I start with two goodies which Melzak taught us in his book, Bypasses. The first concerns the role of bypass in prehistory and history.

Says Melzak, "Man evolved by learning to cope with complexity. .... It may even be that the bypass principle, in its various aspects, was so successful a means of coping with complexity that the evolving hominid ended up by interiorizing it, and so became man." What a conception!

Hommy the Hominid -- who used BYPASS in his primitive tool-making and in his survival tactics -- turned this EXTRINSIC STRATEGY into an INTRINSIC COGNITIVE STRATEGY -- working out "the steps mentally before trying them out in reality". And, allegedly, this CHANGED HOMINID INTO HUMAN!

A BYPASS has the form:

                   difficult/impossible task
                   ------------------------->
        transforn  |                        ^transform back
        to possible|                        |to terms of
        or easy    |                        |original task
        task       |                        |
                   |                        |
                   V------------------------>
                          perform task       

I can show how NONTRIVIAL this STRATEGY is by saying that, in MATHEMATICS, IT DETERMINES THE EIGENVALUES OF A MATRIX OR MULTIVECTOR. In Physics, IT IS THE PRINCIPAL TOOL OF QUANTUM MATH FOR FINDING THE STABLE STATES OR RADIATION STATES OF FUNDAMENTAL PARTICLES.

This can be made more plausible by calling upon that other goodie Melzak taught us in his book: HOMOLOGY IS A SPECIAL CASE OF BYPASS in the form I've sketched above; in the form of the theory of proportions; in the form of kennings in Anglo-Saxon literature; etc.

We need to "flesh out" this ansatz:

1. extensively describe bypasses in the tool-making and survival tactics of animals and hominids;

2. use HOMOLOGY to TRANSFORM THESE EXTRINSIC BYPASSES INTO INTERIOR BYPASSES;

3. show how this process develops its the purest form in LOGICO-MATHEMATICS;

4. find homologies between non-scientific bypasses and scientific ones.

Consider these BYGRAMS.