> Yet the only difference between a FA and a TM is that

> the TM, unlike the FA, has paper and pencil.

> Think about it.

The analogy doesn't works if you really think about it. A TM with a finite tape is equivalent to an FA. The fundamental difference between a TM and an FA is that a TM has infinite space.

(Yes, I know I missed the point and am not very fun at parties.)