What Kind of Infinity? (A Small Infinity - iAPP)

What does the “Infinities” in Small-Infinities mean? What is meant by “Infinite”? What does it mean to refer to a system as infinite? What does it mean to refer to a human as an infinite system, a small infinity?

The “infinite” referred to here is the unfolding horizon of the very large number of possible forms and expressions that a dynamic complex system generates and what this unfolding horizon looks like from the point of view of observers … and what this horizon looks when the observers are themselves part of, or even comprised of, the infinite systems they are observing.

Infinite System?

A system can be described by the total number of its parts and the possible ways these parts can relate, and the forms these parts and relations can give rise to. An Infinite System is a dynamic complex system that has the natural potential to generate such large numbers of parts and relationships, varieties, shapes and forms, that it outstrips the ability of a given observer to track, catalogue and predict. From the point of view of that observer the system generates varieties of states and behaviors which are infinite for all practical purposes (iAPP). The moments and states, the movements, changes and dance, produced by these systems are experienced by observers as the unfolding, outstripping surfaces of Small-Infinities.

This kind of infinity then, the small infinity, arises from the interaction between observers (persons, minds, intelligences) and the complex systems they are comprised of, are embedded in and interact with. Exploring and designing with the insights, implications and ways-forward that arise from taking this state of affairs seriously is the job of Small-Infinites.

A Psychology of Small Infinites?

A very powerful family of questions arise naturally from the infinite for all practical purposes (iAPP) viewpoint. “Is there any real sense in which a human, a mind, a person can be thought of as infinite?” There are many lines of reasoning which lead to a satisfying “No! Humans are not infinite. In fact, almost nothing is truly infinite.” Many of these lines of thought come from the fields of logic, mathematics, information theory, theology, and philosophy. I agree with many of them in the most general terms.

So why then am I talking about a psychology of Infinite Systems? And how can I claim that humans are Infinite Systems? And, if the claim is valid, what are the implications of taking it seriously? What insights, perspectives and questions arise?

These questions, for starters, have led me to explore the possibility of constructing a Psychology of Infinite Systems as applied to the life of persons, the life of minds, the life of dynamic complex systems. This exploration has proven so fascinating, stimulating and liberating to me that I have come to see it as a “Way of Liberation” that arises naturally, easily and dependably from straightforward and immediate consideration of the kind of infinity we are and the kinds of infinities we give rise to.

Surfacing Small-Infinities:

The nature of our lives as small infinities is in a sense continuously hidden from us. One of the great achievements of the human variety of small-infinity is that we play, love, work, create, hope, live and die as if we were simple, as if we were not explosively and infinitely complex. This achievement comes with a possible cost: losing touch with, or never understanding to begin with, the kind of things we actually are.

I want to share some of my exploration of Small-Infinities in a way that allows me and the casual reader to derive benefit from considering the topic from many kinds of angles and perspectives. But how does one think about, describe, live with, those things that by definition outstrip the observer who is doing the thinking, the describing, the living? Really, how?

The very nature of small-infinities shapes the possible ways available to consider infinities, to allow infinites to shape surfaces that we can understand, think about, consider, experience, create with.

The best way that I have found to proceed is kind of like setting up little observation posts all over a mountain range: observation posts that I and others might visit, hang out in, and return to from time to time, and to have a good time looking around, to take in the various views that the mountain range affords, without need to take in the entire thing at once - precisely because it cannot be taken in all at once. This has led me to take a slow-unfolding, axiomatic approach to the topic - the laying out of observation posts along the way - to give myself and others time to stand on the precipice of each insight and look around for ourselves, in our own time, in our own way, to unfold as it were, an infinite number of ways from which to stand and look at the infinities that make up our worlds, our minds, our selves.

A changing collection of these Observation Posts can be found here: Surfaces