That we do associate a sensation with whatever idea we have previously connected it with, even though that idea be that of the number of objects producing it, is clearly shown by some experiments which I performed in the laboratory of Columbia University. I took three little round pieces of wood and set them in the form of a triangle. I asked the subject to pass his right hand through a screen and told him I wanted to train him to perceive one, two, three and four contacts at a time on the back of his hand, and that I would tell him always how many I gave him until he learned to do it. When it came to three I gave him two points near the knuckles and one toward the wrist and told him that was three. Then I turned the instrument around and gave him one point near the knuckles and two toward the wrist and told him that was four. As soon as he was sure he distinguished all of the points I stopped telling him and asked him to answer the number. I had four subjects, and each one learned very soon to recognize the four contacts when three were given in the manner mentioned above. I then repeated the same thing on the left hand, except that I did not tell him anything, but merely asked him to answer the number of contacts he felt. In every case the idea of four was so firmly associated with that particular kind of a sensation that it was still called four when given on the hand which had not been trained. I gave each subject a diagram of his hand and asked him to indicate the position of the points when three were given and when four were given. This was done without difficulty. Two subjects said they perceived the four contacts more distinctly than the three, and two said they perceived the three more distinctly than the four.
It seems very evident that the sensation produced by three contacts is no more complex when interpreted as four than when interpreted as three. If that is true, then it must also be evident that the sensation produced by one contact is no more complex when interpreted as two than when interpreted as one. The converse should also be true, that the sensation produced by two contacts is no less complex when interpreted as one than when interpreted as two. Difference in number does not indicate difference in complexity. The sensation of four is not made up of four sensations of one. It is a unit as much as the sensation of one is.
There remains but one point to be elaborated. If number is not a quality of objects, but is merely a matter of attitude of the subject, we should not expect to find a very clear-cut line of demarcation between the different numbers except with regard to those things which we constantly consider in terms of number. Some of our associations are so firmly established and so uniform that we are likely to regard them as necessary. It is not so with our associations of number and touch sensations. We have there only a vague, general notion of what the sensation of one or two is, because usually it does not make much difference to us, yet some sensations are so well established in our minds that we call them one, two or four as the case may be without hesitation. Other sensations are not so, and it is difficult to tell to which class they belong. Just so it is easy to tell a pure yellow color from a pure orange, yet they shade into each other, so that it is impossible to tell where one leaves off and the other begins. If we could speak of a one-two sensation as we speak of a yellow-orange color we might be better able to describe our sensations. It would, indeed, be convenient if we could call a sensation which seems like one with a suggestion of two about it a two-one sensation, and one that seems nearly like two but yet suggests one a one-two sensation. Since we cannot do this, we must do the best we can and describe a sensation in terms of the number it most strongly suggests. Subjects very often, as has been mentioned before, describe a sensation as 'more than one but less than two,' but when pressed for an answer will say whichever number it most resembles. A person would do the same thing if he were shown spectral colors from orange to yellow and told to name each one either orange or yellow. At one end he would be sure to say orange and at the other yellow, but in the middle of the series his answers would likely depend upon the order in which the colors were shown, just as in determining the threshold for the perception of two points by the method of minimal changes the answers in the ascending series are not the same as those in the descending series. The experiments have shown that the sensation produced by two points, even when they are called one, is not the same as that produced by only one point, but the difference is not great enough to suggest a different number.
If the difference between one and two were determined by the distance, then the substitution of lines for knobs of the æsthesiometer ought to make no difference. And if the sensations produced by two objects fuse when near together, then the sensations produced by lines ought to fuse as easily as those produced by knobs.
In regard to the higher numbers difficulties will arise unless we take the same point of view and say that number is an inference from a sensation which is in itself a unit. It has been shown that four points across the ends of the fingers will be called four or less, and that four points, one on the end of each alternate finger and one at the base of each of the others, will be called four or more—usually more. In either case each contact is on a separate finger, and it is hardly reasonable to suppose there is no diffusion when they are in a straight row, but that when they are in irregular shape there is diffusion. It is more probable that the subject regards the sensation produced by the irregular arrangement as a novelty, and tries to separate it into parts. He finds both proximal and distal ends of his fingers concerned. He may discover that the area covered extends from his index to his little finger. He naturally infers, judging from past experience, that it would take a good many points to do that, and hence he overestimates the number. When a novel arrangement was given, such as moving some of the weights back on the wrist and scattering others over the fingers, very little idea of number could be gotten, yet they were certainly far enough apart to be felt one by one if a person could ever feel them that way, and the number was not so great as to be entirely unrecognizable.
FOOTNOTES.
[1] Brückner, A.: 'Die Raumschwelle bei Simultanreizung,' Zeitschrift für Psychologie, 1901, Bd. 26, S. 33.
[2] Tawney, Guy A.: 'Ueber die Wahrnehmung zweier Punkte mittelst des Tastsinnes mit Rücksicht auf die Frage der Uebung und die Entstehung der Vexirfehler,' Philos. Stud., 1897, Bd. XIII., S. 163.
[3] See Nichols: 'Number and Space,' p. 161. Henri, V., and Tawney, G.: Philos. Stud., Bd. XI., S. 400.