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.

Fatness, In Perspective

Someone wants to be the world’s fattest woman.

And to do it, she’s going to consume 22,000 Calories per day, until she reaches 1,600 lb.

Breakfast: 6 x eggs scrambled, cooked in butter 468 cals. 1/2 pound bacon 1,168 cals, 4 x potatoes as hash browns 672 cals, 6 x pieces toast with butter 600 cals, 32 ounce cream shake 1,160 cals. Snacking 1 x bag of animal cookies 1,950 cals, 2litre bottle of soft drink 800 cals, 1 x 10.5 ounce bag of barbecue flavour crisps 1,650 cals, 3 x ham and cheese sandwiches 1,576 cals.
Lunch: 3 x beef, bean and green chilli burritos with 1 x cup of sour cream 1,453 cals. Salad (1 head lettuce, 1 cup cherry tomatoes, 1 cup carrots, 1 cucumber, 1/2 cup ranch dressing, bacon bits, 1 cup crumbled cheese, 1 cup chicken 1,479 cals.
Dinner: 12 x filled tacos + 1 x cup sour cream 4,906 cals, 2litre bottle of soda 800 cals, Dessert 8 x scoops vanilla ice cream 2,080 cals, 1 x small pan of brownies 1,200 cals.
Total: 21,962 calories

That’s ridiculous. So, in the spirit of my discovery earlier today that 500 Calories = 2000 kJ (2 MJ), I decided to see how much 20,000 Calories can do. For reference: 1 MJ = the kinetic energy of a 1-ton vehicle travelling at 100 mph. Source

I did a little Wolfram Alpha’ing.

So 20,000 Calories = ~90 MJ = [notables:]
…the rest energy of 1 microgram of mass. That may not sound like a lot, but that’s about 1016-1017 molecules, on average, of an average substance.
…an extra $3.74 of electricity (electricity is cheap!)
…26 kilowatt-hours
…the amount of energy that could light up a 60-watt lightbulb for 1500 hours, or a little over 2 months.
…the energy combusted by 2/3 of a gallon of gasoline (about 0.69 gallons). You can drive about 14 mi on a 20-mpg car with that much!

That’s a LOT of food… and a lot of energy for someone who’s on a wheelchair all day.

The Nature of Reality – Unorganized Thoughts

So I was having a conversation about Vicki about a few things, and I kinda had this epiphany, which I will share here. I’ll start by citing Heisenburg1 and his divide between a “subjective” reality, grounded in an ethical dimension, and an “objective” one, grounded in a mathematical, scientific dimension. Note that the “subjective” reality may not always be subjective – we can all agree that the Norway massacre was bad. Nor is the “objective” reality always objective, because of the nature of data and its biases and uncertainties.

Now as usual I’m going to start from a quantum mechanical perspective, that is, the world can be described by specific states represented by solutions to the Schrodinger wave equation. Likewise, we can also think of the world as a linear superposition of states. There is nothing wrong with this since you an either analyze a state by looking at its constituents (elements) or looking at it as a whole (a kind of a Gestaltic wholism). Indeed, quantum mechanics (QM) serves as a good proxy for the workings of the world in general. What QM tells us reflects what is readily obvious in front of our eyes. We cannot know everything; the reality is the superposition and the constituents, but our observation (read: bias, analysis, etc.) often collapses this into one single element.

But for now we consider specific states rather than the superposition. And we use this idea to look into the nature of the “objective” and “subjective” reality. I will expand Heisenburg’s definition, and I will expand the meaning of objective to include the idea of a Fact. Meanwhile, I shall expand the meaning of subjective to include the idea of an Opinion. Now granted, this has ambiguity too… the statement “God loves us” is Fact to a Christian, while Opinion to an Atheist. So I will define Fact as something which is truely true, as in what really is true from an omnipotent perspective. So if the Christian God actually does exist as described in the Hebrew Bible, “God loves us” is Fact. Now Opinion I will define as a *variable* qualifier or label to something that is truely true. (If God does not exist, “God loves us” is neither Opinion nor Fact, as it would not be part of any reality.) Note that objective labels (“there are 4 ducks in this pond”) that are absolutely true are Fact.

Examples: “I think this banana is sweet” is Fact because you actually do think that. “This banana is sweet” is Opinion in that you’re labeling the banana as sweet or not sweet.

Facts describe the objective reality. As such, in the QM perspective, Facts are synonymous to States. There is an infinite amount of states, because we can describe the reality around us with an infinite amount of Facts. Opinions describe the subjective reality. Now here’s the kick. Reality is by definition independent of what you or me say. So I’m going to turn my entire post upside down by saying that there is no such thing as subjective reality! (Well, as we have it now – I’ll change up its definition later.)

