The Chemistry of Relationships/Friendships

There is a reason why we call friendships “bonds”. It’s an incredible thing to think about, and I’ve been pondering about this topic for a few years, since high school. First, I must give mad props to Joyce for helping me polish this idea in my talks with her. Now before we delve deeper into this [surprisingly complex] topic, we have some preliminary stuff to take care of.

We begin by considering the idea of change. I’ve already set this discussion up here. Recall that we can think about a change as a difference in states – \Delta A. But we can take the limit of \Delta A for small deltas – we can take the instantaneous change and track that through the interval of \Delta A. This is idea of integrating dA to obtain \Delta A.

In life the difference between dA and \Delta A is encapsulated in this: “Do the means justify the ends?” \Delta A skips everything in between. It is path-independent; it specifies just the beginning and end states. On the other hand, in examining dA we look at the path between states and how we get from A to B. So we ask, does the path, do the means, matter? Or is the change between State B and State A the more dominant question?

In chemistry the state-oriented vs. the path-oriented mindset separates thermodynamics from kinetics. Chemical kinetics looks at the rates of reactions, which is highly dependent on the mechanism – the path the reaction takes. On the other hand, chemical thermodynamics studies the relative favorabilites of reaching different states.

So now we can look at the idea of interpersonal relationships through the eyes of chemistry. Bonds don’t just form out of thin air, after all. They require favorable thermodynamics – state B must have lower energy than state A. They also require favorable kinetics – the reaction path must not have too many bumps or barriers. Likewise, friendships form only when the conditions are right. And there are two ways to examine why friendships happen: from a kinetic viewpoint, and from a thermodynamic viewpoint. We will take a look at both in more detail now.


We have a bunch of atoms, each with some kinetic energy. Now according to collision theory, atoms must have the right orientation and the right amount of kinetic energy, known as the activation energy, for a reaction to occur. Once the reaction occurs, the atoms form what is known as the activated complex, which can undergo a transformation either backwards, reforming the original atomic constituents, or forwards, entering a product state.

Initial social interaction works the same way. Through the course of our lives, we meet many many people. And in many cases, we will not have enough energy to form an activated complex. Or maybe our “orientations” aren’t right – there is some steric hindrance, the alignment of atomic orbitals just isn’t ideal, or maybe one atom only sideswiped another. For instance, if I talk with someone on an airplane for a couple of hours, I will probably never see them again. The conditions just aren’t ripe. (This actually did happen to me – I met a very nice lady with a poodle on my plane ride home from Berkeley last summer. But of course, I never saw her again.)

Now, sometimes two people hit it off very well and become acquaintances, because everything went right. I guess the best way to describe the activated complex is the awkward phase in between friendship and stranger. You’re definitely not familiar enough with this person to invite him/her out to a meal, or to do any “friend” stuff. It’s not a comfortable phase. Not surprisingly, the activated complex is a high energy state. And physics doesn’t like high energy states. Many times, you lose contact with the acquaintance, and you go back to what you were originally: strangers. But sometimes, you go forward, and enter your friendship product state.

Some remarks follow. Collision theory states that the rate constant, which is proportional to the reaction rate, is exponential in the activation energy. A small change in activation energy does wonders for how fast the reaction proceeds. That’s what catalysts, such as enzymes, do – by lowering the activation energy just a tad, they increase the reaction rate by many orders of magnitude. The activation energy for stranger to friendship transformation is immense; reaction rates are slow, initial awkwardness is high. Catalysts are almost always essential for friendship formation. Sometimes these catalysts are other friends (chemistry example: the presence of a functional group that polarizes a covalent bond is essential for an organic reaction to occur; hydrocarbons themselves are relatively nonreactive). Other times, they are shared experiences or shared interests. A very dull person with few experiences requires high activation energies to reach an activated state. The presence of a common interest provides an alternative pathway for people to connect.

This was one of my first discoveries when I first looked at the social interaction problem in high school. The people who were popular had stuff to talk about, and ways to connect with people. They had all types of catalysts that lowered the activation energy of reactions. I didn’t. So that made me sad for awhile.

Thankfully however, I soon discovered another aspect of chemical reactions – thermodynamics.


