Complexity_ A Guided Tour - Melanie Mitchell [98]
FIGURE 13.11.
Figure 13.11: Indeed, not much later in the run this happens: the c–j correspondence has been broken and the c–J correspondence has been restored. In addition, the proposed whole-string correspondence between abc and mrrjjj has been built; underlying it are the mappings whole ⇒ whole, successor-group ⇒ successor-group, right ⇒ right (direction of the links underlying both groups), successor ⇒ successor (type of links underlying both groups), letter-category ⇒ length, and 3 ⇒ 3 (size of both groups).
The now very coherent set of perceptual structures built by the program resulted in a very low temperature (11), and (probabilistically) due to this low temperature, a codelet has succeeded in translating the rule according to the slippages present in the Workspace: letter ⇒ group and letter-category ⇒ length (all other mappings are identity mappings). The translated rule is “Replace the length of the rightmost group by its successor,” and the answer is thus mrrjjjj.
It should be clear from the description above that because each run of Copycat is permeated with probabilistic decisions, different answers appear on different runs. Figure 13.12 displays a bar graph showing the different answers Copycat gave over 1,000 runs, each starting from a different random number seed. Each bar’s height gives the relative frequency of the answer it corresponds to, and printed above each bar is the actual number of runs producing that answer. The average final temperature for each answer is also given below each bar’s label.
The frequency of an answer roughly corresponds to how obvious or immediate it is, given the biases of the program. For example, mrrkkk, produced 705 times, is much more immediate to the program than mrrjjjj, which was produced only 42 times. However, the average final temperature on runs producing mrrjjjj is much lower than on runs producing mrrkkk (21 versus 43), indicating that even though the latter is a more immediate answer, the program judges the former to be a better answer, in terms of the strength and coherence of the structures it built to produce each answer.
FIGURE 13.12. A bar graph plotting the different answers Copycat gave over 1,000 runs, each starting from a different random number seed.
Summary
Via the mechanisms illustrated in this run of the program, Copycat avoids the Catch-22 of perception: you can’t explore everything, but you don’t know which possibilities are worth exploring without first exploring them. You have to be open-minded, but the territory is too vast to explore everything; you need to use probabilities in order for exploration to be fair. In Copycat’s biologically inspired strategy, early on there is little information, resulting in high temperature and high degree of randomness, with lots of parallel explorations. As more and more information is obtained and fitting concepts are found, the temperature falls, and exploration becomes more deterministic and more serial as certain concepts come to dominate. The overall result is that the system gradually changes from a mostly random, parallel, bottom-up mode of processing to a deterministic, serial, focused mode in which a coherent perception of the situation at hand is gradually discovered and gradually “frozen in.” As I illustrated in chapter 12, this gradual transition between different modes of processing seems to be a feature common to at least some complex adaptive systems.
Analogies such as those between Copycat and biological systems force us to think more broadly about the systems we are building or trying to understand. If one notices, say, that the role of cytokines in immune signaling is similar to that of codelets that call attention to particular sites in an analogy problem, one is thinking at a general information-processing level about the function of a biological entity. Similarly, if one sees that temperature-like