But there is such a thing as a subjective and objective qualifier. Let’s go back to the “banana is sweet” thing. It’s objective in the context of what is really sweet – perhaps quantified by sucrose concentrations or XXX ion activation in taste buds. In a more general twist, a statement such as “banana is good” can be dissected into objective facts. Perhaps the quality of something can be objectified by its effects, but that’s beyond the point. C.S. Lewis argues in Mere Christianity that some things are universally good or bad. We just disagree on the more minor issues. Other times, we are oblivious to what is really good or bad – female genital mutilation, for example. Our subjective qualifier clouds the more objective qualifier, and the lack of universality among humans doesn’t change the objective qualifier.

The objective qualifier, then, is what I’m going to redefine as the “subjective” reality. It’s the part of reality that is still there, but is often disputed. “There is a lamp on my desk” is Fact. “This lamp looks good” can be objectively weighed against other lamps based on geometry, compositional qualities, and balance. That is the subjective reality, or the objective qualifier.

Objective qualifiers in the QM world represent, ultimately, energy levels. Each state can occupy at most one energy level, but these are discrete at the most generalized level – the level of good and evil. The two cannot mix. In QM, energy levels represent eigenvalues of the Hamiltonian operator in the Schrodinger equation. Each state, or [non-superposition] solution to the Schrodinger equations, spans eigenspaces of those eigenvalues. Together, these sum of all the eigenspaces of all the eigenvalues of the Hamiltonian make up reality. And so, each Fact can occupy an objective qualifier level. Perhaps “this lamp is on my desk” would occupy the eigenvalue “Neutral”. “80 people were killed by a madman in Norway” would occupy the eigenvalue “Evil”. Something like that. Eigenspaces may have arbitrary amounts of dimensions depending on the number of linearly independent eigenfunction solutions that form the basis of that set (this is called degeneracy). In reality, the eigenspaces are infinite-dimensional – there are an infinite amount of evil and good things in this world, and the degeneracies are infinite.

There are some other little things I have to mention. Some things can be more good or more bad or more sweet than others. The eigenfunctions that form a basis set in an eigenspace may have different lengths, which we will interpret here as the amount of good or bad or sweet in a Fact. In QM, the functions are orthonormal. However, normalization is achieved by changing the weights on each of the basis functions, and is a separate consideration, and so we can ignore this discrepancy.

Finally – and apologies for the post’s length – we talk about subjective qualifiers, which do not consist of reality. Imagine what happens in a computer program. There is an objective bunch of executable code somewhere in the computer’s memory, but this is all abstracted in the higher levels by stuff like objects. In OOP languages, these objects can be referred to by a variable. These variables refer, to the object itself. You can change or swap references all you want, but the object itself remains unchanged. Likewise, subjective qualifiers act as references to the eigenfunctions of reality. We do not know the workings of reality itself, just as for beginner programmers, you do not know what goes on in object instantiation. A legit computer program will swap references and variables all the time, just as people change subjective qualifiers. The nature of reality remains however independent of the references you put on it. We see pointers, not the eigenvalues themselves.

1See Physics and Beyond: Encounters and Conversations, by Werner Heisenburg, pp 82-84.

The Nature… of God?

For this post I will be making two key assumptions…

1) Special Relativity (hereafter, SR) is valid. SR operates under the tenet that the speed of light c is absolute, and thus every speed < c is reference frame dependent.
2) The Christian God, as described in the Bible, is valid.

Now with that said, let’s get on to the post.

Taking the tenets of SR, the following relationship can be derived:

“…where Δt is the time interval between two co-local events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on his clock) – this is known as the proper time, Δt ’ is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer, [and] v is the relative velocity between the observer and the moving clock…” (Wikipedia)

This is known as time dilation. Simply stated, if I were travelling very very fast (close to c), my clock will start to tick slower than a stationary observer on Earth. Time gets extended.

Another relationship can be derived, as follows:

L is the proper length (the length of the object in its rest frame),
L’ is the length observed by an observer in relative motion with respect to the object,
v is the relative velocity between the observer and the moving object,
c is the speed of light,” (Wikipedia)

This is known as length contraction… if I travel fast, space itself will contract around me.

But here comes the million dollar question – what if I was traveling at c? Forget for a moment that this is impossible, and imagine a photon looking down on Earth. Now let’s say the photon measures a time of three seconds. How much time would have elapsed on Earth? What about five seconds? No, wait, the denominator goes to zero! Likewise, let’s wonder if the photon measures a piece of space. No, forget about that — forget about the Earth — the whole UNIVERSE will have collapsed to a singularity! The photon knows of no time, nor does it know of space, because these things don’t make sense to a photon from the relativistic perspective. Instead, it sees all infinity of space, and all infinity of time – at any single “moment”.

