Chapter 2: Features of Connective and Binding Interactions

The Wholeness of Bonds

The fact that objects are fastened together in a bond becomes evident when an external force acts on them and they do not respond individually. Rather the bond responds as a whole so as to allow its constituent objects to remain within their constraint. The bond responds while its constituent objects remain relatively unmoved within it.

For example, in the case of a proton and an electron, it becomes evident that they are bound together in an atom when an external force that should affect them individually affects the atom as a whole instead.

Consider that an external force is also occurring in the context of an interaction - with one or more external objects - and when the bond responds as a whole the external objects respond to it as a whole rather than to its individual constituents.

A bond may thus participate in external interactions as a single object in its own right, while a connective always participates in external interactions as the collection of its individual objects. The objects of a connective may appear to respond as a group when their responses are similar, but they do not respond as a single object. The participating objects of a connective are free to respond without constraint and so always respond individually.

Since a bond may participate in an external interaction as a single object in its own right, any object may in fact be a bond. Protons, for example, are bonds of quarks utilizing the strong nuclear force for their binding.

Bonds can be Disrupted

The constraints of bonds have limited strengths, known as their binding strengths, beyond which they become unstable and break down. A relevant external interaction more energetic than a bond's binding strength will overcome its constraint and release its objects from their bond, in which case I say that the bond has been disrupted.

(Bonds sometimes offer a number of possible ranges for constraint, with each range having a different binding strength, so that an external interaction may cause a bond to switch to a constraint range having a binding strength able to withstand the external interaction. But should there be no range available with a strong enough binding strength, the bond is disrupted.)

Once an external interaction has disrupted a bond, the erstwhile bond's objects can respond completely freely to each other and to the external interaction, for their interaction is now connective. But breaking the constraint will have drained some if not all of the energy of the external interaction. Energy is expended in disrupting a bond.

For example, it is possible to exert a force on an atom that is so strong that its electrons and protons are freed from their bond. Those electrons and protons continue to interact with each other (courtesy of the electromagnetic force between them) but now interact connectively, moving without constraint in a plasma, and respond freely to each other and to what remains of the interaction that disrupted their bond. But the atom they constituted is no more - the bond between them, the bond that made them an atom, has been disrupted.

Bonds do not disrupt spontaneously. It takes an external interaction to disrupt a bond. There is nothing that a bound proton or electron can do unassisted to escape their atom. Bonds last until an outside influence disrupts them. (The apparently spontaneous disruption of radioactive isotopes can be seen as the stronger electromagnetic forces repelling their protons exceeding the constraint of the nuclear interaction binding them.)

To remove an object from a bond its constraint must be broken. In which case the bond (and the whole object it constituted) ceases to exist (though the remaining objects may then establish a new bond). When removing an object from a connective there is no constraint to break and the same connective interaction continues among the remaining objects. Connectives do not cease to exist when objects are removed (until of course there is only one object left).

It is important for my story to stress that for a bond to be disrupted a constraint must be broken. We often picture an electron and proton in an atom orbiting each other in the way that the Earth orbits the sun, but there is a significant difference: An electron and proton in an atom are locked in constraint while the Earth is not locked in constraint with the sun. The Earth may have settled into a regular orbit around the sun but is not fasted to the sun or constrained to a particular orbit. The Earth could imaginably be nudged to another orbit, or even removed from the solar system entirely, say by the gravitational force of a rogue planet passing close by, which need only expend enough energy to shift the Earth without having to break a constraint as well. Electrons and protons are locked in atoms but planets and suns are not locked in solar systems. The presence of a rogue planet would affect each planet individually rather than move a solar system as a whole. An atom exemplifies a bond while a solar system exemplifies a connective.

The composition of a bond - the collection of objects that are bound by it - remains unchanged until the bond is disrupted. Removing an object from a bond disrupts it while adding a new object can be viewed as an aggregation to the bond - the establishment of an additional bond with the new object (as will be described shortly). A bond can be seen to persist with the same objects it was initially established with until it is disrupted, with no objects entering and no objects leaving for as long as it endures. A connective, on the other hand, persists, and its composition changes, as objects join or leave.

