The game-board, naturally, tries out only the units that maneuver on the ocean; it does not try out the mechanism inside those units, because they can be tried out best by engineering methods.  The province of the game-board is merely to try out on a very small scale, under proper conventions or agreements, things that could not be tried out otherwise, except at great expense, and very slowly; to afford a medium, half-way between actual trials with big ships and mere unaided reasoning, for arriving at correct conclusions.  When the game-board is not used, people conferring on naval problems can do so only by forming pictures in their own minds, endeavoring to describe those pictures to the others (in which endeavor they rarely perfectly succeed) while at the same time, trying to see the pictures that are in the minds of the others—­and then comparing all the pictures.  The difficulty of doing this is shown by a little paragraph in “The Autocrat of the Breakfast Table,” in which Dr. Holmes points out that when John and Thomas are talking, there are really six persons present—­the real John, the person John thinks himself to be, the person Thomas thinks him to be, the real Thomas, the person Thomas thinks himself to be, and the person John thinks him to be.  The conditions surrounding John and Thomas are those of the simplest kind, and the conversation between them of the most uncomplicated character.  But when—­not two people but—­say a dozen or more, are considering highly complicated questions, such as the House Naval Committee discuss when officers are called to testify before them, no two of the twenty congressmen can form the same mental picture when an officer uses the word—­say “fleet.”  The reason is simply that very few of the congressmen hearing that word have ever seen a fleet; none of them know exactly what it is, and every one forms a picture which is partly the result of all his previous education and experience; which are different from the previous education and experience of every other congressman on the committee.  Furthermore, no one of the officers uses words exactly as the other officers do; and the English language is too vague (or rather the usual interpretation put on words is too vague) to assure us that even ordinary words are mutually understood.  For instance, the question is asked:  “Do you consider it probable that such or such a thing would happen?” Now what does the questioner mean by “probable,” and what does the officer think he means?  Mathematically, the meaning of “probable” is that there is more than 50 per cent of chance that the thing would happen; but who in ordinary conversation uses that word in that way?  That this is not an academic point is shown by the fact that if the answer is “no” the usual inference from the answer is that there is no need for guarding against the contingency.  Yet such an inference, if the word “probable” were used correctly by both the questioner and the answerer, would be utterly unjustified, because the