It feels a bit sneaky to think of a constant rate of change as an invariance (ie the first derivative is flat). I suppose it's true! But then it seems you could easily take the next step, and treat any constant higher order derivative (eg constant acceleration) as an invariance. Maybe technically so, but then if it *does* vary in the higher orders, it seems you would be further off base than with a bad bet on invariance in lower orders. (In the case of AI capability, whether acceleration is an invariance seems like precisely the big debate!)
LOL - yes, you are quite right, but even so: I am counting steady growth as an invariance, more because it is usually overlooked in future scanning pieces, than because of the mathematics. We tend to focus on discontinuity rather than continuity. Maybe that is the better terminology!
It feels a bit sneaky to think of a constant rate of change as an invariance (ie the first derivative is flat). I suppose it's true! But then it seems you could easily take the next step, and treat any constant higher order derivative (eg constant acceleration) as an invariance. Maybe technically so, but then if it *does* vary in the higher orders, it seems you would be further off base than with a bad bet on invariance in lower orders. (In the case of AI capability, whether acceleration is an invariance seems like precisely the big debate!)
LOL - yes, you are quite right, but even so: I am counting steady growth as an invariance, more because it is usually overlooked in future scanning pieces, than because of the mathematics. We tend to focus on discontinuity rather than continuity. Maybe that is the better terminology!