If so, that makes sociology completely useless for policy. A field which cannot predict what will happen next time can't actually inform a policy maker as to whether their policy is useful.
Math mostly requires reducibility: the ability to split it into small parts and look at these individually.
This is simply false. If this is your criticism of math in economics, it applies equally well to math in geophysics, oceanography, climate science, etc.
That charge could reasonably be made against economics. From 2008: 'During a briefing by academics at the London School of Economics on the turmoil on the international markets the Queen asked: "Why did nobody notice it?"' [0]
[0] http://www.telegraph.co.uk/news/uknews/theroyalfamily/338635...
There's plenty more to the economy, and to economics, and to the crisis than predicting stock prices. Reducing the question to stock prices is avoiding the question, IMO.
> That's like saying physics is invalid because the Newtonian model doesn't 100% accurately reflect reality
Not really. Newtonian physics is inaccurate in ways that are hard to measure at everyday human scale. The 2008 crisis was pretty noticeable, all over the world. I think an apt physics analogy would be something like getting a nuclear explosion out of starting a fire (technically, out of buying a house), something that's been done successfully for millennia without major incident.
http://www.twill.info/wp-content/uploads/2013/03/SOME-ECONOM...
Dean Baker's paper from 2002:
Only in as much as one believes that descriptive results are "completely useless" for policy.
For me they are just as important, if not more, than predictive results. Predictive models only tells us what will happen -- not what is going on, if it is any good, ways of thinking about it, and whether we should ask for more or less of it.
I'm a policy maker. I put an end to slavery.
No prediction involved.
"X prevents women from getting into IT".
I'm a policy maker. I take steps to help women get into IT.
No prediction involved.
Conditions in prisons are bad because so and so.
I'm a policy maker. Let's change the conditions.
No prediction involved.
Sometimes the prediction is obvious and implied (removing X will allow more women to get into IT), other times it's not needed at all (when the change is about doing what's right, like with slavery, not about doing something that we predict will turn things in some specific way).
This critique is similarly wrong. There's a field called "machine learning" - you might have heard of it - which often uses inhomogeneous data points.
So doing statistical studies on a question like "do charter schools work" that treats all these implementations as identical, is often not very useful for actually learning something about policy.
So instead build a model that understands the important factors which make charter schools work/fail. Then use it.
If you can't do this, don't pretend you have anything to say about whether I should implement charter schools.
And I'm not claiming that sociology cannot predict. I'm just saying that they cannot measure the small (CO_2) and extrapolate to the large to make predictions. Their predictions therefore need other methods.