in the corridor of the emergency room of UCSF Medical Center, I tried to remember the name of the hospital advertised in those posters. With an ice pack wrapped around my left ankle, I waited patiently for a nurse’s attendance. There was only one more waiting patient, a man sitting in a wheelchair next to me. “I have been here since six o’clock”, he said, “and I am still waiting.” I was dismayed. It was past ten.

Finally a nurse took me into a room, measured my blood pressure, put me onto a wheeled bed, and pushed me into a ward. Ward 20, as marked on the ceiling. The wards were separated by plastic curtains. There was a small bedside table, and a phone.

I called two friends. I hoped to have someone drive me home after treatment; if I could not have that, I wanted to have someone at least carry my laptop home for me. I called Wendy first. Not only because she had a car, but also because the companionship of a woman is preferable.

I got Wendy’s voicemail. “Hello, Wendy. This is Huafeng. I sprained my ankle and I am in ER. I wonder if you can drive me home tonight.”

Next I called Yu Chen. He did not have a car; but he lived nearby and he could at least take my laptop home for me.

Again, I got the voicemail. “Hello, Yu Chen. This is Huafeng. I sprained my ankle and I am in ER of UCSF Medical Center. If you can stop by on your way home and take my laptop home, it will be great. I am in Ward 20.”

For the next twenty minutes I stared at the ceiling. The ward was surrounded by curtains on three sides and a wall in the back, so I could not see anything outside. Everything in my view was white, including the phone. I imagined myself to be in a modern art exhibition, where the pieces had been variations of the white color on canvases. I imagined myself to be a wounded soldier in a World War, surrounded by dying fellowmen, neglected by the nurses and my government. I let my thoughts drift through the whiteness.

The curtain was pulled open, and a nurse came in. I thought my wait was over. She handed me a walkie-talkie-phone. “You have a phone call from your friend.” Surprised, I took the phone. It was Wendy. She just received my message and wanted to know my condition.

“Since the doctor has not attended to my case, I guess I am not dying.” I attempted humor.

Wendy wanted to know when I would get out of ER, so that she could pick me up and drive me home. I had no idea, and told her that I would call her again if I got out before some reasonable hour. I narrated my embarrassing accident. We chatted for some time. It was wonderful not to be alone in the ward.

After some time, Yu Chen called. He came in after another ten minutes. As usual, Yu Chen spoke of his trouble in finding the ER, and in finding my ward. Then we talked about this and that. Yu Chen stayed until a nurse came to take X-ray of my ankle. He left his Time magazine to me. “Just remember to return it to me when you are done. I want to keep this issue.” He carried my laptop away.

The nurse who X-rayed me was a chubby young Asian girl by the name Jacquelyn. She was either easily amused or professionally polite, laughing at every one of my jokes. As a result, I have forgotten all the jokes that I made to her. Having a nurse who laughed at my jokes at least made me temporarily forget my physical pain. The white, gigantic X-ray machine sat in a spacious room. Jacquelyn pulled the X-ray barrel over my left ankle, put a heavy apron over my chest, and walked into the adjacent operator’s room to push the button. She shuffled between my bed and the operator’s room several times, twisting my left ankle into different positions for panoramic effects. All the time, I tried to keep the jokes flowing.

A few X-ray bombardments later, I was wheeled back into my ward, and was greeted by an unexpected visitor, Wendy. Sitting in a chair, she smiled with genuine amusement when she saw me pushed in lying in the bed. I was very pleased when I saw her: female companionship, the best medicine for a man in pain.

With Wendy’s company, waiting for doctor was far more endurable. The meetings between Wendy and me were always far between, so we had a lot to update each other. I told her about my upcoming marriage proposal. She laughed at the formality of “popping the question”.

Soon came the doctor, a slim, kind-looking lady appearing to be in her late thirties. She introduced herself as Doctor Her-last-name, and informed me that my bones were fine, and the ligaments were badly stretched but not torn off, so I would be fine after sometime on crutches.

Somehow I mentioned I had a Ph.D. in chemistry.

“You should have let us known that earlier. I would have come to you much sooner had I known you were a chemist.” Doctor Her-last-name said.

