Dollar cost averaging: making hay while the sun shines or doubling down?

Over at Scientific Clearing House, Carson posted a pretty proof of the how dollar cost averaging is an optimal investment strategy.  Unfortunately, I think the conditions for this optimization aren’t practical because they are far too optimistic about one’s ability to choose to invest in appreciating assets.

In a long winded comment, I take delight in making the following perverse equivalence between an honest work-ethic idiom and foolish gambling practice,

Under these optimistic assumptions, DCA [dollar cost averaging] is equivalent to the idiom: make hay while the sun shines. Downward price fluctuations are viewed as opportunities to use the same resources to make even more of a good investment. Under less certainty, this is what gamblers call doubling down–when you are loosing, bet more so when you win, you make up your previous losses.

I have advocated DCA as a reasonable investment strategy to friends of mine, but I am increasingly skeptical about the assumptions.  It is starting to seem more like doubling down and less like making hay.