We demonstrate that information loss (error) is minimized in a binary branching network from linear-algebraic (graph-theoretic) and physical perspectives. Nature organizes the network currents to minimize heat loss. Nature has created the human brain, and a set of computational procedures of human natural language (CHL) exists in the human brain. A natural object CHL conforms with the principle of minimal computation (MC) and chooses binary branching structures rather than ternary branching structures. MC prefers efficient (less costly) computation. More information is conserved in the binary branching network. Binary branching structures, and not ternary branching structures, conform with the conservation law. Information means energy, forces, or heat from an engineering perspective. Moreover, we have graphtheoretic (linear-algebraic) and physical reasons for concluding that the syntactic operation merge in CHL must be binary, and not ternary.