Sal Cordova recently speculated on the relationship between the concept of irreducibility as defined in mathematics and physics and Behe's irreducible complexity. Some link-following took me to a paper by Chaitlin describing the ramifications of algorithmic information theory (and its roots in the work of Godel and Turing) for mathematics, physics, and biology.

I'm not as certain as Sal that the work of Godel, Turing, and Chaitlin can be straightforwardly applied to support ID - or that the concept of irreducibility in AIT correlates well with Behes' Irreducible complexity[1].

However Chaitlin's paper certainly illustrates some trends in the sciences that are favorable to ID: the discovery that the world around us (not just in biology but also in physics) is fundamentally informational, and that it can be fruitful to think of biological and physical systems as computers which process that information. The fact that Chaitlin goes so far as to predict the convergence of theoretical physics and theoretical computer science shows just how deep the similarities go. These discoveries provide strong support, I think, that the workings of a mind are behind the phenomena studied by the sciences.

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[1] There seem to be intriguing similarities to specified complexity, though. A system could be irreducibly complex without being algorithmically irreducible (that is, it might break if you remove any one piece, but not be the most efficient method for producing a given result). On the other hand, AIT irreducibility is strongly tied to minimum description length, which is an explicit part of specified complexity.

Update (2/19): I'm reading Dembski's paper Specification: The Pattern That Signifies Intelligence and just discovered that his formulation of specified complexity makes explicit use of the concept of minimum description length as described by Chaitlin (and others). So I'm a little late to the party. Shows how much I know :-)