2. Relatively short chapter and review today. The chapter is basically about a debate that Isaac Newton and Gottfried Leibnitz had over whether space really existed or was just a concept we invoked to compare objects to each other. The force of Newton's person in the 1600s made it difficult for anyone to win against him.
So Newton's bucket scenario asked why the water in a spinning bucket first is flat and then concave, but that if the twisted rope holding the bucket slowed down and stopped, the water continued to be concave. Newton's answer that space was absolute. The water had a position relative to absolute space. So you could feel changes in acceleration because of the change in relation to absolute space.
3. Leibniz believed that space wasn't anything. Space is just what we call the relation between things. Leibniz pretty much lost the bucket argument in the 1600s, but Ernst Mach revived it in the 1870s. Mach suggested that it's only the matter in the universe, its collective gravity, that would make us feel ourselves spinning in space. There is no absolute space.
So Mach argued that we would not know any difference between spinning or not spinning in a completely empty universe. In a universe half as full, we would only be half as much aware, etc. "You feel acceleration only when you accelerate relative to the average distribution of other material inhabiting the cosmos" (37).
4. This sets us up for Einstein, who apparently showed that Mach and Leibniz were the winners on this one, not Newton.
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