I read the following in a review of Lewis Wolpert's new book, Six Impossible Things Before Breakfast: The Evolutionary Origins of Belief: "There are more molecules in a glass of water than glasses of water in the oceans." Apparently, Wolpert uses this as an example of the almost miraculous breakaway of scientific thinking from our intuitive understanding of the world.
And, indeed, when you think about it, there is absolutely no way one could make a statement like this without the full array of mathematical reasoning and quantitative observation that has characterized the scientific way of thinking since the time of the Alexandrians. Archimedes, for example, might have made a reasonable guess for the number of glasses of water in the oceans. (He had a fair idea of the size of the Earth and might have made a decent stab at the depth of the oceans.) He would not, of course, have been able to estimate the number of molecules in a glass of water.
Anyone even modestly trained in science today can do both. By my back-of-the-envelope calculation, there are about 10 to the 25th water molecules in a glass (1 followed by 25 zeros), and about 10 to the 22nd glasses of water in the oceans.
No shaman, magician or high priest of yore had such power at his fingertips.