Instead, we must consider the full statistical ensemble of possible world, and quantify to what extent the butterfly shifts that ensemble.
add some small stochastic noise to it at all times t to generate the statistical ensemble of possibilities
In the typical scenario, the impact of this single perturbation will not rise above the impact of the persistent background noise inherent to any complex real-world system.
I think these quotes illustrate the mind projection fallacy. The “noise” is not an objective thing sitting out there in the real world, it is a feature of your own uncertainty.
Suppose you have a computational model of the weather. You make the simplifying assumption that water evaporation is a function only of air temperature and humidity. Whereas in reality, the evaporation depends on puddle formation and plant growth and many other factors. Out in the real world, the weather follows its own rules perfectly. Those rules are the equations of the whole universe. “noise” is just what you call a hopefully small effect you don’t have the knowledge, compute or inclination to calculate.
If you have a really shoddy model of the weather, it won’t be able to compute much. If you add a butterflys wing flaps to a current weather model, the knowledge of that small effect will be lost due to the mass of other small effects metrologists haven’t calculated. Adding or removing a butterfly’s wingflap doesn’t meaningfully change our predictions given current predictive ability. However, to a sufficiently advanced future weather predictor, that wingflap could meaningfully change the chance of a tornado. The predictor would need to be tracking every other wingflap globally, and much else besides.
We are modelling as probabilistic processes that are actually deterministic but hard to calculate.
I think these quotes illustrate the mind projection fallacy. The “noise” is not an objective thing sitting out there in the real world, it is a feature of your own uncertainty.
Suppose you have a computational model of the weather. You make the simplifying assumption that water evaporation is a function only of air temperature and humidity. Whereas in reality, the evaporation depends on puddle formation and plant growth and many other factors. Out in the real world, the weather follows its own rules perfectly. Those rules are the equations of the whole universe. “noise” is just what you call a hopefully small effect you don’t have the knowledge, compute or inclination to calculate.
If you have a really shoddy model of the weather, it won’t be able to compute much. If you add a butterflys wing flaps to a current weather model, the knowledge of that small effect will be lost due to the mass of other small effects metrologists haven’t calculated. Adding or removing a butterfly’s wingflap doesn’t meaningfully change our predictions given current predictive ability. However, to a sufficiently advanced future weather predictor, that wingflap could meaningfully change the chance of a tornado. The predictor would need to be tracking every other wingflap globally, and much else besides.
We are modelling as probabilistic processes that are actually deterministic but hard to calculate.