Mathematically a dimension is a vector of measurement. In the “real world” a dimension is a vector of existence. Mathematically any measurement you can take, plug into a formula and plot on a graph, can exist in it’s own dimension. Mathematically you can have an infinite number of dimensions.
In the “real world” dimensions must have “real” properties, and their numbers are limited to what we can measure. At this time scientists are only able to take measurements in four recognized “dimensions”, height, width, depth and time. But what if there are more? Science and mathematics are hinting that there are.
Scientists recently created a mathematical model of the way the brain creates and accesses memories, and discovered that the mathematics involved requires as many as 11 dimensions to do so. The mathematics of string theory also requires as many as 11 dimensions. Scientists will trip over themselves to assure everyone that this doesn’t meant that there are 11 actual vectors of existence, that’s just the current state of the mathematics involved.
Science fiction has long speculated about the existence of other dimensions, dimensions that function almost as separate universes where anything is possible. But one must understand that other dimensions, if they exist, are all variables in the same equation, or set of equations. All the variables are connected, and while some may be 0’s or negative numbers, they can’t be isolated, one from another. Other dimensions, if they exist, don’t represent discreet universes, they are an indivisible vector of our current existence.
There are theories which suggest that there are 12 dimensions, and that the 12th dimension is unknowable, or undefined. There is even a mathematical symbol for this.
In this humble layperson’s opinion, “If it walks like a duck and quacks like a duck…” If the mathematics and the science are pointing to the existence of eleven dimensions, then perhaps they actually do exist, and are more than just an arbitrary tool for solving equations. And perhaps, just perhaps, inserting a twelfth, undefined dimension might be the key to a final proof for string theory and who knows what else.