Throughout this part, the movement does not proceed through the smooth accumulation of properties.
A new order arises when an existing structure exhausts the distinctions available within it and a radical distinction is put forward over its elementary state.
Not every section names such a leap. Some sections unfold the consequences of a distinction already retained. Others mark the point at which an existing order can no longer continue through its own variations and must be radically restructured.
The Transferred and “This”#
Proto-transfer introduced direction into relation.
A distinction arising through one relation could become operative toward another. But as long as the act of transfer and what is transferred remain indistinguishable, transfer cannot acquire determinate content.
Directed transfer may repeat, yet every repetition reproduces the same undivided operation.
Transfer reaches an elementary state: it continues to operate, but can produce no difference between carrying and carried.
A radical distinction is put forward over transfer as a whole.
In the line followed here, this distinction is retained as the difference between:
- the operation that transfers;
- that which is transferred.
The transferred receives a minimal mark:
This.
“This” is not yet an object with properties.
It is an abstract indication that something is being held as distinct from the act that carries it.
Here the first germ of boundary appears.
The distinction remains unstable. What is transferred is still a product of the same movement that transfers it. Yet the movement now retains its product as something other than itself.
At later stages, this mark may become stabilized and treated as an independent thing.
For now, it is only the transferred distinguished from the act of transfer.
Transfer has become more than direction.
It is the directed operation of marked content.
Qualitative States#
Marked content can now be transferred throughout the differentiated relational field.
The mark “This” passes through densifications, sparse regions, and oriented relations.
But if every transferred mark remains equivalent to every other, transmission merely reproduces the same contentless indication.
Repetition again reaches exhaustion.
Transmission continues, but nothing within what is transmitted distinguishes one transfer from another. The marked content falls into an elementary state.
A radical distinction is put forward over the transmitted as a whole.
In the line followed here, it is retained as a distinction within the transferred content itself.
“This” can now be determined in different ways.
These determinations are proto-states.
A state is a way in which transferred content differs while remaining transferable.
Different states can propagate through the same relational organization and affect subsequent transmission differently.
The field no longer carries only marks.
It carries qualitative differences.
Once distinct states can be transferred, patterns of propagation become possible.
Proto-Waves#
Transferred states do not remain isolated.
Their directed propagation forms organized patterns.
We may call these structures proto-waves.
The term is analogical.
A proto-wave is not a physical wave moving through matter. There is not yet a developed physical medium, spatial distance, velocity, frequency, or wavelength.
What exists is the poorer structure of differentiated states propagating through oriented relations.
If propagated states cease to remain distinct, their movements merge.
If their distinctions persist, they may combine, reinforce, cancel, or transform according to the relations through which they propagate.
Repeated propagation produces complex patterns.
These patterns may never repeat exactly, yet regularities arise within them. They anticipate structures later described through terms such as periodicity, interference, superposition, and resonance.
Under a physical unfolding, such patterns may be realized as physical waves.
Under an informational unfolding, they may be realized as signals and structures of transmission.
Under social or psychic unfoldings, they may be realized as recurring patterns of imitation, opposition, attention, or affect.
These are not reductions of one domain to another.
They are developed realizations of a poorer common structure under different conditions.
As propagated patterns multiply and interact, their elementary state becomes increasingly rich.
Exhaustion no longer appears as the simple homogenization of one repeated distinction. The field may remain intensely active while its current organization produces nothing structurally new.
Rest becomes difficult to distinguish from continued movement.
Rest Within Movement#
Rest does not first appear when propagated states become complex.
It is already a moment of movement itself.
For a distinction to occur, something must remain while something else changes. Without a retained moment, movement could not differ from what it leaves or from what it becomes.
Rest is therefore not the absence of movement.
It is the self-retention of movement: the way movement remains sufficiently itself for change to be distinguished as change.
At poorer stages, this relation appears directly.
Repetition increasingly preserves one form while producing less new difference. In exhaustion, movement falls into its own retained form: distinction continues to be repeated, but no longer distinguishes.
The elementary state is the rest of a particular movement.
It is the point at which the retained identity of that movement has overtaken its production of further difference.
In a complex field of propagated states, this rest is concealed by variation.
The field continues to change, yet certain contours persist through those changes. Further propagation adds movement, but does not alter these retained contours.
The field has reached an elementary state with respect to its current organization.
A radical distinction is put forward over the field as a whole.
In the line followed here, it is retained as the difference between what varies and what remains through variation.
What remains is an invariant.
The radical distinction does not create rest for the first time. It makes explicit the rest that has always been internal to movement.
An invariant is therefore a developed form of rest within movement.
It is not absolute immobility, but the way a movement remains itself across variation.
Several invariants may now arise.
