You've just touched on the fascinating subject of sampling rates and aliasing. The computer monitor flicker you observe when videotaping it comes from the fact that the refresh rates on your computer monitor (there are many different ones for different computers) is different from that of your video camera. Video (NTSC TV, used in America) updates the whole frame every 1/30th of a second; all the even scan lines on a TV screen are drawn in 1/60th of a second, and then your TV (and video camera) go back and fill in the odd ones in the next 1/60th of a second. If your computer monitor updates, say, the whole screen one line at a time once every 1/70th of a second, then the video camera when it scans its lines will only pick up those lines on the computer screen that are updating while it is "looking" there. The other bits of the screen will be darker. Depending on how far mismatched the refresh rates of the video camera and computer monitor are, the light and dark areas of the screen can appear to crawl slowly up or down the screen, or they may appear to flash rapidly. Movie cameras take one frame every 1/24th of a second and are therefore never synchronized with televisions or computer monitors. Special televisions and monitors are needed if they are to be used on movie sets, so as not to look very strange.
Incidentally, the TV refresh rate was chosen to match the frequency of electrical power out of the wall socket. If some flaky component in the TV, like a power supply, oscillates with the power frequency, and it is not exactly the same as the picture refresh frequency, you may see a slow wiggle of the picture on the screen with a frequency that is the difference between the power line’s frequency and the refresh rate frequency. If it is a slow wiggle, it can really give the viewers a headache! Computer monitors seem to be better manufactured and do not require synchronization with the input power.
And yes, the multitude of shadows of your pen are caused by the refreshing of the computer screen -- it only makes a shadow when the screen is being updated. The reason your screen looks on "all the time" to you when in fact it is really flickering very rapidly is due to physio-psychological effect called "persistence of vision" in which an image is stored in the visual cortex long enough so that if it is removed ever so briefly and then brought back, the brain thinks the same object has been there all the time ("interpolation between frames"). If it is too slow you will notice flickering. 24 frames/second is near the lower edge of what is comfortably viewable without noticeable flicker (which is why the movies are at that rate). The pen shadow you describe does not fall in that category because it moves rapidly -- each update of the screen casts a new shadow of your pen in a different place. Your eyes and brain then interpolate the "fixed" computer screen with several shadows of the pen that are cast within the amount of time your brain takes to process an image.
Physio-psychology experiment: How many pen-shadows can you make simultaneously visible if you shake your pen rapidly in front of your computer screen? (this tells how long it takes your eyes and brain to acquire and process an image).
Another interesting thing to do is to look at your TV screen while "blowing a raspberry" (i.e. sticking your tongue out, closing your lips over it, and blowing hard to make a flatulent sound). Since blowing the raspberry causes your head to vibrate at a frequency that is not too different from the refresh frequency of the TV, and you will see some interesting results.
Please see our own answer to the aliasing question.
(published on 10/22/2007)