The fog on a mirror is the condensation of water vapor as it touches a colder surface. That's okay if you are trying to make ice cubes, but hey brother, we want to shave. Fog - bad!
In 1998 we thought, hmm, what if we heated the mirror, not with a hairdryer but from behind with a thin heater. That's what we did. The mirror is heated by hot dry air, and then the condensation says, "I'm moving on" and lands haplessly somewhere else. The dew point of the mirror is higher than the heated water droplets. Thousands of units later, we've been making men and women from around the world more beautiful and helping them get out of the bathroom faster.