3 ms·

Shortcuts 100% exist. Imagine another physical problem. Simulating a sand grain and how it bounces off other sand grains or lodges against them. If you want

Shortcuts 100% exist. Imagine another physical problem. Simulating a sand grain and how it bounces off other sand grains or lodges against them. If you wanted to simulate a sand mountain, you could use a massive amount of compute and predict the location and behaviour of every single grain. Or, you could take a bunch of well-known shortcuts and just know that sand sits in a heap at the angle-of-repose. That angle decides how steep the mountain will be. any steeper and it will tumble till it's at that angle. Suddenly, the computation is dramatically reduced, and you get pretty much the same result.

tovej 3y ago
The point was that weather, unlike a sandheap, is a chaotic hydrodynamic system with turbulent flows, that means it's computationally intractable to do exactly, which is why weather forecasts are only good for a few days anyway. The example you gave does not really explain anything.
- londons_explore 3y ago
  The sandheap is chaotic too - just one sand grain tumbling can be enough to start a landslip. But the end result tends not to depend on the minute details - if sand grain A didn't cause the landslip, then a few seconds later sand grain B would have.
  - tovej 3y ago
    That's not chaos, the outcome is the same even if the input varies. Chaos is when the outcome differs greatly with small changes in input.
twayt 3y ago
You get the same result in a short span of time, heck you may even get a reliable error bound. Where this falls apart is that error accumulates over time and not just for one heap of sand but for many such heaps of sand that also interact with other heaps of sand. Predicting weather for the next hour is trivial. Aviation runs on the fact that you can forecast fairly accurately into the next hour most of the time. The difficulty scales superlinearly over time due to the error accumulation over predictions

tovej 3y ago

The point was that weather, unlike a sandheap, is a chaotic hydrodynamic system with turbulent flows, that means it's computationally intractable to do exactly, which is why weather forecasts are only good for a few days anyway. The example you gave does not really explain anything.

londons_explore 3y ago
The sandheap is chaotic too - just one sand grain tumbling can be enough to start a landslip. But the end result tends not to depend on the minute details - if sand grain A didn't cause the landslip, then a few seconds later sand grain B would have.
- tovej 3y ago
  That's not chaos, the outcome is the same even if the input varies. Chaos is when the outcome differs greatly with small changes in input.

twayt 3y ago

You get the same result in a short span of time, heck you may even get a reliable error bound. Where this falls apart is that error accumulates over time and not just for one heap of sand but for many such heaps of sand that also interact with other heaps of sand. Predicting weather for the next hour is trivial. Aviation runs on the fact that you can forecast fairly accurately into the next hour most of the time. The difficulty scales superlinearly over time due to the error accumulation over predictions