SETI's blind spot: Technological Acceleration and fleeting technosignatures

The search for extraterrestrial intelligence (SETI) has traditionally framed the detection challenge with a focus on the parameter $L$ in the Drake equation - the communicative lifetime of a civilisation. I argue that the more pertinent quantity is $\tau_d$, the duration during which a civilisation produces technosignatures that are \emph{actually detectable by us, now}. Modelling technological progress as an exponential process, we show that $\tau_d = \alpha^{-1}\ln(K_{\rm max}/K_{\rm min})$, where $\alpha$ is the rate of technological acceleration and $[K_{\rm min},K_{\rm max}]$ brackets the technology levels accessible to our instruments. As $\alpha$ increases, $\tau_d$ can shrink to mere decades, dramatically narrowing the window in which civilisations overlap technically. This ``technology mismatch'' has implications for future search strategies, emphasising broadband and technology-agnostic approaches, as well as anomaly detection across multi-wavelength/messenger survey data.