Wolfram Computation Meets Knowledge

Date Archive: 2011 January

Education & Academic

Breaking Secret Codes with Mathematica

Mathematica can make you feel like a computational superman. Armed with that attitude and some schoolboy knowledge of cryptography, I turned my attention to cipher breaking this week, only to discover buried kryptonite. The weakness of ciphers (where you swap every occurrence of a particular letter in your message with the same different letter) is that they don't change the patterns of letters. The simplest attack that exploits this fact is frequency analysis. The most common letter in English is "e", and so it follows that the most common character in an encoded message (assuming the message is written in English) will correspond to "e". And so on through the alphabet. Mary Queen of Scots famously lost her head when Queen Elizabeth's spymaster broke Mary's cipher using frequency analysis. I figured that if sixteenth century spies could do it by hand, I should be able to automate it in Mathematica in about 10 minutes.
Leading Edge

Stabilized Inverted Pendulum

Can you balance a ruler upright on the palm of your hand? If I concentrate, I can just barely manage it by constantly reacting to the small wobbles of the ruler. This challenge is analogous to a classic problem in the field of control systems design: stabilizing an upside-down (“inverted") pendulum. One of the best things about Mathematica is that it makes specialist areas like control systems accessible to non-specialists. This lets you freely combine and develop new ideas without needing to be an expert in everything. It also makes Mathematica a great platform for learning and exploring new areas. Using the new control systems features (one of several new application areas integrated into Mathematica 8), I've been experimenting with models of stabilized inverted pendulums. I'm no expert in control theory, but you'll see that one doesn't need to be.
Education & Academic

The Benefits of Free-Form Input for Precollege Teachers

After talking with community college educators recently at the national AMATYC conference in Boston, I'm reminded, once again, that time is the most valuable commodity in a teaching setting. It takes time to plan a lesson for students, time to refine this lesson such that it has the most impact, and time to plan what technology will accompany a lesson and how to guide students through the process of using that technology. Any wrinkles with using the technology will greatly distract students from the course concept at hand. As a concrete example, community college faculty are used to explaining to students the four menus, and roughly eight steps, to visualize a function and its derivative using a calculator, which is a significant time investment. (The examples are from my own TI calculator I've kept all these years.) It seems that most community college educators know how powerful and useful Mathematica can be to support lectures or individual student projects. But this year, more than anything else, we talked about how Mathematica 8's new free-form input will reduce or eliminate a teacher's preparation time and will help students who are new users access Mathematica's powerful functionality immediately.