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shminux comments on Counterfactual resiliency test for non-causal models - Less Wrong
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This pattern-matches in my mind to the Stability theory, only you try to use large changes instead of tiny ones, which might be too much of a jump.
It might be worth considering small changes in the initial conditions (is that what you call T?). In the Reformation example, would having 94 theses make a difference? What if Luther's proclamation was not translated to German? Etc.
Suppose you establish that a model is stable to small perturbations (how? seems to need math), you can then try to see where the tipping points are. If there is no such stability, the model is probably useless.
Hum... That is one suggested way of going. But it does seem to ignore the fact that these non-causal models are claimed to be correct, without needing to know anything much about the underlying processes.
Maybe "small" should be calibrated by the claims of the model?
At least for the three examples you cited, I seem to remember them bring called approximations, not "correct".
What's the difference between a singularity, and an approximate singularity? :-)
In the former case, it progresses asymptotically, while in the latter, it progresses exponentially or super-exponentially but not asymptotically.