Yesterday's post about Imagery and Math made use think about Jacques Hadamard's inquiry into mathematical creativity. His description was quite similar to Daniel Tammet's account. In Hadamard's interviews with other world class mathematicians, he found that "Practically all of them...avoided the use of mental words ...as I do, (as well as) the mental use of algebraic or any other precise signs... The mental pictures...(used) are most frequently visual, but they may also be of another kind, for instance, kinetic. There can also be auditive ones, but even these quite generally keep their vague character."
Not surprisingly periods of drowsiness or dreaming can also be a powerful source of new ideas and insights for many inventors, scientists, or mathematicians. It may be when the concepts are vague and floating, and associations can float more freely.