A person at the local shopping mall knows that she needs to move north-south, east-west, and up-down, to reach the desired store. There is a fourth dimension, time, because unless she arrives within business hours, it is a wasted trip. It appears that we live in four dimensions, or do we?
Secret Dimensions explains that possibly six or more additional dimensions exist. Somehow we cannot sense them. Mathematicians are accustomed to N dimensions, and although readily grasped, (and exploited) it is difficult to imagine what living in ten dimensions actually implies. To be a little different, I have called them dark dimensions, to be consistent with dark matter. The designation 'dark' implies they are unseen, or that we know very little about them. Perhaps I could write a novel about vampires living in these curled dimensions, but I digress ...
String Theory explains the original string theory had space-time consisting of ten dimensions, and the 11th dimension was an almost insignificant line or circle. Bosonic string theory insists space-time has 26 dimensions. Theorists believe the extra dimensions are necessary to explain mass-less objects such as photons. The theory being, that they are only mass-less in flat space, but in full space, they have mass.
Wiki explains the extra dimensions may be very short or curled. Imagine a long hose viewed from a distance in empty space. The observer might conclude the hose has only a single dimension, or length. But a close observer would note the hose has all three physical dimensions. A gnat flying inside the hose would experience all three, despite the far-away observer deducing there was only one relevant dimension to the object.
Since we are so much larger than the sub-atomic world, the extra dimensions experienced by photons and other particles may be irrelevant to our daily life, just like the extra dimensions of the hose. Yet gravity may lurk within those hidden or secret dimensions, causing the paradoxes we note between the microscopic and macroscopic observations.
Do Hidden Dimensions Exist? explains there are thousands of possibilities of what the hidden six dimensions could look like. Astronomers are attempting to look at past history from the Big Bang to identify the single multi-dimensional geometry defined for the physical world. In Search of Hidden Dimensions suggests that the strings of string theory may be less than a millimeter in length.
Physicists fervently hope the Large Hadron Collider will prove the existence of hidden dimensions. How? - through violation of the law of conversation of energy. If energy disappears, then it had to leak into the unseen dimensions. Mmm. That's what happened to my homework years ago.