Let inspiration be your compass

This book is about the lost lecture of Richard Feynman on the motion of the planets around the sun. It is not a book by Feynman but by David and Judith Goodstein. The book contains Feynman’s elementary proof that planets move in elliptical orbits around the sun (being one of the focus points) by first showing that the so-called velocity orbit of each planet is a perfect circle. For this fact he “only” needs the famous laws of Newton and the law of gravity. Elementary, but not simple at all. Feynman's reasoning is based on the work of Sir Isaac Newton, however he deviates at the point where he could not follow the arguments of Newton anymore. Feynman challenged himself in providing a geometric proof in the tradition of the ancient scholars instead of using the nowadays more custom analytical methods. As he states himself his proof is elementary but not simple. The whole idea behind this proof is truly elegant. Instead of focusing on the orbit swiped out by the "position...

This book is about the life and work of Kurt Gödel. And what better way to start a book on Gödel’s Incompleteness theorems, by adding, as a first note in your book, a self-referencing note? That is what Rebecca Goldstein does in “Incompleteness”, by ending her first note with an additional note that there are two types of notes used in her book, namely footnotes and endnotes. But in her charming book she does much more than only adding notes to some theorems, by explaining that self-reference, and the logical paradoxes it leads to, are really at the heart of Gödel’s proof of his incompleteness theorems. She outlines the proof very well leaving out the technical details, but in such a way that an interested layman can still appreciate the crux of it. Next to her explanation on the incompleteness theorems, she does a great job by putting the work done by Kurt Gödel in its historical context and describing the man behind the theorems. And what a man Gödel was: closely befriended with Al...

In this age of technology, this era of digital revolutions, the question becomes more and more relevant how far technology can get us and what its limitations are. Surprisingly enough, already one century ago, even before the first computers existed, these limits have been settled. These had been found by Kurt Gödel and Alan Turing. They proved that so-called “self-reference” was always inevitably leading to logical paradoxes destroying the rigorous foundations of both mathematics and computer science. Self-reference is the ability to completely describe yourself - stepping back and reflect on yourself. Their proofs are ingenious, both simple on the high level as complicated on the detailed level. But let’s take some time to step back and reflect ourselves; bear with me and try the following thought-experiment to better understand what Gödel and Turing were saying. Suppose I would offer you the perfect VR device, that is one where you cannot not tell the difference between the "...

This book is about quantum electrodynamics, the theory which describes how light and matter interact on the smallest scales. As can be expected from any book by Richard Feynman, this book is a joy to read. Feynman manages to explain in clear layman's terms why it seems that light travels by straight lines, how light reflects from surfaces, why it behaves wave-like and how light-particles interact with electrons. In the final part of the book he concludes with an appetizer on the so-called quantum chromodynamics (QCD), which is the theory of the (strong) interaction between even more exotic particles. Feynman takes the reader by the hand starting with simple examples and step-by-step advance on those examples pointing out the strangeness of the theory when scales or distances get very, very small. It would not make sense to summarise here what is so perfectly described in his book, best is to read it yourself. However I want to mention the main take-out for me, which is that the ...

Were you ever, when taking a bath, suddenly struck by the insight that the upward force on your body by the surrounding water is equal to the weight of the water displaced by your body? It’s a matter of balance between the displaced weight and the induced upward force. It inspired Archimedes to his law of up-thrust. Were you ever, when taking a nap, suddenly awaken by the fall of an apple on your head, and came to realize that you were hit by the force of gravity? The same gravity holds the moon into orbit, and, less distant, our airplanes. This was also a matter of balance, which inspired Newton to his famous laws of gravity. And did you ever look at a pocket compass and wondered what it was in the surrounding empty space that was moving the needle? Where do you go to when there is nothing surrounding you? This wonder inspired Einstein to his theories of relativity and gravitation.All these great men were inspired by Mother Nature to represent the real world by simple models. Their i...