I gathered that chemists had more vulnerable ankles.

After Doctor Her-last-name, a young, strapping ER technician brought me a pair of brand-new aluminum crutches. He smiled broadly, his dental braces flashing with a metallic sheen above his thick goatee. He sympathized with my sprained ankle. “But at least you have your wife here with you.” He tried to comfort me.

“Wendy is a friend of mine.” I corrected him.

“So you are dating this guy?” The technician said to Wendy. Apparently he did not believe in pure friendship between sexes.

Ten minutes later, I moved out of ER on the new crutches. Wendy drove me home.

Wendy

Wendy was one of my fiancé’s best friends. I met Wendy in Columbia University a few months after I came to the United States, even before I met my fiancé. Later, through my fiancé, Wendy and I became better acquainted, although we rarely met. She moved to San Francisco after college. Two years later, I came to San Francisco for postdoctoral study in the University of California. We had met a few times since then.

Wendy was a rarity among my friends. She had more academic concerns for the world than pragmatic concerns for her own life. Three years after Columbia, two years after Berkeley, Wendy was still only half way descending the Ivory Tower. She worked as an engineer in P.G. & E., but aspired to a career in writing and journalism. Not completely a wild dream, since she had already published a few political essays in newspapers.

Like all Columbia graduates, Wendy was an ardent feminist. Although in heart I am a women’s rights activist, I sometimes speak to the contrary with Wendy just to instigate a more interesting debate.

But the ride to my home was too short for any debate of the political sort. Wendy helped me upstairs to my room, left Shere Hite’s book on female sexuality and a movie set in the Chinese Civil War, and drove back home.


Life on the crutches

The next morning I woke up with my left leg raised by four pillow cushions. The pain was still on my ankle. I clasped my crutches, sat up slowly, stood up on my right leg, and balanced myself on the crutches. I needed to go to the bathroom. Going to the bathroom, so easy before, now seemed a tremendous undertaking. Opening and closing each door, lifting up and setting down the toilet seat, getting down and getting up, between each action, I had to pause and rebalance. As I moved back step by step to my bedroom, I had an inkling of the difficult days ahead.

Going to work was out of the question. I lay in bed and read Shere Hite’s book. But the pulsating pain in my ankle made sexuality uninteresting. I flipped through the pages, nonchalantly reading women describing their sexual fantasies and orgasms. Later in the morning, Yu Chen stopped by and dropped off my laptop and two more movies. I ended up watching three movies on that day.

At noon I tried to fix myself some lunch. It was Mission Almost Impossible. I carried a pitcher of water while walking on my crutches, and I spilled water all over my pants and the floor. I managed to boil some dumplings in my rice cooker. But as I stood on one leg and scooped the dumplings into a bowl, I knew that was the last meal I would cook for myself for days to come. I left the rice cooker open and unwashed. In ten days, when I finally had the strength to clean it, I found a dead black spider in it.

In the evening, Yu Chen brought me dinner, a juicy cheeseburger from Sliders. He continued to bring me food for the next two days. He was a true friend.

For two days, I remained in my little room, venturing out no further than the bathroom. Immobilized, I began to realize how much of our lives depended on mobility. With a sprained ankle, my life was reduced to no more than a hundred square feet. I had no internet access. I had no desire to read. I was bored. On Saturday morning, I stared out of the window and looked at a beautiful Californian day. I normally would run six miles on such mornings, but not on that morning, not on the Saturday mornings of many ensuing months. I felt like an impotent man lying in bed with a beautiful woman, tormented by lust and shame. I was shrinking, body and mind.

On Sunday, the confinement became unbearable. With Yu Chen’s help, I walked outside on my crutches. Getting down the stairs was a challenge, but by the last few steps I had mastered a technique for descent. We went to the closest restaurant. I rested a couple of times along the way. When we finally reached the restaurant, my back was damp with sweat, my armpits sore. But I was as happy as a drowning man who surfaces above the water and takes a breath.

I stayed on the crutches for the next three weeks. When I crossed the streets, cars waited patiently. When I hopped on a bus, other passengers yielded the front seats to me. When I flew to New York, I enjoyed priority boarding. I was granted the convenience given to the handicapped, but I was not an object of pity. Because struggling as I was, I would soon rid of the crutches, and walk again.

