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Tweedledum and Tweedledee: Symmetry in Behavior Analysis

Tweedledum and Tweedledee: Symmetry in Behavior Analysis. M. Jackson Marr Georgia Institute of Technology mm27@prism.gatech.edu. Maxwell’s Equations. Symmetry between electricity and magnetism: Explained the nature of light as electromagnetic waves moving at speed c.

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Tweedledum and Tweedledee: Symmetry in Behavior Analysis

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  1. Tweedledum and Tweedledee:Symmetry in Behavior Analysis M. Jackson Marr Georgia Institute of Technology mm27@prism.gatech.edu

  2. Maxwell’s Equations • Symmetry between electricity and magnetism: Explained the nature of light as electromagnetic waves moving at speed c.

  3. Einstein’s Principles of Relativity • (1) Laws of physics independent of states of motion. • (2) Constancy of the speed of light, independent of states of motion. • One implication: Equivalence of mass and energy. E = mc2

  4. SYMMETRY AND CONSERVATION LAWS • Emmy Noether’s Theorem: For every symmetry exhibited by a physical law, there is a corresponding observable quantity that is conserved. • Momentum: translations in space (including rotations). • Energy: translations in time. • Many other examples of symmetry/conservation, e.g., in particle physics (e.g., CPT—charge, parity, time—all together.).

  5. SYMMETRIES IN BEHAVIOR ANALYSIS Positive and negative reinforcement Positive and negative punishment Reinforcement and punishment Discrimination and generalization Shaping dynamics Three-term contingency Equivalence and n-term contingency Schedule performance Generally, invariances in behavior-analytic principles (contingencies, species, intra- and inter-individual, and socio-cultural behaviors)

  6. MEN ACT UPON THE WORLD, AND CHANGE IT, AND ARE CHANGED IN TURN BY THE CONSEQUENCES OF THEIR ACTION.B. F. Skinner, Verbal Behavior, 1957, p. 1

  7. Operant Conditioning

  8. O-rules, functional relations B = f (r) r: feedback B: output E-rules, feedback functions r = g (B) Figure 1. The behavior-environment feedback system Operant Conditioning

  9. SD SR Ro SD: discriminative stimulus Ro: operant class SR: reinforcer Three-term Contingency F: force m: mass dv/dt: acceleration Newton’s Second Law of Motion

  10. The Equivalence Relation: Ordered pairs of all elements that participate in the reinforcement contingency

  11. EQUIVALENCE RELATION GIVEN SETS: A, B, & C A = A; B = B; C = C (reflexivity or matching) AND A = B → B = A; B = C → C = B (symmetry) AND IF A = B and B = C, then A = C (transitivity)

  12. Operant Conditioning

  13. Operant Conditioning

  14. Scale Invariance in FI Schedules with  = 1

  15. If f (x) = c xα then, log f (x) = log c + αlog x. This is a linear function on a log-log scale, with slope  (the scaling factor).

  16. Scaling Rate and Response Number in FI Schedules

  17. Scaling in IRT>t Schedules IRT>t Scheduled Value

  18. MATCHING LAW • R1 / R2 = r1 / r2 Herrnstein • R1 / R2 = b (r1 / r2)a Baum

  19. HERRNSTEIN’S HYPERBOLA Conservation of Behavior: Exclusive choice is conserved; either you do one thing or another, each action with differential consequences (r and r0), and total behavior in the situation is constant (k).

  20. FI 10 (FR 20: Sp)

  21. Symmetry, as wide or as narrow as you define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection. Hermann Weyl, Symmetry (1952, p. 5)

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