1 + 1 = 2 but does 1 man + 1 woman = love?
That's the difference between science and social science.
Remember that when you hear an economist (sociologist, political scientist, et al.) tell you that they've "got a model that shows 1+1=2."
Models (and other academic superstructures on which ideas are draped) are useful for thinking about how humans behave, but they cannot be used without caveats, cautions, interpretations, etc.
Some people may say that too much caution makes models useless. Yes, that's my point.
Bottom Line: Models are fun to play with but put away the toys and engage with human complexity if you want to really understand/cause change.
Sunday, August 9
The False Security of Mathematical Precision
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5 comments:
Without models, in every branch of science, you are left with the need to remember every experiment and its subtleties and caveats. This is hard.
Remembering the model, e.g. F=MA, allows you to spend more time on things that work and are predictive and less time on remembering.
F=MA and quantum mechanics are two models of the universe that have been spectacularly successful. There are not a significant number of incorrect predictions.
In trying to predict human behavior based on no model and only the instinct of your gut, people make characteristic errors over and over again. A model can be discarded. Gut instinct, not so much.
On the other hand, many 'social science' models seem to fail because the proposed model is equivalent to F=MA while the modeled behavior is much more complex. The complexity of the real world is thrown away to arrive at a simple to explain model--hedge fund algorithms demanded by sales people.
The simplification makes the model non predictive while a predictive model inhibits sales.
To me, all models have to be tested stringently against real world behavior. Those that are predictive and that encompass the existing data are kept; others are not.
F=MA survives because it continuously and correctly predicts events. For a while Black-Scholes did the same thing, but then the predicted events showed more of their complexity and the prediction worked less well. The inverse square law of gravity and the Standard model of physics may not survive current experimental results that challenge the universal validity of these models.
Bottom line - keep what works, discard the rest.
"Essentially, all models are wrong, but some are useful."
George E.P. Box, Professor Emeritus of Statistics at the University of Wisconsin.
I think your bottom line (and Eric's) miss the mark. The quote from Prof. Box is dead-on. The key to using any model (and as Eric points out, it's essentially impossible to do any kind of science without using models) is to recognize how the assumptions inherent in the model differ from the reality being modeled. Always list and justify the assumptions - then you'll gain a sense of how far off you are likely to be.
Among the more deadly assumptions: Normal distribution. Every time you talk about an average, you're assuming a normal distribution. How often is that assumption violated, unknowingly invalidating the model?
@albionwood
I agree.
When I construct models, I list all the assumptions and caveats. I only talk about these assumptions when someone asks, but I always have them.
As to normal distributions, I model biochemistry and biology. Normal distributions usually do not apply. Normal distributions tend to throw away all the important biology. So, for more than a decade now, I have used Bayesian and bootstrap approaches. Most recently, I have been using agent based modeling, which is fraught with caveats but useful.
As you may have guessed, this discussion is far longer than a blog post.
@Eric -- great first comment!
@CB -- I've heard Box a million times from Richard Howitt -- often as a rationalization for the results he's about to offer.
@abionwood -- indeed. what's the distribution of behavior and beliefs among people? :)
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