The Work of Betty Tuller The Work of Betty Tuller and Complex Systemsand Complex Systems

John CadwalladerJohn Cadwallader

PSB 4065PSB 4065

Complex SystemsComplex Systems

• Composed of a large number of simple agents interacting with one another according to specified rules.

• Share universal patterns.

Complex SystemsComplex Systems

• Examples:– Molecules in a liquid– Genes in a cell– Organisms in an ecosystem– Buyers/sellers in an economy– ISPs on the internet– Neurons in a brain?!?!?

Complex SystemsComplex Systems

• Share Common Properties:– Phase transitions– Order parameter(s)– Control parameter(s)– “Slaving”– Enhanced contrast– Hysteresis– Others…

Phase TransitionsPhase Transitions

• Rayleigh-Bernard Instability

Order and Control ParametersOrder and Control Parameters

SlavingSlaving

• Analogy: state of an army can be described without reference to any individual soldier. The state of every soldier is a slave to the state of the army. In understanding the system we don’t have to worry about every single degree of freedom.

HysteresisHysteresis

How does all of this apply to How does all of this apply to behavior?behavior?

Speech Categorization: Tuller et al. Speech Categorization: Tuller et al. 19941994

• How do we determine what a person’s utterance means?– Different people say the same word

differently.– The same word can sound different in

different environments.– Same-sounding words can have different

meanings.

Speech Categorization: Tuller et al. Speech Categorization: Tuller et al. 19941994

• Used a “say” – “stay” continuum

• Varied the gap between the “s” and the rest of the word.

Speech Categorization: Tuller et al. Speech Categorization: Tuller et al. 19941994

• Order parameter: interpretation of stimulus

• Control parameter: interval between s and rest of word

• Patterns:– Hysteresis– Enhanced contrast

• Indicative of complex systems-like behavior

Speech Categorization: Tuller et al. Speech Categorization: Tuller et al. 19941994

P. Kruse et al 1996P. Kruse et al 1996

• The perception of multistable visual objects• Different groups of lights flash alternately

P. Kruse et al 1996P. Kruse et al 1996

• Percepts range from:– No apparent motion– Alternating motion– Unidirectional motion– Bidirectional motion– All lights appear on

simultaneously

P. Kruse et al 1996P. Kruse et al 1996

• Order parameter: type of motion observed

• Control parameter: interval between lights

P. Kruse et al 1996P. Kruse et al 1996

Freeman 1997Freeman 1997

• Olfactory coding• How does olfactory bulb recognize

different odors?• No one-to-one correspondence between

odorant and cells in the olfactory bulb.• Even lesioning areas of the bulb that are

most activated by a particular odorant does not prevent the animal from recognizing the odorant.

Freeman 1997Freeman 1997

ConclusionsConclusions

• Complex systems approach offers powerful method for understanding macro-scale brain function

• Also offers direct path for simulating brain function on computers, something the cognitive approach and behavioristic approach do not allow (in any straightforward manner)