The Separateness of Bonds

By not responding to external interactions and not venturing beyond their constraint, the objects in a bond separate themselves from the rest of the world.

By fastening to each other and not to any other objects, the objects in a bond establish a special relationship that distinguishes them from the rest of the world.

By shielding its constituent objects from the influences of external objects, a bond keeps external objects out of its interior. A bond holds a volume from which external objects are excluded. Multiple bonds/objects cannot occupy the same space at the same time. (This will later be clarified to be only objects that are interacting with each other being excluded from each other's interior. Also, at scales where quantum effects prevail, it is not possible to say exactly where an object is so it is also not possible to say with certainty that objects cannot occupy the same space at the same time. However, atoms are known have measurable volumes from which they exclude other atoms (see Van der Waals Volumes) so we can say with certainty that interacting objects cannot occupy the same space at the same time at least at the atomic scale and larger.)

A connective does not shield its participating objects from external influences and so does not have an excluding spatial volume of its own - only its participating objects do, from which they exclude each other (and any external objects they interact with).

Bonds/objects collide but remain separate when they meet because they exclude each other from their volumes. When connectives meet they may merge into a shared volume and may even pass through each other, though their participating objects may collide in the process.

Emergence

The properties of a bond-as-a-whole can be very different to those of its constituent objects. An atom, for example, displays properties very different to those of its constituent protons and electrons, and its excluding volume can be much different than the volumes of its protons and electrons added together. Water comprises molecules that are bonds of hydrogen and oxygen atoms and is a liquid (at room temperature), while hydrogen and oxygen are gasses. A mixture of say 50 litres of hydrogen gas and 25 litres of oxygen gas has a mixed volume of 75 litres, but get them to bond (with a spark) and they cram into only a tablespoon of water.

The properties a bond displays in its own right are termed its emergent properties. It is the emergent properties of water that makes it different to an unbound mixture of hydrogen and oxygen. We can say that water emerges from a bonding of hydrogen and oxygen. Some of the emergent properties of a bond may be entirely novel - not displayed by any of the bond's constituent objects - while some may be shared with its constituent objects, or there may be properties of the constituent objects missing from the bond's display.

The properties displayed by a connective on the other hand, are not any different to those of its participating objects. A connective does not have emergent properties. A connective displays the properties of its participating objects, perhaps summed as a group, but does not have emergent properties of its own. In the above example, the mixture of two connectives, 50 litres of hydrogen gas with 25 litres of oxygen gas, is itself a connective gas, having a combined volume of 75 litres - the simple sum of 50 and 25 - and the properties of the mixture (in the absence of the spark) are not any different to the properties of hydrogen gas and oxygen gas mixed together.

Though molecules of water are bonds of hydrogen and oxygen atoms, a collection of water molecules is a connective - a liquid - at room temperature. Simply because hydrogen and oxygen atoms have bonded does not preclude the emergent water molecules - as objects in their own right - interacting connectively. Freezing the water would indeed cause the water molecules to bind together into crystals of ice, which would have emergent properties very different to those of liquid water.

While the properties of an atom are different to those of its protons and electrons, the properties of a plasma, not being a bond, are those of its participating electrons and protons even though they are interacting. A plasma may display an overall electric charge different to the charge of any one of its participating electrons or protons (and perhaps even no charge at all if they all happen to cancel each other out) but in any external interaction the force arising from its overall charge will be no different to the combination of forces from the charges (and motions) of its individual electrons and protons. A connective cannot participate in external interactions as an object in its own right or have emergent properties. A connective can engage in external interactions only as the collection of its participating objects, utilizing their individual properties to do so (which may change as they move) while the emergent properties of a bond persist for as long as the bond endures.

The Identity of Bonds

It's relatively easy to distinguish things that are separate from each other - and bonds/objects are - while distinguishing merging connectives can be very difficult. Sorting a puff of smoke from the air around and between it would be impossible without some very sophisticated technology, and ultimately only becomes possible because each particle of smoke has some properties different to those of air.

