That is an exceedingly optimistic hypothesis.
The people who are competent at math are probably N types on the MBTI, people who are good at abstract reasoning, but who might be less competent at focusing on empirical data and specific concrete situations.
Might be, indeed. This hasn't stopped physics, chemistry, engineering, biology, astronomy, etc. all of which have empirical data and concrete situations, and are chock-a-block with maths.
The sciences, especially the social sciences, need people who are good at observing/collecting data
Indeed they need such people. If you have evidence that the present selection procedures prevalent in the social sciences select for such people, I would be delighted to hear it.
Observing and collecting data is stereotypically something that maths types are good at. Consider google, data science and data mining.
Let me refer to Why is machine learning not used in medical diagnosis?
The top voted answer in the Quora discussion is from a medical student (...) describing the complexity of a diagnostic decision, and claims “the human body is incapable of being defined by any algorithm, no matter how bloody brilliant it is.”
The expert systems in question supposedly outperform human doctors!
The problem with machine learning in medicine is not the machine learning. Machine learning and AI have come a long way since the 80′s, and even then automated systems outperformed doctors in experimental settings.
I hypothesise as follows : the non-mathy fields maintain a group dynamic that causes a certain hostility towards mathematical ideas, even when such ideas are objectively superior. To an extent, this also prevents objective judgement of people's abilities within the field, and steers these fields away from a desirable meritocratic state. We end up with fields that select against mathematical ability (those with mathematical ability flee as soon as they realise that the entire history curriculum does not contain a single course on radiometric dating - I wish I were kidding), and that may not select for other desirable qualities instead.
Part of the sequence: Rationality and Philosophy
Bertrand Russell
I've complained before that philosophy is a diseased discipline which spends far too much of its time debating definitions, ignoring relevant scientific results, and endlessly re-interpreting old dead guys who didn't know the slightest bit of 20th century science. Is that still the case?
You bet. There's some good philosophy out there, but much of it is bad enough to make CMU philosopher Clark Glymour suggest that on tight university budgets, philosophy departments could be defunded unless their work is useful to (cited by) scientists and engineers — just as his own work on causal Bayes nets is now widely used in artificial intelligence and other fields.
How did philosophy get this way? Russell's hypothesis is not too shabby. Check the syllabi of the undergraduate "intro to philosophy" classes at the world's top 5 U.S. philosophy departments — NYU, Rutgers, Princeton, Michigan Ann Arbor, and Harvard — and you'll find that they spend a lot of time with (1) old dead guys who were wrong about almost everything because they knew nothing of modern logic, probability theory, or science, and with (2) 20th century philosophers who were way too enamored with cogsci-ignorant armchair philosophy. (I say more about the reasons for philosophy's degenerate state here.)
As the CEO of a philosophy/math/compsci research institute, I think many philosophical problems are important. But the field of philosophy doesn't seem to be very good at answering them. What can we do?
Why, come up with better philosophical methods, of course!
Scientific methods have improved over time, and so can philosophical methods. Here is the first of my recommendations...
More Pearl and Kahneman, less Plato and Kant
Philosophical training should begin with the latest and greatest formal methods ("Pearl" for the probabilistic graphical models made famous in Pearl 1988), and the latest and greatest science ("Kahneman" for the science of human reasoning reviewed in Kahneman 2011). Beginning with Plato and Kant (and company), as most universities do today, both (1) filters for inexact thinkers, as Russell suggested, and (2) teaches people to have too much respect for failed philosophical methods that are out of touch with 20th century breakthroughs in math and science.
So, I recommend we teach young philosophy students:
(In other words: train philosophy students like they do at CMU, but even "more so.")
So, my own "intro to philosophy" mega-course might be guided by the following core readings:
(There are many prerequisites to these, of course. I think philosophy should be a Highly Advanced subject of study that requires lots of prior training in maths and the sciences, like string theory but hopefully more productive.)
Once students are equipped with some of the latest math and science, then let them tackle The Big Questions. I bet they'd get farther than those raised on Plato and Kant instead.
You might also let them read 20th century analytic philosophy at that point — hopefully their training will have inoculated them from picking up bad thinking habits.
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