I've always wondered if this simply isn't a case of having the causality wrong, that is to say people in old age who don't have alzheimer symptoms are more intellectually engaged.
Well today is your lucky day, because you can cease your wondering! The answer is "no".
In fact, any question you have that relies on thousands of doctors and professors in the field missing something obvious is always "no" (cf "never a compiler error").
The latter of course. Everyone who has given more than 10 seconds of thought to the issue has considered the opposite relationship because it's so obvious.
