Pep Pàmies’ blog: Curious bits and pieces...

Persons, nucleation and growth, crowd

Thu, 9 Jul 2009 08:22:14 -0400

Some events are typically uncontrollable and occur at a seemingly-unpredictable moment. For example, traffic jams sometimes happen with no apparent reason in a crowded but still fluid highway. Or a stock-market index dips suddenly, only to recover a few hours later, with nobody to blame for it. Sometimes a song from an obscure band becomes a hit overnight.

These sort of events have another common characteristic besides appearing capricious. When they happen, they happen very fast. A good example of this is the following video, in which you will see a crowd go wild.

It is clearly difficult to guess a priori when (and if) the crowd will go dancing. Naively, one can look for a sudden change in some variable. For instance, the speed at which people join the dancing group: during the first minute and 12 seconds, up to three persons dance, but it takes only another minute to get a few hundreds to join. Thus, we can say that minute 1:12 is the onset of the dancing madness. But, because from the onset time on, the number of people standing up and joining the dance grows very fast, watching for this sudden change becomes pretty useless. Once we realize that the stock market is crashing or that we are involved in a traffic jam, it is already too late.

It turns out though that this rather infrequent but quickly-happening events are not totally unpredictable after all. Physicists have been interested in this so-called rare events for some decades, not only because they would like to avoid traffic jams when driving to the lab., but also because rare events are not that rare in nature: the formation of rain droplets, the crystallization of water into ice, or the formation of air bubbles when boiling pasta have a lot in common. The basic understanding of this phenomena can be very-well described by the theory of homogeneous nucleation. The theory can be understood in very simple terms, and I next attempt to do this by referring to the dancing event in the video above.

Let’s assume that the sitting crowd is in the mood for dancing. This means that happiness increases when people move from ‘laying down and chilling out’ to ‘up and dancing’, and this increase is proportional to the volume of people dancing. However, there is a cost — a decrease in happiness — associated to the group in the ‘up and dancing’ state. This cost is related to the embarrassment of dancing while being observed by a crowd — we all have experienced that feeling. The ‘embarrassment cost’ also grows with the size of the group, but in this case it is not proportional to the volume of people dancing as a group, but only to the number of people dancing at the boundary of it. This is because only those at the boundary feel being observed by the sitting crowd. In the schematic graph below I have drawn the ‘embarrassment cost’ (labeled interfacial cost) and the volumetric ‘happiness cost’ (which is, in cost terms, negative). Clearly, the interfacial cost grows slower with size than the volumetric cost. The sum of the two is the total cost, and it displays a maximum.

The shape of the total-cost curve explains nucleation phenomena qualitatively. For sizes smaller than the critical size S*, increasing the size of the dancing group comes at an interfacial cost. Beyond S* all is downhill, and the slope heading down is steep. In the video above, S* is 3, which is the critical nucleus of people needed to jump start rapid growth toward group happiness. From minute 1:12 on, the size of the group grows as fast as people can stand up and join the dancers. Before the critical nucleus is reached, only very few persons seem to have enough energy (or alcohol) to overcome the barrier to nucleation.

Similarly, when the temperature of water is below that of at which it crystallizes (zero degrees Celsius at atmospheric pressure), ice forms via a nucleation process. Molecules of water jiggle in the fluid, and fluctuations in their energy can drive a few molecules to order likewise they do in ice (the image at the top of this page shows this for hard spheres). The size of this small nucleus of ice-like molecules will fluctuate — shrink and grow back again — if there is not enough energy available to overcome the interfacial cost of forming a critical nucleus, which is the energy needed to form the ice-water interface. This is why water does not freeze spontaneously at its freezing temperature, but some degrees below it. Decreasing the temperature below the freezing point increases the negative volumetric cost and diminishes the size of the nucleation barrier, making it easier that spontaneously-forming nuclei of ice reach the critical size.

For technical information about nucleation theory, follow this link to a scientific talk by professor Daan Frenkel, who works at the University of Cambridge, UK, and was my scientific advisor some time ago. (You will need a basic knowledge in thermodynamics to understand it.)

