The Problem of Zeno: Part I

There is an argument called Zeno's Paradox which shows unequivocally that motion cannot exist. Hold on, you say, I can move about quite nicely, so how can it be that motion does not exist? Consider this post and see for yourself. Achilles the hero and the tortoise were very good friends in Zeno's day. Achilles always had the upper hand when it came to physical toughness, but the tortoise had a very crafty mind. One day, Achilles challenged the tortoise to a race. Achilles was so sure that he could beat the tortoise, he offered to give the tortoise a head start. The tortoise then politely let Achilles in on our paradox. He said that if Achilles were to give the tortoise a head start, he would never pass the tortoise and thus the tortoise would win the race. Achilles thought this was foolish and demanded an explanation from the tortoise. His explanation may have gone something like this.

"Now Achilles, is it not true that when the race begins, I will be some distance ahead of you?"

"Yes that is true, for I will give you a head start."

"Indeed, but before you can pass me, you must first pass the point where I start the race, correct?"

"Yes, this is true."

"But in that time, I will have moved forward."

"If you intend on participating in the race!"

"Quite. However, in order to pass me, you will then have to reach my new position."

"Agreed."

"But by that time, I again will have moved forward some distance."

(It is at this point that Achilles begins to realize that he will not win the race.)

"But-"

"And so you see Achilles, you will never pass me, because you will have to reach a point I was at previously before passing me."

Begrudgingly, Achilles responded, "Tortoise, you are correct, I cannot win if I give you a head start. I concede the race."

Examine this argument, try to understand what is going on here. See how the tortoise wins. Is there a flaw in his argument? If so, what is it? And if there is a flaw in his argument, why did Achilles miss it? I will publish my interpretation in my next post two weeks from now. In the interim, I am presenting a talk for Student Research Week at Texas A&M discussing this subject. It will be Wednesday the 29th around 9:00 AM in Rudder tower. I will present my interpretation in the hopes of showing, under a careful formulation, that this is not a paradox after all, but a genuine theorem of mathematics.

The Peculiarities of Podcasting

Podcasting is a new buzzword which has been floating around the internet since 2004. To many, or at least to me, this word may initially sound like a marketing tool for Apple's iPod. While this is not totally false, this use of the word does not aptly describe what podcasting has become. In Wikipedia a podcast is described as a web feed of audio or video files placed on the Internet for anyone to download or subscribe to, and also the content of that feed. (The feed portion generally refers to RSS which is an XML file format which allows computer programs to read sites which change often and synchronize with them accordingly.) A few misconceptions about podcasting are that you can only listen to a podcast on an iPod and podcasting is just a new word for streaming audio. I was duped by the first one until quite recently, but it is true that an iPod is NOT required to listen to podcasts. The other misconception will be addressed below. The popularity of podcasting has grown considerably in the last year which many people attribute to the freedom podcasts offer. One major difference with podcasting and older forms of audio/visual media served on the Internet is that a user is not required to be online while enjoying a podcast. Podcasts in many ways are more dynamic than these other forms which include streaming internet radio and static, prerecorded files. Podcasts fill a niche that lies somewhere between radio, television and the always accessible internet and for this reason a person can listen to content on his schedule or lack thereof. For instance, on a recent three hour trip I decided to listen to a few episodes of the FrenchPodClass which worked out quite well as it was educational during a time I would normally be doing nothing productive. Clearly, podcasts fit quite well into my schedule, as I'm sure they will fit into yours in the future.