Again, this suggests an analogy with human behavior: experiencing the most emotion-packed events first and then tapering off may be more tolerable than the reverse. Other variations of input also suggest interpretation in terms of human psychology. Sandwiching a low-emotion event between two high-emotion events, say 7 2 7, can make the total sequence tolerable; by contrast, the events 7 7 2 and 2 7 7 produce mad behavior. The mathematics underlying this TEMPER model can be exposed quickly and naturally. For example, after some experimentation with the program, one might wonder: How many 5s can the program take before it 'blows its top?' [image] A sequence of 5s builds up EMOTION to higher and higher values, but never reaches 10. This process parallels the well-known geometric series 1 1/2 1/4 1/8 1/16 1/32... the sum of which converges to 2. Exploring in this way, a child may gain some insight into the nature of infinite series in an active and interesting (at least less abstract) setting. Some simple modifications of the TEMPER program students might make are to: (a) change the threshold, e.g. from 10 to 25 for higher tolerance, or to ?25 (a random number) for unpredictable behavior; (b) modify the model, e.g. from EMOTION ÷ 2 to EMOTION ÷ 3 to express stronger 'forgetting'; (c) adapt the program for use by others, e.g. inserting conversational statements such as 'ENTER NUMBERS FROM 1 TO 9' or even 'CAUTION! THIS PROGRAM MAY BECOME EMOTIONAL. . .', and (d) make the program dynamic, e.g. automatically resetting EMOTION to 0 after an emotional catharthis. Possible extensions of TEMPER include: (a) writing related programs, such as a version with multiple emotional dimensions like ANGER, FEAR, and LOVE, and (b) writing companion programs, such as two TEMPER-like programs which interact with each other so that one's output is the other's input. CYBERNETICS In the area of cybernetics, students can be introduced to some sophisticated ideas by using simple computer programs. Scene analysis, for example, is an important part of robotics research. ln designing vision machines, it is important to know what types of scenes can be computationally distinguished. Consider the two scenes below: SCENES [image] One scene is "connected"; the other is not connected. Note that the same line segments comprise the two scenes, but that they are in different positions. Suppose one of these two SCENES is PICKed at random. Call it MYSTERY. Further suppose that you are permitted to PEEK at small portions of the MYSTERY scene -- called "microscenes" --but you are not told where the microscenes came from. For example, [image]PEEK MYSTERY PEEKing at MYSTERY is like using a flashlight to illuminate small unidentifiable places on a much larger unknown scene. PEEK MISTERY PEEK MISTERY After a period of probing, the question arises: Can you determine which scene it is that you are looking at?' (The answer is postponed so that the reader may ponder this question.) The APL programs which facilitate exploration of this question in scene analysis are simple indeed: This program will PICK one of 2 SCENES at random for the result called MYSTERY. MYSTERY PICK SCENES  MYSTERY SCENES[?2;;] This program will PEEK at some two-dimensional SCENE and produce a random 4 by 4 portion for the result called MICROSCENE. MICROSCENE PEEK SCENE  MICROSCENE SCENE The enterprising student might elect to automate the production of MICROSCENEs. [image]AUTOPEEK AUTOPEEK  ''  PEEK MYSTERY  ''  »i Soon it should become clear that these two SCENES cannot be distinguished on the basis of random microscenes This question is treated as a theorem by Minsky and Papert in their book Perceptrons, MIT Press, 1970. Perceptrons are theoretical machines which can be trained to detect features of a scene by computations in a layered network of logical elements.