Human beings "can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols."
The words "innumerably finite" mean "countable using integers perhaps extending to infinity." Here, Boolos and Jeffrey are stating that an algorithm provides instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be chosen from 0 to infinity. Using this concept as a component of a quantum theory of mind, we might expect an algorithm to be an algebraic equation such as y = m + n - two arbitrary "input variables" m and n that produce an output y.
With respect to our inherent nature, humans may possess internally contained algorithms and capabilities to find, decode, and then calculate arbitrary input integers or symbols m and n, symbols + and = and produce an output-integer y at a specified place in a specified format. This inherent nature or algorithm opens toward a further question of whether we are also composed of the necessary algorithms to execute algorithms beyond our physical density that, in turn, provide us with the ability to perform an action that allows us to adjust matter within ourselves, resulting in an expanded alert cognitive state in which we are aware of unseen states of materialistic reality.
(If I didn't understand what I was saying here, I think I'd be totally lost reading this mixed bag of gallimaufry offering. So, if you have made it this far out of the sheer kindness of your heart, feel free to skip the rest of this theory and know that no one will begrudge you or even question your genius status).
The inherent genetic algorithms of problem solving in coping with nonlinearity, leave us bedeviled to find a method for determining how to expand our present cognitive state toward an expanded state of awareness (okay, I'm bordering on Eastern theology here, but I'm determined not to cross over) of the material universe. While humans exhibit a remarkable versatility due to evolution and natural selection, crossover (the fundamental mechanism of genetic rearrangement [beyond the crossover point] for both real organisms and genetic algorithms) presents a multitude of strings, which may be curved by the distribution of mass and energy resting in them, to be deciphered in an already simultaneously evolving population.
"Despite this complexity, it is the fact that a single string belongs to all the regions in which any of its bits appear. For example, the string 11011001 is a member of regions 11****** (where the indicates that a bit's value is unspecified), 1******1, **0**00* and so forth. The largest regions - those containing many unspecified bits - will typically be sampled by a large fraction of all the strings in a population. Thus, a genetic algorithm that manipulates a population of a few thousand strings actually sample a vastly larger number of regions. This implicit parallelism gives the genetic algorithm its central advantage over other problem-solving processes." John H. Holland
Before I get into why crossover complicates the effects of implicit parallelism; duh, those of you actually following this post might say; I'll now take this moment to thank the Consciousness Whisperer for his or her calming presence, felt through a series of hushed, intimate utterances of agreement and gentle, tender, harmonious keystrokes leading to the next section.