The collection of properties (and their values) displayed by an object constitute what I call its identity. The properties of a book, for example, would include its shape and size, its title, the colour of its cover, its subject matter and author, the price that was paid for it and who owns it. Many of these properties could be shared by other books, for example if they are by the same author, but at least one property of every book will be unique - exactly where it is at any one moment - simply because no two books can occupy the same space at the same time. Generally speaking, every object's identity is ultimately unique if only because objects cannot occupy the same space at the same time, though there are likely to be other points of difference. The uniqueness of an object's identity persists for as long as it is not disrupted.

Even when connectives are distinguishable from each other, they do not display properties in their own right. They may also occupy the same space at the same time. So connectives do not display a unique and lasting identity as objects/bonds do, but their participating objects, being objects, do.

The Aggregation of Bonds

Objects can bind together in many different combinations, and by binding in different combinations different objects with different properties emerge. A molecule of water, for example, is a bond of two hydrogen atoms and one oxygen atom, while a molecule of aspirin is a bond of nine carbon atoms with eight hydrogen and four oxygen atoms. Even when binding different numbers of the same object, objects with different properties may emerge.

And what distinguishes a hydrogen from an oxygen atom? Both are atoms but each has emerged from a bonding of protons and electrons in different combinations. An atom of hydrogen is a bond of one proton with one electron while oxygen is a bond of eight protons with eight electrons. All the chemical elements, such as hydrogen, oxygen, carbon, phosphorus and uranium, are bonds of differing numbers of protons and electrons (as well as differing numbers of other subatomic objects such as neutrons).

A cornucopia of difference, novelty and variety emerges when objects bond in different combinations.

The explosion of novelty doesn't stop there. Bonds, being objects in their own right, can then bond with other bonds. It's not just that objects create something new when they bond, or that bonding in different combinations gives a variety of newness, but the new objects so created can then bond with others to synthesize even greater confections of novelty. Protons and electrons bond in different combinations to create many varieties of atoms. The atoms so created can bond with each other - again in many different combinations - to create molecules of even greater variety and complexity, and the molecules can bond with different molecules to create extremely complex structures such as the proteins we are made of. A plasma, on the other hand, being a connective, is not an object in its own right and so cannot engage in a bond. It may merge with another plasma, but plasmas of plasmas are just bigger plasmas and do not become anything significantly different when they merge.

When bonds bond with bonds, I say that they aggregate. The resulting aggregate is an object in its own right, having emergent properties of its own and an identity of its own; it is able to bond with yet other objects to aggregate into more complex objects, and so on.

An aggregate is just a more complex bond, so the term 'aggregate' is really also equivalent to 'object' and 'bond' (and from here on I may use the terms interchangeably).

Aggregates are constructed in a series of discrete, singular events, each being the establishment of a bond.

Aggregates may destruct rather than construct. When an aggregate is disrupted, it leaves behind smaller bonds that were the aggregate's constituent objects. These smaller bonds may disrupt into even smaller bonds, and so on. Each step in the destruction of an aggregate is also a discrete event, being the disruption of a bond.

It is the emergent properties of atoms as different to the those of their component protons and electrons that opens up the entire arena of chemistry - by which we distinguish one kind of atom from another, by which atoms bond with atoms (using their atomic properties) to create molecules, and by which molecules bond with molecules using their molecular properties.

The Architectures of Aggregates

As bonds aggregate they can be seen to build in levels. In the example above, the protons and electrons are at the lowest level, the atoms they comprise are at the next level up and the molecule that the atoms constitute is the topmost level of the aggregate.

The levels of an aggregate are thus arranged in a hierarchy, and every object within the aggregate can be allocated a rank according to its level in the hierarchy.

With each aggregation event the number of levels rises by one. With each aggregation event a new object emerges at a new topmost level, having an identity different to those of its constituent objects on the level below (and different to those of their constituents on the level below them, and so on). The rank of any two objects in the hierarchy can then be compared, according to whether one object is internal to the other, is bound to the other, or has emerged from the other.

