DVD Classes/Zero and Infinity

I bought a few courses from the Teaching Company. I know for many of you sitting on your couch and watching a professor talk at the podium on your DVD for 24 lectures (at 30 minutes a pop) is enough to set you running for the remote, but I think it sounds like great fun. I bought them as a Valentine's Day present for myself since I don't have a sweetheart for this most Hallmark of holidays.

Here's what I bought:

• The History of European Art
• Einstein's Relativity and the Quantum Revolution (I looove quantum physics!)
  
• Zero to Infinity: A History of Numbers
• Foundations of Western Civilization (from earliest civilizations to 1600)
• Museum Masterpieces: The Louvre
• Museum Masterpieces: The Met

Keep in mind 24 lectures is a short course. Foundations of Western Civilization is 48 lectures long. I can't wait for them to arrive at my doorstep. The Teaching Company folks also sent a web link to "Course Starter Materials" for your class. These course materials have an overview of the class, book recommendations and links to websites. Since I'm chomping at the bit, I've already done some reading and surfing around for my first class: Zero to Infinity: A History of Numbers.

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As many of you know I'm terrible at math. I can barely figure out the tip for the restaurant meal. When I was much younger I read a book about mathematics which I didn't understand very well, BUT there was a half a chapter on the history of counting. This half chapter was so riveting and interesting to me I never wanted it to end, but rather than explore further I told myself I couldn't do math and left it alone. I can't WAIT to learn more about the history of counting in my DVD course.

As a seventh grader with an overactive imagination and an inability to do fractions, I figured out one morning in math class that the number line, that is negative numbers, zero, positive numbers both extending into infinity in both the negative and positive directions, is really not a line at all. Instead it's a massive oval because the numbers bend back on themselves. Everything always comes back to zero.

For the first time my very good math teacher had no idea what to say, and I couldn't readily explain why I thought this was so. She asked me for specifics. I couldn't give her any. I just knew everything comes back to zero. Then, somehow, I was able to explain why. My explanation was simple and made complete sense. Or so I thought, but my friends thought I was completely out of my mind and spent a good deal of time telling me so.

When I became an adult I completely forgot about this incident. Every once in a great while I would recall it, but I completely forgot why everything comes back to zero.

While reviewing the course starter materials for my DVD course, due on my doorstep any day now, I read a line about how when it comes down to it zero and infinity are very similar numbers.

A light went on (this happened about 30 minutes ago). It sputtered for a moment and then burned brightly. The reason why everything comes back to zero is because zero and infinity are mirror images of each other. Since negative and positive numbers are mirror images of each other so is zero and infinity. This is why the numbers bend back on each other.

Now I know you're thinking this is all well and good, but you're probably wondering if it's true. Can it be proven with an equation or series of equations? The answer is I have no idea. I don't know if it's true and I have no way of finding out. I'm hoping to get a clue on my DVD class, but if the professor doesn't mention this idea I'll send him an inquiring email when the class is over.

Huh. Too bad I can't do math. I have a feeling I would have really enjoyed playing with numbers and theories and things.