Thinking Woman's Crumpet

Do you believe you could be solely attracted to a person for their mind? I mean honestly, their sense of humour, outlook on life and intellect, but nothing physical, at all?

I was wondering this whilst talking to a friend the other evening, thinking everything with this person, except for the traditional things you would base a relationship on, like sexual attraction, that certain je ne sais que, is there. All boxes ticked but for one: Jumpability.

It's very weird to find yourself with an intellectual crush.