"E and the Builder" (February 2000) is Steve Baer's essay on the constant e and the fraction 1/e = 0.37 — what he calls "the share not done, at the deadline we ignorantly count on." The essay applies exponential decay to cooling, ventilation, daylight shading, and even the path of a trailer, arguing that builders who think linearly will always be disappointed.
Baer's central metaphor: many processes promise to finish on a schedule but never do. "Our schedule: 5, 4, 3, 2, 1, 0, (blast off); Nature's pace: 5, 4.09, 3.35, 2.74, 2.246, 1.84 (oops)."
Objects cool rapidly when hot, slowly when merely warm. Subcontractors work fast at first, then slow. "The time to completion promised by the present rate of progress, whether to cool a pot of soup or clean a garage is called the time constant. After one time constant the job won't be done, 1/e will remain. It will never be done."
| Domain | How 1/e appears |
|---|---|
| Cooling | A hot object sheds heat quickly at first; after one time constant, 37% of the temperature difference remains. |
| Ventilation | Blowing one fresh volume into a smoky room leaves 1/e (37%) of the smoke. Two volumes leave 1/e² (14%). |
| Trailer tracking | Driving one tongue-length forward straightens a trailer to within 1/e of its starting angle — almost exactly. |
| Daylight shading | A shade that blocks all direct sun can admit at most 1/e (37%) of diffuse daylight. Baer derives this as the limit: (N/(N+1))^(N+1) → 1/e as N → ∞. |
The essay argues that the world is "too complex" for linear counting: "the roads aren't straight to straighten out on, and background temperatures [aren't] steady to cool off to." Patterns only emerge through study. This framing matters for the archive because it pushes toward time constants, coupling coefficients, and flow rates instead of simple before-and-after thinking.
Baer also connects e to architecture through Gaudi, whose catenary models use the equation Y = (eˣ + e⁻ˣ)/2. Gaudi "went where mathematics invited and showed off its beauty" — suspended models that computed compression forms by gravity. Baer contrasts this with Gehry's Bilbao: "In Gaudi, form is mathematical perfection; in Gehry, a mathematical headache conquered by computer."
The study of exponentials … clarifies only one tidbit of the world at a time and works best on things subsiding to equilibrium. Other things grow exponentially, at least for a time, but those who predict geometric explosions of either wealth or poverty usually deceive.