College students were presented a series of problems consisting of two numbers to be added (A + IB) and a comparison number (C) ranging 13-153. They were to choose the larger, A 4-B or C, as rapidly as possible. Errors and latency increased with size of numbers, except when A + B and C were on opposite sides of 100. Speed and accuracy increased with the difference between A and B, but were also high when A = B. Errors and latency increased when the absolute difference between A + B and C was relatively small, requiring high accuracy on the part of 6". The results were interpreted in terms of an analog operation in which 5s place the magnitudes symbolized by numbers on the number line (an imaginary analog) for manipulating and judging.

When college students learn patterned sequences, they divide them into subparts. Each subpart has the property that it can be generated unambiguously by simple rules. Such a rule system consists of E, the set of elements or events forthcoming, and I, the set of intervals leading from one event to the next. Parts or their generating rule systems can be the elements of higher order rule systems. This produces the "recursive E-I theory." One part is generated from another by any of a class of transitions such as repeating, transposing, or inverting. By applying such transitions as compound functions, one generates structural trees, which give a particularly simple account of certain regular patterns. Experimental results show that the difficulty of learning a transition within such a pattern depends on how high it is in the tree. The theoretical results are applied to the theory of music. 481 1970 by the American Psychological Association, Inc.

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"A stochastic model for the solution of cue learning problems by the selection of strategies was stated and developed. Errors were shown to constitute a system of uncertain recurrent events in Feller's sense. Three models, one strategy-at-a-time, all-strategies-at-once, and a-random-sample-of-strategies, were formulated and shown to yield the same system of recurrent events to be identical in terms of data."

It is possible to construct a line drawing that represents one object partly hidden behind another, and most subjects complete the interrupted figure and see the hidden object as whole. This article is addressed to two problems: (a) What are the necessary and sufficient conditions for such figural completion to occur, and (b) exactly what will be seen behind the occluding figure---that is, what completion will be made? Leeuwenberg's coding model for line drawings was used to analyze a number of such figures, along with the hypothesis that figural completion occurs whenever it results in a simplification of final code of the whole figure. Data from previous experiments along with results from two new experimental studies were collected and shown to agree with this hypothesis. Of various possible figural completions or "mosaic" interpretations, subjects chose the ones resulting in the simplest overall code. However, the above conclusions are correct only if "simple" is precisely defined as the smallest information load in a completely reduced code. Other possible theories of figural completion, both structuralist and Gestalt, may invoke familiarity, particular "cues," like T-shaped intersections, simplicity of the hidden figure, symmetry, and good continuation. All such possibilities were considered in the experiments and shown to fail, wrongly predicting at least one figure. The coding-theory analysis, on the other hand, made correct predictions for all of the 25 figures used.