The thermodynamics of a reaction, abstracted by the Gibbs Free Energy \Delta G, is intrinsically linked with the reaction’s equilibrium constant, defined as the ratio of the population in the product state to the population in the original state at steady-state, zero-forcing conditions. Now, the kinetics state the pathway that gets you to steady-state conditions, but we are going to ignore that for now. We aren’t going to ask how we get to friendship. We’re going to ask how many times we get there, assuming the path is laid out for us.

Picture someone who is affable. Who do you think about? I think of all the people on the floor I live on. If I were to redo my experience with “6th floor”, the probability of my entering a friendship state with the people here would be very high. But then think about all the jerks you’ve met. What is the probability in that case?

This is the essence of the thermodynamic viewpoint. For a friendship to occur, good orientations and shared experience catalysts are not enough. The two sides must “jive” together if they meet, and this happens every time regardless of circumstance (read: kinetics). Sometimes the energetics is very favorable, as was with me and Vicki, and you feel comfortable with them immediately – you enter a lower energy state fast. Personally, I find low \Delta G in people who are bubbly, smiling, and enthusiastic. Not surprisingly, some of my best friends I’ve met at Berkeley fit that description. People look for different things in other people, which makes \Delta G between pairs of people difficult to calculate.

Nevertheless, some personalities are naturally low in Gibbs Free Energy – they are naturally more sought after. Remember the jerks? People typically don’t like jerks. I discovered in high school was that being nice and smiling actually netted me friends. As did knowing calculus and science – people looked up to me for academic assistance, which I gladly gave. What I lacked in kinetics, I overcame with a heaping helping of thermodynamics. And that is the good news about thermodynamics. Kinetics (aside from catalysts) are often out of our control – you still have to collide with the right circumstances to form friendships. But thermodynamics are something we can control. If you want more friends, you can always improve your thermodynamics so as to increase the probability of forming and sustaining a friendship when you meet a new person.

One final thing about thermodynamics – in general, we live our lives interacting and friending people (not on FB, in real life). Likewise, the almost all the world is made of bonded chemicals. The sum of all the free energies of bonded states on Earth must therefore be less than the sum of all the free energies of the non-bonded states. Back in the friendship scheme of things, this means we have natural affinity towards social interaction and friendship forming in general. Most of your encounters will be of the near-zero or negative \Delta G type. Only kinetics stops you.


Finally, to conclude, we will examine the extrovert vs. introvert problem. For the longest time I thought extroverts had more friends, because they liked to talk with people more. But then I found an article that claimed extroverts and introverts have similar amounts of close friends. And then I met Joyce – who has many friends due to her bubbly, happy personality. But she is nevertheless an introvert. How can this be?

The extrovert/introvert problem is one of kinetics. Extroverted people have more kinetic energy and so are more likely to reach activation energy. They like to talk to people and interact. On the other hand, introverted people have less kinetic energy and so do not interact/collide as much. The physically equivalent idea is Temperature (\propto kinetic energy). In fact, the rate constant is goes by exp(1/T), where T is the temperature, so extroversion helps a lot, just like shared experiences. But neither guarantees friendships – that is the job of \Delta G once the kinetic barrier has been breached. Meanwhile, temperature does not affect the energetics*, so the amount of good low \Delta G product states will be about the same for both the high- and low- temperature environments.

The extrovert/introvert problem provides some of the most compelling evidence for the chemistry of relationships/friendships, and some of the best applications too. I think it is astounding that we can draw as many parallels as we have done here. There is still much to be figured about the dynamics of friendships.

* For those more familiar with chemistry, we ignore entropic effects. Since \Delta G = \Delta H - T \Delta S, the temperature dependence vanishes if we drop the \Delta S term, which is allowed here since entropy has little to do with our analysis.

P.S. 1700+ words, ~3 pages single-spaced on a Word doc. Yay!


Thoughts on [In]stability, Extrema; Sports; Precipitation Prospects

I’m just going to clump everything in one post, my first in over a month.

Consider a harmonic oscillator, for instance a mass-spring system. If you took a snapshot of it at any random time, you’d most likely find the mass furthest away from its equilibrium point. Why? The oscillator has the most kinetic energy at its equilibrium point – meaning it will also move the fastest at that point. As a result, it doesn’t spend much time there, but rather, it will spend a great deal of time at its turning points when all its energy is in the potential form.

