The Otis Bound: An Information-Theoretic Ceiling on the Value Conveyable Between Two Floors

It is folklore that a good idea can be pitched between two floors of an elevator. We show that this is not folklore but a capacity theorem. Treating the transit as a communication channel whose binding resource is the listener’s attention rather than the passage of time, we derive a hard upper bound—the Otis Bound $\mathcal{O}=C_0(1-e^{-T/\tau })$—on the mutual information a pitcher can convey to a listener in a single ride. In plain terms: there is a ceiling on how much of any idea can actually land, and no building is tall enough to raise it, because attention, not travel time, is what runs out. Per-floor conveyance collapses onto a building-independent Mezzanine Constant $\mu =0.61\pm 0.03bits/floor$; half of every successful pitch arrives before the cab clears the first inter-floor gap. Ideas whose intended content exceeds $\mathcal{O}$ do not arrive truncated—they obliterate, collapsing into self-similar repetition through a second-order phase transition (order parameter $\Omega$, critical exponent $\beta =\frac{1}{2}$). Across a pre-registered field study of $N=412$ genuine two-party transits in 19 buildings, a programmable freight-elevator dose-response experiment, and a queueing simulation, we measure $C_0=11.4\pm 0.6$ bits and $\tau =9.8\pm 0.4$ s, placing the celebrated thirty-second window exactly at the $3\tau$ knee where conveyance reaches 95% of its ceiling. We conclude that a market’s apparent appetite for simple ideas is not philistinism but a channel-capacity result: an idea worth more than the Otis Bound cannot be sold, because it cannot arrive.