Now, what happens when we boil water to cook pasta and add salt right before the water starts to boil? Yes, nucleation at work again, but this time helped by the small grains of salt.

Broaden your big thinking

Sun, 15 Feb 2009 23:03:16 -0500

Last week I attended an event in which individuals were pitching new ideas to a big audience. It was refreshing to listen to clever people coming up with innovative ideas to bring a product or service to the market, and aspire to make money with it. Most of the ideas were about building up new services on health care, networking, kid’s education or real state. Ideas on products contemplated green alternatives to existing ones.

Though a few of the pitches raised a silent ‘oh, that’s cool’ in my head, I found many ideas somewhat lousy. Let me detail two of those:

Pitch A. The US government spends hundreds of millions of dollars on making coins and people keep jars of coins at home. The idea is to introduce a ‘change keeper’ which keeps the balance of coins. At stores, people pay only dollar amounts. If the balance of the keeper is enough, the customer pays a little less and the balance is reduced. If it is not enough, the customer pays a little more and the balance is increased. Since its balance never goes beyond $1, no heavy security is necessary. Thus, the payment can be fast, even faster than using coins. This idea helps the government save some money, customers be freed from jars of coins and stores receive money more quickly at the cashier.

Pitch B. A system for using cold air from outside to keep refrigerators and freezers cold. It could be a small box which is retrofitted onto existing refrigerators and has an air duct leading outside, similar to a dryer. It would of course only activate when it’s cold enough outdoors, but that’s a large part of the year in areas like New York.

At first hand, the two ideas seem worth considering. Pitch A proposes to eliminate the hassle of dealing with small change. Pitch B proposes to reduce the energy bill in houses by improving the efficiency of refrigerators. Now, what both have in common is that they are products of narrow thinking. Not only are these ideas likely unprofitable, but also doomed to failure.

The ‘change keeper’ generates obvious problems. For instance, it can only work if businesses accept the law of large numbers – or what I lose with you, I gain it with the next customer. It also should be implemented globally, otherwise any user could be off by much more than one dollar if done in a per-business basis. This makes putting the service into practice very difficult if not impossible.

The idea on the ‘refrigerator box’, regardless of the details, is not going to work. Refrigerators operate at 3 degrees Celsius, and the refrigerant is at about -25. This big difference in temperature is part of the reason why refrigerators are mostly silent (the compressor has to turn on only occasionally). Now, air, being not that cold, and a poor thermal conductor, will have to be pumped in significant volumes inside the house. One big problem will be noise. And, what’s more, the ‘refrigerator box’ will have to be insulated as much as the refrigerator itself. Letting many other engineering problems aside, it is not easy at all to determine how much can one save on the electricity bill – and thus will likely have little appeal for customers.

In summary, both ideas generate more problems that they solve. Actually, they don’t solve any real problem. If somebody hates coins, he pays with bank cards. If anyone wants to save some dollars on the energy bill, cranks down the thermostat of the heating system or turns lights off. You don’t change people’s habits with small improvements. For a new idea to have chances of being successful in improving an existing service or product, it better be really, really good.

The pitch event made me realize that we all think narrow more often than we believe. For instance, some try to save a few pennies in the supermarket by buying possibly inferior products while spending tenths of dollars more in that flight booked too late, or in that magazine subscription rarely read, or in that expensive restaurant one ends up at because of lack of patience to look for a cheaper offer around. The advice is: forget about little savings in groceries. They are likely insignificant compared to the fluctuations in other costs. But the reason most of us save a few dollars in groceries is that it is easy to compare two numbers next to one another in the shelf of a supermarket, but it is not so easy to evaluate savings with many other expenses.

Other ideas are narrow minded when, as with the groceries, involve clear savings in one aspect, but omit to add expenses in another, because they are difficult to measure, or just not easy to see. For example: it is easy to find the cheapest insurance, but difficult to measure the cost of the risk of taking that option versus a more expensive one. Or it is easy to count how much one saves by booking that cheap flight, but not so easy to see how much will we have to pay for extra expenses because of the constraints involved with the cheap option (extra transportation or meals, or time lost). Or that claim that obesity is contributing to global warming, which fails to realize the contribution of physical exercise of the non-obese.

