You can now say “If the 7 of diamonds is the 5th card in the pack of diamonds, then the 5 of spades is the 7th card in the pack of spades,” and, in short, each pack serves as an index to the other.
From the point of view of this proceeding, multiplication appears as a continually repeated addition. Now let us ask what will result from continually repeating multiplication. As before lay the 11 diamonds in their proper order face down on the table, and take the 11 spades in their proper order in your hand. Deal the spades into 2 piles and gather them up. Put the back card, the 2, down on the table and replace it by the top diamond. Again deal the cards in your hand into 2 piles and gather them up, and put the back card (the 4) upon the one lying face up, and replace it by the top diamond. Proceed in this way until you have laid down all your spades except the knave which you never can get rid of in this way. You will now find that the spades run in geometrical progression, each the double of the preceding
2 4 8 5(≡ 16) 10 9(≡ 20) 7(≡ 18) 3(≡ 14) 6 1(≡ 12).
In fact, if, as before, x be the place, y the face-value,
y = 2x.
Then, in the other pack we ought to have
x = log y/log 2.
In fact, for these the face-value is increased by 1 when the place is doubled. For the order is
10 1 8 2 4 9 7 3 6 5.
You may now do this surprising trick. Ask Celarent to cut the pack of diamonds (with the knave of spades but without the knave of diamonds). Then, ask how many piles she would like to have the diamonds dealt into. Suppose, to fix our ideas, she says 5. You obey and gather up the cards according to rule. You then cut so as to bring the knave of spades to the face; and in doing so you notice the face-value of the card carried to the back. In the case supposed it will be 4. Then carry as many cards (i.e. in this case, 4) from the face to the back of the pile of spades. Then ask Celarent what diamond she would like to find. Suppose she says the 3. Count to the 3rd card in the pack of spades. It will be the 6. Then say, “If the 6 of spades is the 3rd card, then the 3 of diamonds is the 6th card,” and so it will be found to be.
I have not given any reason for anything, my Barbara, in this letter. In your family you are very high in reasons and in principles. But if you think I have said anything not true, it will be a nice exercise in the art of reasoning to make sure whether it is true or not.
1. Published at Heidelberg in 1496, at Freiberg in 1503, in Strassburg by Grüninger in 1504, in Strassburg by Schott in 1504, in Basle in 1508; etc.
2
Ribot’s
Psychology of Attention
| 19 June 1890 | The Nation |
The Psychology of Attention. By Théodule Ribot. Authorized translation. Chicago: The Open Court Publishing Company. 1890. 8vo, pp. 121.
Every educated man wants to know something of the new psychology. Those who have still to make acquaintance with it may well begin with Ribot’s little book on “attention,” which all who have made progress in the new science will certainly wish to read. It is the chef d’oeuvre of one of the best of those students who have at length erected psychology into a science.
Ribot regards the doctrine of attention as “the counterpart, the necessary complement, of the theory of association.” He means that attention is related to suggestion as inhibition to muscular contraction. Physiologists, however, would scarcely rank inhibitibility with contractility as an elementary property of protoplasm. Besides, though suggestion by association may be likened to muscular action, how can the analogy be extended to the process of association itself, or the welding together of feelings? This welding seems to be the only law of mental action; and upon it suggestion and inhibition of suggestion alike depend. Attention is said by Ribot to modify reverie’s train of thought by inhibiting certain suggestions, and thereby diverting their energy to suggestions not inhibited. This makes the positive element of attention quite secondary. At the same time, we are told that the sole incitement to attention is interest. That is to say, a preconceived desire prepares us to seize promptly any occasion for satisfying it. A child’s cry, drowned in clatter of talk for others’ ears, attracts the mother’s attention because she is in some state of preparation for it. Ribot, however, does not remark that to say the mind acts in a prepared way is simply to say it acts from a formed association, such action not being inhibitory. If interest be the sole incitement to attention, it is that the energy spent upon the interesting suggestion leaves none for others, rather than that a positive inhibition of the latter throws waste energy into the former. This only happens when attention is controlled for a conscious purpose. If, in the beginning of his inquiry, Ribot had discarded the unscientific word “attention,” and with it his feeble antithesis of association and attention, the truth would have shone out that the main phenomenon is emotional association, aided in certain cases by acts of inhibition.
The most interesting and valuable parts of the book are those devoted to corporeal concomitants of attention. Evidence is that in this act parts of the brain receive increase of blood. This must be due to stimulation of the vaso-motor nerves, belonging to the sympathetic system, under the influence of the desire in the interest of which attention is excited. Moreover, in intense attention the breath is held, and in every case respiration is slackened. There are, besides, certain muscular actions: in external attention, the eyebrows and the skin of the forehead over them are drawn up, the eyes opened wide and directed to the object, the jaw more or less dropped, and the whole body held immobile in an attitude as if approaching the object. In internal attention, the brow is contracted, the eyebrow lowered, the lid at least partially closed, the jaw clenched, the lips pursed up, the body usually immobile, preferentially in a sitting posture with the whole arms close to the trunk. There are, however, often motions, as walking up and down. These muscular states are indispensible conditions of attention. “It is impossible to reflect while running at full speed or climbing a steep ascent.” “A child, seven years old,” not able to breathe through its nose, owing to a tumor, “had succeeded in learning, during a whole year, only the first three letters of the alphabet. Having been operated upon for its adenoid tumor, the same child in a single week learned the entire alphabet.”
According to Ribot, these muscular actions are not aids to attention, but constitute attention. The notion that we think with our muscles is very attractive to the whole new school. Ask why, and you are told, because “every act of volition, whether impulsive or prohibitory, acts only upon muscles and through muscles; any other conception is vague, incomprehensible, and chimerical.” This little burst of emphasis signifies defective evidence. When positive evidence is at hand, it is calmly put in; when prejudices have to be addressed, warmth is in order. The truth is, all these physiological psychologists are “monists.” For theory of connection of soul and body, they have struck a happy compromise between materialism and spiritualism, in holding that mind and matter are simply two aspects of the same thing. If the balance were really preserved between the opposing tendencies, the result would be a doctrine in harmony with philosophic pessimism, but not easily reconciled with observed facts. But is the balance held even by the psychophysicists? They say, for example, that unorganized matter feels, if at all, very little. But when we expect them to balance this by cases in which mind is barely, if at all, connected with matter, they insist,