Which integral?

Every minutest moment we can perceive, there is a burning question that each of us evaluates without effort and redefines or reaffirms our actions to align with the outcome of that effort. The burning question is where we think we fit in the world, which also, in a way, is how the world is with respect to us and vice versa. Then, we do actions that reinforce that belief in that position and avoid actions that weaken it.

Now, with this starting point, there are several other questions that emerge. First, the ranking and the problem of compatibility in social relationships. Say there is a unique numbering system that everyone concurs with, but there is a perceived rank that each individual gives to every other individual. But, because that ranking itself brings with it the biases of the observer/judge, the rank that one individual perceives will be very different from what another perceives for the same observed person. This is the first level of error. Then, this perception is conveyed to the observed itself through the observed’s own perceiving faculties, and his position is gauged. This position is then acted upon, and the closeness to this position is achieved. Then, the perception of the observer also changes with the pivot being some other position, and thus the perception moving closer to this and so on and on. This goes like a parallel mirror system with infinite reflections. Every communication theory talks about just two sources for the error: the encryption and the decryption points. But, what is prevalent is not two distinct things but one highly complex web that influences with a countably infinite number of threads, thus blurring the lines between the real world and the perceived world. That theory is for a different day.

What is more interesting is the application of this to the perception of your discretisation rank. When we look at anything in the world, our view of it depends on how deep we let the continuousness exist before discretisation kicks in. In the world of psychology, this is very similar to the idea of bounded rationality, where we depart from perfect rationality because of limitations to our mental capabilities or even resources to extend the depths of our rationality assumptions. (Rationality works on the idea that you know you are rational, and you know that (the other player) B is also rational and that B knows you are rational and you know that B knows that you are rational, and so on and on forever. But, if we keep recursively doing this, it never ends, and we can’t have infinite time to choose. Thus, we prune our rationality to bounded rationality) Now, similarly, when we discretise the world, we discretise it, keeping in view the ideas of our perceived “discretisation rank,” which is also determined based on others’ perceptions, etc. Now, eliminating the dynamic aspect of this game, we find ourselves with a snapshot of everyone’s discrete rank. (The irony here is not lost on me. The very act of extracting a snapshot view is discretisation, the wide prevalence of which says something about our collective consciousness’s rank on the discretisation scale). Then, whatever the unit of discretisation is, as long as we have buckets of such discretisation and the population distribution along this possibility of discretisation, there can be some crowding at some discretisation levels, but the mere transience of them makes one indifferent to the tribe close to one’s discretisation rank.

This makes one wonder, how would the possibility of infinite computation improve us? Or does it even improve us when it removes all the apparent imperfections? Does being able to integrate more and more dimensions make one a better player? This fits very well within the idea of the “absolute” being the integral of an infinite order. And as you keep discretising it, the lower-order integrals come out. So, the two unknowns are on the either side of the spectrum. The infinite range on both ends then leaves a more fundamental question — Does integrating as much as I can or discretising as much as I can take me closer to the promised land of freedom? However, we know from Integrating experiences and discretisation experiences that integrating experiences, empirically speaking, makes the world look better and feel better for the individual. But, having this longing for the absolute but at the same time not knowing the relative position ever, it becomes an immortal prison.