NOT.5:5 - Archetypal Grounding

NOT.5:5.1 - Translate a dependency drawing without inventing geometric meaning

A drawing has named nodes A, B, C and D. An arrow X→Y means that Y takes X’s result as its direct input. Box positions carry no meaning. In one drawing the arrows are A→B and B→C; D is isolated. The receiver must determine C’s direct input using ordinary text.

Construct this textual notation:

nodes: A, B, C, D
direct-input pairs (supplier, receiver): (A, B), (B, C)

The reading rule selects the pair whose receiver is C and returns its supplier, B. Translating back draws one node per declared name and one arrow per pair. This recovers the named directed structure, including isolated D. It need not recover the original layout.

A list of node names alone fails. The second drawing with A→B and A→C would give the same list but a different answer for C. Retaining the pairs repairs that loss. Retaining only pairs would create a different loss: isolated D would disappear from a reconstructed drawing.

Now suppose horizontal position additionally records a planned start time. The earlier translation still answers the direct-input question, but it cannot reconstruct that timing. Add a start-time value for each node if timing is now needed. That extension follows a changed interpretation or question; it is not evidence that the original drawing already specified times.

NOT.5:5.2 - Keep a useful count without pretending it preserves a rhythm

A toy score is a sequence of four equally spaced cue positions. D and T name two distinct sounds; there are no rests. Translate a score into the counts of D and T. Both D T D D and D D T D become D:3, T:1.

The target answers how many sounds are required: four. It cannot answer which sound occurs second. In the first score it is T; in the second it is D. No reverse choice made from the counts alone can recover both originals.

For this family with one T, retain its position as a supplement. Counts plus T-position:2 reconstruct D T D D: place T at position 2 and fill the remaining positions with D. This permits both the count and the second-cue question. If the score may contain several T cues, retain their positions, check that they are distinct and within the score, and check that their number agrees with the count. If rests or unequal intervals become relevant, the chosen description needs further distinctions.

The counts remain a sufficient result for inventory. Reconstructing performance order requires the supplement; reconstructing tempo would require a time scale that this toy score never supplied.

NOT.5:5.3 - Choose what a backward update preserves

A plan describes two successive phases by [A:3; B:5], in whole minutes. A summary notation shows only their total, 8. The recipient changes that total to 10. Several source plans fit: [A:3; B:7] and [A:5; B:5] both do. The new total does not choose between them.

Suppose the work requires A to remain fixed. Retain A’s duration, 3, and reconstruct B as new total - 3. The requested total 10 gives [A:3; B:7]. Returning the unchanged total 8 recovers [A:3; B:5]; summing the updated plan returns 10. If instead B must remain fixed, the other update policy gives [A:5; B:5].

Assume phase durations must be nonnegative. A requested total of 2 is incompatible with retaining A at 3. Report that conflict and obtain a changed requirement if the work allows one. Substituting B = -1 would preserve the sum while violating the admitted source plan.