Our mathematical models of physical reality are far from
complete, but they provide us with schemes that model reality
with great precision - a precision enormously exceeding that of
any description that is free of mathematics. There seems every
reason to believe that these already remarkable schemes will be
improved upon and that even more elegant and subtle pieces of
mathematics will be found to mirror reality with even greater
precision. Might mathematical entities inhabit their own world,
the abstract Platonic world of mathematical forms? It is an idea
that many mathematicians are comfortable with. In this scheme,
the truths that mathematicians seek are, in a clear sense,
already "there...." To a mathematical Platonist, it is not so
absurd to seek an ultimate home for physical reality within
Plato's world.What Penrose doesn't acknowledge is that some
convergences are coincidences--and that mathematics can be
entirely internally consistent, yet need not map onto any
external reality, or are adaptable to en