Thanks. I should clarify that the computer is deterministic, so as to avoid building randomness into the definition of randomness!
I skimmed over an example too quickly, but your intuition is about right. For that sequence, two possible programs are:
- Compute and print the first 40 digits of pi.
- Decompress the following string according to a Shannon code with probabilities (1/36,1/18,1/12,[etc]): [insert code]
First, the paragraph that begins with "At first blush, the requirement to use..." Seems to be a non sequitur. I don't fully understand how the previous section creates a requirement to use deterministic programs, so I could use more explanation on how that requirement is established.
Second, a very simple concrete example of what one of these programs would look like would be immensely helpful. After re-reading the article a bit I have a mental image of a program that contains a long, compressed string and a decompression algorithm that somehow models the system you're interested in. I can imagine how you might get a useful interpretation of probability from the decompression system, but there are enough open questions there that I'm not sure I have the correct interpretation.
Hope that helps!