Blog Archives

How Transistors Work

Suppose you learned that transistors are a fundamental building block of modern electronics, and you decided to learn about how they function. If you looked at the first result in a google search you would see this Wikipedia article filled with technical details, but not that much beginner-friendly clarity. As with many such important concepts, explaining it at just the right level of detail to be both technical and accessible is a serious challenge.

To the rescue comes Derek Muller, creator of the Veritasium Youtube channel, who demystifies the idea behind transistors. His video features just the right type of animations and visual props to make a point without getting lost in technical details that would only be relevant to graduate students or scientists. If you’re interested in electronics, this six minute video is as good a starting point as any textbook or lecture.

A Short Animated Introduction to Reading Music (And a Bit of Bach)

Although numerous studies have shown the importance of music education in schools, few students learn the basics of music theory as part of core curriculum requirements. Apart from the obvious reasons, this is unfortunate because music is so intertwined with math and science and has been a source of inspirations for many great mathematicians and scientists. In fact, Albert Einstein once said that “the theory of relativity occurred to me by intuition, and music is the driving force behind this intuition. My parents had me study the violin from the time I was six. My new discovery is the result of musical perception.”

If you have never learned how to read music, the following animation by Tim Hansen does a good job of conveying the essentials. After you watch it, listen to some Bach (i.e. mandatory music for mathematicians) and watch an incredible visual representation of music that is rich in mathematical structure. Enjoy!


A Simple Animated Explanation of Free Falling and Zero Gravity

As children we first learn about the notion of weightlessness in outer space and the idea of zero gravity, but these concepts are actually a bit more nuanced than may appear. For example, why satellites orbit Earth instead of crashing into it because of Earth’s gravitational pull can be a mystery if you have never studied physics. The following TED Education animation does a good job of illustrating the basic principle behind orbiting objects without going into too many details.

If you’ve been exposed to high school physics, the Wikipedia article on weightlessness is uncharacteristically clear on some of the more advanced aspects of the subject. In particular, you may be surprised to learn that Einstein in developing his theory of relativity realized that gravitational interaction cannot be felt when all other forces are removed and this led him to consider the possibility that gravity is the result of the curvature of space. If you’re interested in the details of relativity and a modern interpretation of Newtonian mechanics, Leonard Susskind’s set of physics lectures is the best place to start.

An Animated Introduction to Ontology: Is a Copy the Same as the Original?

Questions of equality and equivalence are of fundamental importance in mathematics and computer science. In everyday use we are usually comfortable with a vague definition of equality, but in programming for example, two objects may be identical in one instance and different in another. This is usually a great source of confusion for inexperienced programmers. In mathematics, equality has multiple meanings and uses and even basic subjects like high school geometry introduce the notions of similarity and congruence that represent two different levels of equality.

Of course, equality and equivalence are also part of the branch of philosophy called ontology. In the following classic animation, John Weldon presents the topic as a fun thought experiment that asks the question: what does it mean to be? Watch it and be amazed by the philosophical nuances of existence.

Two Minutes of Thermodynamics: Heat Versus Temperature

Sometimes a simple drawing or animation is all that it takes to understand a previously confusing idea. A good illustration of this principle is the following video by Henry Reich which does a good job of explaining the difference between heat and temperature. These two concepts are clearly related but students often erroneously equate them, especially when they first start thinking about them in science class.

A similar, but much older animation from the Eureka! Science series also addresses this thermodynamics issue, but from a slightly different perspective. If you have five minutes to spare, you won’t regret getting a better grasp of this fundamental area of physics.

The Seasons Simply Explained

The fact that certain months are hot and others are cold is so deeply ingrained in our brains that we take it for granted. Fortunately, it doesn’t take advanced science to explain the basics behind this phenomenon. In the “Reasons for Seasons” animation below, Rebecca Kaplan talks about the science of seasons as if she is reading a fairy tale, not giving a serious lecture. This makes for wonderful bedtime learning even if you’re already a serious adult.

Dimensions: A Beautiful Excursion Through Geography, Geometry, and Topology

Unfortunately, some of the most beautiful mathematics is hidden from most people because it is so difficult to visualize. A good explanation has limited reach when the discussion at hand is about geometry, especially when it spans more than two dimensions. We may have an abundance of technology to help illustrate the subject, but someone still needs to spend an enormous of time and energy creating the kind of visualizations that are mathematically accurate, yet breathtaking. Fortunately, a group of French engineers, mathematicians, and education enthusiasts have done some of this hard work and produced Dimensions, an incredible nine part animated film that is nothing short of a visual feast featuring some of the most important and beautiful ancient and modern mathematics

The first chapters of the film introduce geography and the geometry of the sphere. Later chapters extend our intuition about two and three dimensions to four dimensions. The final chapters are more advanced but present a fairly elementary treatment of complex numbers and some topology. Every new idea is presented by an important mathematical personality, putting the whole narrative into a historical context. Although you can watch all nine chapters in one sitting, they are not all connected and it might be easier to watch them separately. The film website has a useful guide to help you choose what to watch, and we can’t recommend watching it enough.

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.

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.