 Why would we compute at all, if according to our known information measures, deterministic computing does not produce new information? The question could be rephrased as: should we use Kolmogorov or Levin complexity (Levin 1973, 1974, 1984) as our basic information measure? In fact both choices lead to relevant, but fundamentally different, theories of information. When using the Levin measure, computing generates information and the answer to the three questions above is a “yes”, when using Kolmogorov this is not the case. The questions are related to many problems both in mathematics and computer science. Related issues like approximation, computability and partial information are also studied in the context of Scott domains (Abramsky &amp; Jung 1994). Below we discuss some relevant observations. 