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.

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***[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.]