Understanding Karma through probability
I have long been fascinated by the idea of karma. The notion itself is just built on simple empiricism (that of causality), but once you accept a single metaphysical prior – that of rebirth and the quest for moksha from the cycle – it changes into a beautifully complex meme.
Now as a man is like this or like that, according as he acts and according as he behaves, so will he be; a man of good acts will become good, a man of bad acts, bad; he becomes pure by pure deeds, bad by bad deeds; And here they say that a person consists of desires, and as is his desire, so is his will; and as is his will, so is his deed; and whatever deed he does, that he will reap. [Brihadaranyaka Upanishad 4.4.5]
Now let us take a not so straightforward approach to thinking of karma. If you have been reading my blog, you would have gotten the impression that I am a Bayesian. If you haven’t, I am a Bayesian, which is no different (at least in my mind) from saying “I believe in karma”.
First a brief foray into probability, so that the terms I have used become a little clear. This is a bell curve otherwise known as a Normal Distribution or a Gaussian Distribution. It has this nice property that when you find the x value at the centre of its hump (which is called its mean) the y value that you get, which is its probability P(x), is the highest, higher than any other point. The width of this curve is given by its variance. A higher variance means a really fat curve.
Bayesianism is a philosophy within probability that is different from the frequentist view you probably know from 10th standard mathematics. Let me use a subset of the very popular SLAM problem in Robotics to illustrate how to think of Bayesianism. If a robot was placed in a room, which it had no map of, that is to say it has no previous idea of how the room looked or where within the room it was located then it would go about figuring out these two things in the following way. It would assume a prior belief that it was in position X. It would then observe the world around it and take a measurement through its sensors. Using the measurement, it would then update its belief giving it a posterior belief of its actual position X’. This is what is meant by a Bayesian update. In this manner it would move and explore the room around it, constantly updating its prior beliefs of the room and the objects. Note that after computing its posterior belief, that belief becomes a prior when the robot takes its new measurement.
Now we can proceed. Let there be an event A, which non-trivially occurs in a significant number of people’s lives. Let’s take the life of someone in Brahmacharya Ashrama. Now for the said person, he getting married is a non-zero probability event i.e. it will happen at some point in time. According to the Hindu newspaper, the average age of marriage in urban India is about 29-30 for men. When paternal age effect kicks in, in about 2 generations, things are not going to be looking good for these urban Hindus. Some good advice taking this into account is; get married early and have kids early. But that is a discussion for another time.
What this means is if we took time as our x axis, you would see that the graph would have its mean at around 29 years. Let’s narrow our view and select one particular persons probability distribution for event A = marriage. Here’s where things get a little tricky. Marriage in itself is not something that just occurs at random. There are factors influencing it, which is captured by the curves mean and variance. What do I mean by this? Well, let’s say we have a chap Rohan with a Gaussian curve, which describes event A (marriage), but it is hidden from us. He comes from a very conservative family in Haryana, who believe that he is best married off as soon as possible, to a nice comely girl at say age 23-25. Well then his Gaussian curve has a mean at around 24 with high probability of marriage in the ages around 24, but the probability of him getting married at say age 30 is practically 0 and this is exactly what the Gaussian curve captures. Beautiful, isn’t it?
What influenced Rohan’s mean and variance? His family. What influenced Rohan being born into that family? His karma, specifically his Prarabdha karma, otherwise known as the karma which is bearing fruit.
There are an infinite number of events that can occur in one’s life and therefore an infinite number of Gaussian distributions. Life, and therefore karma is a multivariate Gaussian distribution.
So where does Bayesianism come into all of this? It comes in relation to the Agami karma of Rohan, otherwise known as the actions he performs in the present. Well, let’s say when Rohan is 21, his mother catches him with a girl. After the initial shock, she starts finding a girl for him to marry. Now this latent curve of his marriage event is updated, and its mean and variance changes. His variance becomes lower and his mean shifts towards the left of the graph i.e. it is going to happen earlier than 24. His new distribution is an abstraction of both his Prarabdha karma as well as his Sanchita karma, which is the store house of all your karmas performed till now, but, which are yet to bear results.
You can trivially think of a converse example, say his parents have a bit of financial stress, when he is of age 23 and he is forced to work and forgo marriage temporarily, so his graph shifts to the right i.e. he will get married at age 25 or more than that.
While my illustration is a little silly, it captures the beauty of Gaussian distributions and how you can model all life events as a Gaussian curve that gets updated, as and when events occur in one’s life. But a consequence of accepting karma as a prior is that there are predetermined mean and variances for each distribution. Not only this; these distributions influence each other. One life event happening influences a subset of the multivariate distribution and updates it in a Bayesian fashion. These predetermined mean, variance tuples are simply measures of your past karma because of … you guessed it, Bayesianism. Perhaps now you can understand my Twitter bio: “Kismat is Bayesian. Get to work.”
