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Just for fun. The equations are simple, basic high school extended course, or an elementary, entry college level course. I can write a physical model for a bullet (I have in my video game hobby). Now, that model will behave exactly like a bullet, for the purposes of a video game simulation. No one would no the wiser, indeed, the US Army has their own little FPS game where they train young adults to be merciless killers. The video game Americas Army is actually one of the best simulators around.
You could take a thousand bullets in real life, fire them on a shooting range, and they will compare to the video game simulation, in fact, over a long term average they should be identical (randomness is inserted into the bullet trajectory, as in a first person shooter with a gun that isn't stable). And that's where the models come in.
The models themselves are static (as in, the code itself doesn't self-modify, or whatever), there's only one model, though the results are always going to be different, it isn't the model itself that changes, simply the simulation run.
Now, just like with those bullets in the video game, one run is not going to be representative of real life. A thousand runs? A million runs? They average is where the accuracy lies.
And every single model follows the temperature record to the tee, well within any margin of error.
It would take a quantum computer, or a second planet to actually "run our model" in real time, with exact results. Likewise, it would take a quantum computer, or more computing power in the world to render the trajectory of a bullet exactly. Every atom in the bullet, every atom in the air that it passes through, ever atom in the combustibles, every atom in the gun shaft and triggering mechanism.
This is why, when people say 1) the models aren't perfect simulations or 2) they can't predict weather (distinct from climate), I wind up shaking my head. Because you're not going to get that in a million years.
We landed on the moon with 2 kb of RAM, this is less ram than what is in a modern calculator. You don't *need* absolute simulations to be able to achieve accuracy.
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