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.

The Five Second Rule: A Simple Everyday Question Leading To Quantum Mechanics and Biology

Sometimes the simplest question can lead down a deep rabbit hole to new worlds. How fast germs contaminate food that falls on the floor is a good example of such a question. When you start to think about it, you realize that you don’t quite now what it means for two objects to touch, and when you start analyzing the microscopic and then the quantum mechanical details, you cross multiple scientific disciplines.

This is the intellectual journey that Michael Stevens goes on in his video that debunks the “five second rule,” a popularly held belief that food that falls on a dirty floor is safe to eat if it is picked up quickly enough. One of the main benefits of this type of video is its ability to connect seemingly unrelated issues and motivate viewers to conduct their own thought experiments. You may think it’s a silly question, but you’re sure to be surprised by at least some aspects of the answer.

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.

A Comprehensive Introduction to Information Theory for Complete Beginners

The term ‘information age’ is a modern cliche, yet few realize that the word information has a precise mathematical meaning with far-reaching consequences. Information theory is one of the great developments of the twentieth century that spans multiple disciplines including mathematics, computer science, electrical engineering, and biology. Unfortunately, although some of the fundamental ideas of this subject are easy to convey to even the youngest students, it is completely absent from the school curriculum.

Luckily, the filmmaker, Brit Cruise has created “The Language of Coins,” a series of videos about information theory that is accessible to a general audience. The series begins with a close look at the way we communicate and continues on to more advanced topics like Markov chains, which is an important modern tool of applied mathematics. In all, there are sixteen videos; twelve are already available online and the remaining ones will be posted soon (the complete playlist is available on Youtube). You need to know about information theory and if you don’t, you should start with this excellent series.

10 Science Tricks for Entertainment and Further Exploration

In the era of iPhones and iPads, magic tricks involving everyday items may not be as exciting as they once were, but in a classroom they are still an effective teaching tool. Richard Wiseman has created a video featuring ten science-based stunts which are an excellent demonstrations of various principles of physics. Some of these tricks were once popularized by the great Martin Gardner and you can learn more about the science behind them in his books. Our favorite stunt, which is more mathematical than the others, involves cutting a hole in a small postcard so that a person can climb through it. Watch the video and start your next science conversation or class with one of the tricks in it. Any science knowledge gained from it is sure to be more memorable than a boring science textbook.

Richard Feynman on the Differences between Mathematics and Physics

As previously discussed, mathematics is not a science in the same way as physics, chemistry, and biology, yet because it is treated as a scientific discipline in school, students rarely understand it’s role. If you’re a math teacher, ask your students the following question: “Biology is the study of living organisms, physics is the study of matter, motion, energy, and forces, but what does math study?” You are certain to elicit a great deal of confusion.

In the following video, Richard Feynman, one of the great physicists of the twentieth century, attempts to answer the question by differentiating between the mental models of mathematicians and those of physicists (and by extension other scientists). Feynman, whose mathematical abilities stood out even among other elite physicists, was supremely qualified to compare the different approaches and to elucidate the peculiar nature of mathematical research. His lecture was recorded almost half a century ago, and lacks the polish of more modern science productions, but it more than makes up for it in both substance and Feynman’s impassioned lecture style. This is a must-see lecture for high school students who have an interest in a math or science career.

Vacuum Cleaners, Cannons, and the Quantum Mechanics of Empty Space

The force exerted by air molecules is something that we take for granted every day, but it is a surprisingly powerful force with equally surprising applications. For example, a vacuum cleaner “sucks” dirt in by creating a partial vacuum that allows the air outside the vacuum cleaner to push dirt into it. Similar reasoning can be used to create a vacuum cannon that relies on air pressure to eject a projectile at great (even supersonic) velocity. The following video from the Sixty Symbols Youtube channel illustrates this and provides further technical details.

If you’re interested in learning more about vacuums, Sixty Symbols has a follow up video that reveals their surprising quantum mechanical nature. You may be surprised to learn that a complete vacuum cannot really exist and that empty space actually contains energy. The conversational nature of the video doesn’t allow for a rigorous treatment of the subject, but instead offers an enticing glimpse into the exciting world that research scientists get to explore.

Is Mathematics Real? A Thought-Provoking Discussion for Any Math Class

Mathematics is so frequently put into the same category as the sciences that students often assume that it is one of the many scientific disciplines, just like physics, chemistry and biology. This can become a problem when students try to understand the reason for studying mathematics. Most students can immediately see that biology is the study of living organisms and the immediacy of that subject makes it both instantly appealing and comprehensible. In mathematics, however, as soon as the studied objects become sufficiently abstract and far removed from everyday experience, students fail to see their significance. As layers of abstraction are added, visualizing mathematics becomes even harder than picturing microscopic cells.

When confusion arises about the nature of mathematics, it can be helpful to introduce a few ideas from the philosophy of mathematics. That is exactly, what the following PBS Idea Channel video does. The question of whether mathematics is a science that studies objects that exist in this universe or is a mental construct that is aesthetically elegant and just happens to be the best language we know for describing nature, remains unanswered, but the discussion is important. Without it, students may never suspect that mathematics plays a unique role in human history and that it spans almost all disciplines. For those who want a deeper take on the nature of mathematics, Eugene Wigner’s classic paper on The Unreasonable Effectiveness of Mathematics in the Natural Sciences will provide much more food for thought.