Selected Mathematical Topics of the Universal Theory of Innovation
The SP innovation map
The SP-map is constructed as a graph of indefinite size where vertices represent innovation challenges (IC) and edges represent a parent-child relationship between a source (parent), and a derived (child) IC. For each such pair it holds:
p' + p|p' < p
where p is the effort to resolve the parent IC without first resolving the child IC, p' is the effort to resolve the child IC, and p|p' is the effort to resolve the parent IC after having resolved the child IC.
This relationship expands ancestrally:
pn+ pn-1| pn+ ...pi| pi+1+ ...+ p0| p1< p0
The innovation strategy is to find an innovation pathway on the SP-map such that the effort to resolve the original IC will be minimized.
Functional Extension
Innovation challenges may be resolved by combining them with functionally similar challenges of more advanced knowledge. Mathematically we seek isomorphism based on the following premise: given two random entities, A and Z, one would seek to establish a functional similarity between them by identifying entitles B, C, D, which are functionally related to A, and also identify entities W,X,Y which are functionally similar to Z, then search for a functional similarity between the two sets:
A' = {A, B, C, D} and Z' = {Z, W, X, Y)
If A' and Z' are isomorphic sets they establish a similarity between A and Z. Otherwise one could repeat the process for A' and Z', searching for respective entities: B', C' and D' as well as W', X', Y' such that the sets:
A" = {A', B', C' , D'} and: Z"= {Z', W', X', Y')
are isomorphic. If successful the process stops, otherwise it continues.
The fewer iterations are needed before isomorphism is established, the closer A and Z are.
In the innovation process one tries to resolve challenge A, by seeking for a challenge Z for which a resolution is known, or is closer, where Z is as functionally close to A as can be found.
