A plan is a cone: narrow now, wide later. Click something inside it and the cone inverts into a funnel — everything that must be true, and by when. Scroll to change the horizon (which coarsens the calendar and the map together), drag empty space to travel through time, drag an event toward the centre line to say it is likelier. Every number is computed live, not illustrated.
A possibility cone widens away from its anchor. That geometry was already there — the code grew
σ with |Δt|, so the object was really a bicone, opening in both directions.
The half pointing backward had no meaning attached to it.
Give the anchor an orientation and the backward half becomes the funnel. A forward cone from now answers what is reachable. A backward cone into a target answers what must still hold to arrive. Their intersection is Hägerstrand's space-time prism.
A correction. This work was scoped around “the narrowest waist of the prism is the last responsible moment”. That is wrong, and drawing the cross-sections is what showed it: a prism is pinched at both ends and fat in the middle, so its narrowest points are the endpoints and the claim says nothing.
The pivot — where σforward = σbackward. Before it the binding constraint is capability: you cannot be there yet. After it, it is commitment: you must be heading there. Freedom peaks exactly here, which makes it the honest “from now on, waiting costs you options” date. Found by bisection — the difference of an increasing and a decreasing function is monotone, so it converges without a derivative and works for any curve.
The commit deadline — the last moment you could set out and still
arrive. This one is closed-form: invert the growth curve. For the radiant cone,
u ≥ ln r / ln ρ. It satisfies a check worth stating —
reachable ⟺ deadline ≥ origin — which is how you know the two numbers are the same number
seen from different ends.
Zooming out in time while still claiming to know which building you were in is a specific kind of lie. So the two ladders step together: at a fortnight the axis is ruled in days and places bucket by venue; at a couple of months, weeks and cities; at a year, months and countries; beyond that, quarters and continents. The readout above the cone always says which pair is in force.
Buckets are made coherent rather than merely quantised. A grid alone has a boundary artifact no amount of coarsening fixes — two points eight kilometres apart can straddle a cell edge and stay separate forever — so groups within the grain's own length scale are merged afterwards. Two things in Berlin read as one Berlin, and Berlin and Tokyo never do.
An unlikely event is one someone agreed to that may not happen. A proposed one is a suggestion nobody has agreed to at all. Those are different facts and they get different ink: proposals are hollow and dashed, and they do not read as occupying the calendar.
The funnel's rungs are Padovan-spaced: cell widths grow by ρ = 1.3247, the real root of
x³ = x + 1. Run that ladder backward from a deadline and it gets finer as the
deadline approaches — pick a city, book flights, confirm the venue, send the agenda, final headcount.
The spacing is derived rather than written down by hand.
But only the spacing. A visa takes 45 days because a consulate says so, not because of a cubic. The ladder places checkpoints when nothing better is known; a real lead time always overrides it. Conflating the two would be numerology.
A constraint with no lead time is not quietly assumed fine — it is unverifiable, and it says so. A constraint whose moment has already passed is not filed under “missing metadata”; it gets its own band at the waist, because it is the most important thing on the screen. And the headline verdict folds in both failure modes: a plan whose constraints are all pending but whose target is out of reach reads unreachable, not “on track”.