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Complexity_ A Guided Tour - Melanie Mitchell [96]

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built, represented by solid rectangles around the letters. For graphical clarity, the links between letters in a group are not displayed. The existence of these groups creates additional pressure to find new successorship and sameness groups, such as the rr sameness group that is being strongly considered. Groups, such as the jjj sameness group, become new objects in the string and can have their own descriptions, as well as links and correspondences to other objects. The capital J represents the object consisting of the jjj group; the abc group likewise is a new object but for clarity a single letter representing it is not displayed. Note that the length of a group is not automatically noticed by the program; it has to be noticed by codelets, just like other attributes of an object. Every time a group node (e.g., successor group, sameness group) is activated in the Slipnet, it spreads some activation to the node length. Thus length is now weakly activated and creating codelets to notice lengths, but these codelets are not urgent compared with others and none so far have run and noticed the lengths of groups.

A rule describing the abc ⇒ abd change has been built: “Replace letter-category of rightmost letter by successor.” The current version of Copycat assumes that the example change consists of the replacement of exactly one letter, so rule-building codelets fill in the template “Replace _______ by _______,” choosing probabilistically from descriptions that the program has attached to the changed letter and its replacement, with a probabilistic bias toward choosing more abstract descriptions (e.g., usually preferring rightmost letter to C).

FIGURE 13.6.

The temperature has fallen to 53, resulting from the increasing perceptual organization reflected in the structures that have been built.

Figure 13.6: Two-hundred twenty-five codelets have run. The letter-to-letter c–j correspondence has been defeated by the letter-to-group c–J correspondence. Reflecting this, the rightmost ⇒ rightmost mapping has been joined by a letter ⇒ group mapping underlying the correspondence. The c–J correspondence is stronger than the c–j correspondence because the former covers more objects and because the concept group is highly active and thus seen as highly relevant to the problem. However, in spite of its relative weakness, the c–j correspondence is again being considered by a new team of codelets.

Meanwhile, the rr group has been built. In addition, its length (represented by the 2 next to the R) has been noticed by a codelet (a probabilistic event). This event activated the node length, creating pressure to notice other groups’ lengths.

A new rule, “Replace the letter category of the rightmost letter by ‘D,’ ” has replaced the old one at the top of the screen. Although this rule is weaker than the previous one, competitions between rival structures (including rules) are decided probabilistically, and this one simply happened to win. However, its weakness has caused the temperature to increase to 58.

If the program were to stop now (which is quite unlikely, since a key factor in the program’s probabilistic decision to stop is the temperature, which is still relatively high), the rule would be adapted for application to the string mrrjjj as “Replace the letter category of the rightmost group by ‘D,’ ” obeying the slippage letter ⇒ group spelled out under the c–J correspondence. This yields answer mrrddd, an answer that Copycat does indeed produce, though on very rare occasions.

FIGURE 13.7.

Codelets that attempt to create an answer run frequently throughout the program (their attempts are not displayed here) but are not likely to succeed unless the temperature is low.

Figure 13.7: Four hundred eighty codelets into the run, the rule “Replace letter-category of rightmost letter by successor” has been restored after it out-competed the previous weaker rule (a probabilistic event). However, the strong c–J correspondence was broken and replaced by its weaker rival, the c–j correspondence (also a probabilistic event). As a consequence,

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