Probability Distributions as Sieves of Reality.

Lately it has come to pass that I should work with a lot of concepts in probability theory and with probability functions. One thing I could not help but notice is this idea of filtration done by probability distributions.

Suppose there is distribution which acts on set of random variables. Even though I want to relate these random variables to some physical quantities, it seems that I would be doing injustice to this idea. So yeah, suppose you have some random variables and a probability distribution governing them.

The probability distribution is in some sense, filtering these configurations. Okay do not let me confuse you, look at the picture below. To solidify this analogy I have very conveniently chosen a two-dimensional grid, which looks like a sieve, but play along things might get interesting.

Suppose now you were to place a whole lot of sand on top of this sieve, some holes would allow a lot of sand to pass through them quickly and some holes would not. The holes (I am repeating this word way too much, i know) which are big would let a lot more sand pass through than the gaps (lets mix things a little bit) which are smaller. Now you might say that this might depend on the size of the grains of the sand and what not, but as I said earlier, play along.

So in a way the distribution is acting like a sieve, the probability P(X=6, Y=5) is 0.6 and P(X=2,Y=9) is 0.01, we can read these statements in a stand alone fashion and we can read them together, but things happen in a comparative nature in reality (more on that further ahead and maybe in some later post). So what our sieve is saying is that the first configuration is 60 times more likes to pass through than our second configuration.

Now lets leave the numbers alone for a little bit and think about these distributions as physical phenomenon. Particularly lets talk about the phenomenon of genetic expression. Also, a quick note, I am no expert in molecular biology. There is a certain probability that a gene is going to be expressed depending on its need to get expressed, these needs are read off by thousands of sensors in our body. There is sieve attached to each of these steps, the probability of the sensor reads what it is supposed to read. The probability that the sensor is successful in delivering its signal. The probability that the signal is read correctly and finally the probability that this signal is acted upon. What evolution has done is tune the holes in these sieves, and further-more made these sieves so sophisticated that the pattern on them changes on the fly.

A word of caution, this paragraph is pure mind jackery. There is even a possibility that it might rain fire next moment, but the sieve of common-sense does not let that possibility pass through to the realm of possible futures that might happen. There might be numerous such things that can be cooking up in the simulation sections of your brain, but the sieves of common-sense do not let them present to you as reality. But there are some moments (maybe under the influence of certain molecules) when these common-sense sieves are altered and they let through uncommon thoughts and reality experiences. There are even techniques (like meditation) that claim to tune your sieves in a permanent manner, so that you have better thoughts and experiences.

On a final note, think of this. Somewhere far-off the sieves of reality were altered (through a set of unlucky coincidences) in such a way that the possibility a virus can jump species was made a reality, and that changed the sieves further in such a way that you ended-up reading this article.

Hate reading prologues.