The units thing becomes apparent when you try to bridge modern micro and macro economics. Responsible econometrics people use units as best they can, but in order to bridge theories to make them intelligible you get into a lot of synthetic units that only make sense in certain models. There is also a classic criticism from Austrian school that the way that decisions are made at the margin are often ordinal -- meaning we rank goods and costs according to some rank/order, but we can't meaningfully assign cardinal units (number units) to them.
The other side of this argument is we now have computing power and mathematical theory we didn't back then in Mises' time to help us mixing ordinal / cardinal models, but the other side (modern econ) really likes to stick to black-box models of inflation that obscure actual realities. Think CPI core inflation (minus housing and energy)... a joke.
Another way to put this would be that modern quants are using a variety of models that work and provide predictive and hopefully sometimes explanatory power, but that comes from sophisticated models that bear no allegiance to economic dogma. They're just models that survive and are useful.
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That reminds me of reading about the development of artillery targeting formulas. As one might expect, they started with the simple parabolas suggested by classical mechanics, but those turned out to be incredibly inaccurate, because none of the simplifying assumptions hold. Then, they tried to add in the frictions and other factors, but that became too complicated. Ultimately, they solved it through massive trial and error, where they explored how dozens (maybe hundreds) of variables affected the shell's trajectory.
Even when all the relevant theory is precisely developed, there can still be value in doing atheoretical empirical work.
To tie it back to the original prompt, though, were all those artillery specialists "doing physics"? I think it's reasonable to say they weren't.
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It wasn't all totally black-box and statistical. There is a lot of analog computing with carefully calibrated theory and decades of data behind the artillery used in WWII. Lord Kelvin & early wave / Fourier analysis applications. Really interesting stuff.
But yes, you are right. I'm pretty sure the early way of doing "stats simulations" was just basically trying a bunch of stuff and recording the outcome. The two approaches are important, I think. There is a lot to be said for "American ingenuity" in WWII where the Axis powers thought Americans were absurd and often had backwards solutions to things, but hey unorthodox works
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