What does this equation mean?

A processor held at fixed altitude near a black hole’s horizon runs slow. Not metaphorically: its proper time $\tau$ , the time its own internal clock and its own quantum gates actually tick through, elapses more slowly than the coordinate time t used by a bookkeeper stationed far away, by the ordinary gravitational redshift factor $\sqrt{f(r)}$ . A distant observer watching that processor through a telescope sees every one of its gates run in slow motion. Turn the statement around, though, and something more interesting appears to fall out. If the processor’s own clock is the one that is running normally — and by the equivalence principle, locally it is — then from the processor’s point of view it is the distant observer’s second that has become enormous. Every proper second the processor spends near the horizon corresponds to a large number of the distant observer’s seconds. If the processor can run some fixed number of quantum operations per proper second, and a proper second down there buys many coordinate seconds up here, then a computer near a horizon appears to have found a way to think for the distant observer for free.