Inner time and outer time: SMM/DTT and McTaggart’s A-series and B-series

01The question behind the comparison

The distinction between producing an event and having a record of it is the most useful entry into dual time. A measurement apparatus can undergo internal changes before a stable pointer value becomes available. Calling these two descriptions inner and outer is initially an explanatory distinction. The stronger DTT claim is that spatially articulated objects themselves emerge through such production, so the apparatus is already part of the resulting world rather than the ultimate source. The philosophical attraction is that becoming is placed in the constitution of events, not added afterwards to an already complete spatial inventory.

A clear account therefore separates three orders. Dependence orders the nested operations required for completion. Succession orders the accessible records. Duration compares changes with a physical clock. These orders need not coincide simply because the same symbol t appears in their description. Two operations may depend on one another without having separately measurable durations. Conversely, records may be separated by unequal clock intervals despite containing the same number of abstract updates. This distinction protects DTT from concealing a conventional external clock inside the word generation.

A constructive interpretation of the six levels treats later capabilities as presupposing earlier ones: a retained contrast can support a relation, and a sufficiently organized set of relations can support a spatial readout. That is a possible functional architecture, not a claim that any arbitrary six operations automatically make a universe. The explanatory burden is to identify operations, retained memory and a completion condition together. When those ingredients are specified, inner time can acquire content through which partial histories it distinguishes and outer time through which records it exposes.

02The single-source and nested-time proposal

SMM begins with one nonspatial generative source. DTT distinguishes its inner production from the outer order in which completed results become accessible. The six inner levels are nested functional dependencies within that production; the seventh denotes outer completion. They are not six independent clocks, six spatial directions, or six simultaneously occupied temporal axes. This distinction makes the framework more specific than a general claim that everything changes: it asks how a world of persistent relations can be generated before its spatial representation is taken for granted. ^[2]

03The comparator’s explanatory structure

McTaggart distinguished tensed positions—past, present and future—from the relations earlier than and later than. His argument challenges the coherence of taking passage as a changing possession of incompatible temporal properties. For the comparison here, the distinction is a tool for asking what DTT’s completion adds to an ordered history. A sequence can be fully ordered without specifying which member is now present.

Consider a list of event labels A, B and C. The facts A precedes B and B precedes C do not change when a reader moves down the list. What changes is the reader’s relation to a particular entry. If a completion theory adds an objective change in actuality, it needs to say whether that change is another event, an irreducible feature of events, or a change in a meta-time. These alternatives expose the regress question without assuming that McTaggart’s conclusion is correct. His analysis is philosophical; it supplies no Hamiltonian, physical clock or information-processing mechanism. ^[1]

04The precise agreement and difference

Inner generation is not simply McTaggart’s A-series, and outer observation is not simply his B-series. The A/B distinction classifies ways of ordering or qualifying events; DTT distinguishes the constitution of an event from its completed accessibility. An inner dependency can remain tenselessly describable, while an outer observer can speak in tensed language. The two distinctions therefore cross rather than coincide.

DTT’s distinctive answer would be that completion makes a difference to what can enter later relations, not merely to where an observer stands in a list. This avoids reducing becoming to the movement of attention, but it raises McTaggart’s further question: in what sense does the change from unfinished to finished occur? If another temporal parameter is needed, the account must explain its status. If completion is primitive, it should be stated as such. The useful outcome is a clearer ontology of actualization and an operational record relation, without claiming that two temporal labels alone dissolve McTaggart’s regress. ^[1]

05Worked example: what follows and what does not

Consider an idealized detector with a two-step preparation followed by registration. Its internal path is blank → armed → latched, while the public display changes only at the last transition. If the detector can be delayed while armed, the public record count remains unchanged even though the physical clock advances. Thus a completion count and a clock interval are independent measurements. If a proposed source law fixes their ratio without adjusting the detector separately, that is a substantive relation. If one simply defines a second time to be twice the first, the relation is a convention. The example is intentionally modest: it identifies what a dual-time mechanism must add beyond a two-stage description, without claiming that a laboratory detector is the Single Monad.

06What this comparison contributes

This makes the comparison answerable in a precise way. A framework may agree that events possess an internal explanatory structure while denying that this structure is temporal in the same sense as measured duration. It may also agree about record order while disagreeing about whether unrecorded possibilities already exist. The productive DTT contribution is to connect these questions through completion. Its strongest mathematical development would specify which differences among inner histories survive as different outer correlations, and which are unobservable descriptions of the same process.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

• The duality-of-time postulate →

  Connects this comparison with the author’s discussion of inner.

• source and memory →

  Connects this comparison with the author’s discussion of inner.

• How a protocol can reveal dual-time structure →

  Connects this comparison with the author’s discussion of inner.

• A checklist for claims of two physical times →

  Connects this comparison with the author’s discussion of inner.

• Relational time: order, clocks, and shared duration →

  Connects this comparison with the author’s discussion of inner.