DTM.6:5 - Archetypal Grounding

DTM.6:5.1 - Restricting both variants can favor the less sensitive one

Consider a hypothetical community sharing procedures. A and B denote normalized execution activity inside one group, with A+B no greater than one. Remaining capacity is R=1−A−B. A yields useful results in this case; B produces specified errors. These are descriptions of practices and outcomes, not classes of people.

Suppose a shared checking response a affects them differently:

A' = A(2R − 0.2 − a)
B' = B(R − 0.3 − 0.2a).

These illustrative coefficients are stipulated, not measured. Two connections are now visible: both use R, and a restricts A more strongly. Holding activity fixed, an increase in a lowers both instantaneous growth rates. Over time, loss of A also releases capacity for B. The sign of B’s eventual change cannot be read from its direct response term alone.

DTM.9 completes this example by modeling how a is formed and calculating the later outcome. If a real procedure catalogue does not have the assumed capacity competition or differential checking effect, this model is not its explanation. A distinguishing investigation must recover those relations.

DTM.6:5.2 - Compatible partners can make an unfamiliar method worth adopting

Suppose the proposed method gives a group a benefit of 2 units over a fixed horizon and costs 0.5 to adopt. Exchange with a partner using the old method remains possible through manual conversion. The switching group bears conversion cost 3 per unit share of old-method partners.

If f is the share of its relevant partners already using the proposed method, its gain relative to continuing is:

g(f) = 2 − 0.5 − 3(1−f).

An independent estimate that omits partner conversion gives 2−0.5=1.5. The coupled estimate instead gives −0.9 at f=0.2 and 0.9 at f=0.8. At the lower share, ignoring compatibility therefore reverses the sign of the choice. Here other adopters facilitate adoption by reducing conversion work. No shared defensive response is needed.

An available adapter costing 0.4 over the same horizon and reducing the conversion coefficient to 0.2 changes the gain to 2−0.5−0.4−0.2(1−f), or 0.94 at f=0.2. The participants, cost allocation and horizon are unchanged. If costs instead shift to old-method partners, both parties’ consequences must be recomputed.

A comparison that records conversion work and partner composition can distinguish this account from an unrelated reluctance to adopt. Adoption still requires opportunity, capability and authority; a positive gain is not a transmission event. DTM.2/.4 supply those further questions.

DTM.6:5.3 - A notation practice can facilitate another method’s transmission

A group encounters a useful construction but cannot reconstruct its diagrammatic operations. A notation-learning practice may change that capability. The proposed connection is therefore capability → reconstruction of the transmitted method, not contact → uptake alone.

Compare subsequent reconstruction on suitable tasks, while retaining differences in prior knowledge and exposure. If only familiarity with the example increases, the evidence does not establish general facilitation. Human learning and AI training use their respective subject methods; this pattern does not prescribe one learning algorithm.