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

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.