Leibniz, in his Essais de Théodicée (1710, I), says:
Il demeure toujours vrai … qu’il y a une infinité de Mondes possibles, dont il faut que Dieu ait choisi le meilleur; puisqu’il ne fait rien sans agir suivant la suprême Raison.
[It always remains true ... that there are an infinity of possible Worlds, from which it must be that God would have chosen the best, since he does nothing without acting in accordance with supreme Reason.]
Leibniz has been roundly ridiculed for this sentiment. Apparently he rejects the desirability of finding optimal subproblems, in the logical sense, within moral philosophy. Coming from the coiner of the term differential and what remains (300 years on) its modern symbol, this seems inconsistent. Then again, maybe it is Leibniz’s detractors who fail to see the possibility of optimal subproblems in the order of the universe, because they are distracted by the immediacy of human suffering. Perhaps Leibniz thinks that all this really does even out algorithmically.
The question of efficiency strategies is much on my mind these days, as I have been trying to master the units on dynamic programming and greedy algorithms before tomorrow’s final exam in Algorithms. There has been ample time, but somehow I never use time as effectively as I might, and I wonder if the subject itself does not contain lessons for me, going forward.
In the past year, calendar 2011, I have made headway clearing my desk of obligations from my past academic life. My mind is clearer, too. Though not as clear as I wish, since it has been cluttered with the new learning I have taken in during two semesters of Data Structures and Algorithms this year, the heart of the mathematical poetry that underlies computer science. It has been a good year and I think it will remain a memorable one for me, if perhaps not the best of all possible years.
I use the word “cluttered” advisedly above, since it seems to me that while I am perhaps able to study with preplanned efficiency, my mind does not learn that way itself. In particular, my mind seems to require a distinctly inefficient period of “shaking down” what I have learned before it displays any comfort with new learning, to say nothing of mastery. A really efficient learning strategy would include provision for that process.