The method of erasing a hard drive is the subject of some controversy and evolves as the technology evolves. The National Bureau of Economic Research criticized Peter Gutmann, a security expert, for claiming that hard drives with overwritten data could still be read by the government. Gutmann's method's method of erasing hard drives entails writing over the entire hard drive 35 times with patterned inscriptions. As Gutmann notes, while the technology evolves, expecting that his method will work without understanding the technology is to treat his technique "as a kind of voodoo incantation to banish evil spirits..." [see Gutmann's Secure Deletion of Data from Magnetic and Solid-State Memory.]
Hard drives are inscribed by a planographic method: smooth surface reversals of magnetic fields inscribed by a writer hovering over the smooth surface. The surface is layers of glass platters. Increasing storage volume requires weakening the magnetic field, making reading and writing more precise. Two categories of erasure methods: overwriting (patterns and schemes) or degaussing (using a strong magnetic field).
Completely erasing a hard drive may be impossible as the physical trace becomes smaller and smaller, but then finding that trace after erasure becomes progressively more difficult as drive densities increase. Or as Gutmann puts it: "if you've got 10KB of sensitive data on a drive and can't erase it with 100% certainty, the chances of an adversary being able to find the erased traces of that 10KB in 80GB of other erased traces are close to zero."