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No one should offer pronouncements about what it means to be well-educated without meeting my wife. When I met Alisa, she was at Harvard, putting the finishing touches on her doctoral dissertation in anthropology. A year later, having spent her entire life in school, she decided to do the only logical thing . . . and apply to medical school. Today she is a practicing physician -- and an excellent one at that, judging by feedback from her patients and colleagues.

She will, however, freeze up if you ask her what 8 times 7 is, because she never learned the multiplication table. And forget about grammar (“Me and him went over her house today” is fairly typical) or literature (“Who’s Faulkner?”). After a dozen years, I continue to be impressed on a regular basis by the agility of her mind as well as by how much she doesn’t know. (I’m also bowled over by what a wonderful person she is, but that’s beside the point.)

So what do you make of this paradox with whom I live? Is she a walking indictment of the system that let her get so far -- 29 years of schooling, not counting medical residency -- without acquiring the basics of English and math? Or does she offer an invitation to rethink what it means to be well-educated since what she lacks hasn’t prevented her from being a deep-thinking, high-functioning, multiply credentialed, professionally successful individual?

Of course, if those features describe what it means to be well-educated, then there is no dilemma to be resolved. She fits the bill. The problem arises only if your definition includes a list of facts and skills that one must have but that she lacks. In that case, though, my wife is not alone. Thanks to the internet, which allows writers and researchers to circulate rough drafts of their manuscripts, I’ve come to realize just how many truly brilliant people cannot spell or punctuate. Their insights and discoveries may be changing the shape of their respective fields, but they can’t use an apostrophe correctly to save their lives.

Or what about me (he suddenly inquired, relinquishing his comfortable perch from which issue all those judgments of other people)? I could embarrass myself pretty quickly by listing the number of classic works of literature I’ve never read. And I can multiply reasonably well, but everything mathematical I was taught after first-year algebra (and even some of that) is completely gone. How well-educated am I?