Our Mathematical Universe, by another physicist. The basic notion of the book looked interesting to me. Could it be that the universe is not just able to be described by mathematics. Could the universe be mathematics, a "giant mathematical object" (6).
I took the author to be a Pythagorean of course, not too different from Plato, for whom ideas were the ultimate reality. For Pythagoras, though, number was the ultimate reality.
1. Two chapters in, the book isn't what I'd really expected. But I think I should finish it. The guy's agent suggested he write the book in a somewhat personal style. I'm sure I'll appreciate it.
2. The title of this post relates to the second chapter, "Our Place in Space." In it, Tegmark reviews the process by which we came to infer the size of the earth, the moon, and the sun. He explains where our sense of how far away the sun and the stars comes from. Lastly, he asks what space is. Is it infinite or finite?
It is truly amazing to read of how ingeniously these measures were made. I certainly puts my limited smarts in their place. Even more sobering is to realize how many Americans of unremarkable intelligence somehow feel competent to dismiss such things.
"How far away are the stars and what are they made of?" Can't you hear some wise ignoramus sitting in a bar saying, "There's no way they can know that. They're just making it up."
In the 200s BC Eratosthenes in Egypt used the distance between two cities in Egypt and the number of degrees difference in the angle between the two cities and the sun to calculate the circumference of the earth.
Aristarchus of Samos at the same time used lunar eclipses to figure out the distance to the moon and its size. Using trigonometry, he made a good attempt at inferring the distance to the sun and its size. The result was a proposal that the earth goes round the sun two thousand years before Copernicus.
On and on the chapter goes. The ability to break down a spectrum of light in the 1800s answered our questions about the composition of stars. Many other deductions, simply following our knowledge of how things work here, helped answer other questions of temperature, pressure, mass, distance, etc.
3. The chapter ended with some anticipation of how general relativity has changed our sense of space, particularly how space bends. Space would not need to go on infinitely because it could possibly bend back on itself. In other words, if you went far enough in one direction, you would eventually come back from the other. Tegmark doesn't actually lean that way, as I think we'll see.
A final observation is that we should not expect common sense to be of much good when it comes to the greatly small or massively big. Human experience was not designed to have common sense about such things. Human experience is designed to work in the "our size" world.