Why, for example, should we suppose that just because our minds can only apprehend three dimensions (four, if you count time) that that's all there are? Could the world not consist of numerous dimensions that we can not only not perceive, but we can't even imagine? Could there not actually be entire worlds integrated with our world but closed off to us because our minds lack the necessary structure to perceive them?
One way to try to imagine what reality might be like if there are actually more than three dimensions of space is to imagine how a three dimensional object would appear to a two dimensional being as illustrated in this short video:
If we actually do consist of more than three dimensions we would look completely different to a being who could perceive those other dimensions than we do to each other. There could literally be, in other words, far more to you than what meets the eye.