Image zoom Anthony Harvey/Getty

Look, and you will not find Jon Hamm on social media — a real, official account run by the former Mad Men star that is, no matter how many fake accounts may exist.

The privacy-minded actor, 46, tells PEOPLE in this week’s issue that while he understands why people enjoy following celebrities on the various social media platforms, he’s not comfortable sharing information with millions of potential followers.

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“I actually just prefer the act of connection with real people, whether I know them or not,” says Hamm. “I like talking to people.”

Hamm does however concede to having one small, private presence on the photo-sharing app, Instagram.

Image zoom Wilson Webb/Sony

For more on Jon Hamm and his post-Mad Men life, pick up the latest issue of PEOPLE, on newsstands now

“I get why people like Instagram,” he says. “I have an Instagram account that I use to follow beautiful places and baby animals and things that make me feel joy.”

The Baby Driver star, who was 36 when he landed the career-making role of Don Draper on Mad Men, says he is still trying to make peace with public interest in him.

“The only way I can be Zen about it is to disengage from it,” Hamm says. “I don’t read about myself on the Internet. Not having a Twitter account is nice. I don’t have to deal with Facebook. I don’t have to deal with any of that stuff and honestly not engaging with it means, for me, it doesn’t really exist.”

Hamm admits he feels that fame is “a bell that can’t be unrung,” and that he’s trying to learn to deal with it.

“Like all things that are disruptive, you can either manage it effectively, or sometimes it gets the better of you,” he says. “I’m incredibly grateful for and happy with the career that I’ve worked for. It’s my job to find the balance.”