I call the hierarchy of an aggregate/object/bond its architecture or architective hierarchy. The architecture of an aggregate offers a clearly defined map of all the bonds used in its construction.

(This discussion of the aggregation and architecture of bonds is overly simple but is sufficient to convey the gist of my argument. If you are interested, some complexities are discussed in Appendix 1.)

I speak of an aggregate's internal objects being its constituent objects at all levels, so as to include the constituent objects of its constituent objects and so on.

Disrupting a constituent object of a bond will disrupt the bond itself, since a bond persists with its same constituent objects until it is disrupted. Disrupting any of an aggregate's internal objects will destroy the whole aggregate. (If this statement seems a little strong see Appendix 1 for some justification.)

The ranking of an aggregate's internal objects cannot be changed without disrupting one or more of the aggregate's internal bonds, which in turn would change the aggregate's architecture, so an aggregate's architecture persists unchanged for as long as the aggregate exists. An aggregate's architective hierarchy contributes to its identity.

Objects of a lower rank in an aggregate's architecture are more numerous, while those of a higher rank contain more internal objects than those of a lower rank. There is only one object at the very top of an architecture and it contains all the others.

There is a time-line implicit in an aggregate's hierarchy, for the object that emerged most recently is always at the top of the hierarchy, and those of the next level down are the next most recent, and so on.

The Integration of Connectives

Connectives are not objects in their own right and so cannot interact with each other - but their participating objects can. The participating objects in one connective may bond with those in another or may interact with them connectively.

When the objects in multiple connectives interact connectively, the connectives effectively integrate or merge into a larger connective. It matters not whether all or only some of the objects interact, for if only one object from each connective is involved then all the objects of all the contributing connectives will be interacting at least indirectly with each other.

The participating objects of one connective could alternatively bond with those of another, to form a connective of different, larger objects, or they could all bind together to form a single large object; but the connective itself cannot bind with another object or connective.

The capacity for external interaction of an integrated connective is not any different to the capacities of its contributing connectives, which is the capacities of their participating objects. One plasma integrating with another creates a larger plasma that is not any different to the sum of the integrating plasmas in its capacity for external interaction.

Each object in an integrated connective directly or indirectly interacts with every other object in the integrated connective, no matter which of the contributing connectives each object originally belonged to. The contributing connectives may become indistinguishable once integrated, or their original groupings may be maintained, to some degree, or for a while. If more connectives join in, the merged participating objects may pass through so many arrangements that it may be impossible to discern the original contributing connectives or any sequence to their merging. In fact, the arrangement of objects in a connective may change so much, even without any integration taking place, that discernible groupings of its participating objects may simply appear and disappear with its flux. In a connective there are no constraints to hold the groupings in place. Lasting identification of groupings or of the contributing connectives is impossible. It may not even be possible to say whether a connective is the result of a prior integration.

When connectives meet they may pass through the same space whether or not their participating objects interact.

The 'Visages' of Connectives

Since objects in a connective always respond to a relevant external force, whether or not the arrangement of the connective will be disturbed by an external force is not dependent on the strength of the force. The arrangement of objects in a connective will be disturbed to some degree by every force that acts on any of its participating objects. And if one object changes its position relative to the others then the others will adjust themselves accordingly. While a connective is not identifiable as an object in the way that a bond is, I say that it may be discernible in the sense that all its participating objects respond to a disturbance even though each responds as an individual.

Though subgroupings of its participating objects may appear and disappear with its flux, the subgroups are sometimes distinguishable from each other. We distinguish constellations in our galaxy and swirls in streams and rivers, for example. I call any distinguishable subgroup of a connective a visage of the connective. A visage describes a temporary or arbitrary arrangement of the participating objects in a connective, like a cluster or a swirl, rather than a lasting identity. A visage may last a long time as in the case of a stellar constellation or pass quickly as a swirl in a water stream.