Saturday, March 12, 2005

Letter Writing in the Digital Age

Don't write beyond the subject line.

In the information age, brevity comes first. I sent the following message to invite my friends to a popular Peruvian restaurant:


Near the intersection of Valencia and the 17'th Street sits the legendary Limon restaurant, whose succulent ribeye steaks and tender grilled scallops have earned its reputation far and wide in the Bay Area. To this restaurant I invite you to join me, on the wondrous Thursday of March the Tenth, at the felicitous hour of 7:00pm.

......


Soon, I received a reply asking why I sent an email talking about a restaurant. It dawned on me that the person did not read beyond the first sentence.

Email was just getting popular when I entered graduate school. My very first emails were sent to American schools inquiring about their application procedures. Internet was still a rarity in China at that time, and I paid 20 cents per minute to type my letters in the terminal room of the chemistry department of my college. I wrote short messages to save money.

Then I went to Columbia University. Immediately I had a free email account with unlimited letter writing privileges. I could write for free to all my friends who were similarly blessed with an email account. The internet revolution had started in earnest. Two and a half years after its launch on the Independence Day of 1996, Hotmail had more than 30 million active users. It seemed that suddenly everyone in the States was sending emails, and our inboxes exploded. Our workdays were transformed: the morning would begin with composing, reading, replying to and deleting emails; frequent visits to the inbox would punctuate the day; one last peek of the inbox would invariably precede our departure from work.

With the advent of every new technology, an old way of life must die. The victim of email is the post; email is killing letter-writing. Before email, I corresponded by hand-written letters with my friends and family. The letters were infrequent but thoughtfully composed. In them, I not only narrated the most significant events happening in my life, but also told of my ideas and opinions. Every letter was an intimate conversation, and the delay in the reply provided anticipation and suspense.

To send a postal mail, one has to seal the letter in an envelope, write down the send and the return address, put on a stamp, and drop it in a mailbox. Emails, in contrast, are different. Push one button and the message is on its way. This ease exercises a subconcious pressure on one's mind: the letter can, and therefore should, be sent as soon as possible. As a result, one rushes to complete the letter, pushes the send button, and moves on to the next message. Convenience is the enemy of depth.

I am probably one of the few surviving dinosaurs from the postal age who still read my friends' emails from the beginning to the end. But I have an advantage: my friends' emails tend to be short. They average two paragraphs, consisting of no more than three sentences each. They fall into the following general format:


I did some cool stuff. The stuff I did was really cool. I wish you did the same cool stuff too.

Want to do some cool stuff together sometime?


After proposing to my fiancee, I sent an email to my friends, telling my engagement story with details and great excitement. I fell cold on seeing the following reply:

Congratulations! So how did you do it?


The subject of my email was: "I am engaged!" The narrative of the full experience began in the first paragraph of the text.

Friday, March 11, 2005

Harvard Exchange

Harvard University did not offer me a job, for one good reason.

This year I looked for faculty positions. I sent my application to Harvard University. It lead to the following exchange of letters.

*********************************

Department of Chemistry and Chemical Biology
Harvard University

Dear Members of the Search Committee:

Please consider my application for the junior faculty position in Physical Chemistry advertised by your department in C&E News. I have enclosed with this letter my curriculum vitae, a list of my publications and patents, and a statement of my research interests.

I look forward to hearing from you.

Sincerely,

Huafeng Xu

*********************************

Department of Chemistry and Chemical Biology
Harvard University



Dear Dr. Huafeng Xu,

Thank you for your application for our assistant professorship in Organic Chemistry. We have received a very large number of excellent applications this year and can only interview a few candidates.

Unfortunately, the Department is not in a position to offer you an assistant professorship at this time.

Our best wishes for your future plans.

Sincerely,

Akira R. Shave

*********************************

Dear Dr. Shave,

I recently received a letter from you which stated to the effect that your department was not in a position to offer me an assistant professorship in organic chemistry. I am writing to assure you that the regret in your letter is completely unjustified and unnecessary.