But their coexistence does not yet make them comparable.
Each remains a distinct organization within its own movement.
Extensity as Witness#
Rest names what remains within movement.
Extensity names the holding through which what remains can persist and leave a trace.
For anything to differ, something must hold while something else changes.
This holding functions as a witness in a minimal sense—not as an observer, but as the retained continuity through which movement can be distinguished and its result preserved.
Basal extensity does not yet require chronological time or spatial extension.
It is only the continuity sufficient for one state to differ from another and for this difference not to disappear immediately.
At the stage of invariants, extensity acquires a developed form.
The traces of several invariant patterns may now be retained within one continuity without their complete organizations being reproduced within it.
Developed extensity is therefore not an empty container in which patterns are placed.
It is the continuity of a structure capable of retaining several encounters together.
Basal extensity makes retained distinction possible.
Developed extensity provides the holding within which different structures may enter a common interaction.
But common retention alone is not comparison.
The invariants remain fully distinct, and nothing yet determines which of their differences should matter together.
Mediated Comparison#
The multiplication of invariants produces a new limit.
Each invariant retains a contour through variation, but invariants considered only in themselves remain mutually incomparable.
Adding more invariants adds more distinct organizations without producing a common order among them.
The field of isolated invariants reaches an elementary state with respect to their relation.
A radical distinction is put forward over this plurality.
In the line followed here, it is retained as a common mode through which one structure can interact with several different patterns.
Comparison therefore arises only through mediation.
A mediating structure encounters different patterns through the same mode of relation.
In each encounter, it retains certain effects while other differences remain indifferent to its operation.
The patterns become comparable only with respect to what the mediating structure can distinguish in both.
Nothing is comparable in every respect.
Every structure contains distinctions that no other structure reproduces completely. Direct and exhaustive comparison would require identity and would abolish the difference that comparison presupposes.
Comparison is therefore not a fundamental operation added to distinction.
It is a particular organization of interaction:
- different structures remain distinct;
- a mediating structure relates to them through a common mode;
- the same distinction operates across the encounters;
- differences that do not affect this distinction remain indifferent.
What appears as similarity arises when different patterns produce the same retained result within the mediating structure.
What appears as difference arises when the same mode of encounter produces different results.
Similarity and difference in comparison are not exhaustive statements about what the patterns are.
They are results of a definite interaction.
Every comparison is partial.
A change in the mediating structure may make previously irrelevant differences operative or make previously decisive differences indifferent.
Comparison does not reveal two structures from nowhere.
It reveals how they differ in relation to a third organization capable of encountering both.
Measure#
Mediated comparison initially distinguishes only whether its results coincide or differ.
As the same operation is repeated, many comparative traces accumulate. But an undifferentiated collection of differences does not yet determine how one difference relates to another.
Further comparison adds results without producing an order among them.
Comparison reaches an elementary state.
A radical distinction is put forward over the field of comparative traces.
In the line followed here, it is retained as a distinction among differences themselves.
Differences can now be ordered.
This is the beginning of measure.
Measure is a stabilized and repeatable form of mediated comparison in which the results of a common operation are placed into an order.
“A differs from B by this much” becomes possible when:
- the same operation can be repeated;
- its results can be retained;
- differences among those results can themselves be distinguished.
A unit arises as a retained form of the repeated operation.
It is not necessarily an indivisible quantum.
It is a stable distinction through which different encounters can be related to one another.
Different orders of measurement may establish different units. What functions as a unit within one order may itself be unfolded into a complex structure within another.
A genuine quantum arises only where the order of measurement admits a minimal distinguishable step.
This is a further determination, not a consequence of comparison alone.
Measure therefore requires:
- patterns stable enough to enter repeated interaction;
- a mediating structure capable of relating to them through a common mode;
- a repeatable operation;
- retained traces of the encounters;
- a unit or scale;
- an order among the resulting differences.
Measure is not a property lying fully formed inside the measured structure.
It is produced through interaction under a common mode of distinction.
This does not make measure arbitrary.
The structures being measured resist and constrain the operations through which they can be encountered. Some operations preserve stable differences; others produce no coherent result.
But no measure exhausts what a structure is.
It retains only what becomes operative through a particular organization of interaction.
Proto-Geometry#
Each measure orders one mode of interaction.
But different measures may remain isolated from one another. Each can organize its own differences while providing no common orientation with other measures.
The field of separate measures eventually reaches an elementary state.
More measurements add determinations, but do not yet produce a coherent medium in which their different orders belong together.
A radical distinction is put forward over the field of measures as a whole.
In the line followed here, it is retained as an organization of relations among measures.
This coordinated order is proto-geometry.
