You are pushing me hard! :) > And if you had two separate copies of the universe, you could measure this compounding. > But even if it did ruin cyclic behavio

You are pushing me hard! :) > And if you had two separate copies of the universe, you could measure this compounding. > But even if it did ruin cyclic behavior, how long are your cycles? The universe is only 1e61 planck times old. A discrepancy of 1e-100 would have no effect yet, let alone 1e-1000. When this is true: When there are no threshold conditions, then discrepancies accumulate just as you have described. And for any given t, a small enough discrepancy can be chosen so that it does not impact measurements of a given accuracy. When it is not true: For any system with thresholding conditions, any discrepancy can have profound immediate effects. A collision can result in a particle heading off in an entirely different direction after a collision, cascading into an entirely different system state. How critical constraints change structure: When pi, i and e are used structurally, i.e. "pi" represents traversal of a cycle, "i" a quarter turn traversal, "e" a positive feedback traversal, each of them represent something invariant: for "pi" some sum of two squared units is conserved (the squared radius on two units), for "i" a position may be conserved while an orientation rotates, for "e" some feedback value maintains an invariant relation between its position, its rate of change, and its accumulation. These relations define the system itself, not just some proportions. So for those cases, where constants define structure, any change to those constants changes the structure. Suddenly, there are differences where they did not exist before, non-unity proportions where they did not exist before. The system has new state values, new interactions. The system itself has changed, not just proportions. The system likely has more states. Structural change is threshold change: Changing the system's structure is the most significant threshold-type change one might imagine. The entire system is different starting at time = zero. Can a structural constant be changed in a way that leaves it only proportionally changed? So that discrepancies simply accumulate, until they are measurable? Sometimes, yes. But will that hold in general? No. In general, the difference between interactions that exist, vs. interactions that do not exist, states that exist vs. states that do not, includes systems that can behave qualitatively differently from the very first time step. Does that make sense? (I rewrote this several times!) Sometimes numbers define structure. They define what interacts with what. And what does not interact. Not just proportions. Changing structure is a threshold-type change: 0 to something, equal to unequal. A state that didn't exist, to one that exists. No interaction, to interaction. That might result in a system that simply accumulates discrepancy. But it may also result in entirely different behavior from the first step onward.