Statistics about human height are not a good analogy, since the concepts are simple and straightforward enough that they can be readily dissolved and their connection to reality re-evaluated if necessary. But many other "social science" numbers are indeed as bad as those found in economics, in the sense that even a casual rational evaluation of these numbers will reveal critical problems that are nonchalantly ignored in the regular "scientific" practice in these areas. (Though it would probably be hard to find anything as perverse as the epistemic rat's nest that economists have built around various numbers they operate with.)
As for measuring how much richer people are than in the past, you can provide information that will leave readers with more or less correct intuitions about such things, by describing at length how much people in various occupation had to work and in what conditions, what they could afford with typical wages, etc., etc. But the idea that you can describe this with a single scalar number and then treat this number as a real physical quantity that features in models and theories is obviously complete nonsense.
But the idea that you can describe this with a single scalar number and then treat this number as a real physical quantity that features in models and theories is obviously complete nonsense.
It's not obviously complete nonsense. It's obviously part nonsense and part sense, and without further argumentation it's not obvious how large a part nonsense and how large a part sense.
Just because a quantity is defined in a rather arbitrary way, that doesn't mean it carries no information. You can take the position that an informal analysis would incorporate the ...
A Wall Street Journal article by Harvard professor of government Harvey Mansfield claims that the social sciences and humanities are inferior to the sciences. The article implicitly urges undergraduates to major in science. From the article:
Do you agree with this? As a game theorist I probably have a rather biased view of the situation. It's certainly true that the ideal of the scientific method is vastly better than the practice of economists, but I think that majoring in economics provides better training for a rationalist than majoring in any of the sciences does.
Economics explicitly considers what it means to be rational. Although it infrequently considers ways in which humans are irrational, I'm under the impression that the hard sciences never do this. Furthermore, because economists can almost never perform replicable experiments we have to rely on what everyone in the profession recognizes as messy data; therefore we’re far more equipped than hard scientists to understand the limits of using statistical inference to draw conclusions from real world situations. Although I have seen no data on this, I bet that a claim by nutritionists that they have found a strong causal link between some X and heart disease would be treated with far more skepticism by the average economist than the average hard scientist.