The figures in which the observers reported their judgments of absolute number have a value that is chiefly qualitative. The marked inconsistencies and disagreements are our guarantee for this statement. With all the observers there was but the loosest association between group-appearance and number-name. The innumerable variations in internal space-relations were of course responsible. For one observer a particular name probably had a quantitative significance far in excess of its value for another observer in this respect. To one man 100 might have meant about the same as 60, for example, to his neighbor. On the whole they were parsimonious; but Baldwin decidedly not.
A more or less constant influence was exerted on any given judgment by the comparison of the presented group with the traces of the preceding still in mind. The observers felt, however, that the judgment was largely independent of such comparison, and its fluctuations give some credence to this feeling.
The numbers chosen ranged by fives, from 25 to 100. In four cases a number was immediately repeated that rough suggestions as to the definiteness of the judgment and its dependence upon the actual number might be gained. These were indeed but rough suggestions, since, with certain exceptions to be noticed later, the arrangement was disturbed between times; but they made possible a closer watch upon the flickering of the judgment than could be kept by a mere repetition of the series. In the latter case it might be unstable and yet relatively firm in the other. A standard series is here recorded. Its order was determined by drawing the numbers out of a heap, but the repetitions were inserted arbitrarily.
- 1. 95
- 2. 25
- 3. 35
- 4. 65
- 5. No change
- 6. 30
- 7. 90
- 8. 85
- 9. 45
- 10. 100
- 11. 50
- 12. No change
- 13. 60
- 14. 40
- 15. No change
- 16. 70
- 17. 80
- 18. 55
- 19. 75
- 20. No change
1. Absolute Number under Standard Conditions.
An indispensable preliminary for the present study is the establishment of a standard. Unless we know something in advance about the characteristics of the judgment of absolute number in relatively simple conditions, we shall be unable to tell what influence, if any, to attribute to the modifying factor in later experiments. Having then decided as to the general conditions under which we will study the problem we must make these the standard conditions of our work; and having discovered the nature of the judgments given under them, measure up to these results in all that is to follow. These standard conditions have already been set forth in the introduction to this section. The results are recorded in Tables XIX and XX.
TABLE XIX
| Subject = Baldwin | Subject = Miller | ||||||
|---|---|---|---|---|---|---|---|
| Trials with each number | 6 | 3 | 3 | 4 | 2 | 3 | |
| Original Numbers | Standard | Scattered | Compact | Standard | Scattered | Compact | |
The figures recorded Baldwin never under- | 25 | 1 | 0 | -6 | -10 | -6 | -4 |
| 30 | 3 | 5 | -5 | -12 | -7 | -6 | |
| 35 | 10 | 7 | -3 | -14 | -4 | -7 | |
| 40 | 10 | 13 | -8 | -15 | -8 | -11 | |
| 40 | 10 | 8 | -8 | -14 | -10 | -12 | |
| 45 | 10 | 18 | -3 | -21 | -13 | -10 | |
| 50 | 17 | 23 | 2 | -19 | -15 | -17 | |
| 50 | 15 | 22 | 2 | -17 | -15 | -14 | |
| 55 | 27 | 40 | 0 | -18 | -3 | -12 | |
| 60 | 19 | 33 | 5 | -20 | -23 | -17 | |
| 65 | 27 | 53 | 2 | -18 | -3 | -7 | |
| 65 | 24 | 57 | 5 | -13 | -13 | 2 | |
| 70 | 38 | 77 | 0 | -19 | 8 | -8 | |
| 75 | 31 | 73 | 0 | -24 | 10 | -20 | |
| 75 | 28 | 78 | -5 | -24 | 8 | -8 | |
| 80 | 36 | 83 | -5 | -14 | 5 | -18 | |
| 85 | 54 | 85 | 5 | -19 | -8 | 0 | |
| 90 | 54 | 90 | 5 | -13 | 8 | -3 | |
| 95 | 48 | 73 | 5 | -30 | 20 | -15 | |
| 100 | 61 | 87 | 7 | -13 | 10 | -7 | |
Turning to these tables we notice at once, as characteristic of all the observers, the following facts: (1) Wide variation from objective correctness. (2) A far wider discrepancy with the larger numbers than with the smaller. Miller does not wholly agree here. His judgments by series show inconstancy, tending at first to follow the rule, but in the last two series to a maximum error near the middle. Certain remarks of this observer suggest that possibly in the latter case reflection as to the convenience of certain actual numbers for manipulation may have had influence. The three earlier series of Hutchison conform to the rule. The remainder, on the contrary, show no definite progression in tendency. It should be noted here that both Miller and Hutchison were more inclined than the other two observers to rough calculation. The effect of its adoption or of increased practice in it is shown by the disappearance of the characteristics of the earlier series. We have thus in these two cases a doubleness of standard that we must not fail to consider in our later comparisons. (3) There is a pronounced instability of judgment, as shown by the fluctuations for the same number in different series, and especially in successive judgments, of the same in any given series. (4) There is a general tendency to judge in multiples of five. That there should be any splitting of fives, particularly in the large numbers, might be regarded as mere caprice. Not so did it seem to the observers. They were conscious of an apparent absurdity in it where judgments were necessarily so vague; but they insisted that this stood for a kind of qualitative shading in the perception which threw out the choice of the round numbers just above and below. (5) The number is on the whole underestimated, three observers agreeing in this respect; but the fourth shows a very large and consistent tendency in the opposite direction.