So what does this have to do with God?

The Bible says many things about God. He is all-knowing, all-powerful. Paraphrasing, he knows the number of hairs on our head and [something else I forgot] before we are even born. He knows each of us by name, on a personal level. He listens to each and every one of our prayers. He knows what we are going to do before we even do it. Now a lot of people have a beef with this – and for good reason; it doesn’t sound very logical that God can do all this at the same time. C.S. Lewis provides a rebuttal: God is out of time (167-171). God knows of no time, and He knows of no space either – He knows our destiny before we can act on it, and He sees the order of the universe and the cries of our hearts all at the same time. Now this sounds familiar…

Wait. Am I implying God is a photon?!

Well, not really, because photons can’t do things like love us and stuff. BUT what we can assume from this, is that many inconsistencies about God can be accounted for by believing that God is a massless being traveling at the speed of light. Massless, because SR proves that massive particles can’t travel at the speed of light, but more importantly, because it creates a distinction between what we are made of – mass, and what God is made of – not mass. Theologically, we can then recognize that the Creator and the created are separate things.

Another thing is that SR effects are symmetric between reference frames. If infinite time and zero space on the Earth is seen from a photon in its frame, the photon of speed c will appear to us in our rest frame as something that goes through infinitely many lives every second, but can never be observed to have a finite dimension*. For those who ask why God never reveals Himself to us – He can try, but if He is traveling at c, we will never be able to see Him.

I can’t say much beyond “science can reconciliate Christian notions of God if He travels at the speed of light”. It’s a pretty random hypothesis, anyway. We can even argue that God is energy if we want, or even better, that He is outside of our Universe. There’s plenty of hypotheses out there, and thankfully we’ll never truly know the inner workings of God. But it’s something cool to think about.


*If SR is correct, we could never be able to observe massless particles such as photons traveling at c, because they would be size zero in our reference frame. I don’t know if I’m missing something and we’ve actually observed and measured photons, or if I’m right and “seeing” a photon is physically impossible. I suppose that, if photons are a quantum construct, they don’t actually exist in reality except to make bundles of energy mathematically and logically easier to handle. This is an entirely different discussion though.

The Nature of Light

I had this epiphany long ago, but it took this line from Surely You’re Joking, Mr. Feynman to remind me of it.

They gave out dark glasses that you can watch [the first atomic bomb test] with. Dark glasses! Twenty miles away, you couldn’t see a damn thing through dark glasses. So I figured the only thing that could really hurt your eyes (bright light can never hurt your eyes) is ultraviolet light. I got behind a truck windshield, because the ultraviolet can’t go through class, so that would be safe, and so I could see the damn thing. (134)

And I was thinking about the bold part, and I came to realize he was right. You see things when light of some wavelength enters your eye and hits a molecule called retinal (the aldehyde form of the most common form of Vitamin A). The 11-cis form of retinal is isomerized to its most stable all-trans form, and the conformational change ultimately leads to the nerve impulse that registers as vision.

The key to realizing what Feynman says is that retinal absorbs at a specific wavelength. If you think about the photoelectric effect, electrons in a metal are “knocked out” by light only of a certain minimum energy or above. Likewise for a certain piece of light to be registered by retinal photoisomerization, it must have a certain amount of minimum required energy. Isomerization has a certain activation barrier.

As it turns out the intensity of light has nothing to do with its energy. From studies done of the photoelectric effect, it was determined that the frequency of light is what determines its energy, and that these come in discrete “lumps” (as Feynman puts it), known as photons. Each photon has a set frequency – a set energy. The intensity, on the other hand, is determined by the probability of finding a photon. A brighter light is simply more photons of the same energy. So it cannot possibly hurt your eye, because you’re still seeing photons of energies that your body already knows how to deal with – just many more than you’re used to.

But that wasn’t my epiphany. Let me explain what exactly is.

In church we are taught to bring light in a world of darkness. And there’s this nice, optimistic belief that while we can light up the darkness, the darkness cannot smother the light. Now this is great and all – but is it true? We investigate with the photon idea.

In [my favorite interpretation of] quantum theory, we see that classical light waves are actually propagating probability distributions of photons. Classical physics teaches us that the intensity of a classical wave is proportional to the square of its amplitude, which itself is proportional to the wave’s energy. If we allow energies to be quantized in discrete particles, and the wave to be propagating in an arbitrary space, then we can see how amplitude becomes related to the number of particles per unit space. We can imagine how this in turn is related to the probability of finding a particle. So with this established…

In darkness, the intensity is zero, so the probability of finding a light particle – a photon – is equivalently zero. From here I deduce that if we add light to darkness, we add photons, increasing that probability to a nonzero number. Yay we can do this! If I want to shine my light onto others, I simply add some of my unique photons. That’s quite nice.

