Folding, Unfolding, and the Economy of Distinction

Every determinate form retains some distinctions and leaves others undistinguished. This does not necessarily indicate an inadequate description. If every movement required the form’s entire internal organization to be unfolded anew, no continuation could remain local.

A form acts as a whole precisely because some of the distinctions that produced it no longer have to be repeated in every new relation. But the boundary between what is distinguished and what remains undistinguished is not final. What can remain folded today may become necessary for continuation tomorrow.

This moving boundary can be considered through folding and unfolding.

Form as a Fold#

By a fold, let us mean a form distinguished as a whole while some of its internal organization is not held explicitly in the movement at hand.

It is not the form itself that is folded: the form has already been distinguished and can enter into new relations. What is folded are those internal distinctions that do not presently need to be produced anew.

A tool, a rule, a concept, or an established way of acting may be available as a single whole even though the movements through which it arose are no longer represented within it as a sequence of separate steps. We can use a tool without repeating its manufacture, apply a rule without reproducing the history of its formation each time, and proceed from a concept without simultaneously unfolding every distinction it retains.

In the limiting sense, every finite form is a fold. It is determinate only because it draws a boundary between what is distinguished and retained and what does not enter with the same degree of explicitness. Yet it is useful to speak specifically of folding when the possibility of further disclosure becomes relevant to continuation.

Explicit and Implicit Folds#

In one case, the internal organization is not unfolded now, but a determinate relation to it is retained. It is known which distinctions can be disclosed in greater detail, how they can be reached, and under what conditions it may become necessary to return to them. This may be called an explicit fold.

In another case, the form also acts as a whole, but some significant internal organization has not yet been articulated at all. No determinate path by which it should unfold is retained. Such an implicit fold becomes apparent only when continuation proves impossible or produces an unexpected result.

The difference between these cases lies not in the amount of hidden detail, but in whether the form retains a relation to the possibility of its own unfolding.

Unfolding Relative to a Distinction#

Unfolding begins not because every form must eventually reveal its complete content. It begins when the available determinacy of a form is insufficient relative to a distinction that has arisen.

Let $C$ be an available folded form and $\Delta_u$ a distinction that requires greater internal determinacy. Unfolding then has the general form of a possible continuation:

Here, $G_{\Delta_u}(C)$ denotes the field of possible directions of disclosure, $g_u$ a distinguished continuation, and $C'$ a form in which the necessary internal organization has been articulated more fully.

What matters is that unfolding is directed by the current distinction. It does not unfold a form as such, but distinguishes only what the present continuation requires. Another distinction could direct disclosure differently and lead to another articulation of the same form.

If an established way of acting ceases to work under new conditions, there is no need to recover the entire history of its formation at once. The first task is to distinguish where the available determinacy is insufficient: in the conditions of applicability, in an internal relation among parts, in the expected result, or in the organization of the movement itself. Not everything is unfolded, but only the region toward which the arising distinction leads.

Unfolding Is Not Restoration#

Let $C=\operatorname{Fold}(X)$. The fact of folding alone does not entail that unfolding will restore the original organization:

Exact restoration is possible only when the internal organization of $X$ and the relations of access to it were retained with sufficient determinacy. But this is a special case.

Ordinarily, a new unfolding is a new act of distinction. It proceeds from a different present form, relative to a different distinction, and under changed conditions. It may therefore articulate internal organization differently from how that organization first arose or was previously retained.

A fold does not contain a single ready-made unfolded original within itself. It retains an achieved organization and some possibilities of continuation. What will be disclosed later is determined not only by its origin, but also by the new distinction.

An important limitation follows: if exact provenance, repeatability, or recovery of a path is essential to a future movement, that path must be retained separately as a form. The presence of a result does not by itself preserve the history of its formation.

Directed Unfolding#

A complex form need not be a flat enumeration of everything that could in principle be distinguished within it. It may retain relations of possible access: which internal forms have already been distinguished, how they are related, and in response to which distinctions they may become relevant.