Ideas are easy to generate, and easy to find – just look at 999 business ideas for inspiration (# 917 is the funniest idea ever) – but please, if you want to invest time and money on them, give it a second, broader thought.

Political inclination, a (not so) free choice

Mon, 3 Nov 2008 22:47:27 -0500

Nobody questions that, in democracy, citizens are free to cast their vote for the option they personally think is best. The common belief is that, ultimately, political inclination is a personal choice, and a choice that we consider rationally.

However, recent evidence points out that this is not always the case: some physiological traits — feelings of disgust and fear to threats — have a connection with strong political inclinations. In an article recently published in the journal Science, a team of researchers from various US universities found out that people showing stronger reactions to threatening images and sudden noises were more likely to approve conservative political attitudes than those having less physical sensitivity to the same frightening images and startling sounds. Fearful individuals, then, seem to have a biological drive toward the right side of the political spectrum (and the unalarmed toward the left side), at least for those with strong political convictions. The link between fearfulness and socially protective policies is sound — as I wrote in a previous post (see here), fear is a common word among Republicans.

This does not suggest that physiological responses influence political beliefs. Indeed, correlation does not imply causation. Why both are connected is not clear yet. The researchers hypothesise a single origin: genetics. Physiological responses to threat derive from genetically-influenced neural activity patterns in the amygdala, and social attitudes may have a heritable component too. Thus, it is a possibility that physical and social sensitivities to threat are in part transmitted from parents to offspring.

Evolutionary biologist Olivia Judson, in her blog in the New York Times, hypothesizes further. She makes a point of linking obesity in pregnant women to politics, using the fact that the hormonal environment in the womb is known to affect aspects of adult personality, and thus social attitudes. Although very interesting, this seems a far-fetched possibility.

In the last years, multiple evidence is indicating that genetics is limiting freedom of choice more than ever thought possible. Still, even if our genetic glasses give us a somewhat distorted vision, we can still decide to close our eyes.

Buffet’s wisdom

Tue, 14 Oct 2008 23:34:31 -0400

Given the recent stock market volatility, with many indexes regaining in one single day (Monday 13th) a substancial part of the big losses they had in the catastrophic previous week, I can’t help but posting an interview to the great investor Warren Buffet. The interview was aired a few days before the US Congress approved the financial bailout, which happened on October 3rd.

Watch it. If you appreciate economic wisdom, I promise it will be an hour of your time well spent. Buffet is as sharp as ever and great at communicating simple ideas. Below the video, I quote a few of the wisdom he shares in the interview.

By the way, the image above is as funny as untrue these days, when market is clearly reacting to ‘real’ news.

Warren Buffet quotes

About markets:

- “You wanna be greedy when others are fearful and you wanna be fearful when others are greedy. Is that simple.”

- “It's a lot like Cinderella fable. I mean, midnight, everything is gonna turn to pumpkins and mice, right, but, as the evening goes along, I mean, the guys look better all the time, the music sounds better, it's more and more funny, and you think, why the hell should I leave at a quarter to twelve? You know, I'll leave at two minutes to twelve, but the trouble is, there are no clocks on the wall.”

- “Confidence in markets, and in institutions, it's a lot like oxygen. When you have it, you don't even think about it, I mean, it's indispensable, you go years without thinking about it. When it's gone for five minutes, it's the only thing you think about.”

- “You had all these types from Wall Street, they had advance degrees, they look very learned, and they came with this things that said gamma, and alpha, and sigma and all that. All I can say is, beware of geeks, bearing formulas.”

- “As long as you have markets, you will have excesses. People went crazy with tulip bulbs, they went crazy with this house state bubble, went crazy with internet stocks, they went crazy with uranium stocks back when I was first getting started. I mean, you are not gonna change the human animal, and the human animal really doesn't get a lot smarter.”