Proto-geometry does not yet mean a particular mathematical geometry.
It is the emergence of a field in which meanings such as nearer, farther, between, beside, boundary, region, center, periphery, direction, and contour can operate together.
These meanings are not imposed upon an empty space.
They arise from stabilized relations among mediated measurements.
Some of them were anticipated earlier.
Modes of non-indifference suggested something like proximity.
Directed relations anticipated orientation.
Relational densifications anticipated regions.
But at those stages these meanings were poor and disconnected.
Through coordinated measures, they become moments of a common order.
A difference can now be located relative to other differences.
This illustrates an important feature of the unfolding: later stages often return to structures that appeared earlier in a poorer form.
The return is not repetition without change.
A previously abstract possibility becomes integrated into a richer organization.
Reality gains content through the deepening and coordination of distinctions.
Proto-geometry provides the first developed order in which stable configurations can be retained as configurations.
Forms can now arise.
Form#
Within proto-geometry, some configurations persist across the transformations available within the common order.
These stable configurations are forms.
A form is an organized continuity of distinctions across change.
Its stability does not mean complete immobility.
A form may preserve itself through constant internal transformation.
A whirlpool persists while the water composing it changes.
An organism replaces material while retaining a living organization.
A social institution persists through changing participants.
A concept survives through different formulations.
In each case, the form is not identical to any particular element through which it is realized.
What remains is an organization.
A configuration becomes a form when its internal relations remain stable enough for it to be distinguished as one configuration rather than as a transient coincidence.
Form is therefore an unfolding of the order already established in proto-geometry.
It is the persistence of a configuration within that order.
But not every form actively maintains itself.
Some forms endure because surrounding conditions happen to remain favorable.
Others respond to differences in ways that preserve their organization.
The first kind persists passively.
The second kind is a self-preserving form.
Self-Preserving Form and Locality#
Passive persistence has a limit.
A form that remains stable only because its surroundings remain favorable contains no internal distinction through which it can preserve itself when those surroundings change.
Under repeated disturbance, passive persistence reaches exhaustion.
The form remains organized, but nothing within its organization yet distinguishes differences according to their consequences for its continuation.
The form enters an elementary state with respect to passive persistence under disturbance.
A radical distinction is put forward over the form as a whole.
In the line followed here, it is retained as the difference between what supports the continuation of the form and what threatens or interrupts it.
The form begins to respond to differences in ways that maintain the organization through which it remains this form.
It becomes a self-preserving form.
A bounded form may already contain a complex internal structure. It may move, expand, contract, or undergo extensive change.
None of this alone makes it a locality in the developed sense.
The decisive question is whether differences affecting the boundary enter into the operations through which the boundary itself is maintained.
A locality has at least three moments:
- a boundary
It distinguishes the form from what lies outside it. - an internal organization
Its distinctions cooperate in maintaining the form. - a mode of encounter
Differences arising at the boundary alter the internal operations through which the form continues.
Locality begins when the boundary becomes operationally recursive.
The principle through which inside and outside are distinguished enters the field affected by the distinction.
The boundary enters the field it organizes.
Encounters at the boundary can now modify the operations through which that boundary is maintained.
This return does not require an explicit image or symbolic representation of the self.
A minimal locality may register its own condition only through changes that support or threaten its continuation.
Locality is therefore not simply a position inside a pre-existing space.
It is a position produced and held through the work of maintaining a distinction between here and not-here.
Identity arises in the same way.
Identity is not a substance hidden beneath change.
It is the active retention of a contour across transformations.
A locality may replace many of its elements and alter many of its operations while remaining itself, provided that these changes continue the work through which its boundary and organization are held.
Locality is therefore not isolation.
Its boundary belongs to the work of encounter and connection as much as to the work of separation.
Locality and the Possibility of Choice#
The same recursive structure that makes locality possible also makes local choice possible.
A difference encountered by a locality can return upon the operations through which the locality continues.
Its consequences can therefore concern not only what the locality encounters, but what the locality itself will become through the encounter.
This does not mean that every change within a locality is an actual choice.
Local choice begins when different continuations become operative as alternatives and one continuation is retained in a way that alters the locality’s own continuation.
Such choice does not yet require consciousness or an explicit representation of the alternatives.
It requires only that the distinction among them participate in the locality’s self-maintaining organization.
The possibility of locality and the possibility of local choice therefore arise together.
The depth of choice depends on how deeply the distinction reaches into the locality’s organization.
A peripheral choice changes an operation while leaving the organizing principle intact.
A deeper choice changes the way the locality maintains its boundary and responds to its outside.
A radical choice reaches the distinctions through which the locality constitutes itself as this locality.
The development of this possibility into self-determination belongs to the life of locality.