  We consider the solution to a stochastic heat equation. This solution is a
random function of time and space. For a fixed point in space, the resulting
random function of time, $F(t)$, has a nontrivial quartic variation. This
process, therefore, has infinite quadratic variation and is not a
semimartingale. It follows that the classical It\^{o} calculus does not apply.
Motivated by heuristic ideas about a possible new calculus for this process, we
are led to study modifications of the quadratic variation. Namely, we modify
each term in the sum of the squares of the increments so that it has mean zero.
We then show that these sums, as functions of $t$, converge weakly to Brownian
motion.
