How to Avoid Tachions in String Theory

The square root of a negative number leaves you with an imaginary answer. Any theory that has tachions in it is a sick theory, a broken theory, and you have to throw it out. To understand why the number of dimensions comes into play, it really has to do with a zero point energy. If you have more dimensions that you can vibrate in, quantum mechanics says you're going to vibrate in all of them.