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ChristianKl comments on Rationality Quotes May 2014 - Less Wrong
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Empty water bottles don't exactly fall faster than full water bottles.
But my point isn't about whether you rely or authority or don't but on how people actually make decisions. There literature on phenomenological primitives in physics.
The one time we tested the theory of gravity experimentally in school I did not get numbers that the Newtonian formula predicted. At the same time I don't think those formula are wrong. I believe them because smart people tell me that they are true and I don't care enough about physics to investigate the matter further.
Through air full water bottles do fall faster than empty ones.
LOL. "Who are you going to believe, me or your lying eyes?"
A bit maybe but I think they should have roughly the same speed. How much faster do you think they would fall?
Sometimes you have to make hard choices...
There was a time were I thought it was about picking sides and being for empiricism or against it. I'm well past that point. There are times when believing the authority is simply the right choice.
If the fall is sufficiently long, they reach different terminal velocities, which are proportional to the square root of their masses.
According to the Teh Interwebz, an average 0.5 litre empty plastic bottle weights about 13 g. A full bottle weights 513 g. Therefore, at terminal velocity it falls about 6.3 times faster.
What does sufficiently long mean in practice?
It depends on the drag coefficient and forward projected surface area of the bottle. My mildly informed guess is that it would take between 20 and 30 seconds.
EDIT:
Actually, I've just tried dropping 1.5 litre bottles from an height of about 1.8 m. Even if the fall lasts perhaps one second, the empty bottle starts to tumble much more than the full one, and hits the ground a noticeably later.
In epistemic matters? I don't think so.
Information isn't free and there are many cases where gathering more information is too expensive and who have to go with the best authority that's available.
On the other hand it's worthwhile to be conscious of the decision that one makes in that regard. Most people follow authorities for all the wrong reasons.