OK, so for the oscillator its easy. We can see why the mass likes its extrema. But for other phenomena it’s a little harder to explain. We start by reflecting on one of the greatest nights in baseball history last Wednesday. Down by one, and with only one strike left, the Baltimore Orioles – last place in the AL East – manages to score twice off Boston Red Sox closer Jon Papelbon to snatch a victory out of the jaws of defeat. And then four minutes later, Evan Longoria of the Tampa Bay Rays, also down to one strike in the bottom of the 12th, snatches a victory for his own team as he hits a walk off home run against the first-place Yankees. Just four innings before, the Rays had been looking down the barrel of a 7-point deficit; now they were looking at a trip to the ALDS. And so it was that in one night, the Red Sox, who were ahead by 9 1/2 games in the AL Wild Card race on September 1st, watched as their 2011 postseason hopes went up in flames. [And this comes a week after Tom Brady throws 4 picks in a game where the New England Patriots give up a 21-0 lead in the first half. Brutal.]

You see, Boston sports, like the harmonic oscillator, is amazingly bipolar. 10 years ago they were blessed when Tom Brady comes out of nowhere and leads the Patriots to a postseason birth. Then the Tuck Rule happened, and they miraculously win the divisional game against the Oakland Raiders with two consecutive field goals in a raging snowstorm. Afterwards they go on the win the Super Bowl against the heavily-favored Rams on a last-minute… you guessed it… field goal. And that would begin a dynasty, as the Patriots would win two Super Bowls in the next three years. And again one of them was won on a last-minute field goal.

Meanwhile, in baseball, the 2004 ALCS was marked by a massive Red Sox comeback as the Yankees, up 3-0 in a 7-game series, blew a 9th inning lead in Game 4. The Red Sox walked off that game, and the next. Then in Game 6, a game-tying run by the Yankees was nullified due to interference, which allowed the Red Sox to hold onto the lead and win, and the Red Sox won Game 7 handily. This was the first time any team had come back from a 3-0 series lead in the postseason, and Boston subsequently swept the Cardinals in the World Series.

Crazy-assed luck, if you tell me. So you can guess my reaction to the 2007 18-0 Patriots season after the Red Sox swept the World Series earlier that year. PLUS the Patriots defeated my Chargers 21-12 in the Championship game. I was all out for a big F-U to the Patriots in the Super Bowl, and my wish came true as the Giants pulled a major upset victory with a miracle catch and a last minute touchdown. Incredible.

Well, since then, the Patriots have not won a single postseason game and the Red Sox have been trippin. In 2007 I vowed never to root for a Boston team again. I might be getting to that turning point where I will put in exceptions… such as when the Patriots are up against loser teams like the Jets. But yeah, bipolar extrema galore! Don’t know why, but Boston pulls out the greatest championships and the greatest chokes.


The other extreme I wanted to discuss relates to rain. Empirically, I’ve observed that major heat waves often precede rain chances. I’ve somewhat come to expect that if there’s a heat wave, some type of rain will follow in 1-2 weeks. In places like India and Arizona where there is a distinctive monsoon season, this is not just an empirical observation but a well-known: the summer “heat dome” must be present for the year’s first monsoonal moisture surge to commence. (This is why Phoenix always gets to 110 degrees in June.)

In San Diego, such a warm period would be followed by either an anomalous monsoon surge from the east (if it was in Jul/Aug), or a thunderous upper-level low (if it was in Sept/Oct — and I mean thunderous quite literally). For the monsoon surge, this would entail sprinkles from decaying storms coming off the mountains, fun nonetheless as decaying anvils made for wondrous sunsets at dusk. As for the cutoff upper-level lows, they brought some pretty fun shower and thunderstorm activity. Climatologically they are most common in SoCal from September-early November, which correlates well to peak season for Santa Ana Winds. One such low brought relief to firefighters about 1.5 weeks after the devastating wildfires in 2003 killed 16 overnight, which will serve well as a prime example of the phenomenon I’m referring to here.

Well, now, we just had a major heat wave in the Bay Area, and guess what’s looming on the horizon?

This might be one of the bigger October rainstorms since that epic one in my freshman year at Berkeley. At the very least, looks like heat waves will be good predictors of the start of the rainy season.