pertinent, though possibly unnecessary, to point out the inherent contradiction between the operations that a successful reply is supposed to involve and the absurdity of the failures or wrong answers that occasionally occur. Thus, this most intelligent Berlin horse, who is supposed to be acquainted with difficult mathematical relations, occasionally makes mistakes. Now when a child makes a mistake, it is in regard to some operation just beyond its capacity, while the simpler additions and subtractions are readily accomplished. On the other hand, Hans, immediately after giving an answer in square-root, fails to count the buttons on an officer's coat, and insists, until repeatedly corrected, that a man has three ears and not two; or again, after making the minute distinctions of German orthography, puts K for J; and further, if this miraculous horse really distinguished the sounds and converted them into letters, why should he not be phonetically misled and occasionally substitute, let us say, a ck for a k, which would mean all the difference between 2 pawings followed by 1, and 3 followed by 5. Yet such objections are indeed superfluous, or would be were they not so commonly disregarded by the prejudice in favor of taking such absurd pretences at their face value. In brief, it is difficult seriously to investigate these limitations in any other spirit than that of pointing out how unmistakably they indicate an unreasoning, unrelated method of reaching the answer through some system of signs.
This statement of the facts of the case does not at all imply that in this performance we have reached the limits of the horse's education. Very likely the intelligent horse may be taught to go very much farther than this in the direction of his natural ability to associate signs with actions. It would, for example, be very interesting to know whether 'Jim Key' could be taught, in selecting one after the other the letters that spell his name, to go of his own accord for the 'I' after he has been led to the 'J' and then to the 'M' and so on; that is, whether he could learn to perform a series of selections by associating each with the one following. This would still be a task of the same order, but a more complicated one; and in investigations of this kind earnest students of animal intelligence have obtained important evidence as to the capacities and limitations of animal thinking. Such psychological questions are asked in a different temper from that which prompts the stage performances, and lead to far more useful results.
And so we come last to the other side of our inquiry, why this kind of a performance is so generally accepted at its face value, why educated persons will attribute to the horse (as they do to the Berlin horse), the insight to recognize that 27 divided by 7 gives 3 with a remainder of six, that 1⁄4 must be added to make a unit out of 3⁄4, or that at 12:17 one must wait 43 minutes for one o'clock! Indeed, so wide-spread were the misleading accounts of this learned animal, that a commission of
