bah, this reminds me of trying to analyze motion in accelerating reference frames in physics.
Taking challenging classes is good. Taking the same physics class freshman year in college with a good portion of the class having placed in/won the national physics Olympiad…and not even haven had taken AP physics…slightly more questionable. my poor, poor GPA 
The professor was awesome though.
Still gyroscopes completely baffle me. I know mathematically, why they work, but there are some completely unintuitive situations you can create with them. (gyroscope precessing horizontally when attached to a rod hanging from a string, for example)
anyways, this talk of relativity made me remember what I think of as one of the more fun paradoxes.
I think its called the runners paradox, or something along those lines.
may or may not be well known. If you already know it, don’t spoil it for a little bit.
preface: an object moving close to the speed of light relative to your reference frame will appear to contract in the the direction parallel to the relative motion.
(paraphrased, and possibly botched)
A guy owns a barn, 10 meters in length with doors on either side (magic doors that can open and close instantaneously)
There is a runner, who is holding a pole 11 meters in length. This runner can run at speeds approaching the speed of light.
bar owner says to runner
“you know, if you run fast enough, you’ll be able to fit your entire pole lengthwise inside my barn”
“no way!”
“sure, just run close to the speed of light, In my reference frame, you’ll contract and be short enough to fit in the barn”
“In your reference frame maybe. In my reference frame the barn is moving at me at near light speed and it will contract, making this even more impossible.”
They agree to a test. The runner will run towards the front door of the barn at close to the speed of light. The front door is open and the back door is closed. When/if the barn owner sees that he is entirely inside of the barn, he will trigger a mechanism that will simultaneously open the back door and close the front door, allowing him to run through safely.
runner takes out a life insurance policy.
So, who’s right? Are both right? Does our runner survive? Are any doors left intact?
justify your answer.
this is left as an exercise for the reader (that phrase and its equivalent appear far, far too often in math and physics textbooks :P. That and “by inspection we see that…” ughh)
EDIT: its called the ladder paradox, or barn-pole paradox apparently. No cheating with wikipedia though!