Debunking a bogus encryption statement

deviantphil writes: Recently where I work someone tried to assert that encrypting a file twice with a 64 bit algorithm in equivalent to encrypting it once with a 128 bit algorithm. I know enough about encryption to know that isn't true but I am having difficulties explaining why and how. Doesn't each pass of the encryption having a separate file header make this assertion not true? Can anyone point me to references that would better help me explain this?