Appendix 1

I have made my argument in simple, stark, black-and-white terms in order to convey it more easily. No special cases, no ifs-and-buts were addressed and someone with a knowledge of physics would probably be aghast at my brevity. I ask you please to read between the lines. For example, I have not used the term 'force' in its strict physics textbook definition nor should the constraint of a bond be understood to apply only to the distance between its constituent objects - it could well be their momenta or energies that are the subject of their constraint - and so on.

I am happy to address questions you may have by email (my email address is on the title page of this book), and would rather you email me than abandon the main argument, for the argument may deliver overall outcomes that are not dependent on the missing details.

However, there are some matters of detail that I feel should be covered here.

The Limited Flexibility of Bonds

The main text describes how a bond prevents its constituent objects from participating in external interactions as the bond s constraint prevents suitable responses to the external interaction, effectively negating them. The external interaction then affects the bond as a whole instead of affecting its constituent objects, and behaves as if the interaction was with the bond as a single object rather than with its individual constituents.

Now the constraint of a bond holds its constituent objects to a range of values rather than to a single value, meaning that there can be some response by the constituent objects to the external interaction within the range allowed by the constraint, however small that may be. That is, a bond need not completely negate the effect of an external interaction on its constituent objects. The external interaction could affect both the bond s constituent objects and the bond-as-a-whole, such that the bond-as-a-whole only responds to the external force to the degree that it negates the force on its constituent objects. The more that the effect of the external force on the constituent objects exceeds the constraining range of the bond, the greater is its effect on the bond as a whole.

The degree of the negation may of course be so great, or the range of a constraint so narrow, that for all practical purposes, the bond s constituent objects are comparatively undisturbed by the external interaction and the bond as a whole appears to respond fully. On the other hand, if the constituent objects are allowed a significant response to the external interaction, then both the bond and its constituent objects can respond to the external interaction.

In the case of a partially negated external interaction a bond displays a spatial volume of its own as well as the spatial volumes of its constituent objects (and perhaps those of their internal objects if they are partially negated). Outside objects are excluded from the spatial volume of the bond-as-a-whole as well as from the spatial volumes of its constituent objects. The excluding spatial volume of the bond may be enlarged by the volumes of its constituent objects and made less rigid by them.

While there is a degree of flexibility in the spatial volume of a bond, it is always only a degree. A bond can never be as flexible as a connective, for in a connective there are no constraints at all, meaning that the flexibility of a connective is limitless while any flexibility to a bond, even when sublimated, is limited.

In the discussion below, I describe how bonds can be made very flexible, like rubber bands, by chaining them together.

Indirect Bonds

Objects may participate in more than one interaction simultaneously.

In the case of connective interactions, multiplicity is straightforward, allowing objects to be linked in a network of different interactions utilizing different forces rather than all being direct participants in the same interaction. There may be an indirect connection between all the objects in a network with the connection between some objects mediated through others.

In the case of a bond, its constraint may prevent its constituent objects from participating in external interactions. But this is so only if the force utilized by the external interaction relies on properties that the bond is constraining, because of possible conflict with the constraint. If it relies on unconstrained properties, the constraint of the bond is not challenged and the external interaction is not negated. So the constituent objects of a bond may yet participate in an external interaction if that interaction utilizes properties not constrained by the bond - and that second interaction may also be a bond.

A bond's constraint will also not prevent its constituent objects from participating in an external bond when the external interaction does utilize properties the bond is constraining but the external bond's constraint ranges are the same as the bond's so there is no conflict maintaining both constraints.

An external interaction by a bond's constituent object may well be with the constituent object of another bond, with the result that the two bonds aggregate via a bond between their constituent objects. Both or either of these two bonds may aggregate in this same way with yet other bonds, to create a chain of bonds aggregated via their constituent objects rather than their topmost objects. In this way bonds can bond with each other in horizontal chains rather than in vertical hierarchies, with the bonds at either end of a chain linked to each other indirectly through the mediation of other bonds.

Both connective and binding interactions can thus also be indirect, that is, mediated through a chain of interacting objects.

An indirect bond can also interact as an object in its own right with its own emergent properties. But the overall constraint of an indirect bond is a composite of the constraints of its composite bonds, so any leeway in each component constraint adds to the total leeway in the indirect bond. The greater the number of bonds in the chain, the more the composite constraint can widen. A very long indirect bond can be very flexible indeed, like a balloon or a long polymeric molecule, though ultimately its flexibility remains limited.

Since an indirect bond can interact as a single object in its own right, it may be a constituent object of a direct bond, and so reside within its hierarchy, while the whole hierarchy of a direct bond may be just one link in the chain of an indirect bond.

The architective hierarchy of an aggregate offers a clearly defined and fixed map of all the direct and indirect bonds in its construction. Indirect bonds may be more flexible, but their architectures remain fixed.