out mentally before any diagram or word of
the solution was committed to paper.

The author says that his usual practice was to write down the
_answer_ first of all, and afterwards the question and its
solution. His motive, he says, for publishing these problems was not
from any desire to display his powers of mental calculation. Those who
knew him will readily believe this, though they will hardly be
inclined to accept his own modest estimate of those powers.

Still the book was intended, not for the select few who can scale the
mountain heights of advanced mathematics, but for the much larger
class of ordinary mathematicians, and they at least will be able to
appreciate the gifted author, and to wonder how he could follow so
clearly in his head the mental diagrams and intricate calculations
involved in some of these "Pillow Problems."

His chief motive in publishing the book was to show how, by a little
determination, the mind "can be made to concentrate itself on some
intellectual subject (not necessarily mathematics), and thus banish
those petty troubles and vexations which most people experience, and
which--unless the mind be otherwise occupied--_will_ persist in
invading the hours of night." And this remedy, as he shows, serves a
higher purpose still. In a paragraph which deserves quoting at length,
as it gives us a momentary glimpse of his refined and beautiful
character, he says:--

Perhaps I may venture for a moment to use a more serious
tone, and to point out that there are mental troubles, much
worse than mere worry, for which an absorbing object of
thought may serve as a remedy. There are sceptical thoughts,
which seem for the moment to uproot the firmest faith: there
are blasphemous thoughts, which dart unbidden into the most
reverent souls: there are unholy thoughts, which torture
with their hateful presence the fancy that would fain be
pure. Against all these some real mental work is a most
helpful ally. That "unclean spirit" of the parable, who
brought back with him seven others more wicked than himself,
only did so because he found the chamber "swept and
garnished," and its owner sitting with folded hands. Had he
found it all alive with the "busy hum" of active _work_,
there would have been scant welcome for him and his seven!

It would have robbed the book of its true character if Lewis Carroll
had attempted to improve on the work done