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Our concepts are very much simpler than reality; an infinitude of laws would, in fact, decribe reality rather than just a scientific lab experiment.

Our concepts would have to be much simpler than reality, if reality is comprised of an infinite number of dimensions, while we humans are pretty much stuck with three of space and one of time, making four. That would be a very severe handicap for human understanding -- so severe, in fact, that I'd wonder how a scientist could even summon the will to get out of bed in the morning, knowing his entire day will be spent in an exercise in virtual futility....

Thanks for the tip re: random = uniform = chaos??? I suppose this interesting problem you raise might be soluable if we propose that most dimensions "extra" to our own normal perceptive apparatus could hang out in "imaginary time" -- like the "extra" dimensions of string theory.... But working out the details looks like it'd be a whole lot of work to me.... Apparently, it's already hard enough WRT the 11 dimensions of string theory....

Alternatively, one could simply take the "theist's way out" and simply assume that God would not have made a world that man would find very difficult to understand. Oooooppss! My anthropocentrism is showing....

Technically, random need not be uniform. "Chaos" is now (in mathematics and physics literature) used to mean something like: "not random but with sensitive dependence on initial contitions." Chaotic as an informal term may mean essentially the same as random as an informal term. In the scientific literature, the meanings are more precise and much different. (I know this sounds pedantic, but science is pedantic.)

"I may didact, but I never pedant." - Norman Squire

Alternatively, one could simply take the "theist's way out" and simply assume that God would not have made a world that man would find very difficult to understand.

The complexity of the world is just exactly sufficient for it to work, just as a man's legs are exactly long enough to reach the ground. No need to confuse is with ought.

reality is comprised of an infinite number of dimensions, while we humans are pretty much stuck with three of space and one of time, making four

There are other dimensions. Weight, for example. Electrical charge. Utility-futility. Importance-inherence. Quantizing the qualities: to measure.