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Yes, it is true that the four conditions I gave for twist measures

don't guarentee that the function will behave anything like the kind

of complexity measure we are looking for. I was only trying to show

how some of the properties you might expect of a twist measure could

be used to generate a metric, so I didn't actually need strong enough

properties to ensure reasonable twist measures. The additional property

I have been using to assure reasonability is the following:

5) For all M, if T(M) > 1, then there exists an N such that 0 < T(N) < T(M) and T(N) + T(N'M) = T(M).

Note that N'M has the property that 0 < T(N'M) < T(M) (easy to show)

so the two manipulations N and N'M are both "simpler" than M. We can

thus easily show that any manipulation M can be expressed as the

product of T(M) twists (where a twist is defined as a manipulation

such that T(N) = 1).