Harvard is not the only school that is not in a position to offer me a job in organic chemistry. No institution on this planet is: I am not even an organic chemist! Sure, I took organic chemistry in college, and spent some time making pheromones in an organic lab. But that's it. I have not been near any toxic chemicals since graduate school. Consequently, I have decided to accept an offer in computational chemistry from another institution, and continue my chemical-free career.

I wish you success in identifying the best organic chemist in the world.

Sincerely Yours,

Huafeng

Friday, May 28, 2004

Angels in Katana Ya

Sitting with an empty wallet in a restaurant that only accepts cash, I thought of calling a friend, who was at that moment desperately looking for his missing cell phone.


It happens to us all. Seeing that "Cash Only" sign hanging on the restaurant door at the end of our solitary meal, and finding to our great dismay that, despite those "accepted everywhere" major credit cards and except for a few loose pennies, we are out of cash. We blush, anticipating the embarrassing moment when the friendly waitress brings the bill with a big smile; we panic, knowing that the nearest ATM machine is at least twenty minutes away; we regret not having checked our wallets before entering and not having come with a friend; we ask ourselves, what are you gonna do?

Well, I could call my friend Yu Chen, I thought as I regained my composure. At that time, I was eating by myself in the restaurant Katana Ya. I had almost finished my meal before I opened my wallet and found no cash in it. I contemplated my way out of this dilemma, and Yu Chen came into my mind. After all, he was partially responsible for my situation. Had he let me use my credit card to pay for the meal that we had together the previous night with a few other friends, I would not have depleted my cash reserve. No, he had to make those award points, he explained complacently as he collected cash from us. Of course, the other benefit of paying the group meal with one's credit card is to get cash without a visit to a bank ATM. Yu Chen took advantage of us all.

Yu Chen was my instinctive choice of rescue for other reasons too. He lived close by, no further away than the closest ATM of my knowledge. He was always ready to help his friends in need. He knew the location of the restaurant, since we had dined in it together. (He had a funny way to say the name of the restaurant -- "Kata--naya" -- making the name sound Polish instead of Japanese.) He had cash in his pocket, those very twenty dollar bills that he had harvested from us the night before; therefore he would not be delayed by a detour to his bank.

The thought of Yu Chen gave me back comfort and appetite. With ease I ingested the last few bites of my meal. Having washed down the food with ice water, I took out my cell phone to summon help. I dialed, and eagerly listened to the long ring tones. Three rings without answer. My waitress gracefully put down my bill tray and took away my plate. My anxiety grew. Five rings, still no answer. Six rings, I hang up. Where was Yu Chen?

Yu Chen was, at that very moment, pressing his face against the restaurant window to assure my presence at the table. Presently he pushed open the door and entered.

“I am in a hurry.” he said, “I could not find my cell phone. I am really worried that it might be stolen.”

“No wonder”, I smiled. But my inappropriate comment was lost on Yu Chen, who continued with urgency.

“I was at work. Then I realized that my cell phone was not with me. So I took the bus back immediately. I must go home now and check if I have left it there." he said, and was on his way out again.

Confronted with his distress, I had not for a single second forgot my own. "Hold on a second", I grabbed the back of his shirt, explained my problem, and asked for a loan. As Yu Chen opened his wallet, I had a glimpse of all the greenbacks that he had happily taken from us the night before. He offered me a twenty, the same bill, I suspected, that had been transferred from my wallet to his. My waitress witnessed our transactions with a tinge of relief on her face. I offered Yu Chen to call his cell phone to see if anybody had it. He said that was the first thing he had done once he found his phone missing. I bid him good luck, and told him that I would stop by his home later to return his money and to see if he would have found his phone. This I did. Expectedly, Yu Chen had left his cell phone at home and had found it. He thanked me for calling it, not knowing the true purpose of my call.

But is there someone to whom I should be grateful? When my call went to a cell phone far away from its owner, when my intended rescuer was not at home nearby as I had hoped, who made him pass by the restaurant, and who made him turn his head to see me in there? Angels in Katana Ya.

Monday, May 10, 2004

The Chinese Language Exam

I had one night to fear my imminent devastation.

