Discrete moments and continuous experience: SMM/DTT and Presentism and the growing-block universe

01The question behind the comparison

A discrete sequence can describe a continuous-looking process without deciding whether reality itself is discrete. Film frames, sampled signals and numerical time steps all illustrate the distinction between a representation and its represented object. DTT gives the distinction an ontological ambition: completed moments would arise from inner generative structure, while outer observation encounters an effectively continuous world. The central question is therefore what supplies continuity across completions. Merely making the steps very short does not explain how records remain related or why a particular smooth evolution appears.

Continuity has several meanings. A trajectory can be continuous in position, differentiable in velocity, continuous in quantum probability, or phenomenally continuous to an observer. These properties are logically separable. A sequence of quantum states connected by small unitary updates can approximate a differentiable evolution even though the update label is integer valued. A sequence of unrelated images can be shown equally quickly without generating the same temporal understanding. Persistent memory and lawful correlations do much of the explanatory work usually hidden by the phrase high refresh rate.

In SMM/DTT, the six nested inner levels should be understood as the organization within a completed moment, rather than six perceptual frames following one another. A physical account then needs both an internal completion map and a rule connecting successive completions. Otherwise one has described six ingredients of a snapshot without explaining motion. The constructive opportunity is to show how stable low-frequency observables emerge while rapidly varying inner distinctions remain inaccessible. That would make continuity a controlled limit with an error estimate instead of a visual analogy.

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

Presentism restricts concrete temporal existence to the present; the growing-block view includes the past and present while excluding the future. The distinction is decisive for a record-based ontology. A present record of yesterday and yesterday’s continuing existence are different claims. Broad’s treatment of becoming supplies the historical growing-block comparator; the presentist alternative sharpens what an archive does and does not establish.

Suppose a stone bears an inscription describing a vanished ceremony. A presentist can treat the inscription as a current object with a history. A growing-block theorist can additionally include the ceremony itself in reality. Both can agree about what the inscription says. The disagreement therefore cannot be settled by pointing to a stored record alone. SMM/DTT gains precision by stating whether renewal preserves past events, preserves only present traces, or uses another form of persistence. Relativity adds the separate question of how a privileged present, if proposed, relates to spatially separated events. ^[1]

04The precise agreement and difference

Discrete presentism could treat only the current completed stage as actual. A discrete growing block could retain all completed stages while adding a new one. Both can be represented with the same sequence of stage labels, so discreteness does not settle the ontology. DTT’s emphasis on renewal favors asking what exactly remains between completions: the earlier event, a current trace of it, or a persistent source relation.

Continuity of experience places a constraint on either interpretation. If each present has no inherited relation to earlier ones, an observer cannot hear a melody or remember an action. Presentism can accommodate current memory; a growing block still needs to explain why the present observer accesses some past events and not others. DTT’s source memory is useful in both cases. Its distinctive contribution would be a law preserving the relations needed for continuous experience while generating new completed states. The comparison therefore concerns inherited structure and access, not whether a sequence looks like a film or whether the philosophical position uses the word present. ^[1]

05Worked example: what follows and what does not

For a finite-dimensional system with bounded Hamiltonian H, let one update be Uδ = exp(−iHδ/ℏ). After n updates the state is Uδⁿψ = exp(−iHnδ/ℏ)ψ. At the sampled times t = nδ this exactly agrees with ordinary unitary evolution. The integer n therefore does not by itself predict a new effect. An alternative update, an observable restriction between samples, or a physical limit on δ would be needed to distinguish a fundamentally discrete theory. This calculation also fixes the units: Hδ/ℏ is dimensionless. A dimensionless stage number becomes seconds only after a clock calibration or an independently derived timing law.

06What this comparison contributes

For experience, a different argument is required: an observer must integrate successive changes into an experienced event. The same word continuous should not make a mathematical limit do the work of a theory of perception. DTT can usefully connect the levels by modelling an observer as a record-bearing subsystem, whose accessible temporal resolution follows from its own dynamics. That is a stronger and more informative claim than saying that an invisible universal movie simply runs very quickly.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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