Objects, Scale, Abstraction

This is a big post for me, because it articulates the basis of my amateur practical philosophy. I've been working on this since 1999. I'm particularly interested to learn from you where I'm sloppy and where I'm naïve, but without further ado ...

Let an object be a thing, an entity, and let a property be a characteristic of an object. Objects are composed of other objects, and require certain properties of their constituent objects in order to exhibit their own properties.

Scale is a property, and it is the size of an object relative to a given frame, where a frame is an arbitrarily bounded hierarchy of objects. For example, here are a few objects in a frame, listed in order of scale, decreasing:

• country club
• golf course
• hole
• putting green
• blade of grass

Each object has a relative size within the frame bounded by "country club" and "blade of grass." Each lower-order object is a constituent member of the next-higher object, forming a hierarchy.

Abstraction is the process of fitting an object into a higher-order object. Abstraction always entails a loss of information (nuance, subtlety, detail, complexity), and a gain in simplicity and usefulness. The putting green may be crafted by so-and-so, contoured thus-and-such, with a certain variety of grass or another, of a particular hue, in soil that is some part sand, clay, and organic matter, and which absorbs water at such-and-such a rate. However, these details of the green only matter within the hole insofar as they affect the properties the hole actually requires of the green: that it be smooth, that it be located at the far end, that it have a cup, etc. An abstraction, then, is a summary, an abbreviation, a short-hand, an objectification, and it serves the purposes of the higher-scale object.

I mean “object” in the most generic sense: a putting green, a government policy, a business decision, an ecological system, a value system, a religious practice. Therefore, these few simple terms enable an analysis that applies quite broadly. Given an object:

• What properties does the object have?
• What higher-scale objects does/could it contribute to?
• How do its properties relate to each higher-scale object?
• How does contributing to each higher-scale object change the object over time?
• What objects compose the object?
• How do its constituents' properties relate to its properties?
• How would changing its constituents change the object?
• How does the object change its constituents over time?

Prof. Anant Agarwal's lecture entitled "Introduction and Lumped Circuit Abstraction" is the most directly related discussion of these themes that I've found. Systems theory also appears to be related, though afaict it has more to do with the internal workings of a system (read: object) at a given scale, rather than patterns across scales. Certainly I'm skirting the edges of ontology. I've got plenty more BS as above, but where do you think I should go from here?