This is what happens when a science generalist puts stuff up on the web. According to Dr Shock, my choice could have been better informed. Here’s what he says:
Unfortunately there’s a problem with the first video on the tenth dimension: It’s a) nothing to do with the ten dimensions of string theory and b) completely meaningless as far as I can tell. Sorry :-(
The ten dimensions of string theory are not mysterious at all. There are 9 spatial dimension which can be described perfectly well mathematically, just like the three dimensions we see around us and one time dimension. In special relativity time is described as a dimension just as much as the other three. String theory is completely self consistent with both quantum mechanics and relativity.
Sadly the tenth dimension video is not a good video to advertise either string theory or any good physics.
Woops! Sorry folks.
Jon recommends the Elegant Universe videos by Brian Greene as a nice introduction to String Theory.