and on the notion of a hyperdimensional space, especially one being crafted from the connections, the interrelations, between multiple lower dimensional spaces, what is the nature of such a mechanism? is there a fundamental difference between a hyperdimensional space and a notion of “time”?
of course there is always (given an interpretation of Gödel’s incompleteness theorems) _some_ way to define into existence a difference between hyperdimensional space and time; a more fundamental question might be whether they are fundamentally connected, such that they are simply different ways of looking at the same underlying mathematics.
for instance, one way to conceive of a 3D version of Conway’s Game of Life (the cellular automaton) is to map it as a series of state changes of different timesteps, such that each change in the 2D space can be represented as another entire state in the time dimension.
that is, the result of each timestep can be considered a 2D field, and then the fields can be “stacked” (or ordered in whatever way is desired to display them) in order to show the changes over time as one entire 3D object.
for more complex sequences this can also be shown in a digital reality like VR (virtual reality), where then (because of the higher-than-flat [i.e., not 2D screen] viewing method) the 3D changes can again have another dimension applied to them.
that is, the stack of changes can be finessed at different points in the “time” of the process, providing interesting insight into the nature of timeloops and general finessing of the structure and behavior of time.
that is, if there are a sequence of dimensional spaces that are connected in functional ways (that is, (= sameInput sameOutput)), then a process which exists outside of that sequence (and so outside of the spacetime of it) that can finesse the sequence exists in hyperdimensional time, perhaps.
and so, again, on the topic of connecting multiple spaces in order to create hyperdimensional ones, does time have a connection, here, possibly?
it could be said that time is always very prevalent; perhaps it _seems_ prevalent, but only by necessity (via an anthropic principle, perhaps), and it can be entirely modeled as one framework, as one spacetime, always. if so, a simpler model of space (or a more generalized model of spacetime as a whole, perhaps) may hold all the underlying attributes, fundamentally, and so it may be more helpful to consider it when building broader theories and models, and then consider the time angle when it is helpful to do so.
in other words, if a hyperdimensional geometrical space can hold all the information of a spacetime model, and the hyperdimensional space can be more easily finessed in mind, then perhaps use that generally, and break out the more specific spacetime model when it provides additional insight.
by generally thinking in terms of hyperdimensional space, and gaining a more and more robust intuition for it, higher-order thinking can occur, because there are direct places for connections between connections, perhaps.