Just to make sure, I searched for "interaction" in "On computable numbers...", and it's not in there. And, like I said, in the general case, interaction is "more powerful" than algorithm as often as it is "less powerful".

Edit - Example: You're on "'Who Wants to Be a Millionaire?" You're in "algorithm mode" for most of the questions, but you're granted one "interaction", via a phone call. On the show, you're allowed to call anybody you want, and if you know to call somebody who's really clever, chances are that interaction will be more powerful than computation. But that's not the general case: the general case would be for you to call a random phone number, and chances are that won't help you - so, in that case, not more powerful.