Blog Archives

One Hour With Richard Feynman: Imagining How Nature Works

Once in a rare while, a genius unlocks a secret of nature, moves humanity forward, and secures a prominent place in the annals of science. Sometimes, more rarely, that same person, also conveys the excitement of discovery and the most complex phenomena in the simplest most beautiful language. Richard Feynman, one of the greatest physicists of the twentieth century, is that extremely rare person. In this one hour documentary he talks about the wondrous ways of nature with the air of someone who is both the keeper of its secrets and who is at the same time as fascinated by it as a child. Feynman talks about the jiggling of atoms to explain heat, surface tension of water, and how fire work. He discusses magnetism and reveals why any “why” question can lead to an infinite rabbit hole of explanations. This video should be mandatory viewing for anyone studying science and should be a powerful reminder about the power of imagination, not just the power of theory.

For the Love of Physics: Science as a Performance Art

Inspiring future scientists takes great teachers who are often talented performers. The beauty of physics as an academic subject is that it lends itself well to awe-inspiring demonstrations and performances. Walter Lewin, an MIT physics professor and legendary lecturer, is one of those talented teachers and performers who squeezes out of physics every drop of excitement that can be conveyed to a lay audience. In this lecture, filled with some of his most famous demonstrations, he puts his life on the line to illustrate the principles of classical mechanics, explains why the sky is blue while clouds are white, and leaves the lecture hall on a rocket. The lecture does not require mathematical sophistication, which makes it accessible to middle school students, but it will inspire anyone to pursue physics.

The Origins of Writing and the Development of Language as Technology

We take written language for granted because it defines what it means to be literate in our modern world, but it is a part of our technological and scientific progress, no less important than electricity or algebra. The story of how written language developed is complicated, with multiple interconnected threads and missing details, but it is worth thinking about especially as one studies the language of mathematics. As language develops the ability to express increasingly more abstract ideas, its syntax and semantics have to evolve and this is especially visible in modern mathematics. This short video by Mathew Winkler traces the origins of written language and reveals how it’s increasing compactness led to increased power. It might even spark an interest in linguistics and make you feel better about struggling with new mathematical terminology.

Zeno’s Paradox: Is Movement Possible?

Sometimes when you think really hard about something, you can reach a conclusion so contradictory to everyday experience, that it forces you to reexamine fundamental scientific and mathematical truths. That is exactly the predicament that Zeno of Elea, a Greek philosopher, reached almost two and a half thousand years ago. His famous Dichotomy paradox proposes that getting from point A to point B is impossible because it involves an infinite number of steps, which must take an infinite amount of time. As it turns out, the modern mathematics of calculus and infinite series is required to rigorously resolve this dilemma, but an intuitive explanation that captures the essence of the solution is possible. In his excellent animation, Colm Kelleher illustrates both the paradox and its resolution, and you don’t even need to know any calculus to understand the solution. This video is a good place to start when introducing the topic of infinite series and is also one more way to make a discussion of infinity more concrete.

Street-Fighting Mathematics: Inexact Reasoning Leading to Deeper Understanding

All too often school teaches us to “guess and check” when a simple exact calculation would lead to the right answer. Guessing the answer to a one variable equation may not further our mathematical knowledge, but is it possible that guessing can lead to deep insights? According to Sanjoy Mahajan, physicist and author of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving [PDF], the answer is yes. He makes the case that by using certain basic problem solving strategies one can avoid rigorous and complicated calculations while the result will be the same. Moreover, these strategies and the solutions that they yield lead to a deep understanding of the subject matter. The book is full of examples from mathematics, engineering, and physics and although some parts require knowledge of calculus, it should be accessible to motivated high school students. As a bonus, it is freely available from MIT Press. Here is a TEDx talk that the author gave illustrating the street-fighting techniques in his book.

Why Does Earth Have Deserts and Related Questions Answered

Some facts are so ingrained in our consciousness that we can’t avoid taking them for granted. We accept the existence of deserts, but unfortunately we rarely wonder why they exist where they do and what causes their creation. Once again, Henry Reich brings the subject to life with a brief but beautifully simple animation that attempts to answer these questions. Because the video is fast-paced, you might need to pause it once or twice to make sure you didn’t miss anything, but it is an extremely satisfying feeling to learning something completely new after spending just 2 minutes. Of course in order to be concise, the video glosses over several important details including an explanation for why cold air doesn’t hold moisture as well as warm air (here is an explanation and two instruction activities to go with it), but this leaves room for further exploration.

A Short Animated Foray into the Physics of Parallel Universes

Before you get into the nitty-gritty of math and physics it helps to get fired up about the subject. Thanks to Henry Reich of MinutePhysics you can get a quick curiosity-arousing peek at the latest thinking on the possible existence of multiple universes. None of the presented theories can be experimentally tested currently, but these flights of fancy will spark anyone’s imagination. After all, imagination, not simply the dry application of scientific principles leads to scientific progress.

A Miniature Introduction To Infinity

Infinity is a topic that has for ages caused a great deal of both fascination and confusion among students. It is a mathematical abstraction that unlike other abstractions seems hard to make concrete. The fact there is more than one type of infinity and that infinity is often treated like a number but is not an element of what we know as the real numbers adds to the confusion. The charming little video below from the Open University takes a sixty second look at Hilbert’s paradox of the Grand Hotel, a comic, yet mathematically serious example of how to think about infinity. The name is a bit of a misnomer as it’s not really a paradox, but simply a question with a somewhat counterintuitive answer. The animation does not explore all aspects of Hilbert’s thought experiment, but it is a good start that will pique anyone’s curiosity.

The Scale of the Universe and How We Measure It

Students often ask about the existence of the largest, smallest, or most distance objects that exist. These questions undeniably provide intellectual entertainment, especially when we can visualize the answers with ease. Take a look at this beautiful interactive animation created by Cary and Michael Huang to get a sense of the the kinds of distances and sizes that exist in the universe, and then look at the Royal Museums Greenwich animation that introduces the physics of measuring distances to macroscopic objects in the Universe. The video skips the details of how some of the distances are calculated but is a good starting point for further geometrical explorations that are not beyond the school curriculum.

The Story of Martin Gardner and Mathematics as Magic

Martin Gardner, one of the greatest recreational mathematicians of all time, is responsible not only for helping popularize mathematics as an art form and as a form of recreation but for inspiring a generation of future mathematicians to pursue it as a profession. He wrote the Mathematical Games column for Scientific American for a quarter of a century, and his mathematical and scientific gems have found their way into dozens of foreign publications as well as numerous research papers. The Nature of Things documentary gives the viewer an up close look at Martin Gardner’s work and the work of other people with whom he collaborated. If you’re looking for some mathematical entertainment with serious mathematical substance, or simply want a glimpse into the playful nature of mathematics and mathematicians, this is a highly recommended film.