James,
Definitely there are assumptions. My worldview is by no means a pure logical deduction from nothing, nor I can think of some result with no preconditions at all (think of math, one starts out of a set of axioms, sometimes not even easy to take by granted). If the question is what are my main assumptions, my main assumption is that the world follows an algorithmic distribution. And even if there is ideology in this position what I'm trying is precisely to detach myself from a purely ideological position and tackle the question with the best tools available from information theory to test this digital hypothesis and make my point.
As you may know from my essay, what I do is to compare empirical datasets to data produced by digital (algorithmic by definition) processes in their frequency distributions of patterns. This allows me to see wether patterns are distributed alike (or not) among the real and the simulated worlds.
The conclusion is that there is some resemblance and that differences can also be explained in information terms. Then I argue that because we have no idea how to compare datasets to an analog distribution (mostly because we cannot even agree on what analog means), and because the world definitely seems far to be random, a strong possible explanation is that, if the world is algorithmic then it is likely to be the result of processes similar to the processes matching the empirical data.
My explanation does not rule out the possibility of an algorithmic analog world (no essay here, I think, rules out each other possibility nor are categorical about their claims), but I argue that an algorithmic continuous world actually forces you to assume more preconditions than the digital one (if someone is categorical it shouldn't be taken very serious).
As you may agree, however, assuming too much is undesirable, at least from the point of view of science and how science has worked out for us in order to understand our world. My purpose is precisely to avoid starting from too many (or too strong) preconditions and Levin's universal distribution is, just as it is the uniform distribution in a random world, the one not making any assumptions when no other information about is known, other than assuming that processes are carried out by an algorithm rather than as the result of a truly random interaction.
Thanks.