How can a system be simultaneously chaotic (and thus unpredictable) and deterministic?

A common trend I've found in attempts to predict states is the obligatory necessity of the variable of time into the equations of said system. How else are we to pinpoint when each successive state should occur? This though seems to be a carryover from an antiquated absolutist perspective rather than one of relativism. Here we encounter a problem of identity. One may very well define states in terms of contributing causative variables, which would be instructive in an if/then sense, however we must eventually relate this information back to a location if any prediction is to be had. I propose recursively analytically redressing the state in question's composite variables into equations descriptive of their own states as being necessary before we may do so with a more abstracted subject. Building up the inputs thusly as equations themselves defines them in terms of time on a more subjective aspect which may then be more correctly combined to a generalized view. Similarly, where time is used to specify location, so too must we necessarily include terms for spatial localization, as one without the other conveys incomplete information. This may very well require us to define equations in parallel while holding all but one dimension as constants. We may then finally combine these equations into it's generalized form. From the assumed 4 dimensions of classical physics, if lack of specificity continues to propagate after all other potential variables have been ruled out we may then be forced to used our best 4space predictive equations and use them to attempt an analysis of some associative predictive value among the 4 known dimensions to infer some hypothetical n extra dimensions (or at some limit as dimensionality approaches some value, etc). Assuming independence of dimensions (as one must for them to be truly unique and so defined) we would only be able to know beyond the observed dimensions probablistically and so would eventually have to identify a means of directly observing said dimensions. As I, for one, continue to perceive with difficulty the 4 that are to be known as such (though I do understand spatial percepts to be just as subject to emotional state as time is known to be) I fear knowledge beyond this to be the domain of any eventual constructed intelligence to ponder. Not to be outdone though we may then set such a successful AI to the task of developing a codec to convey this new perspective to us. If we are to assume, if this point is reached at all, that 5 would be an unlikely maximum we may then see that perception may still be conveyed as a rapidly rotating representation of 3 directly perceivable dimensions at a time, so that others may be seen as represented in terms of our minimally necessarily evolved 3 "known" spatial ones. An analogy of this (itself analogous) construct may here be appropriate. If we, for instance, wished to expand our visually perceivable range of the EM spectrum, this may be accomplished by rotating views of the usual range, a red-shifted "thermal" range, and a blue-shifted "UV" range. By doing do we may begin to form associations between familiar objects of natural experience with their presented representations as seen in outlying spectra. Insodoing we may be actively introducing the very circumstances which will serve to naturally select our own evolution. The requisite area of competition however may be shifted from the domain of survival of subspecies over to an evolving economy subject to market forces associated with the survival of brain-compute interface products. As the level of brain-computer interfacing increases, the relative proportion of organic computation remaining will begin to dwindle, representing a possible completely fluid evolution from organic to synthetic organism. Wow, getting all Ship of Theseus on ya...