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On the basis of what we have just discovered, the solution is very simple. Because of our human bias, our space is defined in terms of fermions.
A fermion with mass, travelling slower than the speed of light in the x direction, needs to spin.
Spin requires a plane in two dimensions, so an additional two dimensions — y and z
So three dimensions arise from the fermion's need to satisfy the rules of special relativity. And, as we define our reality in terms of fermions, our space therefore must have three dimensions, three degrees of freedom.
One or two dimensions of space would not be enough as the fermion would not be able to spin. Three dimensions is the smallest number of dimensions which allows spin perpendicular to motion, thus allowing the fermion to satisfy special relativity.
John Barrow explains this unique characteristic in Dimensionality:
"There is one simple geometrical property unique to three
dimensions that plays an important role in physics: universes
with three spatial dimensions possess a unique correspondence
between rotational and translational degrees of freedom . Both
are defined by only three components."
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