Information Theory Models of Instabilities in Critical Systems

The following sections are included:

• Preface
• Contents

Here, we introduce ideas from information theory that prove useful in describing both machine and biological cognition, imposing necessary conditions on the transmission of signals that carry meaning. The Data Rate Theorem further relates information and control theories, and we examine as well the implications of Feynman's (2000) (and Bennett's) identification of information as a form of free energy. We close with a striking example of the hidden symmetries to be found in cognitive systems — natural or artificial.

Forthcoming generations of massively parallel `Self-X' machines will be expected to program, repair, and protect themselves while managing a broad range of critical systems in real time. This is, far more than industry sales-men will openly admit, very much terra incognita: we simply do not know how to reliably supervise and stabilize such systems. Animal — and human — models can provide insights, albeit having had the relentless benefit of a half-billion years of evolutionary selection pressure acting on structure and function. This chapter presents an extended meditation on high level animal cognition that will provide a background for later descriptions of complex machine behaviors and pathologies.

The following sections are included:

• Introduction
• A Modular Network Model
• Punctuation
• A ‘Cancer’ Model
• Implications

The following sections are included:

• Introduction
• The Baars Model
• Cognition as Language
• The Cognition Groupoid
• Internal Symmetry Change
• External Symmetry Change
• Emergence
• Multiple Workspaces
• The Dynamical Groupoid
• The Rate Distortion Manifold
• No Free Lunch
• Directed Homotopy
• Implications

The following sections are included:

• Introduction
• Cognition Redux
• Global Broadcast
• Coevolution
• Basic Model
• Programming as `Farming'
• Second Order Programming
• Implications

The following sections are included:

• Introduction
• Epigenetic Inheritance
• Groupoid Free Energy
• Real-Time Dynamics
• Tunable Epigenetic Catalysis
• Implications

The following sections are included:

• Introduction
• Models of Development
• Phase Transitions in Cognitive Systems
• Real Time Systems
• Distortion Dynamics
• Rate Distortion Coevolution
• Multiple Time Scales
• Flight, Fight, and Helplessness
• Machine Psychiatry
• Cost of Regulation
• Cost of Maintenance
• Implications

The following sections are included:

• Introduction
• More Context
• Impact of the Rand Models
• Response to the Disaster
• ‘Delocalization’ of Fire Service Demand
• Control Theory Perspective
• Implications

The following sections are included:

• Introduction
• Data Rate Theorem Redux
• Phase Transition
• Turbulence
• Information Bottleneck
• Reconsidering V2V/V2I Systems
• Implications
• Summary

The following sections are included:

• Introduction
• Information Catalysis
• The Fuzzy Lock-and-Key
• Symmetries of the FLK
• Phase Transitions and Reaction Dynamics
• Implications

A multitasking hierarchical cognitive model appropriate to institutional or massively parallel machine cognition is considerably more complicated than individual human or animal consciousness, biologically limited to a single shifting, tunable second order giant component. Human institutions, by contrast, appear able to entertain several, and often very many, such global broadcasts simultaneously, although these generally operate at a much slower rate than individual consciousness. Highly parallel cognitive machines, according to this model, would be able to function as efficiently as large institutions, but at or near the rate of animal consciousnes.

The following sections are included:

• Groupoids
• Stochastic Differential Equations
• Morse Theory
• The Groupoid Atlas

The following sections are included:

• Bibliography
• Index