The Mason's Arithmetic

Our lighthouse's crown looked almost right, which is the most dangerous kind of wrong. Almost right survives casual inspection; it fails the moment someone who loves the building looks at it for longer than a second. This week we retired "almost" — with a wash-profile scan of an 1860 elevation, a section cut through the panel band, and the oldest instrument in construction: counting.

The frieze is plumb

The verdict that opened the week was an observation from the reference photographs: the paneled band under the walkway stands dead vertical, while our model let it lean with the tower's taper. The 1860 elevation settled it — we scanned the drawing's wash shading row by row at its own drawn scale and plotted the silhouette width against height. The batter runs right past the old tower's top, dies at a documented break, a molded belt oversails it, and the frieze above rises plumb to the deck. Our model now does precisely that, and the crown finally sits on the shaft the way a capital sits on a column — because structurally, that is what it is.

Frames, not decoration

The recessed rectangles in that band had been modeled as applied trim: neat stone borders laid over the brickwork. A horizontal section through the band on the same 1860 sheet says otherwise. The frames are the wall itself — an outer course flush with the field, a second course stepping inward, a third forming the panel. The drawing shows the steps nested in plan; the measured widths agree with the photographs to a tenth of a foot. So the trim came off and the bond went in: the frames are now laid brick, in courses, in the same running bond as the wall around them. The building has one construction system, and now so does its twin.

Eighteen courses, no opinions

Whitewash defeats photography — a century of paint fills every joint a camera might count. So the layout was settled by arithmetic instead: the band stands just under four feet; a brick course of the period is two and five-eighths inches; the division lands on eighteen courses. The layout then tallies the way a foreman would call it: three courses of field, one course of step, ten of panel, one of step, three of field. Eighteen. The margins run in brick units too — a course and a half beside each bracket arm. The model's grid now derives from the course module rather than from anyone's taste, which is the point: a dimension argued in feet is an opinion; a dimension counted in courses is a fact.

What the section knew

Two details came straight off the section cuts and into the build. A pair of flanged iron portholes pierce the band's side faces into the watch room — drawn in plan in 1860, confirmed low in a panel by a photograph, now cast twice from one pattern like the rest of the crown ironwork. And the mortar: the real joints are struck flush and read as bright lines, where ours sat recessed in tidy shadows. The joints now stand at true three-eighths-inch scale, flush, with the brick faces varying a few millimetres against them. Perfection, it turns out, is the least realistic finish available.

The four-face problem

One mystery dissolved into geometry. In photographs of the real tower you can often see four of the octagon's eight faces; in our renders, never more than three. The taper was suspected. The taper was innocent. An octagon's face normals sit exactly forty-five degrees apart — and our entire camera ring had been planted on compass points, which is to say, aligned dead-on with a face normal at every station. Every camera we owned was standing in the one family of positions from which a fourth face cannot be seen. The ring now sits half a facet off, corner-on, and the model photographs like the building.

Reproducible, verifiably

The week closed with an audit of a claim we like to make: that the entire model rebuilds from source — scripts and a dimensions registry, every value carrying its provenance — on any machine, any time. The audit found the usual embarrassments (absolute paths with a home directory in them) and removed them. The build now runs from a bare clone with one command, deterministic down to the seeded jitter on each brick. One component remains on notice: the Fresnel lens, the only geometry not yet born from code. Its rebuild is scheduled, from first principles — a bullseye, its concentric prism rings, a bronze cage. A lighthouse should not keep secrets from its own drawings.