Words, Episode 3: Linear

One of the obstacles to learning in mathematics and physics is the fact that there are many closely related concepts, although logically distinct. Additionally, the same structures (logical or mathematical) occur over and over again in our mathematical models of the world. For both reasons, the same word is sometimes used to mean several different … Read more

Black Earth Into Yellow Crocus

Perhaps my favourite joke of all time is actually an anecdote that I read in the wonderful book Thirty Years that Shook Physics, by George Gamow. The book is available in an inexpensive Dover edition, and would make a fine complement to a course textbook in modern physics, which amounts to introductory quantum mechanics. Gamow … Read more

The Power of Abstraction

One of the reasons mathematics is powerful and useful is that it is abstract. A collection of abstract symbols may seem sterile, but the power is in the hands of the practitioner, for you can give the symbols whatever meanings you please. Consider Boolean algebra, an abstract system of rules for symbolic expressions. As an … Read more

Helping People Get Things Done

Seth Godin has a fantastic blog, and today’s post makes pointed comments about education, although it is more generally intended to discuss how to help people get things done. Check it out here. (This post first appeared at my other (now deleted) blog, and was transferred to this blog on 25 January 2021.)

The Field Concept in Physics

Let’s continue the story in the previous post about Newtonian mechanics. In Newton’s theory of gravity, two objects that have mass attract each other with a gravitational force simply by virtue of their mass. The strength of the force is proportional to the product of the two masses, and inversely proportional to the square of … Read more

Newton’s Vision

Science has revolutionized the way we live thanks to its influence on technology, but it’s perhaps less well-known how science has utterly transformed the way we think about the world. For example, in ancient times it was thought that the earthly realm was separate from the heavenly realm. God, or the gods (depending on belief) … Read more

Scott Aaronson’s Doofusino Theory

Scott Aaronson has a delightful blog, where he discusses quantum computation and computational complexity in a very light-hearted style. He’s a great writer and very instructive. A good example of his satire is his classic creation, doofusino theory. (This post first appeared at my other (now deleted) blog, and was transferred to this blog on … Read more

The Disney World of Good vs. Evil

One of the traditional purposes of culture is to educate. Before books were common, the spoken word was the essential tool for teaching. Stories are memorable, and so telling stories was an effective way to pass on life lessons, particularly moral lessons. But in recent times, “information media” have been used overwhelmingly often only for … Read more