We just took a voyage through scales, noticing structures in cloud photographs and wiggles on graphs. Collectively, they spanned ranges of scale over factors of billions in space and billions of billions in time. We are immediately confronted with the question: How can we conceptualize and model such fantastic variation? Two extreme approaches have developed. For the moment, I call the dominant one the new worlds view, after Antoni van Leeuwenhoek (1632– 1723), who developed a powerful early microscope. The other is the self- similar (scaling) view by Benoit Mandelbrot which I discuss in the next section. My own view— scaling but with the notion of scale itself an emergent property— is discussed in Chapter 3. When van Leeuwenhoek peered through his microscope, in his amazement he is said to have discovered a “new world in a drop of water”: “animalcules,” the first microorganisms (Fig. 2.1). Since then, the idea that zooming reveals something completely new has become second nature. In the twenty- first century, atom- imaging microscopes are developed precisely because of the promise of such new worlds. The scale- by- scale “newness” idea was graphically illustrated by K. Boeke’s highly influential book Cosmic View, which starts with a photograph of a girl holding a cat, first zooming away to show the surrounding vast reaches of outer space, and then zooming in until reaching the nucleus of an atom. The book was incredibly successful. It was included in Hutchins and Adler’s Gateway to the Great Books, a ten- volume series featuring works by Aristotle, Shakespeare, Einstein, and others. In 1968, two films were based on Boeke’s book— Cosmic Zoom and Powers of Ten (1968, re- released in 1977), encouraging the idea that nearly every power of ten in scale hosts different phenomena. More recently (2012), there’s even the interactive Cosmic Eye app for the iPad, iPhone, or iPod, not to mention a lavish update: the “Zoomable Universe.”
