More on innumeracy
Given all the comments on my post about people who readily admit to being bad at math, as well as the discussion occurring on various other blogs, I figured it was time to respond to some of what’s been said.
There were some people who expressed skepticism of the phenomenon I was complaining about. These comments (both here and elsewhere) were things like “I always talk about how bad I am at writing” or “I’m an English major, but I know plenty of science.” I have no doubt at all that the incidents cited in the comments really did happen, and they do go against the trend I talked about, but I think they are the exception rather than the rule.
Putting aside for a moment the question of how much knowledge someone should have about any particular field, I want to give some clear support for my assertion that math/science people do know more about the humanities than humanities people know about math and science. I should first be clear about what I’m counting as what. By “humanities” I mean not only literature and fine arts, but also history, social sciences and languages. While there are some arguable cases (economics comes to mind), I think it’s pretty clear that that stuff clearly goes on the humanities side of the divide. When I refer to “sciences,” I mean technical fields in general, including both theoretical and applied math, computer science, engineering, and applications like medicine.
It’s obviously impossible to compare levels of understanding in two different fields. How much calculus do you need in order to equal the amount of knowledge that encompassed by fluency in a foreign language? It doesn’t make any sense to compare these things directly. Still, I believe that we can make the general claim that some incredibly basic, simple science is considered “equivalent” to much more advanced levels of humanities knowledge. Z commented to this effect, using Jeopardy! questions as a proxy. Something a little more quantitative (ha, ha) would of course be preferable.
The best metric I could come up with was simply to look at how much effort was being put into learning material on the other side of the divide, rather than how much material was actually being learned. I decided to look up core curricula at some of the country’s most prestigious universities. These curricula seem as good a proxy as any for what the intellectual class feels a well-educated person should know. The humanities part of the core requirement generally determines how much time a science student has to spend on humanities, while the reverse is true of the science part of the requirement. Of course, many on both sides choose to learn much more than is required, but I think the requirements are a good proxy of what is considered necessary in order to consider yourself well-educated. I tried to vary the colleges I looked at. I chose two schools with a technical focus (MIT and Caltech), three general top universities (Harvard, Princeton, and Yale), and two of the top liberal arts schools (Swarthmore and Williams). Results below:
| Caltech | Science: | 14 courses, including 5 math, 5 physics, 2 chem, 1 bio, and 2 labs |
| Humanities: | 12 courses, including 2 writing, 2 social science, 2 “advanced humanities”, 2 “advanced social science” Also, not sure how to place it – 2 science writing courses |
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| Harvard | Science: | 3 courses, one in each of the categories Science A, Science B, and Quantitative Reasoning |
| Humanities: | 8 courses, one in each of the categories Literature and Arts A, Literature and Arts B, Literature and Arts C, Foreign Cultures, Historical Study A, Historical Study B, Moral Reasoning, Social Analysis | |
| MIT | Science: | 8 courses, including 2 math, 2 physics, 1 bio, 1 chem, and 1 lab course |
| Humanities: | 8 courses, including a distribution requirement and a depth requirement | |
| Princeton | Science: | 3 courses, including 1 quantitative reasoning, 2 science with lab |
| Humanities: | 7 courses, including 1 epistemology and cognition, 1 ethical thought and moral values, 1 historical analysis, 2 literature and arts, 2 social analysis | |
| Swarthmore | Science: | 3 courses, including 1 lab |
| Humanities: | at least 6 courses, including 3 humanities and 3 social sciences, and 3 writing courses which may overlap | |
| Williams | Science: | 3 courses, including 1 quantitative/formal reasoning class |
| Humanities: | 6 courses, including 3 in languages and the arts, 3 social studies, including 1 “peoples and culture” and 2 writing | |
| Yale | Science: | 2 courses, and a 2 course quantitative reasoning requirement that (I think) can overlap with the 2 science courses |
| Humanities: | 2 courses in the social sciences, a 2 course writing requirement that (I think) can overlap, and an unclear foreign language requirement |
First, my apologies to anyone from these schools for any errors in interpretation I may have made. Most of these things are not explained very clearly. I should also say that to really compare these things properly, you’d need to look into how demanding the courses in each of these areas are (for example, I’m skeptical of the math requirements labeled “quantitative reasoning”), how easy they are to get out of with AP scores or whatever, and a variety of other factors. Nonetheless, I think the result is incredibly obvious. MIT and Caltech both have large requirements in both sciences and humanities. Everywhere else expects a minimum of twice as many humanities courses as science courses.
I am sure Z or I will be posting more about this soon. There are a lot of issues that need addressing. I could go on for quite a while about the fact that almost no one actually knows what math is (hint, from commenter Dan: not accounting), and in general the case needs to be made that this disproportionate focus on humanities is actually bad, rather than justified in some way. For now though, I simply wanted to dispel any doubt that the level of humanities study necessary to be considered well-educated in America really is greater than the level of study in the sciences. I think that will be obvious to anyone who looks at the chart above.
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I am quite good at math. I have the BS and the MS in math. Like you I get bothered by the number of people who NEED to tell me how they never got it. And yes, even more bothered that it is said with pride. In fairness, however, I do consider math to be my hobby and since I view it as a hobby I don’t want to force my hobby on others. I don’t really feel that people should be forced to learn algebra if they are truly much more interested in spending their time on the great works of literature or world history. Similarly, I would not want someone forcing me to play golf instead of allowing me to play my piano instead. However, it is the pride in being unable to do everyday math that really does bother me. In answer to the age old question, “Why do we have to learn this stuff?”, my father responded “So that when you go to the store you don’t get ripped off by someone taking advantage of you.” If you have math sense you notice the scams and if you don’t have math sense you can sometime depend on the “experts”. As an example, our sales tax recently increased from 5% to 6.25%. Now although this is a 25% increase, this does NOT mean that the sales tax rate is 25%. But at the time that this legislation was being passed I read many articles in newspapers that alluded to this being the case. Now either the writer was taking advantage of a math phobic public (he was opposed) or the writer did not understand the distinction himself. I have no problem with people not understanding algebra, geometry, calculus etc. but I do have problems when people brag about not being able to do the math that was taught in 4th, 5th and 6th grade. Just like a believe that everyone should be able to read well enough to read signs and fill out the necessary applications that life requires, I also believe that people should be able to do simple arithmetic in their heads — multiplying and dividing by 2, multiplying and dividing by 10 as well as being able to figure out the tip at a restaurant and know what 20% off means when they go shopping.