Cinnamon Buns, Bagels and Pretzels
Recently, the Nobel Prize for the year 2016 in physics was awarded to Michael Kosterlitz, Duncan Haldane and David J. Thouless for theoretical discoveries of topological phase transitions and topological phases of matter. Thors Hans Hanssen, a member of the Nobel Prize committee, explained the concept of topological invariance using his lunch of a cinnamon bun, a bagel and a pretzel. It was a funny and a simple way of explaining a complicated concept.
“Everything must be made simple, but not simpler” goes a famous quote by Albert Einstein. The quote rings true across various walks of life, especially in STEM education. People across the world are fascinated and intrigued by science and technology. The curiosity of a kid begins the very moment when he starts to observe things. “Why is the sky blue? Why is fire hot? Why shouldn’t I stand too close to the platform when a train is moving into it? Why does the apple fall?” –these are questions that every child has pondered at a certain point during his childhood and these questions form the very basics of scientific inquiry.
The answers to these questions are obtained from various sources — from science teachers, through constant pestering of parents and mostly from books that are often titled like “100 scientific questions and answers”, “How do things happen?” etc. When the same child goes to middle and high school, the questions become much more complicated. “Where did human beings come from? What are all the things in the world made of? How does the earth exist?” — the answers to these questions are explained in bits and parts to the seeker in the child. “Humans evolved from monkeys, atoms constitute everything, the universe started with a big bang” — the seeker in the child grows up watching “Bill Nye — the Science Guy” and “The Magic School Bus” and proceeds to read “A Brief History of Time” and “The Short History of Nearly Everything” and “Cosmos” and more such popular science.
There is a famous anecdote about “A Brief History of Time”. Simon Mitton, the publisher of the book warned Stephen Hawking that for every equation that he included in the book, the readership would be halved. Hawking just included a single equation, the famous mass energy equivalence, in his final draft. Most of popular science very specifically avoids equations and mathematics in general. It is understandable that they would like to explain concepts in a simple and an entertaining manner, but does that really do justice to original science? It also sounds cool to say “the cat can be both dead and alive until you open the box” and “an electron can be both a particle and a wave” than “the wavefunction of the electron after being operated upon by an operator like momentum just gives a complex number and not a vector”. Yes, “A Brief History of Science” and other books by famous science writers including Brian Green, Sean Carroll, Leonard Susskind et al are all great books, there is no question about that. But, in an attempt to simplify concepts, do they not dilute it too much?
Allegories and comparisons are important in an attempt to illustrate any concept, let alone one in science or engineering. They let you visualize things, put them in perspective to a certain extent and help you relate to them. But, there are certain things that comparisons, allegories, illustrations or any amount of linguistic explanations simply fail to do. Sometimes, it’s just not easy to explain things using the traditional narrative and convey the exact sense that the math and equations are trying to portray. It’s easy when you’re talking about Newton’s second law. “Force is proportional to acceleration” can simply be stated as “F=ma”. But, it gets more complicated as you start explaining something like “Navier Stokes equation” in simple English. The language that curl and divergence of vectors speak needs to be intuitively explained in terms of numbers and mathematics rather than comparisons or allegories.
Why does this matter? Because, it determines the way and the methodology by which STEM classes are taught. People say they get bored when they see math and equations. It kind of confuses them and there are complaints that all of the math has no relevance with what the observable world around them. People tend to say “That’s just a bunch of stuff that I neither get to see nor use anywhere in the world.” And I, to a certain extent, agree. When I did my bachelors in engineering, all they had throughout the four years were equations and math which seemed extremely different from reality. That disconnect between the reality and pragmatic applications of science can be bridged using comparisons and allegories that help you visualize things.
So, what can be done to improve the state and the style of STEM education? Of course, experiments help. But, they are just part of the solution. I would say a way of helping the curious kids see the numbers around them can be a great start. For example, you can intuitively answer certain questions by observation. “What is the mass of an adult human being?” is a question for which an estimate can range anywhere between 50 to 100 kg. Similarly, “what is the temperature outside?” is something that you could guess pretty easily relying on your senses. That was learnt by observation and intuition. Let’s try the same with some other quantities. “What is the magnetic field of the fridge magnet that you just saw at the kitchen? Would it be 1 tesla, 10 tesla or 1000 tesla? What could be the resistance of a single transistor that is used in the device which you’re using to read this article? 22.4 ohms? 224 ohms? 22.4 kiloohms?” — these are questions that cannot be answered intuitively. Of course, you can look at the datasheet to determine what it is, but guessing these values while a specific concept is being taught at class can comparatively help dispel a fear of numbers and provide much needed practical experience.
Next step would be to do the math alongside concept demonstration experiments. One of the popular science demonstration experiments is where a person lies down on a bed of nails with a force applied upon him to demonstrate the concept of pressure. As the surface area increases, the pressure decreases and that doesn’t harm the person. Making the students experiencing the demonstration calculate the total pressure being applied by the person would be great in this case. I am trying to describe a reverse methodology of what Walter Lewin prescribes. A quick hand calculation will let the learners have an experience of what to expect and how to design systems later if they choose to pursue a STEM degree. Quick calculations in simple experiments not only make the students not afraid of math and numbers, but also build an inherent intuition that will be extremely reliable in the long run.
All this could be very helpful at middle and high school level, but what do we do with respect to undergraduate STEM degrees, where the gap between equations and visualization and realization through visualization is much more prominent? How would you try to visualize, demonstrate and explain most of the natural phenomena which are differential equation based? Like, for instance, heat transfer between two bodies or the energy levels required for electrons in silicon to start conducting? We have Arduino boards and Raspberry Pis and sensors and competitive programming for us to be able to learn programming and digital design and circuitry, but what about concepts for which we have no visualization aid? The moment I see a sine wave, I automatically fix a wavy curve within my head. How do I associate it with rotational motion that would help me visualize Fourier transforms? Technology enhanced learning will help. So will running quick experiments on simulation software. (I had trouble trying to visualize JK flipflops, which became pretty easy once it was simulated on PSPICE). But, ultimately, I will have to conclude that the abstractness of math is inevitable and trying to visualize it analytically is going to take a lot of effort.
Science is beautiful. It really is. It is the tool that helps us observe the world around us, make sense out of it and make technological advances that make the world a better place to live in. STEM education and pedagogy really needs to express that beauty of science to its learners by somehow balancing the math and equations along with visualizations and linguistic explanations. We need a bridge between these two facets of science. And that can be achieved only through repeated practice and experimenting with and perfecting our teaching techniques and methods.