Cyclic time and recurrence: SMM/DTT and Eternalism and the block universe

01The question behind the comparison

A cycle repeats a configuration or operation; recurrence returns a system sufficiently close to an earlier state. Neither necessarily repeats the entire history. A clock hand can complete a turn while its counter advances. A biological rhythm can recur while the organism changes. SMM/DTT’s inner cycles can therefore coexist with an outer history that does not close. The key is to specify what cycles and what retains information from one completion to the next. Without that distinction, a circle in a diagram can misleadingly imply that all events recur exactly.

A compact inner variable may represent a periodic phase rather than a closed timelike curve in spacetime. Identifying phase values separated by a period is an algebraic or topological statement. It does not mean that a traveller returns to a past physical event. If a retained state changes after each traversal, the full state space includes both phase and memory. A projection onto phase alone then hides the accumulating history. This is especially useful for a theory that interprets stable matter as organized repetition: persistence can depend on a repeatable pattern without reducing the pattern’s biography to one closed orbit.

The six nested levels suggest cycles within cycles, but their periods need not be independent observables. A slower completion may require the successful closure of a lower operation. This structure can produce a hierarchy of effective timescales, although the values and ratios of those timescales still require dynamics. Counting six roles does not determine a frequency spectrum. A physical model would specify the recurrence condition, the stability of the cycle and the rule that carries memory between completions. These ingredients let cyclic generation support novelty rather than merely oppose it.

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

Eternalism treats events at different times as equally real. A block representation displays a history as a spacetime whole. Relativistic geometry provides powerful reasons to be careful about a universal present, but it does not by itself prove every metaphysical claim associated with eternalism. An eternalist can describe local causal processes, change and the internal experience of time without supposing that objects are motionless within each event.

A complete trajectory is a relation among positions and clock readings. Representing all its points together does not eliminate the difference between walking and standing: the trajectories remain different. The relevant issue for DTT is whether generation adds a physically consequential relation that a complete history omits, or instead offers an explanation of how such a history is constituted. A block description can contain all the records an observer ever accesses. It need not contain an additional moving spotlight. This makes completion, rather than the mere presence of change, the sharp point of comparison. ^[1]

04The precise agreement and difference

A block may contain periodic trajectories, quasiperiodic motion or a universe with no exact recurrence. Eternalism does not decide among them. DTT’s cyclic generation likewise does not by itself refute a complete-history representation. The relevant mathematical question is whether the full state, including retained records, returns to its original value or only a projected phase does.

If only the phase repeats, an eternalist can represent the successive cycles as distinct events in an open history. DTT can add an explanation of why a stable cyclic mechanism underlies those events. If the entire state repeats, including all records, the account faces a different question about whether the cycles are distinguishable at all. These alternatives have different implications for identity and memory. The six nested levels can help organize repeated operations, but cannot substitute for a recurrence theorem with stated state-space and dynamical assumptions. The comparison therefore supports a disciplined treatment of periodic source activity within a temporally extended world, rather than a forced choice between all change and a static block. ^[1]

05Worked example: what follows and what does not

Consider a state (θ,m), with θ an angle and m an integer record count. One update advances θ by π/2; after four updates θ returns to its original value and m increases by one. The phase is periodic, but the full state is not. If an observer reads only cos θ, the display repeats every four steps. If the observer can also read m, successive cycles are distinguishable. This elementary model explains how circular inner organization and ordered outer history can coexist. It does not fix the physical duration of a cycle: assigning four milliseconds requires an additional clock relation, whereas four updates is only a count.

06What this comparison contributes

The strongest comparison focuses on identity across recurrences. Is a repeated form the same event, a new event with the same structure, or merely an observationally indistinguishable event? DTT’s language of renewed creation favors a new completion carrying inherited relations, but a particular model must state what is preserved. This perspective avoids treating recurrence as evidence for an eternal return of every experience while retaining the explanatory value of periodic organization.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

• Circular Time and Cyclical Time →

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

• The Four Main Time Cycles →

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

• The Week as the Primary Time Cycle →

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

• Space-Time and Creation in Six Days →

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

• Time Chest →

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