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Clarity comments on Open Thread, Jun. 8 - Jun. 14, 2015 - Less Wrong Discussion
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Let's have fun offering what-have-you questions for Fermi estimates! If we are here for fun, at least partially, let's save some in quantifiable form. Here's mine:
Would a standard piece of soap (neutral pH, lens-like shape) sink to the bottom of the Mariana Trench, or will it get dissolved on the way down?
The soap keeps more or less constant density as it sinks, but the water is denser the deeper you go. And the density of soap is really close to that of water, so I expect that there is some depth at which the soap has the same density as the water, and when it gets to that level it stays there. And eventually it dissolves or gets eaten.
Dissolved, 60% probability. (I guess the quantity of soap does not diminish as easily through friction with water as through friction with skin, but still, that's a boatload of water.) Sink, 30% probability. And here and now I announce to the world that I don't have good enough intuitions for the Law of Archimedes, so 10% it would float. (And eventually dissolve. Maybe.)
Here's mine: Without looking it up, what percentage of Chinese adults are employed in manufacturing? Is it more or less than 30%? Data that would be accurate for any year between 2006-2015 is a good answer.
Some soap floats, most soap bars sink.
Although I didn't find any international standard, it appears most soap bars weigh 4 oz, which is Yankee for 113.4 grams. However, my research was stopped by this graphic of Pacific oceanic currents. The downward trajectory of that soap bar isn't going to be vertical at all; an additional question could be: where in the Pacific should you drop your soap bar for the currents to take it to the Mariana Trench?