The 50-year-old actor claims he's "pathetic" at all things technology-related and stays away from the internet because he worries he might read an upsetting rumour about himself.
He told Tele 2 Semaines magazine: "I've never googled myself and I never will! I would be too scared to discover lies and horrible things written about me."
The newly-engaged star, who is set to tie the knot with his 'Rum Diary' co-star Amber Heard, also admits his children Lily-Rose, 14, and Jack, 11, roll their eyes at him whenever he attempts to help them with school projects.
He joked: "I'm pathetic! You should ask my children! Before, they used to ask my help to do research on the computer - for a class project, for instance. These days, they've realised there's no point. The last time I asked if they wanted help, they told me, 'Go and play your guitar, dad!' "
The 'Transcendence' hunk is an iPhone convert, however, even though he doesn't remember the name of his favourite application, Instagram.
Asked about his must-have app, he said: "I've forgotten it's name. It allows you to retouch photos automatically."
Probed as to whether his favourite subject is Amber, he replied:
"Among others, but Amber doesn't need any retouching! The photo is perfect every time."