In many systems you can predict larger scale events (when the pot of water will boil) despite being unable to predict smaller scale ones (turbulent flow inside the pot).
Your pot of boiling water prediction is based on past experience, not modeling of the smaller scale system. Climate science is akin to modeling turbulent flow inside the pot to predict when the pot will boil.
All modelling is based on past experience. The usefulness of a model is the degree to which you can abstract it from that experience.
In the case of the pot of water, you can observe the energy input into the system and combine that with some very generic, simple, and reliable physical models to determine when it will boil.
I'm not claiming that climate science is that simple, of course. My point is that some systems are more easily predicted at a larger scale than a smaller one.
To take a similar example, you can derive the ideal gas law from the kinetic theory of gasses. Which is to say, you can start from the idea that gasses are composed of small particles that move constantly and collide with each other and with their container, and turn that into an accurate description of macroscopic behavior. This works well despite the fact that it remains impossible to predict the motion of an individual gas particle for more than an extremely short distance or time.
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In many systems you can predict larger scale events (when the pot of water will boil) despite being unable to predict smaller scale ones (turbulent flow inside the pot).
Your pot of boiling water prediction is based on past experience, not modeling of the smaller scale system. Climate science is akin to modeling turbulent flow inside the pot to predict when the pot will boil.
All modelling is based on past experience. The usefulness of a model is the degree to which you can abstract it from that experience.
In the case of the pot of water, you can observe the energy input into the system and combine that with some very generic, simple, and reliable physical models to determine when it will boil.
I'm not claiming that climate science is that simple, of course. My point is that some systems are more easily predicted at a larger scale than a smaller one.
To take a similar example, you can derive the ideal gas law from the kinetic theory of gasses. Which is to say, you can start from the idea that gasses are composed of small particles that move constantly and collide with each other and with their container, and turn that into an accurate description of macroscopic behavior. This works well despite the fact that it remains impossible to predict the motion of an individual gas particle for more than an extremely short distance or time.