There is no problem with assuming such a Turing machine exists so long as you compare only measurements of information with respect to that Turing machine. Gene

There is no problem with assuming such a Turing machine exists so long as you compare only measurements of information with respect to that Turing machine. Generally what is relevant to study is entropy differences anyway. I don't know much about AIT in specific, but it seems that Chaitin 1975 (https://dl.acm.org/doi/10.1145/321892.321894 https://dl.acm.org/doi/10.1145/321892.321894) acknowledges this, as the algorithmic entropy differs from the usual Shannon entropy by a constant term, which one might imagine is the information needed to encode the Turing machine. I also wanted to mention that because you thought of the information theoretic implications of building a computer, etc., you might be interested to know that this kind of thinking is very interesting and cutting edge in biophysics. Organisms have to essentially build computers to do certain tasks, and in this way they must take into account both Shannon entropy (i.e., information in the abstract sense) and thermodynamic entropy! This is essentially the Maxwell's demon paradox (https://en.wikipedia.org/wiki/Maxwell's_demon) https://en.wikipedia.org/wiki/Maxwell's_demon).