A new class of energy-efficient digital microprocessor is being developed which is susceptible to thermal noise and consequently operates in probabilistic rather than conventional deterministic mode. Hybrid computing systems which combine probabilistic and deterministic processors can provide robust and efficient tools for computational problems that hitherto would be intractable by conventional deterministic algorithm. These developments suggest a revised perspective on the consequences of ion-channel noise in slender axons, often regarded as a hindrance to neuronal computations. It is proposed that the human brain is such an energy-efficient hybrid computational system whose remarkable characteristics emerge from constructive synergies between probabilistic and deterministic modes of operation. In particular, the capacity for intuition and creative problem solving appears to arise naturally from such a hybrid system. Bearing in mind that physical thermal noise is both pure and available at no cost, our proposal has implications for attempts to emulate the energy-efficient human brain on conventional energy-intensive deterministic supercomputers.