A Gaussian surface within a charged distribution.

The addition of charged distributions and Gaussian surfaces provides for much more sophisticated visualizations. This example includes a a charged sphere with inner radius a=20 and outer radius b=50. At the center of the charged sphere is a Gaussian surface of radius 10. Zoom in on the image to see that the electric field does not penetrate the Gaussian surface, and that the Gaussian surface is completely within the hollow center of the sphere.

Working through the details to get a reasonable appearance for nested translucent objects without complex rendering was definitely challenging.

SXSW Feedback

I was able put together a proof of concept and show it off to a lot of people at SXSW, and the feedback was overwhelmingly positive. Based on that feedback I have expanded the documentation, made the project easier to use and more modular, and put it out as an open source project on GitHub.

Next I will be adding the ability to specify charge densities, such as a charged sphere, line, plane or ring, and also the ability to automatically generate the field lines without needing to specify a starting point to trace the field lines.

I also spent some time covering some fascinating material on the interplay between neuroscience and learning. One of the talks drew an interesting car analogy. To paraphrase, pedagogy and psychology are like learning to drive fast, where neuroscience is like opening the hood and understand how the car achieves it's speed. This would undoubtedly make you a better driver.

Some of the more interesting items included

• The Neuroscience of Language and Learning
• Neuroscience, Games & Learning
• Neuroscience, the Science of Learning, Educational Reform
• Educational Neuroscience: How Education Shapes Brain Development

Well, after digesting all that I am going to work out the code to display a charge distribution on a web page – that means a volumetric rendering that will function well on highly limited devices such as a cell phone.

Illustrating the concept

This interactive rendering is generated by
HTML5 JavaScript and WebGL.

A quick internet search for electric field will show a large number images. Most of which are similar to the initial appearance of the example on this page. However, the electric field is an intrinsically three dimensional phenomenon. Making the leap from the standard two dimensional representation to a three dimensional understanding is difficult at best. So start with a clear three dimensional representation. With OpenGL ES on Android or iOS, or with WebGL as done here, a much better representation can be presented. This image rotates and zooms in response to many of the standard browser actions such as a mouse or a finger drag. Though the touch interaction has only been tested under Chrome and Firefox on Android. This provides a differing three dimensional view that shifts in direct response to the user or learner action. This allows a very fast comprehension of the three dimensional nature of the field. This is an early proof of concept to show the general class of examples that can be generated, and with the right choices in the software design, it is easy to modify the presented example and incorporate it into existing content.

Why Visualization

  I can remember the first program I ever wrote when I was about 11 or 12. It solved a physics problem from one of my father's books: m=m₀(1-v²/c²)^½. The program produced a lot of numbers for v and m, but this table of numbers did not provide any great insights. So I decided to graph them. Seeing the the curve of m running to infinity rapidly as v gets close to c immediately gave me a deeper understanding of what the equation really means.

  A few years later in my first real job – the same thing but on a bigger scale. Doing computational physics at the Princeton Plasma Physics Lab. This code produced massive sets of numbers, and once again, simply looking at the numbers was not the best way to digest the data. So we graphed them. Of course we checked the numbers to ensure that the calculations were correct, but the real understanding came from the visualizations. And all of the publications and presentations used the visualizations.

 A few more years later and I was visiting the San Diego Supercomputer Center, and I saw a large screen displaying an interactive three dimensional model of a molecule. I can remember having the flash – wow this would be great for teaching. I knew immediately that many of the advanced mathematics and physics concepts I had struggled with would be understood much clearer much faster if quality visualizations were available.

  Now, graphics capability which was once the exclusive province of large institutions can be carried in your hand. We have a strong focus on STEM education, we have the Internet as a distribution medium, and we even have a graphics API embedded in most browsers. It is a great time to bring together all of this knowledge and experience with the desire to make a difference and build first class visualizations targeted to instruction.