There is a universal metric of information: amount of bits. It's universal in the sense that if we write a piece of information in DNA (4-ary digits), we can simply multiply by 2-log-4 to get the amount of bits.
I'm wondering if there is also a universal measure of the size of a program. I know about Kolmogorov complexity, but this is defined in terms of the size of a Turing machine.
But if we compare this to some other computational model, will the equivalent complexity measure be equivalent to the Kolmogorov complexity measure, in the same way that the 4-ary information metric is equivalent to the binary one?
For example, suppose instead of a Turing machine we used a modern CPU, and we define a similar metric of the size of programs, will it agree with Kolmogorov complexity?
I think what I mean by the metrics being equivalent is that there is one canonical metric for each universal model of computation, and that the order of complexity of programs is the same in each model of computation, or even that it is some scalar multiple of it.