I spent half of my lived life preparing for and taking exams. I excelled in them. They gave me instantaneous satisfaction and self-assurance. From primary school to college, I enjoyed the feeling of triumph after scoring higher than most of my classmates in each exam. Although I was scarcely the top of the class, I was invariably close enough to earn my teachers' favor and my classmates' respect. Through what other convenient means can an ordinary teenager achieve self-confidence, if he does not do well in sports and is not dazzling-looking? Mid-term, final, TOEFL, GRE, bring them on. I was the master of them all.

Not only did my excellence in exams give me confidence, they also let me learn modesty.

Friend: "I heard that you got 2300 in GRE, that's amazing!"
I: "Well, that's just a pleasant accident."

Friend: "How did you get such a high mark in the math final?"
I: "I happened to have reviewed the right problem sets."

This time, of course, should be no different. I have already finished three exams, and I have done well in them. Only the math exam remains, and math is my forte. Time to relax and think of the fun things to do in the summer. Then a classmate comes to me and asks me if I am prepared for the final on the Chinese language.

"You are kidding me, right? I don't remember we have a final on that."

"Hmm, no. The exam is on tomorrow morning."

Panic seizes me. Out of my scrambled memory I retrieve the terrifying truth. I now remember clearly that the teacher has mentioned the final in the class, but I have somehow forgot it altogether. I have not once touched the textbook, nor have I read a single reading assignment. As it is, I owe a reading to three novels, five essays, two monograms, half a dozen proses in ancient Chinese, and scores of poems. I cannot even Xerox all the pages before tomorrow morning, let alone reading and memorizing them. I am going to flunk. My mind goes blank.

This is invariably when I wake up from the dream.

I have had this same dream innumerable times, always at dawn. The scenario is identical: falsely thinking that I have only one more exam to take, I am caught off guard with a second exam. The one exam that I remember is on either math or physics, and the one I forget is always, always on the Chinese language. Details may vary. I may remember the Chinese exam with a friend's reminder, I may walk into the classroom and find that everyone is working on the exam that I am completely unprepared for, or I may remain unaware of the exam until I see a big red zero on my score sheet on the first day of school after the summer holiday.

It was the last semester of college when this dream first invaded, shortly after I had taken what I thought was going to be the last exam in my life. In the beginning, the dream was more lenient, and I was given a week's time to cram for the neglected subject. Like a virus that mutates into more virulent strains, however, the dream increased in malice each time it visited, leaving me less and less time to make up, until it gave me only one evening, not to study, since it would be useless, but to dread my imminent and inevitable failure.

To me, it is no coincidence that the dream came on the heels of my supposedly last exam in life. Until then, doing well in exams had been my primary means of establishing my identity. Sure there were other things too, like having a couple of hobbies. But how else does one demonstrate superiority unequivocally? The exams carry scores, and these numbers can be compared. A tall guy says that he is 6'1, a rich man says that he earns half-million a year, and a basketball player says that he scores 20 points average a game. The height, the earning power, and the sportsmanship can all be measured by numbers. My number was my scores on the exams, and it got me ahead in school. Now I had to adapt to a life without exams, and to search for a new means to measure my success. The dream came, I think, to fill in the void. I might no longer have the exams in life, but at least I could still cherish them in my dreams.

Yet it is not a happy dream -- I flunk in it. It seems to reflect my subconscious and persistent fear of failure in the exams. Excellence in the exams was all I had, and how tenuous was my success. Everything hinged on my performance in an hour or so. It resembles in this sense a game, just one shot, and chance happens to us all.

Monday, April 26, 2004

The Backside of a Puzzle

How some classic puzzles can be solved in different ways.

I am fond of puzzles, and often trade them with my friends of similar propensities. Over the years I have come across a large number of puzzles. As a result, the stream of new ones that flows my way has dwindled to a trickle. More often than not, I will have recognized a puzzle of past acquaintance before my friends are only half way through the narrative. From time to time, I will delight in a "new" puzzle only to realize a few minutes later that it is merely a variant of a puzzle that I have encountered before but have failed to see through the disguise of its new form at first sight. This situation may have given my friends some disappointment, as many of them are waiting to expound the clever solutions they know after I fail to devise my own. But it is more frustrating to me than to my friends, because whereas they are only denied the pleasure of reviewing a familiar cleverness, I lose the thrill of a new discovery, and the joy of an intellectual odyssey through a fresh vista of imagination.

