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 ${\tau }_d={\alpha }^{-1}\ln (K_{\mathrm{m}\mathrm{a}\mathrm{x}}\mathrm{/}{K}_{\mathrm{m}\mathrm{i}\mathrm{n}})$, where $\alpha$ is the rate of technological acceleration and $[K_{\mathrm{m}\mathrm{i}\mathrm{n}},K_{\mathrm{m}\mathrm{a}\mathrm{x}}]$ 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.