Now let’s look at the reverse operation. Can darkness smother light? Darkness is defined as a lack of photons. If there already are photons, you have to actively remove the photons by hand; they won’t go away by themselves (that’s violating conservation of energy!). “Diffusion” (not sure how you can do that with photons “bound” by a probability wave, but for the sake of argument–) will reduce the probability towards zero, but never equivalently zero. You can smother light, but darkness by itself can never smother out light. On the other hand, light can kill darkness.

Optimistic thinking? Yes. Reality? Yes. Hooray! The upshot is, you see aspects of God all around you.

Even in quantum theory.

(And yes, I know that Einstein said that God does not play dice.)

On Flynn and YouTube

Regarding Flynn, did anyone notice that name showed up on both Disney’s Tangled and Disney’s Tron: Legacy (which were both released last year)? I only noticed this when I watched the two movies on consecutive weeks last semester…

Anyway, the main body of this post relates to YouTube. Does anyone else hate the “Whoever dislikes this must be …insert derogatory comment here…?” comments? I actually don’t care, as with many things… but I know some probably do get annoyed by them. Nevertheless, all [heavily-watched/rated] videos, no matter how good or how bad, have at least a few up votes and a few down votes. So I was wondering – why?

The answer (at least in my theory here) lies in an unlikely source – statistical mechanics, which deals with numbers, and thermodynamics – which takes its limit and abstracts it in a concept known as energy. The two can be interlinked in many ways, one of which is known as the Boltzmann distribution.

(n is the number of molecules and U is the energy in the ith state)

What we can see from the Boltzmann distribution is that by taking the log of a probability or count of members in a state, we can loosely define the concept of the state’s energy. Since the latter is linear and counts are often large and cumbersome, science rules by energy. It’s easier to work with, and it’s accurate.*

We extend this to YouTube now and consider the counts of likes and dislikes in a video. We say that there is a state L associated with likes, and a state D associated with dislikes. Summarizing the above points, the following relation can be obtained algebraically from the Boltzmann distribution:

Be careful with the signs. A high-energy configuration will have a very small population. A good video will have a large D state energy relative to the L state energy. On the other hand, a very bad video will have a very small D state energy relative to the L state energy. By taking a look at the difference in D and L state energies, we can approximate how good a video is.

Also note that a Boltzmann-like distribution infers that any state, no matter how high in energy, will be populated by members, since the log of zero is undefined. This goes right to the cusp of the initial problem we asked. By assuming a Boltzmann distribution to like/dislike patterns, we answer the problem of why some videos have likes/dislikes that we cannot explain.

One disclaimer I will make is that we are not talking about literal energies, in the physics/chemistry perspective (for one, the units don’t match up). We are just talking about the concept of an “energy” in regards to how good a video might or might not be. Also, as with physical systems, this analysis is best done with large “systems” – where the total number of votes exceeds, let’s say, a few thousand. (Otherwise, the variability will be too much.) With that said, let’s do some analysis. We will consider a “good” video, Eminem – Love the Way You Lie, and a “bad” one, Rebecca Black – Friday.

As of this writing, the Eminem video has a like to dislike ratio of 704 555 to 21 804. Taking the logarithm of the ratio yields an D/L energy difference of 3.476. For the Rebecca Black video, the ratio is 390 655 to 2 803 696 (an order of magnitude more votes, that’s surprising). The D/L energy difference for that video -1.971. As one can see, the higher the delta-energy, the better the video; once your delta-energy goes below zero, you have more dislikes than likes, and your video honestly stinks. We can even translate this to an overall video “hotness rating” – that’s up to other people to decide though.

Note that this phenomenon can be extended to other concepts as well, and is a good argument as to why different opinions exist in the world – no matter how extreme or weird. Going beyond the scope of this blog post, entropy overwhelmingly favors a Boltzmann-like distribution in physical systems, so why can’t it also do this in systems of independently thinking, random human beings? That for a later blog post however.


***[Optional reading as for why: let’s consider flipping coins. As the number of coin flip trials approaches infinity, the ratio of any certain outcome – i.e. heads or tails – to all total outcomes ought to converge to a number, in this case 0.5. If it does converge, that number ends up being the probability – and from this we can see why the universe allows that to work out. The number of molecules in any system is very very large. We can’t calculate a probability for a very large system, but if we simplify it for a small subset of molecules in which the probabilities are similar, we are able to predict the behavior of the system as a whole.]