Figure 1.

Examples of combinatorial explosion and a catalytic cycle reducing the numbers of possible objects. A shows polynucleotide sequences with increasing chain length n. The number of possibilities is 4ⁿ and thus increases exponentially with n. B presents the numbers of possible C_mH_nO_p compounds, computed from simple minded combinatorial expressions assigning three, two, and one possibilities for introducing oxygen containing functions into CH₃, CH₂, and CH groups, respectively. Clearly, we see an indication of exponential increase. These numbers are compared with those derived in ref. 1 through selection of compounds suitable for a primitive metabolism in early evolution. C presents diagrams for interactions. Here we are dealing with a single class of elements represented by squares. The elements are coupled through their edges to the neighboring squares. We show possible patterns on a two-dimensional (square) lattice. The numbers of these patterns, related to “polyominoes” or “animals” defined in discrete mathematics, increase exponentially with the numbers of squares (2). D, ultimately, represents a cycle of catalytic reactions (3). The catalysts, the enzymes E_n, are synthesized from substrates S_n. Closure of the cycle leads to an autocatalytic ensemble. Self-enhancement discriminates against molecules that are not members of the cycle and reduces the numbers of possibilities.