Wonderology (cont.)

Though I did delete the asinine introduction on the last post, I suppose I'll reintroduce the idea slightly. Wonderology is a half-jokingly generative philosophy that pursues the question of relation and non-relation with respect to the apparent existence of subjectivity. It is both skeptical and positivist.

Yet, it drives at a space where philosophy, mathematics, and complexity intersect. The problem with most other philosophies is they do not take into account the true depth and complexity of the issues of subjectivity, relation, and non-relation. Especially with respect to the underlying forms driving these ideas (i.e. the physical realizations that for whatever reason make us think these bizarre and often ridiculous thoughts). Many simplifying assumptions are made at the grossly macroscopic level (i.e. the internal monologue, and maybe a few layers of subconscious underneath), without taking into account the structure, relation, and non-relation of the entire hierarchy of processes lying beneath the surface of the apparent phenomena of subjectivity. Hence, these philosophies restrict the space of possible interpretations and only scratch the surface of a much larger space hiding beneath the abstract symbol manipulations we perform daily.

As the human race hurtles into an increasingly strange reality these deeper questions beg to be answered, lest we perpetuate mistakes we made before. This will likely be a painful and arduous process, since it will require us to question the most deep-seated truths we hold to be self-evident. Hopefully, this will lead to an increasingly peaceful and wondrous reality for all subjectivities.

The next phase of this philosophy will be to generate a proposition for what systems can attain a state of wonder. I'm not sure the best way to go about this, since I'm not even sure if a system has to be subjective to wonder or not. Maybe.

Wonderology

Preliminaries
Define phenomena as any realization of a well-defined process. A well-defined process being a process that does not suffer the agonizing (or not) state of being internally inconsistent. For example, a machine that runs under the assumption 1+1 = 3 (keep in mind inconsistencies can be much much more subtle).

Define inconsistent as being in a state of (human) logical fallacy. It may not necessarily be true that human logic is the end all when it comes to understanding all possible phenomena, but it is the best we've got so far when trying to construct systems for evaluating truth. (Though one could argue against this too...)

Define process as any system of rules that takes input (including no input) and produces output (including no output). Examples: computers, systems of differential equations, cellular automata, random number generators, etc...

Define rule as any well-defined relation between objects or processes.

Define relation as the state of not being in non-relation. Relations are a subset of objects. This is tricky, because all of our thoughts are set in a backdrop of relation, so we have to be wary of what non-relation does to what we think, since we can't think it.

Define object as anything that is not in non-relation.

Define non-relation as any object (which includes processes) which cannot be represented.

Define representation as any formalism for encoding relations.

Define primitive as any object that can not be described in more basic terms (e.g. anything below is in non-relation).

Reduct!
Proposition: One can construct new processes from other processes. As long as one maintains the ephemeral quality of internal consistency, any new object pieced together from other processes is a new process itself.

Corollary: Any process can be broken down into sub-processes if and only if the process is not primitive.

Note: The rules for breaking and constructing are non-trivial. Suffice to say, they exist, but may not be obvious for any particular process. Science is often concerned with the breaking of processes down into simpler processes. Engineering is often concerned with constructing new processes from pieces.

Holify!
Proposition: Certain process constructions produce phenomena that do not apply for any particular sub-process. This occurs whenever global and local qualities of a system cannot be transformed into one another. This is a type of symmetry breaking.

Define transformation as any map of one set to another.

Define set as any collection of objects (which is also an object).

Define symmetry as any property of an object that is invariant under a certain class of transformations (e.g. it doesn't change when transformed in certain ways).

Lemma: Symmetry breaking is the destruction of isomorphism.

Define isomorphism as any relation that implies sameness.

Wonder?!
Define wonder as any state of being that acknowledges and desires to reconcile phenomena, processes and sub-processes. In general this will include special attention to production of non-trivial global phenomena, symmetries, and symmetry breaking. A broad synthesis of reduction and holification. This will in general engender the creation of "meta" concepts. Beware the meta...it is a useful tool, but it can lead one to fixate on certain convincing illusions, and to become so captivated by these illusions that one is blinded to essential relationships hidden behind the meta.

Proposition: A state of wonder is a state of maximal (local or global) relation with other objects.

Note: This does not explicitly state the value of maximal relation. This is an open-ended moral question that may be context dependent (which would be a kind of symmetry breaking). It may also be that one must be in non-relation as well to attain a true state of wonder.