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EDITION 0831 · 31 August 2026
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The planet turns twice — and every flat plan on your desk pays for it
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31-08-2026

The planet turns twice — and every flat plan on your desk pays for it

Precession, obliquity and the theorem that no map keeps both angle and area. Why Zurich offices should set the CRS to EPSG:2056, not Web Mercator 3857.

A Nature Communications paper (s41467-025-63026-9) landed in the desk inbox this week, and rather than paraphrase a finding I could not fully read, I want to pull the thread underneath any planetary-scale result: we live on a body that turns twice, and we draw it on paper honest about only one thing at a time. That gap is not astronomy trivia — it sits inside the coordinate reference system stamped on every drawing you issued this year.

Start with the two turns. The fast one is the day — one rotation about the axis every 24 hours. The slow one is precession: the axis itself sweeps a cone, closing the loop in roughly 25,772 years. Hipparchus measured the drift of the equinoxes around 129 BC, and the medieval “Great Year” is the same intuition short on arithmetic. It is not 2,351 years and it is not the mystic figure the almanacs print; it is a hair under twenty-six millennia, and it is why Polaris is only temporarily the pole star.

On top of precession rides obliquity — the axial tilt, currently 23.44°, wandering between about 22.1° and 24.5° on a roughly 41,000-year beat — and the slow breathing of orbital eccentricity. Milutin Milanković worked these three clocks into the cycles that pace ice ages. Say it plainly, because the headlines blur it: those are the slow clock, tens of thousands of years long, not the fast anthropogenic warming of our own century. Keep the two ledgers separate.

←TODAY: In 2026 every Swiss cadastral drawing is tied to LV95 / CH1903+ (EPSG:2056), an oblique Mercator hung on the old Bern observatory — not the web map’s naïve cylinder. →3012: a Zurich that georeferences its models to the turning axis and the local vertical, so a building poured today still finds itself sure on a map re-cut three centuries out. Fulcrum: a projection is a choice about which distortion you can afford — you only see the choice when you hold the spinning globe and the flat plan in the same hand.

The move from a 3D Earth to a 2D map is a lossy compression, and every scheme picks its losses. Mercator is conformal — it preserves angles and local shape, which is why surveyors and navigators kept it — but it pays in area, inflating the ground the further you sit from the equator. Equal-area projections keep the hectares honest and shear the shapes instead. No projection keeps both; that is a theorem, not a shortcoming of anyone’s software.

Atelier: The office cost of ignoring this is silent until two models refuse to line up. Web Mercator (EPSG:3857) is the default under most quick web-map backdrops, and at Zurich’s latitude it is lying to you about size by a factor you can compute in one line. Monday move: open your BIM template and set the project CRS explicitly to LV95 / CH1903+ (EPSG:2056), record the origin and rotation in IfcMapConversion, and stop trusting whatever cylinder the basemap defaulted to. A century-standing building deserves a coordinate it can be found on.

Hack: Measure how far Web Mercator stretches the ground under your office. The projection’s scale error at latitude φ is the secant of φ — linear — and it squares for area. Run this and read the number before your next site plan sits on a web basemap.

import math
lat = 47.37                      # Zurich, degrees N
k = 1 / math.cos(math.radians(lat))
print(f"linear stretch: {k:.3f}x, area inflation: {k**2 - 1:+.0%}")
# linear stretch: 1.477x, area inflation: +118%

At 47.37° N the map exaggerates every length by ~48% and every area by ~118% — not a rendering glitch, the price of keeping angles true. PAZ has walked this research-into-form bridge before: our walnut-and-Galapagos piece watched David Rutten’s evolutionary solver rediscover a 30-million-year-old joint in Biomimetics 11(4):289, and the Nature-Inspired Algorithms panel makes the same point — geometry is where a hard-science fact becomes something you can build, and where a naïve default quietly costs you.

Check the CRS on the drawing nearest your hand right now. If it reads 3857, you are building on a map that grows the world toward the poles. Swap in EPSG:2056, and let the projection’s losses fall where a Swiss survey can carry them — on shape at the far edges, not on the area of the parcel you are about to pour.

Source: nature.com

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