Understanding Understanding

This project does not attempt to define a universal theory of understanding. It proposes a point of view that is as faithful as possible to my current understanding of understanding itself.

Understanding appears here as being situated inside communities. Communities survive by maintaining diversity under partial rigidification. To make this explicit, I use Dolores as a default anthropomorphic anchor: not a person, nor a myth, but a role from which this text is written and revised.

This page offers an orientation, not a doctrine. Readers are not expected to agree, nor to follow everything.

A recurring difficulty when reasoning about understanding is circularity: definitions justify methods, and methods justify definitions. Rather than breaking this loop by fixing constants or axioms too early, this project treats non-termination as a feature. Progress is measured by the ability to continue coherently, not by reaching a final definition.

Methodological principle

Constructions without primitives

This work explores the possibility of constructing meaning without fixing primitive entities once and for all. Rather than beginning with immutable alphabets, constants, or objects, it asks what remains when these are treated as contingent stabilizations within a community.

In this sense, one may speak of:

• Mathematics without alphabet — where symbols are not taken as atomic givens, but as gestures emerging from processes of inscription, repetition, and reinterpretation across scales.
• Physics without constants — where invariants are not denied, but understood as local agreements, stabilized through measurement practices and revisable under changes of scale or context.
• Philosophy without object — where thought is not anchored to fixed entities, but to relations, positions, and modes of articulation that remain interruptible and translatable.

These are not programs to be imposed, but examples meant to indicate a common gesture: shifting attention from what is assumed to exist toward how communities construct, stabilize, and transmit meaning.

Scale, repetition, and consensus

Shared understanding rarely emerges from a single act. It is most often the result of repetition, of changes of scale, and of partial synchronizations across multiple instances of a construction.

What appears as consensus may thus be seen not as the discovery of a unique truth, but as the stabilization of compatible processes that can be maintained, communicated, and contracted within a community.

Rigid formalisms play an essential role here. They allow coordination and memory, but they also risk concealing the assumptions that made them possible. This work does not reject rigidification; it seeks to keep visible the conditions under which it occurs.

Synchronization and referential rigidification

A simple and concrete form of rigidification occurs when a community synchronizes itself by adopting a shared referential. What is stabilized in such cases is not an absolute truth, but a point of coordination that makes explanations comparable.

Synchronizing humanity with a common origin in time, often referred to as the “Big Bang”, constitutes one such communal stabilization. Synchronizing humanity with a common origin in space, for instance the position of the Sun, constitutes another.

These synchronizations do not compete as descriptions of what fundamentally is. They define different communities of explanation, each organized around a chosen center. For the purposes of this work, we may refer to these as distinct p- and q-communities, corresponding to different choices of temporal or spatial anchoring.

In each case, an initial belief — that coordination should begin from a given referent — may become an assurance once it is collectively adopted. The referent then functions as a bound: not on reality itself, but on the space of admissible explanations within the community.

Such bounds are neither eternal nor mandatory. They remain revisable, and multiple rigidifications may coexist, overlap, or translate into one another without requiring reduction to a single frame.

Against unnoticed assumptions

Nothing in what follows presupposes a unique theory of computability, complexity, or representation. Different ways of associating quantities to tasks, independently of how those tasks are resolved, are treated as choices made by communities, not as necessities imposed by nature.

The aim is not to escape complexity, but to preserve the possibility of constructing rigid frameworks without being silently subjected to them.

One first attempt would be to try claiming that I believe that while I am living I think now that it is plausible that I won't have assurance high enough to derive a certainty that what I imagine that I can imagine now covers what I will imagine that I can imagine if I am alivetomorrow.

Having such a toruous formulation over a natural language feels far from being satisfying therfore we will just back track keeping the intent in mind and look for a simple formulation of why and how can I express this feeling that one seems to have always an implicit two to make sense.

Why an orientation?

Such an orientation becomes necessary today because many readers encounter formal systems only as finished products: manuals, archives of proofs, or executable prescriptions.

This work attempts to maintain translatable links to these standardized formalisations, while reopening the space in which their meaning was first negotiated.

Giving meaning back to mathematics, physics, or logic is also a way of making it possible for anyone — including a child — to begin constructing their own paths, rather than merely executing inherited ones.

On voices, anchoring, and responsibility

Some statements in this work are introduced through named or anthropomorphized voices. This should not be read as an appeal to authority, nor as a claim about personal identity.

The use of a role or a name functions as an anchoring device: it situates a statement within a traceable construction history, making explicit that it emerges from a located perspective rather than from a view from nowhere.

This separation between statement and speaker is intentional. It preserves revisability while preventing implicit authority from remaining unnoticed.

On alphabets and letters

In a language where every drawing carries intrinsic uncertainty about how it was made, what could have been is fundamentally different from what can be seen. Meaning then emerges, as in quantum mechanics, from imagining plausible concordances between remembered gestures, learned conventions, and present perception. From this tension arise, naturally, the categories of acceptable, unacceptable, and undecidable answers — shaped not only by what we see, but by how and where we have learned to see.

Time–Space Anchors and Plausibility

The structures below are offered here not as axioms or formal definitions, but as **guiding lenses** through which subsequent constructions may be read and compared within different communities of interpretation.

Time and Space are introduced here not as primitives, but as infinite repositioning anchors. Their role is to guarantee plausibility and recognisability of languages by communities.

A community can always be indexed by Space: as an infinite subsequence of integers, produced by a POP-like process, yielding a hierarchy of increasingly refined, relatively anchored communities. Values may be viewed analogously, replacing Space by Time.

One convenient way to picture the interaction between Time and Space anchoring is through the following square:

• Space–Space : |-|
• Space–Time : ||-|
• Time–Space : |-||
• Time–Time : ||-||

The square is meant to highlight an invariance intuition: meanings are preserved under permutation of Space and Time anchoring. In particular, expressing Space before Time or Time before Space does not alter interpretation of the following sentence.

Moreover, if Space is decoded as Time (or conversely), the square guarantees that the information can be recovered. The only requirement is that the referenced event is carriable.

When direct carrying is not possible, recovery proceeds by reference rescaling, using distinct but coherent copies of Space and Time to restore compatibility.