I was reading Roger Penrose's "The Road to Reality", and was glad that he addressed the philosophical issue of how physics, mathematics, and perhaps even our consciousness interface, in the very first chapter.
In that chapter, he has an interesting diagram of three different worlds, the Platonic mathematical, the physical, and the mental, and how they relate to each other.
I think the majority of physicists, though using completely mathematical methods in attempting to explain the universe, still hold the belief that the stuff they are dealing with is somehow "real" as compared to pure mathematical objects (in other words, the Platonic world, that has an exact correspondence with the real world, obeying the final laws of physics in the same manner).
Thus, the physicist sees concepts like mass, charge, and so on as being something real, and mathematics can only describe "how" they behave, but never "what" they ultimately are. It is almost that the physicist treat these concepts similar to qualia, to use the term loosely.
While a mathematician who programs a computer that simulates the universe may declare mass, charge, and so on, as nothing more than predefined data types , physicists may suggest that these concepts are not just zeros and ones residing in the computer, but might have a deeper meaning that, while not making any material difference to the execution of the program, is nevertheless essential for actually making the program translate to reality, instead of just a simulation of reality.
While many physicists would avoid the qualia/hard problem debate, they unwittingly hold spacetime itself to be something "real", as opposed to being some mathematical structure. Thus, a physicist might not try to explain what "red" and "blue" really are and might even dismiss them, but he would most likely balk at any suggestion that their own perception of space and time as they seem exists only in their minds, and may just be an array of zeros and ones in an ongoing simulation. The physicist is getting duped by his own subjective experience of spacetime and therefore holds it in reverence compared to platonic mathematical objects.
But one cannot blame him for that. All of physics is based on observations of physical phenomena as they happen in our three dimensional universe which flows along time. No one can even imagine a fourth dimension. String theorists have broken this mould, but at present, they are more concerned with trying to explain reality as they happen in our real three-dimensional world. The rest of the dimensions are apparently "curled up" tightly on the order of the Planck length (some 10^-35 m) , so we cannot perceive them.
But then, why cannot we even imagine a fourth or higher dimension? If you are familiar with my previous posts, you probably have guessed where I am headed. Yes, you were right! It is tempting for me to suggest that the platonic qualia space has more than three dimensions, but we have access to only three.
But I choose not to. For the perception of spacetime, in my opinion, is not on the same footing as other qualia, such as the color red or the taste of beer. The access concept doesn't apply to spacetime, as it does for sensory qualia which are bound to the common binding space (CBS) (see this post for an explanation). Here we are dealing with the underpinnings of the CBS itself.
More on this in a future post.