A specific mapping mechanism is defined as the basic unit of “Biological Memory”. This mechanism must account for the characteristic frequency patterns in the organic world, where future probability is a function of past experience. The conditions for the function of biological memory are analysed. It is found that asymmetry, and irreversibility as a consequence of complexity, are the basic principles of memory function. The essential asymmetries in genetic memory are pointed out, and the problem of bilateral symmetry in a (...) basically asymmetrical organization is briefly outlined.Complexity is defined in terms of symmetry. The thermodynamic arrow of time and the biological arrow of time are discussed in relation to elementarity and complexity with their specific types of repeatabilities: non-accumulative in the first case and accumulative as a result of “copy-reproduction” by memory in the second case. The application of terminology from Information Theory and Thermodynamics to Memory Mechanics is critically considered.The immediate and inevitable consequences of memory function are shown to be irreversible expansion and irreversible, unpredictable diversification, leading to growing complexity and size on all but the sub-molecular levels of biological structure. (shrink)