In order for it to be analogous, you'd have to put the contents of the memory for every step of the program as its running on the hard drive. The program itself isn't sufficient.

Since there's no way to get the memory every step without actually running the program, it doesn't seem that paradoxical.

Also, if time was an explicit dimension, that would just mean that the results of the program are spread out on a straight line aligned along the t-axis. I don't see why making it a curvy line makes it any different.