About the bailout:

- “I'd rather be approximately right than precisely wrong (to turn it down).”

- “The patient is on the floor with a cardiac arrest, is not Wall Street, it's the American economy... I don't wanna give a lecture to this body that's out there, who had the hard attack. I wanna get it back functioning.”

Bailout of businesses

Sun, 5 Oct 2008 20:57:31 -0400

Let's imagine that you are a kid again and, as we used to do at that time without Internet (at least I did), you try to grow your dearly loved collection of picture cards.

In this imaginary world, you (and all other kids) strive for finding those picture cards that will make your fashionable collection cooler and unique. It is not easy, because the most desired cards are scarce, and very often you end up with many cards that you already own. So you trade them with other kids.

Now, besides the basic, on-the-spot exchange of cards, some smart kids invent new complicated ways of trading: they convince you and your peers to lend them cards in exchange for more and better cards in the future. As the collection of playing cards grows in popularity, the ‘smartest’ kids learn that, by borrowing lots of cards, they can grow their collection faster. The more picture cards the kid owns, the more he can trade them for the most-wanted ones. His collection gets therefore bigger and better valued, which helps him pay the debt back and still be better off. Hence, the ‘smartest’ kids borrow as much as they can.

For some time, kids are doing well and the ‘smartest’ kids are doing way much better. All kids are confident in trading, and everyone’s collection is growing and getting more precious.

But as time passes and trends change, some kids leave their so far oh-so-fashionable collections behind. They stop collecting more cards. Cards become less wanted. As a result, the ‘smartest’ kids start suffering: they can’t pay back their high debt, because a big bunch of the cards they own became worthless. Nobody wants them. This forces kids to ask more in return when lending cards, or to stop lending at all, fearing that they will not be paid back. Fear leads to a huge decrease in trading.

The company making playing cards has to to something to keep those cards circulating. They first try to make new cards available at low cost, so the ‘smartest’ kids can get those, and pay some of their debt back. But this does not prevent the situation to go worse. Cards decrease further in value. The company, fearing that the collection could become a disaster, decides to buy all those cards that the ‘smartest’ kids own and no kid wants, hoping that trading will restart.

To be continued...

This story is my simplistic view of how we have ended up in this huge credit crisis.
The ‘smartest’ kids of Wall Street relied on what seemed to be an always-increasing house-market value. Thus, they hugely inflated their debt over the value of their equity (common stock) to make big profits. The US government did not oppose to this high leverage, as did not to other very-risky financial practices. When the house market collapsed, companies in very high debt had to be bailed out by the government (AIG), bought by another company (Bear Stearns), or had to go out of business (Lehman Brothers). Fear led to less fluidity in the market: the cost of borrowing money sky-rocketed, and investors sold stocks widely.

The US Congress approved the $700 billion bailout bill last Friday. This taxpayer money will be used to buy those troubled assets from Wall Street financial companies, so that they can rebuild their balance sheets and get on with normal business. Sadly, this money is going to the companies of those ‘smartest kids’ who brought this crisis to us. However, we either save them, or very likely they are going to drag us all to a deep financial abysm. There seem to be no other solutions.

Let’s then hope the bailout works.

Don’t miss the sub-prime mortgage crisis as told satirically by comedians Bird and Fortune in the video below. Big laughter promised.

Hope or fear

Fri, 5 Sep 2008 23:12:13 -0400

I watched both Obama’s and McCain’s recent nomination speeches. Let me summarize their discourses in two words: hope for Obama, fear for McCain. Two words true to their beliefs.
I am going to refrain from discussing typical political issues now and just quote an important passage from each candidate’s speech.

Obama:
“... But this, too, is part of America's promise, the promise of a democracy where we can find the strength and grace to bridge divides and unite in common effort.
I know there are those who dismiss such beliefs as happy talk. They claim that our insistence on something larger, something firmer and more honest in our public life is just a Trojan Horse for higher taxes and the abandonment of traditional values.
And that's to be expected. Because if you don't have any fresh ideas, then you use stale tactics to scare the voters.
If you don't have a record to run on, then you paint your opponent as someone people should run from.
You make a big election about small things.”

