 A system that satisfies these conditions—a usable hypercomputer—may be purely notional. For instance, infinitely accelerating TMs (Copeland 2002) are TMs that perform each computational operation in half the time as their previous operation. As a consequence, infinitely accelerating TMs complete an infinite number of operations (a supertask) within twice the time it takes them to perform their first operation. This allows infinitely accelerating TMs to compute functions, such as the halting function, that are Turing-uncomputable. But infinitely accelerating TMs are usually discussed as notional entities, without evidence that they can be constructed. Purely notional systems, of course, do not falsify Modest Physical CTT. To do that, a system must satisfy at least the fifth and sixth constraints on physical computation: it must be physically constructible, and it must operate reliably.