The Matrix and the Monte-Carlo Simulations

Recently, I watched The Matrix trilogy, again, just for entertainment. The whole series of events, to be honest, was just funny. Taking the "red pill" to "wake up to reality"! OK, anything is fine in a movie. I wonder what those "awaken" human beings are going to do in the "real" world! What are they going to build? What difference it makes! At least, in the first part of the movie, there was one "bad" guy who felt the reality was too unbearable. I liked him. The supposed villains, that is, the machines, are truly not conquered, it seems, in the third part. Maybe, they intended it as a shift in the plot.

Neo and his "simulations"

So much has been discussed about it by now, as the final part of the movie was released eight years back. But there is something interesting in the movie that I would like to ponder upon: the scene where Neo enters "the door with the lights", seeking for the "source", and meets the "Architect" (apparently a computer program) of "the Matrix". The Architect is shown to be an old person god knows why. In that scene, Neo's face is shown in a large number of computer monitors. As the Architect talked to him, each of Neo's images responded in a different way. The actual Neo's response came after a pause. Those monitors were predicting Neo's response, possibly making use of its knowledge of Neo's personality, his behavioural patters and his past. That scene was the only interesting scene to me. Because, what I was seeing was actually a Monte-Carlo simulation of human behaviour!

In Monte-Carlo simulation, we study a random phenomenon by simulating it many times, independently, and recording the output of each simulations. If the number of these iterations is large, we can more or less expect that we have recorded most of the possible outcomes of the particular phenomenon. This gives a fair understanding of what phenomenon that we are dealing with. Monte-Carlo simulations are used in experiments pertaining to various fields such as signal processing, physics, biology, economics, business studies, and so on. To have a nice Monte-Carlo outlook, I suggest you to read Fooled by Randomness, by Nicolas Taleb.

Coming back to Neo's case, Neo is the random phenomenon and the Architect's statements to Neo are the excitations or inputs. Neo's responses are expected output, but, by simulation, the computers generated Neo's responses simultaneously and independently; and they were all quite different! Isn't it the same in our "real" world, outside the movie, too? As we face the everyday life, we respond in some manner. Many believe that a person's behaviour and the way he responds to his surroundings describe him completely. We say, "Oh, he is such a mean person" or "he is a lazy fool" or "she's a pompous girl" by studying people's behaviour. And yet, it is a random outcome! It could be different! Then can we rely on our own judgements of a person? Rather, how "accurate" are our "estimates" of the personality of a person from his behaviour? Maybe, we have to observe a person for a long time and study his behaviour in different circumstances to know him well. Also, we have to see how varying is his behaviour and "mood". What I mean is that a person responded angrily to a simple question today does not necessarily mean that he is short tempered. Maybe, he did not have a nice breakfast in the morning and so he was annoyed. We have to observe him patiently for a few days, on different occasions. It may turn out that he is actually very kind and soft-spoken! Well, statistics describes accuracy in terms of variance -- a measure of how varying the output of a random experiment can be. Do you see the connection? It is in order to study the variance that a Monte-Carlo simulation simulates an experiment many times -- to see all the outputs.

The Architect, perhaps being very old and having seen six older versions of the Matrix and Neo, very accurately predicts that Neo will respond emotionally rather than intellectually to the situation he was facing -- his lover, Trinity , was under attack, and he had to save her no matter what happens to the Matrix and other human beings! yes, his response was emotional. In that he represents the entire human race. The way humans respond to the every day life is more motivated by emotions than intellect (I'm reminded of reading Daniel Goleman's Emotional Intelligence). I remember the sly expression the Architect bore on his face when he saw that his prediction turned out to be accurate. That was the best scene in the entire Matrix trilogy, to me!