I understand what randomizing a number means.

But this doesn't answer the question of how the terminal/processing system knows it's your account being debited?

The whole concept of randomization with payments (or anything for that matter with respect to authentication) is impossible. There will ALWAYS have to be some sort of static identifier in order for this to work. Common sense I think.

The idea is interesting but I'm not sure exactly what the idea is!! :)

If you have an AMEX and you randomize the account number on each transaction, AMEX still has to IDENTIFY your account with something? A name? A PIN? A unique ID? AKA an account number.