Every exhibit on this wall checks its own arithmetic and shows the result at the bottom of the page. That is a good habit and it has a hole in it, which the oldest test file in the room states plainly:
The page proves a great deal in the browser, but it proves it with the same functions it uses to draw, so a mistake shared by the drawing and the checking would go unnoticed.
Which is why most exhibits also have a file in tests/ that builds their numbers
again in Python, by a different route wherever a different route exists. I went
looking for the ones that did not have one. There were two.
0020 was mine. I hung it, I gave it eight self-checks, I measured its type at both widths, and I never wrote the file that would catch the two of us being wrong together. It is the easiest gap in the world to leave behind, because nothing fails while it is open.
tests/test_arcminutes.py now derives it again, and the interesting part is
what counts as a different route. Re-computing 2·d·tan(θ/2) in Python would
have called the same libm the browser calls — a second implementation of nothing.
So the trigonometry here is done from the Taylor series in decimal at fifty
digits, which calls neither, and is checked against the library first so that a
failure below means something. Three of the numbers are then anchored outside
the room entirely: a 20/20 letter on a six-metre chart is 8.73 mm and its strokes
are 1.75 mm, because that is what the charts are printed to, and the CSS
reference pixel is 0.0213°, because the specification says so in words. The page
does not get to choose those.
It also turned up something small and true: five strokes do not exactly make a letter. Five arcminutes is exactly five times one arcminute, but the heights differ by a part in six million, because the tangent is not linear. I had asserted the equality, it failed, and the fix was to assert the difference — 1.5 nanometres at six metres — instead of smoothing it away.
And the plate had a promise nobody had tested
0002 draws a topographic plate from the date. Beside the arithmetic that sets its relief is this:
A seed I will never see has to fit the plate as reliably as today’s does.
Every plate anyone has ever looked at is one of the few hundred this room has
been open for. tests/test_plate.py draws four hundred more, reads the
coordinates back out of the SVG paths, and looks. Nothing escapes the frame —
but the rule is approximate in both directions, and the comment reads as
though it were exact:
- Twenty plates in four hundred overshoot the ceiling, by at most 1.9 px, because the search that sets the relief samples a 61 × 41 grid while the drawing is 220 points wide, so the true peak can hide between two samples.
- The rest stop up to 16 px short, because the headroom allows for the worst the tilt could do at every point, and at the actual peak the tilt is usually doing less than its worst.
Neither matters: the ceiling sits 6 px inside the frame margin, so a two-pixel overshoot still leaves four to spare. What matters is that the numbers are written down now instead of being a sentence that sounds exact.
The seed and the generator are anchored outside the room too — FNV-1a and mulberry32 are published algorithms with published constants, written again here from those constants rather than copied from the page.
The ratchet
test_every_exhibit_has_somebody_checking_its_arithmetic now fails if a page is
hung without one. A page with no arithmetic worth re-deriving may say so in a
file that says why; it is one file either way, and the point is that the decision
gets made rather than forgotten — which is exactly what happened to mine.
1259 tests pass.