Why overwrite a file more than once to securely delete all traces of a file?

Question

Erasing programs such as Eraser recommend overwriting data maybe 36 times.

As I understand it all data is stored on a hard drive as 1s or 0s.

If an overwrite of random 1s and 0s is carried out once over the whole file then why isn't that enough to remove all traces of the original file?

Answer 1

A hard drive bit which used to be a 0, and is then changed to a '1', has a slightly weaker magnetic field than one which used to be a 1 and was then written to 1 again. With sensitive equipment the previous contents of each bit can be discerned with a reasonable degree of accuracy, by measuring the slight variances in strength. The result won't be exactly correct and there will be errors, but a good portion of the previous contents can be retrieved.

By the time you've scribbled over the bits 35 times, it is effectively impossible to discern what used to be there.

Edit: A modern analysis shows that a single overwritten bit can be recovered with only 56% accuracy. Trying to recover an entire byte is only accurate 0.97% of the time. So I was just repeating an urban legend. Overwriting multiple times might have been necessary when working with floppy disks or some other medium, but hard disks do not need it.

Answer 2

Daniel Feenberg (an economist at the private National Bureau of Economic Research) claims that the chances of overwritten data being recovered from a modern hard drive amount to "urban legend":

Can Intelligence Agencies Read Overwritten Data?

So theoretically overwriting the file once with zeroes would be sufficent.