But the two problems we have mentioned, that some people forgot that (1) "We found there is no benefit …" is not the same as there was no benefit and (2) the central limit theorem does not guarantee to kill black swans, are elementary mistakes and more an embarrassment of some social scientists than the challenges of social science problems.

Is it possible to make progress in the social sciences? Actually, yes: For (1), that is just a hypothesis test, and the social sciences have long commonly made good use of that subject, e.g., as in

Sidney Siegel, 'Nonparametric Statistics for the Behavioral Sciences', McGraw-Hill, New York, 1956.

Some people in the social sciences know this material well. The system monitoring communities in computer science and information technology would do well getting caught up on such material.

For more, the recent rapid progress in 'social' applications of computing and the Internet show progress in understanding 'social' phenomena.

Having the social sciences as precise as mathematical physics soon? No. Possible to make progress in the social sciences? Yes.

Who knows? One of these days he might decide to give up his day job and come back and finish up his dissertation. Could happen.

Here is how one of the basic arguments in 'mathematical finance' went:

We assume that there is no free money, no free lunch, that is, no 'arbitrage' because if there were too quickly too many investors would exploit it at which time the arbitrage would no longer exist. So, this assumption of no arbitrage is, maybe, an okay (for some purposes) first cut assumption for how the market works in the large (even if individual traders get rich with individual stocks). So, what is left is that no one knows, or has any way of discovering, what the stock market will do tomorrow, the next day, etc. So, what the market does each day is (something like flipping a coin) probabilistically independent of the past. Next, lacking any information to the contrary (e.g., no 'Monday effect'), we assume that the distribution of the change from one day to the next is always the same. Soooooo, with these two assumptions, and a relatively mild assumption about the nature of the distribution (finite variance is enough and the Lindeberg-Feller result has a tricky weaker assumption) the change in the stock market over, say, 30 days is the sum of 30 changes each of which is independent and has the same distribution so that by the classic central limit theorem the change over the 30 days must start to be approximated by a Gaussian distribution.

Now, with these assumptions, as the number of days, the 30, grows, the actual distribution will converge to a Gaussian distribution as closely as we please.

In particular, if we look at where the market is, say, each 30 days, then what we get will look, just to the eye, something like Brownian motion.

My view is that this argument (really just the assumptions since the mathematics itself is rock solid) is neither completely wrong nor as accurate as is important.

Even if really believe this argument, (and many traders, e.g., naked short sellers, have reason to laugh) we still do not know how accurately the convergence is to a Gaussian distribution. In particular, even we add up the daily incremental changes for a year, say, 250 trading days, we still can't rule out some rare events far out in the tail, that is, a 'black swan'.