Learning ability is a vitally important, distinctive property of biological systems, which provides dynamic stability in non-stationary environments. Although several different types of learning have been successfully modeled using a universal computer, in general, learning cannot be described by an algorithm. In other words, algorithmic approach to describing the functioning of biological systems is not sufficient for adequate grasping of what is life. Since biosystems are parts of the physical world, one might hope that adding some physical mechanisms and principles to the concept of algorithm could provide extra possibilities for describing learning in its full generality. However, a straightforward approach to that through the so-called physical hypercomputation so far has not been successful. Here an alternative approach is proposed. Biosystems are described as achieving enumeration of possible physical compositions though random incremental modifications inflicted on them by active operating resources (AORs) in the environment. Biosystems learn through algorithmic regulation of the intensity of the above modifications according to a specific optimality criterion. From the perspective of external observers, biosystems move in the space of different algorithms driven by random modifications imposed by the environmental AORs. A particular algorithm is only a snapshot of that motion, while the motion itself is essentially trans-algorithmic. In this conceptual framework, death of unfit members of a population, for example, is viewed as a trans-algorithmic modification made in the population as a biosystem by environmental AORs. Numerous examples of AOR utilization in biosystems of different complexity, from viruses to multicellular organisms, are provided.
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