On their internal work tapes MTMs can compute whatever GTMs can
compute. But they commit themselves forever once they print out some
bit. They are ill-suited to the case where the output may require
subsequent revision after time intervals unpredictable in advance
-- compare Example 2.1. Alternative MTMs that print out
sequences of result updates (separated by, say, commas) would compute
other things besides the result, and hence not satisfy the ``don't
compute anything else'' aspect of individual describability. Recall from
the introduction that in a certain sense there are uncountably many
collectively describable strings, but only countably many individually
describable ones.

Since GTMs may occasionally rewrite parts of their output,
they are computationally more expressive than MTMs in the sense
that they permit much more compact descriptions of certain
objects.
For instance,
K(x) - K^{G}(x)
is unbounded, as will be seen next.
This will later have
consequences for predictions, given certain observations.

Theorem 3.2K(x) - K^{G}(x) is unbounded.

Proof.
Define

(10)

where g is recursive.
Then
K^{G}(f'(x)) = O(l(x) + K(g)) (where K(g) is the size of the minimal
halting description of function g), but
K(f'(x)) > logg(x) -O(1) for
sufficiently large x --
compare the proof of Theorem 3.1.
Therefore
for infinitely many
x and quickly growing g with low complexity.