While a bond has a lasting identity by which it differs from every other object, connectives may or may not offer distinguishable visages and may not even be distinguishable from each other since they do not exclude each other from their volumes. Even when visages are distinguishable, the distinction may not last since the participating objects are free to move in response to any disturbance.

Identity is meaningful to a bond in a way that a visage is not meaningful to a connective. A bond's identity emerges with its establishment and disappears with its disruption. A bond's identity remains unique for the term of its existence, while a visage of a connective is ephemeral.

By enforcing its constraint, a bond actively preserves its identity. As long as a bond lasts, it maintains its unique identity even in the face of external disturbance. As long as it is able to avoid disruption, it maintains its identity no matter how many interactions it engages in. Connectives do not act to maintain their visages. Their visages are incidental and easily changed. In fact, any connective having more than two objects can be arbitrarily divided into visages at the whim of an observer.

A connective has no persistent architecture mapping its contributing connectives or its visages. Visages may temporarily display a hierarchy, in that some may be larger than others or some may be spatially contained within others, but these arrangements are not fixed.

Here we begin to glimpse the charm of connectives. They are unremittingly dynamic and responsive. So much so that they cannot be held to any sort of specificity or precision. They are changeable, unconstrained, flexible, vague and ephemeral. I really appreciate the way air makes way for me as I walk through it.

Winners and Losers: The Contests of Bonds

There is effectively a contest going on between a bond and any external force acting on it. For under the external force, a bond either holds its constituent objects to their constraint and thereby keeps itself together, or its constituent objects are forced beyond their constraint and the bond is disrupted. The contest is decided on a test of strength between the binding strength of the bond and the external force.

Now that external force is taking place in the context of an interaction with external objects, and the external objects may themselves be bonds which are being tested in exactly the same way and under the same force of their mutual interaction. If any bond disrupts under the strain, it might happen that one or more of its erstwhile constituent objects then aggregates with one of the other bonds. In this case the other bond has not only preserved itself in the contest but has aggregated and created a new object - while the disrupted bond is no more. There can be clear winners and losers in such contests. A winning bond both maintains its identity and creates another, while a losing bond loses its identity, its emergent properties and its ability to enter into interaction. Losing a contest is catastrophic for a bond.

A contest between bonds can also be seen as a contest between their binding strengths, because all contestants are subject to the same forces under their mutual interaction - and it is the bond having the greater binding strength that wins.

A chemical reaction in which an atom that is a component of one molecule exits that molecule - thereby disrupting it - to aggregate with another molecule, is an example of such a contest.

We could talk of competition between connectives but not of contests in this sense. For example, one might say that two solar systems are competing over which will capture an approaching comet to its orbit. But competition in a connective sense does not involve the undoing of any competitor, and all the competitors' influences continue no matter what the outcome. There are no outright winners and losers, only a change of visage. In a competition between connectives the outcome is a proportional sharing of all the participating influences even though some may be stronger, while in a contest between bonds there is a selection and possible enhancement of one and the destruction of another.

Contests cannot occur between connectives alone - at least one of the contestants must be a bond.

The Hierarchical Authority of Bonds

In a chemical reaction in which an atom switches from one molecule to another, the atom's internal protons and electrons necessarily go with it to the other molecule.

When a bond is in a contest, there may be uncertainty over how the bond will cope and which way its constituent objects will go, but it is absolutely certain that, whichever way a constituent object goes, its internal objects will go with it. If a bond holds its constituent objects it also holds the constituent objects' constituent objects, and so on. If a constituent object breaks free or is absorbed into another aggregate, its internal objects go with it.

I say that a bond has hierarchical authority over its internal objects to take them with it in decisions under contest. A contest can thus also be seen as a tussle for the allegiance of a bond's internal objects.

By contrast, the idea of hierarchical authority has no relevance to connectives. In a close encounter of galaxies, for example, some stars of one galaxy may well be absorbed by the other, and vice-versa, but many might remain with their original galaxy.

