Remembering the Future

A new kind of mathematics/science is starting to form that is based on computation instead of equations. In this new world, mathematical symbols are replaced with identity indicators, like database keys and topic map PSIs. These identity markers are bound to data structures like XML instead of dimensional numeric structures.

These structures are changed by applying transformations like Web Services and XSLT instead of atom numeric and logic operations. While traditional programming operated on programming structures at a local level (changing specific variable bindings) in the new model, data structures are transformed as a whole. A service takes in a coherent structure and returns a coherent structure. The holistic coherence of that structure can be checked before it is accepted for processing by the service, and after it has been transformed.

These transformations also have identity, and can therefore be represented within a data structure. This allows an evolving resource (representation) to contain within itself, the actions that allow it to continue to be transformed.

A data structure may contain links to many alternative services for transformation. This requires that either a human interpret the data to select an action, or that there is some method for automating the evaluation and selection of an action/transformation. In order to be compared, the evaluation of these alternative actions must once again be represented as numeric values that can be given an order (preference).

In applied mathematics, these kind of temporal credit assignment problems are solved through the use of dynamic programming. In computer science, these topics have been studied in research on artificial life and computational models of evolution and reinforcement learning.

See also:
Christopher Alexander on programming
social software: representing relationships, part 3
The meaning of SOA
Workflow, RSS and business documents
Conceptions of a Global Brain: a historical review
The Philosophical Basis of Knowledge Representation and the Web