Global Perspectives on the Ecology of Human-Machine Systems - Vol. 1

By John Flach; Peter Hancock et al. | Go to book overview

Appendix B
A Sketch of the Fiber Bundle Geometry Needed for the Intentional Dynamics

A fiber bundle geometry is the appropriate mathematics in which to express a potential solution to the ecometric (information) scaling problem and the ecomechanic (energy) transduction problem. Using the generalized Hamiltonian and its natural fiber bundle structure, we can define two different fiber bundles on both the control field and the information field construed as base spaces:

Figure 11.B1:Indefinite Ecological Fiber Bundles without Gauging.

Definition: A fiber is defined as a projectivity from one vector field over a base space, containing information flow paths to another vector field over another base space which contains control paths.

Fibers are parallel to one another and independent unless connected by some function. For instance, a goal-path integral which scales information detection flow paths in one base space to energy control paths in another base space. The ecometric scaling problem is to discover the definite magnitude (gauging) to place on the fiber defined over the information field. The ecomechanics transduction problem is to discover the definite magnitude (gauging) to place on the fiber defined

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