Value Bias in Bonds

The bond at the top of an architective hierarchy can control more than the allegiance of its internal objects - it can control the values of their properties as well:

When an external force acts on a bond it may happen that the force continually acts in the direction of one boundary of the bond's constraint range rather than another, so that the constituent objects of the bond are biased, possibly strongly so, to one boundary of their constraint. For example, when a proton approaches an atom, the electrons of the atom will likely spend more time on the side of the atom closest to the approaching proton by virtue of the attraction of their unlike charges.

The same can be said of the constituent objects' constituent objects, and so on, meaning that all of an aggregate's internal objects may have a bias to one boundary of their constraint rather than another. It may even happen that all the internal bonds of an aggregate are biased in the same direction so that, by the topmost object in the aggregate's hierarchy entering into an interaction, a bias to a particular value may be imposed on all its internal objects.

Bonds and Control

We begin to see the depth of a bond's capacity for control: A bond not only controls the motions of its constituent objects by constraining them, it controls their ability to participate in external interactions, their hierarchical allegiances and may even impose a bias to their values. None of these controls are evident in connectives.

The controls in a bond operate between the levels in the bond's architecture. Objects at the same level in an architecture do not control each other while higher ranked objects control those of lower rank. The relationship between objects at different levels in an aggregate is not an equitable one - it is one of subservience and authority. The higher levels control the lower levels and not the other way round. Higher levels of an architecture control their lower levels even though the higher levels have emerged from the lower ones. The objects at higher levels are however structurally reliant the objects at their lower levels to maintain their integrity since the disruption of a lower level object would disrupt the objects above it.

Processions and Flows

The internal arrangements of bonds don't change. Their constituent objects at every level remain confined within constraints for as long as the bond holds. Yet there are ways by which bonds can be considered to change. They can be considered to change when a bond disrupts or is established, they can be considered to change when they switch from one constraint range to another, and they can be considered to change when an aggregate grows or shrinks. In this sense I say that bonds process (rather than change), stepping from one bond to another and from one static architecture to another in a procession of discrete events.

In contrast, connectives flow through their changes in a smooth, unbroken stream.

Sublimation of a Bond

It may happen that an external interaction does not force a bond's constituent objects to test the limits of their constraint so the bond need not respond as a whole to maintain its constraint. This may happen, for example, when an external interaction invokes a vibration of the bond's constituent objects which is so small that the range of their vibration lies well within the imposed limits. The constituent objects respond as if they were in a connective. And as far as the external objects are concerned, it is the bond's constituent objects that are responding to them rather than the bond-as-a-whole.

When an external interaction acts on a bond's constituent objects and the bond does not respond as a whole I say that the external interaction sublimates the bond, acting only on its constituent objects, which respond freely and individually as if in a connective even though they are constrained in a bond.

In a sublimating external interaction the bond is not apparent to the external objects because it does not respond to them and they do not respond to it, so as far as they are concerned, the bond, as an object in its own right, does not exist - and as far as the bond is concerned, the external objects don't exist (in their own right) either. A sublimation is effectively mutual.

In a sublimating external interaction there is thus no interaction between the external objects and the bond itself. The external objects are not excluded from the bond's spatial volume and it is not excluded from theirs. The interaction is between the bond's constituent objects and those of the external objects (assuming the various constituent objects are not also sublimated), with all constituent objects being excluded from each other's spatial volumes. In a sublimating interaction the external objects and the bond as a whole are not interacting with each other while their constituent objects interact connectively. In this way we see that objects only exclude each other from their spatial volumes when they are interacting.

(This description is sufficient to convey the idea. If you want to go there, some complexities are addressed in Appendix 1.)

Stasis and Change

The outstanding feature of bonds is a capacity for stasis. Strictly confined within ranges, a bond's constituent objects can appear to be motionless relative to each other, especially when their range of constraint is narrow. Bonds have identities and architectures that do not change and they can compound into more complex architectures that are just as static and enduring. They preserve their identities and architectures with absolute fidelity even in the face of disturbance (as long as they are not disrupted).

The outstanding feature of connectives, on the other hand, is their extreme susceptibility to motion and change.