If higher dimensions do exist, are you sure that you are not perceiving them? Maybe, having been born in a universe with higher dimensions, you do perceive them but simply assume that what you are experiencing is part of the normal hustle and bustle of 3 spatial dimensional life. For example, if higher dimensions are responsible for gravity being so much weaker than the other forces, then you do perceive higher dimensions - or at least, you can feel their presence by nature of the fact you are not crushed into degenerate matter.