Movement can then proceed from one available form to another and stop unfolding once sufficient determinacy has been reached. Complete enumeration is replaced by successive disclosure relative to a present need.

But relations of access are themselves forms and may also be incomplete. If a relation to the necessary internal organization has not been retained, the required continuation may never appear in the field of possibilities. This lack will become apparent later as an inability to continue, an unexpected result, or a new distinction.

Directed unfolding therefore does not guarantee that everything essential will always be found. It makes local movement possible without requiring everything to be disclosed in advance.

The Economy of Distinction#

Optimization is usually understood as making an already specified operation faster. At a more basic level, however, it answers another question: what part of an organization must be distinguished now?

If some content does not affect continuation, it need not be unfolded. If a fold conceals a distinction required for continuation, its determinacy is insufficient.

This gives rise to two opposed errors.

Over-unfolding distinguishes, retains, or computes more than the operative distinction requires. The movement loses its locality and expends its capacities on articulating an organization that makes no difference at present.

Over-folding leaves undistinguished the internal organization without which a continuation either cannot be determined or cannot preserve the form. The movement remains simple only because an essential complexity has been concealed.

There is no single universally correct boundary between them. What must be unfolded depends on the particular distinction and on what must be preserved: time, memory, energy, precision, completeness, or the form’s very capacity to remain itself through change.

The economy of distinction therefore does not mean the smallest possible number of distinctions. It means organizing what is distinguished so that enough is retained for the present continuation—but not everything.

The Result as a Folded Formation#

Folding concerns not only the internal organization of a form already present. The result of a movement may itself be considered as a folded formation.

Suppose a process of formation has followed the path

The result $R$ is not identical to the path $L$. The intermediate forms, the distinctions that arose, the rejected continuations, and the precise order of movements may no longer be retained explicitly. Yet the result exists as the achieved organization of that process. It can enter into new relations without traversing the entire path again.

A result may therefore be understood as the achieved organization of a process of formation retained in a single present form. This is not an equality between result and history, but a relation of folding between an accomplished movement and its achieved organization.

This allows the manufacture of a tool, the tool itself, and its subsequent use to be described within one ontology. The manufacturing process is distinguished as a path of formation. The tool is the achieved form in which the organization of that path is retained, so the path need not be traversed anew with every use. When the tool is used, it enters the next movement as a present form. What may previously have appeared ontologically severed now appears as different positions within one general form of movement. Their connection is restored without identifying them. The tool is not its own history of manufacture. The process of manufacture is not exhausted by the tool it produces.

A movement achieves a result. The result folds the organization achieved by that movement and then becomes a participant in further movements. The tool’s position in the relation changes from the result of a formation to the means of a new continuation. This does not require process and thing to belong to two different kinds of being.

In general, a unique path of formation cannot be recovered from its result.

The same form may have arisen through different movements. Some distinctions may have disappeared, while some conditions of formation may not have entered the result. If provenance, verification, or reproduction is essential to further movement, the trace of formation must be retained separately. The result is no substitute for such a trace.

The Moving Boundary of Form#

No fold guarantees that it has retained every distinction that will become relevant later. It takes shape relative to the organization already available and the continuations already known.

When a concealed relation becomes necessary, the boundary of the form ceases to be sufficient. The organization of the fold itself then becomes the object of a new distinction: it may be unfolded, reorganized, or replaced.

This is not a return to some final and complete content. The new unfolding remains partial and directed. It changes the boundary of what is distinguished without eliminating the possibility that something else will have to be distinguished later.

Folding and unfolding therefore do not describe an alternation between a hidden state and a fully open one. They describe how a finite form preserves the possibility of local continuation: it retains an achieved organization as a whole, unfolds it relative to an arising distinction, and folds an accomplished movement again into a form available for further relations.

The economy of distinction does not consist in distinguishing as little as possible. It consists in the capacity to distinguish what is necessary without making every possible distinction obligatory, while preserving the possibility of reopening the boundary of a form when its determinacy proves insufficient.