String theory postulates 6 extra dimension, all too small to be observed. The best description of a small dimension is that of an ant walking on a flagpole: The ant observes that the flagpole allows two dimension of motion (forward/back and left/right). From a very far off perspective, the flagpole seems to only have one dimension; the smaller dimension is too diminutive to be visible.
M-theory adds an additional dimension to string-theory: that got me thinking, is it possible to have a dimension that is too large to be noticeable? Consider the following analogy: to inhabitants Flatland, there are only two dimensions. If Flatland were extended to be the surface of a sphere, it would still seem perfectly flat; they would be living in three dimensional space, but only perceive two.
There are certainly weaknesses in the analogy, but it nevertheless has me thinking about if there could be dimensions that are too large to be naturally observable and what implications that might have in theories such a string/M theory or even if such a dimension were part of an even more ambitious theory that might pick up where M-theory ends.
I'm not enough of a mathematician to know if this is feasible, or to explore the implications myself; but I would love to know if it is possible or impossible, and if anyone has considered this.