McCain:
“We face many threats in this dangerous world, but I'm not afraid of them. I'm prepared for them. I know how the military works, what it can do, what it can do better, and what it should not do. I know how the world works. I know the good and the evil in it. I know how to work with leaders who share our dreams of a freer, safer and more prosperous world, and how to stand up to those who don't. I know how to secure the peace. When I was five years old, a car pulled up in front of our house. A Navy officer rolled down the window, and shouted at my father that the Japanese had bombed Pearl Harbor. I rarely saw my father again for four years. My grandfather came home from that same war exhausted from the burdens he had borne, and died the next day. In Vietnam, where I formed the closest friendships of my life, some of those friends never came home with me. I hate war. It is terrible beyond imagination."

Now, running a text analyser for the complete transcripts of the speeches, I found out what words the candidates used most. McCain discourse was about 10% shorter than Obama’s (word count ~2700 for Obama and ~2500 for McCain). But the differences in the most used expressions is striking. Here follows the count of the meaningful words they pronounced more than 15 times.

Obama: you (48), promise (29), America (23), McCain (21), time (17), American (17), change (16), work (16), country (16).

McCain: you (44), country (28), fight (22), Americans (17), work (15).

The two less common words among these are promise (Obama) and fight (McCain). Again, in line with the title of this blog.

Isn’t this a hope-or-fear choice? Which of the two words do you think sells best in this election? (My answer is connected to what I wrote in ‘Fear, hope and love’).

To finish, one more-than-a-curiosity fact: Without considering the traditional ending ‘God bless you. And God bless the United States of America’, McCain spoke the word God 5 times. Obama, zero.

Spot the fake smile

Sun, 3 Aug 2008 16:00:52 -0400

It comes to us so naturally. But laughing is a very complicated process, very difficult to imitate artificially (think of realistically-animated movies). Smiling and laughing seem to be unique abilities of us humans, together with imagination. Do animals laugh? Is smiling and laughing an ability of consciousness beings only? Are fake smiles always distinguishable from the genuine?

There are many answers to these questions. And the most accurate answer is that we don’t know which of the answers are true. What is also right is that we don’t always spot fake smiles. You can take a quick test here to check how good you are at discriminating fake and genuine smiles. It’s fun, and you will likely realize that you are less good at it than you thought. I got 16 correct out of 20.

We are not necessarily good at realizing when a smile is truly genuine. But do we smile and laugh at the same things? A project called Laughlab has come up with the best joke out of forty thousand submitted and rated:

Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy whips out his phone and calls the emergency services. He gasps, "My friend is dead! What can I do?". The operator says "Calm down. I can help. First, let's make sure he's dead." There is a silence, then a shot is heard. Back on the phone, the guy says "OK, now what?"

It’s a good one. But looking for the best joke is something like searching for the best good-looking woman in a beauty contest. There, because the differences are small and subjective, almost any pick is good enough. So here a second pick:

Sherlock Holmes and Dr Watson were going camping. They pitched their tent under the stars and went to sleep. Sometime in the middle of the night Holmes woke Watson up and said: “Watson, look up at the stars, and tell me what you see.”  Watson replied: “I see millions and millions of stars.”   Holmes said: “and what do you deduce from that?”   Watson replied: “Well, if there are millions of stars, and if even a few of those have planets, it’s quite likely there are some planets like earth out there. And if there are a few planets like earth out there, there might also be life.”   And Holmes said: “Watson, you idiot, it means that somebody stole our tent.”

From these two jokes it seems that we all laugh at others when they behave dumbly. We also laugh at situations that seem out of place. But in the end, it is all about creating stronger social bonds, isn’t it?

The geometry of music

Sun, 20 Jul 2008 23:09:54 -0400

A friend of mine, who is an accomplished singer, conductor, and also a mathematician, claims that maths and music are not far apart. But most people would never put both words in the same sentence. Maths demand rationality, exactness, and ideal entities. Music needs imagination, exploits inaccuracies, and is utterly inseparable from feelings.

