Based roughly on some of the writings by the philosopher David K. Lewis at "Paradoxes of Time Travel": http://www.csus.edu/indiv/m/merlinos/Paradoxes%20of%20Time%20Travel.pdf
The writing suggests one factor, determination, to be one of the constituent lower dimensions that compose the third.
In a strictly quadratic system, with a minimal of fuss the fourth dimension has to do with closing the loop between non-exclusive and exclusive concepts of system. If categories one two and three are a somewhat archetypal trinity, the fourth must close the loop, accounting for many exceptions to the rule that occur in all three categories.
Sometimes the fourth category is generic, e.g. when categories one through three are a specialized set. Then it must make a general theory about the nature of all the missing information. But the first three categories simplify this. Conversely, when the first three categories are generic, the fourth category must be a highly specialized theory which accounts for the specialized data missing from all three categories. That is, in the case of a quadratic set of categories, a four-dimensional typology.
Time Travel Quadra:
1. Entities (Mode of Operation)
2. Determination (Volition)
3. Associations (Assumptive References)
4. Pattern of Simulation (Copied from 1-3)
This is designed to be an adequate reference framework even in the case of technologies that mimic subtle or magical time travel.
My assumption is that time travel can be defined cogently as "a mental change of location"---consider how subtle this definition is, and then if it is impossible in extenuating circumstances, for example, for a social pariah, the president, or a yogi in the mountains.
Problems may emerge in this mental-technical concept of time travel, such as:
A. Multiple entities have contrasting associations, in other words, they are not integrable, a form of bifurcation error;
B. Pattern of simulation fails to refer to reality, a lack of omniscience;
C. Determination lacks authority to make meaningful changes to reality (intellectual, social, or technological failure)
D. Entity simply lacks a conceptual framework to utilize time travel, especially the case of lacking any associative framework for comparing the past with the future, with the present, etc. (a failure of ambition).
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