  Kolmogorov complexity and algorithmic probability are defined only up to an
additive resp. multiplicative constant, since their actual values depend on the
choice of the universal reference computer. In this paper, we analyze a natural
approach to eliminate this machine-dependence.
  Our method is to assign algorithmic probabilities to the different computers
themselves, based on the idea that "unnatural" computers should be hard to
emulate. Therefore, we study the Markov process of universal computers randomly
emulating each other. The corresponding stationary distribution, if it existed,
would give a natural and machine-independent probability measure on the
computers, and also on the binary strings.
  Unfortunately, we show that no stationary distribution exists on the set of
all computers; thus, this method cannot eliminate machine-dependence. Moreover,
we show that the reason for failure has a clear and interesting physical
interpretation, suggesting that every other conceivable attempt to get rid of
those additive constants must fail in principle, too.
  However, we show that restricting to some subclass of computers might help to
get rid of some amount of machine-dependence in some situations, and the
resulting stationary computer and string probabilities have beautiful
properties.
