[tortoise]

Even though the Invariance theorem[11, Thm 2.1.1] guarantees that any two UTMs U and V will agree on the complexity of a string x up to a constant independent of x, for any descriptions x and y, there will be two machines U and V disagreeing on whether x is more complex that y, or vice-versa.

This isn't a correct application for our universe. In our universe, two arbitrary machines will always agree on the complexity of a string. I touched on this in previous posts. The Invariance Theorem is misleading in practical application; our universe doesn't contain UTMs as far as we can tell, which has consequences.

[Alamo-Girl]

Thank you for your post on the Invariance Theorum! Except for arriving at some agreement on terms WRT the biological "machine" - the difference of opinion is not troubling to me.