George Malcolm: half white, half black, with messy tousled hair, rumpled and tugged between kind of curly and extremely curly. Once, a year or so before, he'd been at our house and he'd pulled out a lock of his hair and used it to teach me about eddies and helixes. It's a circular current into a central station, he'd explained, giving me one to hold. I pulled on the spring. Nature is full of the same shapes, he said, taking me to the bathroom sink and spinning on the top and pointing out the way the water swirled down the drain. Taking me to the bookshelf and flipping open a book on weather and showing me a cyclone. Then a spiral galaxy. Pulling me back to the bathroom sink, to my glass jar of collected seashells, and pointing out the same curl in a miniature conch. See? he said, holding the seashell up to his hair. Yes! I clapped. His eyes were warm with teaching pleasure. It's galactic hair, he said, smiling.At school, George was legendary already. He was so natural at physics that one afternoon the eighth-grade science teacher had asked him to do a preview of the basics of relativity, really fast, for the class. George had stood up and done such a fine job, using a paperweight and a yardstick and the standard-issue school clock, that the teacher had pulled a twenty-dollar bill from his wallet. I'd like to be the first person to pay you for your clarity of mind, the teacher had said. George used the cash to order pizza for the class. Double pepperoni, he told me later, when I'd asked.
From a philosophical point of view, Leibniz's most interesting argument was that absolute space conflicted with what he called the principle of the identity of indiscernibles (PII). PII says that if two objects are indiscernible, then they are identical, i.e. they are really one and the same object. What does it mean to call two objects indiscernible? It means that no difference at all can be found between them--they have exactly the same attributes. So if PII is true, then any two genuinely distinct objects must differ in at least one of their attributes--otherwise they would be one, not two. PII is intuitively quite compelling. It certainly is not easy to find an example of two distinct objects that share all their attributes. Even two mass-produced factory goods will normally differ in innumerable ways, even if the differences cannot be detected with the naked eye.Leibniz asks us to imagine two different universes, both containing exactly the same objects. In Universe One, each object occupies a particular location in absolute space.In Universe Two, each object has been shifted to a different location in absolute space, two miles to the east (for example). There would be no way of telling these two universes apart. For we cannot observe the position of an object in absolute space, as Newton himself admitted. All we can observe are the positions of objects relative to each other, and these would remain unchanged--for all objects are shifted by the same amount. No observations or experiments could ever reveal whether we lived in universe One or Two.