Data compression—separating wheat from chaff—is necessary in real-time embodied cognition, particularly on rapidly-changing ‘Clausewitz landscapes’ of fog, friction, and deadly adversarial intent. Here, using the asymptotic limit theorems of information and control theories, we demonstrate that, where Weber-Fechner, Stevens, Hick-Hyman, Pieron, and similar compression modes operate in the context of interfering ‘noise’, sufficient arousal will engender Yerkes-Dodson inverse-U response patterns for difficult problems, bracketed at low—or deliberately blunted—arousal by hallucination, and at high, by panic. With further development, the probability models explored here can be converted into statistical tools useful in the analysis of real-world, real-time data for the contrasting operational purposes of clarity or deliberate obfuscation.