“but a lot of very small uncertainties do add up”
In the sciences, uncertainty decreases with the number of repeateable experiments, in other words, uncertainties deminish by the inverse ration of the number of repititions.
Imprecisions can add up (as happens in cumputers), but not uncertainties.
If you think uncertainties can “add up,” can you give an example of how that would happen?
Hank
Sure. Lets take global warming for example.
CO2 is a green house gas. Doubling it will raise the temperature of the Earth apx. .8 to 1.2 degrees. Then the forcing's come into play. Water vapor is a positive forcing in the 1 to 5 times range, but lower level clouds are a negative forcing in the 2 to 5 times range and thunderstorms are also an unknown negative forcing as are most weather patterns like hurricanes. Then there are other variables like cosmic rays, solar radiation, UHI effects, Satellite measuring errors, etc. etc.
Each one of those items listed is known to a reasonable degree of accuracy. And if you think that the uncertainties diminish by the inverse ratio of the number of repetitions then I am sure that you can definitively forecast the exact temperature for Butte Montana June 18th, 2009 at 7 PM.
Heck I will be generous and give you a .10 degree error range : )