01 / LIFT
Prefabricated lifts
Prepare bridge units at a staging area, reserve lifting access, then lift and connect units between the peaks.
Questions left open: lift capacity, wind limits, access and installation loads.
Keeping construction methods open · Essai 02
Can we still change
how we build the bridge?
A high-level bridge must connect two peaks for walkers and an emergency utility service. After partial construction, the lifting service is withdrawn. What earlier choice leaves another method reachable?
A small exact witness, followed by two preserved visual explorations and their limits.
First witness · exact finite rules
Same progress. Different remaining methods.
Two histories have completed 1 of 2 bridge units at time 4, with access at both peaks. The same lifting withdrawal now occurs. One history retained a conversion provision before closing an interface; the other spent the same unit of time recording its lift plan. Reported progress and elapsed time omit that difference.
Selecting a state loads one declared route to it. Use the action buttons to explore another history.
Permitted next steps
Undo navigates this explorer. It does not undo construction in the model.
All completion routes from this state
This inspected history
Start: no work, access not prepared.
Why actions are unavailable from this state
Inspect the complete finite transition graph
Every reached state and every permitted outgoing transition appears below. Zero completion routes means exhaustive failure within these rules. Completed states have one empty continuation. Click a state or transition to inspect it; the JSON includes every completion route from every state.
| State | Time / work | Complete routes | Cable routes | All outgoing transitions |
|---|
Inspect all ten action rules and modelling assumptions
| Action | Duration / demand | Precondition | Effect |
|---|
Actions run sequentially; one crew and one planner remain available. Durations are illustrative units. Peak access, once prepared, stays open. No deadline, cost, load, weather, waiting or expiry constraint is encoded. The withdrawal is an observed event after partial work, not a random variable or an adversary policy.
Ten one-use actions bound every history by ten transitions. Each edge sets a fresh action bit, so the complete graph is acyclic. The engine works backward from completion states; independent tests enumerate forward histories to check every state and route count. There is no search timeout or omitted waiting behaviour that changes reachability under these rules.
The precise result is one remaining route after this observed disruption.
The provision-retaining state can convert, cable-complete and connect the utility service. The matched state without provision has no permitted completion route. This is a fictional finite witness, not real engineering feasibility or a policy that succeeds across all disruptions. The progress measure omits provision, closure, lifting availability and service connection.
Retained exploration · drawing interpolation
Could a change of drawing suggest a change of method?
Keep this visual question separate from the finite witness above. These three paths are illustrations of prefabricated lifts, cable-assisted assembly and advancing from the two peaks. They do not define the permitted actions, states or recovery routes.
Same drawn start. Same drawn finish.Schematic
Dots match by position in the sequence, not by equivalent work. Geometry is illustrative, with no physical scale.
Explore the drawing
Choose two approaches
Prefabricated liftsCable-assisted
Drag or use arrow keys. This changes the drawing, not project progress.
Paused at the starting drawing.
A smooth picture is not a feasible plan.
The two endpoints stay fixed by construction. Intermediate drawings do not establish that crews could switch between these methods.
What the four dots stand for
The correspondence is supplied for the drawing.
- 1 · Prepare bridge work
- 2 · Establish an approach
- 3 · Advance bridge work
- 4 · Complete the bridge
Three imagined approaches
02 / CABLE
Cable-assisted assembly
Stage work at both peaks, establish a cable system, transfer bridge units and connect them across the gap.
Questions left open: anchor design, hauling loads, crew access and staging.
03 / ADVANCE
Advancing from the peaks
Stage teams at both peaks, establish work fronts and advance toward a common connection across the gap.
Questions left open: temporary stability, balanced progress, rescue and peak access.
What survives the change?
A question to investigate,
not a set of green ticks.
The drawing contains no engineering, cost or time model. These counterpart questions remain unmodelled in the drawings; the finite model above supplies no engineering answer:
- Weather resilience
- Unknown · not modelled
- Structural and access safety
- Unknown · not modelled
- Seasonal deadline
- Unknown · not modelled
- Budget compliance
- Unknown · not modelled
The homotopy intuition—and its limit
In mathematics, a homotopy is a continuous deformation between maps within a specified space. For paths, one can require the endpoints to remain fixed. Here, corresponding vertices are linearly interpolated: H(s, t) = (1 − t)A(s) + tB(s), where s runs along the equally partitioned segments and t is the blend. This gives a homotopy of these drawn paths in the unrestricted plane, with the same first and last coordinates.
A space of feasible project plans has not been defined. Nor does this drawing engine encode allowable transitions, obstacles, resources, costs or deadlines. The finite model above is a separate declared system, not a validation of these curves. So this is not a proof that the construction approaches are homotopic as feasible plans, or that safety, budget or completion dates are preserved. Matching the second dot in two drawings does not make “Reserve lifting window” and “Establish cable system” interchangeable activities.
The useful project question is: what would have to remain true while a team changed method? The finite model above takes one small step by declaring states and actions. It neither assigns those meanings to these drawing coordinates nor proves that interpolated points are feasible states.
Explore the companion task-field experimentSixteen tasks, supplied affinities and a reproducible spatial layout
Retained companion exploration · heuristic spatial grouping
What happens when related task dots attract?
The earlier prototype also let sixteen construction tasks move under attraction and repulsion. This version maps every task to the bridge setting and retains all sixteen records, types and supplied priorities. It turns those labels into a repeatable drawing rule, with no claim that a construction sequence emerges.
0.1–2.0. Reset after changing strength to compare from identical starting positions. Repulsion remains active at every setting.
Paused. Seed 190 fixes the starting positions.
0 / 600 steps
Prepare peak anchor points
Foundation / anchoring · supplied priority: critical.
- Foundation / anchoring
- Structural
- Weatherproofing
- Safety systems
The supplied drawing rules
Within 150 drawing units, same-type pairs attract with weight 1.2; foundation–structure pairs with 0.8; structure–weatherproofing with 0.6; other safety pairs with 0.4. Remaining pairs mildly repel (−0.3). A pair involving a supplied critical task has 1.5 times that influence. Short-range repulsion limits overlap.
All positions update from the same prior snapshot, in fixed steps with damping, speed caps and a bounded square. Seed 190 reproduces the start. The same strength and number of steps reproduce the layout. The 600-step stop is an illustration limit, not evidence of convergence.
Attraction is not a dependency
A foundation dot drawing a structural dot closer does not enforce “foundation before structure.” There are no directed prerequisites, start or finish times, crew capacities, loads or completion checks. These are proximity links, not a schedule or construction phases.
Spatial grouping does not prove feasible construction, optimal scheduling or real project self-organisation. The original “optimal phases” and “no central scheduler needed” claims are withdrawn. This experiment can prompt questions about relationships that a separate planning model would need to encode.