FoundationalConceptsNeuroscience

tists that microscopic matter behaves in these strange ways, and the
experimental verification of quantum mechanics has been extensive
and unwavering.
And there’s more weirdness that, unlike the above, is not univer-
sally accepted among physicists. For example, some physicists believe
the next big explanatory breakthrough will involve so-called string
theories that expand the number of physical dimensions from the
four dimensions of space-time as currently understood to ten or
eleven dimensions, describing who knows exactly what. And some
physicists contend that the best way to understand our universe is
to view it as one among an infinite number of parallel universes, and
that new universes in this vast collection are being created all the
time. Though not universally accepted, these theoretical speculations
are taken very seriously within mainstream physics, in part because
they can be tied into some kind of elegant mathematical framework.
Mathematics, it seems, offers at this point the ultimate, the most
compelling guide to what we regard to be truths about physical
reality. No one knows exactly what that is about. Does it mean that
mathematical notions somehow exist as an intrinsic part of the foun-
dation of reality? Are numbers—zero to infinity, real and imaginary,
discrete and continuous—examples of what is really real, the “ideal
forms” posited by the ancient Greek philosopher Plato (about 427-347
B.C.E.)?
Or is mathematics, from the simple to the profoundly esoteric,
solely a product of human cognition—our concept of numbers, ability
to carry out mathematical operations, and capacity to formulate and
discover mathematical truths (such as “rt is an irrational number,”
“there is no largest prime number,” or “x" + y™ = z" has no integer
solutions x, y, z for any integer value of n > 2”)—directly related to
biological evolution of our cognitive capacities and nothing more? No