Let us quickly summarize. Every event that occurs can be modeled as a Gaussian Distribution (GD). Succinctly, this means that at a particular point in time called the mean, the probability of that event occurring is the highest. At any other time (either before the mean or after it) the probability of this event drops. The way the probability is modeled it looks like a bell which is why GDs are often called bell curves. The “fatness” of a bell curve represents the variance of the GD, which essentially models how uncertain that event is. If the GD had a small variance we are extremely certain that the event will occur around the mean value. If we were dead certain of when the event would occur, the GD would degenerate into a single line in the graph and it’s variance would tend to 0. A persons priors, i.e. the (mean, variance) tuple of all his Gaussian Distributions are simply abstractions of his Prarabdha karma. Any action he takes is akin to the robot’s action of measuring its surroundings, which is his Agami karma. When a person takes an action he now has a new set of Gaussian distributions, which are abstractions of his Prarabdha karma as well as his Sanchita karma. But enough of the math, why even choose such a symmetrical function to represent karma?
To answer this one needs to understand how causality works. The most important question here is: what affects you. There is actually a fairly long debate we could have about the definition of you, but we shall leave it to our illustrious ancestors, for they did it better than I could attempt today. We can say that generally the “You” is a combination of your experiences, your possible actions and your possible futures.
From the definition of the curves that I gave earlier you must have noticed that I am assigning seemingly arbitrary priors to each GD i.e. their mean and variance. I noted that the mean and variance of these curves are fixed apriori, and by apriori I mean before you are even born. They are fixed by a hidden function, which takes your past karma and computes the various (mean, variance) tuples and then assigns them to the distributions. So what about free will?
Long story short, it doesn’t exist at least in any absolute way. Absolute Free will is not a meaningful term because of the constraints imposed by a variety of factors, such as and not limited to, one’s biology, one’s society and one’s religion, so “will” is not absolutely “free”. Does this imply that karma is deterministic? Must we now conclude, that since our priors are a function of past karma and are computed without our knowledge, we are completely at the mercies of the gods in their wisdom?
No, and that’s why I used the GD rather than some other function. The GD models uncertainty. It allows for variability of the occurrence of the event. There is already randomness within any system, so there is also randomness within the event’s occurrence and that is captured by the GD in its bell curve.
Even this, however, is a very narrow way to consider karma. This is because karmas influence each other just as events influence each other in a Bayesian manner. For instance, if we go back to our example of Rohan. Let us consider the event B, where B is the event where Rohan disobeys his mother. By definition it has a Gaussian curve associated with it. Here’s the most important piece of the puzzle: event A is influenced by event B, and the priors for event A are actually assigned only after B is assigned. In this manner, we can extrapolate backwards that the first couple of priors that are assigned are the priors, which govern our temperament: known as our Svabhava . After these Svabhava are assigned, the interaction of the infant Rohan’s Svabhava with the external world molds the rest of his priors and indeed molds the priors of whether he is going to listen to his mother or not.
If we ponder on what this all really means, we can derive three separate types of karma :
This type of karma is related to the earlier discussed Svabhava found in each of us. The thoughts we have in our moments of solitude are a function of personal karma. Our tendency to overreact to situations is personal karma. Our ability to set aside negative thoughts and power and work through towards our goal (or lack thereof) are functions of our personal karma.
When we spoke earlier of event B affecting event A (both events specific to Rohan), it logically follows that any arbitrary event B affects any arbitrary event A (even if the magnitude of the effect is negligible). Parallels to chaos theory or butterfly effect are not totally unwarranted, but perhaps imprecise. All this aside, it follows that event B occurring to a close family member affects the event A occurring to the individual in a more significant way than, if it were to occur to any other person. Family karma is thus the effect of the karmas of the individuals within your family or more abstractly within your clan, where I will leave the definition of the term clan open ended on purpose. Practically speaking, family karma is not strictly restricted to blood relations, even extremely close friends affect your family karma. The things that affect them affect you more than any other individual’s karma and thus, it is a separate and distinct type of karma, which plays a huge role in your wellbeing. A very simplistic example is that of a horrible overbearing spouse whose personal karma is somewhat distasteful. Their karma directly affects your mental wellbeing and in some cases physical wellbeing. Perhaps this is why humans for millennia have engaged in arranged marriage practices, and not left such a difficult and important decision to the whims and fancies of their gullible and capricious children.
This is the final type of karma, which can affect any individual. This could also be called transient karma, since its effects are bound by both time and distance. For instance, if you have a bad circle of friends, your likelihood for engaging in delinquent behavior increases in a Bayesian manner. Perhaps this is why Indian mothers are so focused on fitting into a peer group with “good influence”, since they natively understand that you will be molded by the company you keep. Proximity karma changes as you age, because the company you keep changes as you age, but it significantly moulds the priors you will carry with you for life. 
Now that I have illustrated the different types of karmas that I have identified, one can perhaps see the value of modelling karma as a multivariate Gaussian Distribution. As I mentioned in the last post, believing in Bayesian probability is equivalent to believing in karma. So what of free will, what of our predetermined future, what of the will of the gods?
I think we are best off taking one of the greatest lessons the Bhagavad Gita has to offer: Nishkaama Karma.
 The gene determinists among you can think of Svabhava as an abstraction of the genetic makeup
 I do not claim that this distinction is sufficient to describe karma. Simply that it describes karma in an interactive world setting fairly well in my humblest of estimations
 As an aside if this reminds you of ta’veren you are not alone. I find the Wheel of Time to be extremely Hindu. After all, the Dragon is reborn once every age to reset the Age and purge the world of Evil and bring back the Good. Who does that remind you of?
The article has been republished from author’s blog with permission.
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