[enasterosophes]

I don't know the answer, but a couple of things to keep in mind with such speculations:

* Properties of lower dimensions don't always extrapolate to higher dimensions. An example that comes to mind is the result in probability theory that a 2D random walk will always return to the home position an infinite number of times, whereas a 3D random walk has a 2/3 chance of never returning.

* Physics is interested in what is observable and testable. In your grant application, what are you saying are the testable aspects of this 4D bulk space which would validate your theory?

On the other hand, we can already perfectly represent 4D objects in 3D space. Just write down a bunch of 4-vectors. If this seems like it's trivializing what you're saying, then it means you need to provide a clearer definition of the objects which you have in mind, and what it means to represent them.

So overall I think you'd want to be careful with how you're defining the objects you're interested in, and what is the mathematical form of the claim you want to make about those objects, and how to test whether it has any physical relevance.

[lanstin]

For example, the Banach-Tarski paradox can't happen in two dimensions, it needs at least three. Terence Tao's 2nd book on analysis explains it, tho I can't yet understand the explanation. (It (the weird measure expanding rearrangement) can happen for countable # of sets in 2, even 1 dimension, but not for finite # of sets).

https://terrytao.files.wordpress.com/2010/02/epsilon.pdf