As the author of this article, I will reply to this, though it is hard to make much of a reply here, though. (I actually got here our of curiosity when I saw the site logs). I am, however, always pleased to discuss issues like this with people. One issue with this reply is that it is not just randomness we have to worry about. If we are basing a computational interpretation on randomness, yes, we may need to make the computational interpretation progressively more extreme, but Searle's famous WordStar running in a wall example is just one example. We may not even have the computational interpretation based on randomness: it could conceivably be based on structure in something else, even though that structure would not be considered to be running the computer program except under a very forced interpretation. Where would we draw the line? Another point - why should it matter if we use a progressively more extreme interpretation? We might, for example, just want to say that a computation ran for 10 seconds, which relies on a fixed intertreptation (if a complex one), and what happens after that may not interest us. Where would we draw the line? Another issue is that the main argument had been about statistical issues with combining computers when considering probability issues - the whole thing had not been based on Searle - who would not take me any more seriously by the way.
We may not even have the computational interpretation based on randomness: it could conceivably be based on structure in something else, even though that structure would not be considered to be running the computer program except under a very forced interpretation. Where would we draw the line?
We would draw the line where our good old friend mutual information comes in. If learning the results of the other phenomenon tells you something about the results of the algorithm you want to run, then there is mutual information, and the phenomenon counts as a (partial) implementation of the algorithm.
Paul Almond's site has many philosophically deep articles on theoretical rationality along LessWrongish assumptions, including but not limited to some great atheology, an attempt to solve the problem of arbitrary UTM choice, a possible anthropic explanation why space is 3D, a thorough defense of Occam's Razor, a lot of AI theory that I haven't tried to understand, and an attempt to explain what it means for minds to be implemented (related in approach to this and this).