yeah, what makes a trapdoor function has a lot to do with the arithmetic system you use. hash functions use clockwork arithmetic or finite fields (meaning they can overflow and stuff can be lost or mess with the LSB part of the number) . if you allow the number of bits to increase you can reverse it just fine. the bits that a hash function blows off cannot be recovered without trying many (squillions) of candidates. to see if you can figure out what got hashed. and they are called "hash" because this means a mess in english. i'm not sure if that was where it was invented, but i suspect yes. a hash is specifically a type of mess that might be fixable, but probably you will just throw it out and start again.