But even the familiar puzzles can give me the pleasure of surprises. I continue to get unexpected solutions to some classic puzzles from my friends. It seems to contradict a popular belief among mathematicians and physicists: The truth is often so simple and elegant that it cannot be otherwise. I will show you two puzzles, whose canonical solutions are so simple and elegant that they make you doubt if any other solutions are possible.

Puzzle #1. Construct a mathematical expression containing four zeros but no other numerals such that it is equal to 24.

The standard solution to this puzzle, when I first hit upon it, convinced me that it had to be THE solution. (For readers with a desire to solve every puzzle by themselves, I place the standard solution and the alternative solution at the end of this article, so as not to deprive them of the pleasure of an independent discovery, which is so often taken away from me.) With its simple symmetry, and its inevitable and apparent connection with the number 24, the standard solution seems to have left no room for any alternative to fit in. Well, I fell off my chair when my friend Dave showed me his beastly solution. His solution is a monster that has all four zeros in hideous arrangements, and its equality to 24 cannot be easily verified without the aid of a scientific calculator. Nonetheless, with the rules of the puzzle relented slightly, his solution is every bit as valid as the beautiful, standard one. Appearance may be misleading.

Puzzle #2. Consider the following equation, formed by 14 matchsticks.

2 2 / 2 = 11

(Because of the limitations of the display, the matchsticks are not drawn here. Each number "2" is formed by three matchsticks: one horizontal on the top, one horizontal at the bottom, and one diagonal leaning right in the middle; the division sign "/" is made of one diagonal matchstick leaning right; the equal sign "=" is made of two parallel horizontal matchsticks; the number "1"s are just one vertical matchstick each.)

You are to move one and only one matchstick to a different place in the equation, and form a different equality. The emphasis is on DIFFERENT and EQUALITY, and therefore the new equation should be different from 22 divided by 2 equals 11, and it must have on both sides of an EQUAL sign two entities that are EQUAL.

As for the first puzzle, I reveal the standard and the alternative solutions only at the end of this article. Again, the standard solution is clever, exact, and cute. Anyone who discovers the standard solution will find in it harmony and enjoy the graceful twist of his or her brain. But when I told this puzzle to my former colleague and friend Dimitris, as we were drinking a few beers in a noisy restaurant, he gave me a jaw-dropping answer. Admittedly, his solution is not exact, but it happens to be one of the most famous approximations to probably the most famous number of all. It is almost devilish. A couple of years later, the same Dave who took me by surprise with his monstrous solution to the first puzzle gave the same answer as Dimitris's to this second puzzle. Coincidence, or a trick of the devil?

G. H. Hardy once remarked: "Beauty is the first test: there is no permanent place in this world for ugly mathematics." For the theories of physical sciences, beauty is almost as important a criterion of judgement as experimental veracity. We all readily embrace the Greek faith of the unity of beauty and truth. But we must be wary that truth can sometimes be ugly.

Finally, here are the solutions to the puzzles.

Puzzle #1, standard solution: (cos(0)+cos(0)+cos(0)+cos(0))!=24, where n! is the factorial of n.

Dave's beast: floor[ - (0!)0 / cos(0! + 0!) ]=24
where floor(x) is the largest integer smaller than x. (0!)0 should be read 10, the number ten.

Now you wonder how anyone can think of 1/cos(2)=-2.403...!

Puzzle #2. standard solution: move one vertical matchstick from 11 on the right of the "=" sign to a horizontal "-" between the two's in 22, and the new equation reads 2-2 / 2 = 1. Remember the precedence of arithmetics!

Dimitris and Dave's monster: move the bottom horizontal matchstick from the third 2 to over 11 and make it the Greek letter "pi". The new equation is 2 2 / 7 = pi -- the famous approximation to the ratio of the circumference to the diameter of a circle discovered by the ancient Chinese mathematician Chongzhi Zu.