Theme One Program • Jets and Sharks 2

Re: Theme One Program • Jets and Sharks • (1)

Example 5. Jets and Sharks (cont.)

As we saw last time, Theme One reads the text file shown below and constructs a cactus graph data structure in computer memory.  The cactus graph represents a single logical formula in propositional calculus and that proposition embodies the logical constraints defining the Jets and Sharks data base.

\text{Jets and Sharks} \stackrel{_\bullet}{} \text{Log File}
Theme One Guide • Jets and Sharks • Log File

Our cactus graph incorporates a vocabulary of 41 logical terms, each of which represents a boolean variable, so the proposition in question, call it ``q", is a boolean function of the form q : \mathbb{B}^{41} \to \mathbb{B}.  Given 2^{41} = 2,199,023,255,552 we know a truth table for q takes over two trillion rows and a venn diagram for q takes the same number of cells.  Topping it off, there are 2^{2^{41}} boolean functions of the form f : \mathbb{B}^{41} \to \mathbb{B} and q is just one of them.

Measures of strategy are clearly needed to negotiate patches of cacti like those.

To be continued …

References

  • McClelland, J.L. (2015), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, 2nd ed. (draft), Stanford Parallel Distributed Processing LabOnline, Section 2.3, Figure 2.1.
  • McClelland, J.L., and Rumelhart, D.E. (1988), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, MIT Press, Cambridge, MA.  “Figure 1. Characteristics of a number of individuals belonging to two gangs, the Jets and the Sharks”, p. 39, from McClelland (1981).
  • McClelland, J.L. (1981), “Retrieving General and Specific Knowledge From Stored Knowledge of Specifics”, Proceedings of the Third Annual Conference of the Cognitive Science Society, Berkeley, CA.

Resources

cc: Conceptual GraphsCyberneticsLaws of FormOntolog Forum
cc: FB | Theme One ProgramStructural ModelingSystems Science

This entry was posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Theme One Program • Jets and Sharks 2

  1. Pingback: Survey of Theme One Program • 4 | Inquiry Into Inquiry

  2. Pingback: Theme One Program • Jets and Sharks 3 | Inquiry Into Inquiry

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