A Mathematical Basis for Karma

So I've been auditing Jordan Peterson's course "Personality and Its Transformations". Peterson is a wonderful lecturer and while he sometimes drives off into the weeds of multiple digressions, he often just lights up one's skull with insights. (see note below)

Here is a concept that he tossed off in a couple of sentences, just a throw-away line really, around the 59:00 point in Lecture 14. He says,

I also don't think that the connections between people and the society are as abstract and distant as we think, because you might think, well, what the hell difference could it possibly make, you know, the way I behave? Well, you're a node in a network. You're not an individual connected by a linear line to another individual connected by a linear line to another individual, in a line that's seven billion people long. That would make you nothing: just pull you out and the line would reclose, and that would be the end of that. You're a node in a network, and the network's communicating. And we know for example, that you are roughly going to interact with, in some serious way, a thousand people in your lifetime as a minimum, minimum estimate. So, and all those people know a thousand people, so that's a million people that are one person away from you, and two people away from you is a billion people, and as soon as you get to three, well, that's far more people than there are. So, you know, you are only three or four or five connections away from everyone. And so it is very very difficult to know exactly how your behaviors and misbehaviors echo and ripple. And we know that people can be tremendous forces for good; we know that because you see people like that from time to time; and we certainly know plenty about the reverse. So God only knows what role you play in determining, you know, whether the part and the whole of mankind goes seriously wrong or seriously right.

So, he's Canadian, you know? Well, Canadian quirks aside, my mind was caught by that casual remark that you or I will influence at least 1000 people, and they 1000, etc. Which means, one's influence spreads by a power law. What of one's influence, how would it fall off? To work it out formally, let

• E be the total of your influence on one other person
• K be the number of persons you influence in each period Y
• N be a number of periods

The value of Y can vary; Peterson was talking about your whole lifetime, but it could stand for one year without changing anything.

The number of people your influence reaches is K^N. Say you influence K people in one year, they reflect or echo your influence on K people each in the next year, that's K², K³ in the second year, and so on. This rapidly becomes a large number, as exponential functions are wont to do.

Meanwhile, the effect you have on people is being diluted as E^N. Now this is like, but unlike, an epidemiological simulation. Simulating an epidemic, a node in the network is either infected or not infected, and a simulation of an epidemic has little nodes changing from green to red with no in-between. But one person's influence E on another person is only fractional; when you express an opinion, or behave in some way, another person will adopt that opinion or echo that behavior only weakly or with low probability. So perhaps E is a small fraction, 0.01 maybe, i.e. 1 person in a hundred will actually do exactly as you did or said. (It would really be a family of values, one for each kind of influence you might have; the influence of your speech patterns with one value, your habit of kicking puppies another value, your clothing choices another and so on ad infinitum; all relatively weak yet nonzero.)

The point is, your effect on others is E^N, 0.01 on the people you interact with, but 0.01²=0.0001 on the K² people they influence, and so on. It gets smaller, but it never goes to zero—and also, it reaches a whole bunch of people.

In another essay, I wrote something to the effect that you could think of your actions as "seeding your world" with good things or bad things, with health or illness, calm or anger. Here is a mathematical basis for that, and (I think) the real basis for the Buddhist notion of karma.

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Note from 2018: In recent times, Jordan Peterson has emerged as a rather distasteful public personality, much criticized by people whose opinions I respect. But I don't think this more recent criticism invalidates the very particular idea that I quote above.