Nevertheless, my friend’s intuition was certainly on the right track. Not only because pleasing musical intervals can be described with simple mathematical ratios (Phytagoras knew this), but because the succession of musical chords in time appears to be linked to geometry. A geometry that can be related to mathematical entities such as circles, cones, Möbius strips (a circular strip with a half-twist, for instance), and unnamed exotic geometries. This is explained in a paper which appeared last April in the Journal Science (here a non-edited version), by researchers from Florida State University, Yale, and Princeton.

Reading the paper, I learned that the key link between geometry and series of chords are five musical relations that also have a unequivocal mathematical sense: octave shifts, permutation, transposition, inversion, and cardinality equivalence (ignoring repetitions). A musical score is represented by points in a n-dimensional space, where n is the total number of instrumental voices playing at the same time. The succession of points corresponds to the pitch evolving in time. These points are glued together in the n-dimensional space, using the five musical relations that I mentioned above. The result is that the connected points form geometric objects, which can be used to track leading voices, analyze compositions in search for similarities, and design music visualization tools, for instance. A simple example is the following visualization of Chopin’s E minor prelude as pitch in circular space.

You can watch more visualizations on the webpage of one of the authors of the aforementioned paper in music theory.

Now, I want to make clear that this connection between maths and music is just an abstraction, albeit a very important one, that can be used to understand music. In fact, abstraction, or ignoring information, is fundamental to the connection between both fields. But this and other abstractions ignore a lot of stuff that cannot be easily rationalized: expressivity, voice colour, timbre, volume dynamics, and so much more. This is the substance that makes good music sound differently when impeccably interpreted. Conductor Ben Zander makes it extremely apparent in the next video. Don’t miss him playing the same Chopin’s prelude at different levels of expressivity and impulse.

What astrology and Santa Claus have in common

Sun, 27 Apr 2008 19:51:59 -0400

You can easily guess... they both are nice human illusions. It is enjoyable to give presents in the name of Santa, and it is fun to read daily horoscopes. However, there is an important difference between the two: only children believe in Santa Claus.

Indeed, too many adults truly believe that astrology has some obscure truth that we do not know yet. Well, the only truth is that it will remain a belief.

In 2006 there was a large study investigating the relationship between date of birth and individual differences in personality and intelligence. No relevant correlation was found (obviously).

However, we don’t need a complex study to tell that astrological claims are nonsense. One can easily make the following experiment:

Get 12 randomly selected horoscopes, remove the sign of the zodiac, and give them to your friends. Tell them to point at which one best describes the they they had, and then check how many got their correct horoscope according to their birthday. With enough friends, you will get about 8.3% (1 over 12), which means that this experiment will not perform significantly better than chance. The video below shows a similar test.

Even if celestial bodies might have an influence in our lives, this influence is certainly not in line with astrological predictions.

No choice is bad; too many choices, too

Sun, 20 Apr 2008 23:43:27 -0400

Today I spent too many hours in fashion stores. I browsed through many hundreds of shirts, pants, socks, and shoes. Because here in Manhattan I have almost an unlimited number of possibilities, I definitely had to find something perfect. This time I did. Purchased two spring-colored shirts. Returned home tired, but happy. However, last weekend I was not so lucky. Ended tired and frustrated.

Sometime ago I was looking for a good restaurant for a special dinner. TimeOut New York offered me some tens of new possibilities only within East Village. It took me very long to come up with a decision, and what I chose turned not to be as great as I expected. Who’s to blame here? Of course, not TimeOut, but me.

The conclusion here is: too much choice leads to more time spent choosing, and less happiness.

...but why?

Barry Schwartz cannot explain it better. Below a 20-min. speech of his that you will not regret watching. He is crystal clear, funny, and enlightening.

Before you click the play button, let me stress the message, using his own words:

“All this choice [...] produces paralysis rather than liberation.”
“The secret to happiness is low expectations.”