computer forensics question

[Technomage]

ok,
I've been wrangling this question around a while and haven't been able to gain 
any real answers that make sense (and my knowledge base on this is lacking 
due to being 10 years out of date).

so, here goes:

is it possible, given the current understanding of the laws of physics, to so 
erase a hard drive as to make it virtually impossible to recover ANY data of 
any usefulness whatsoever (up to and including either a major government or 
major multinational corporationthrowing huge sums of money at the problem in 
an attempt to recover)?

so far, the only answer I have found is: a conditional no (any or all the data 
can be recovered, including the previously written data multiple layers 
deep).

is there a correct 9and unconditional) answer for this arguement?