# 2 | Michael Anes | July 26, 2008 10:06 AM

I agree wholeheartedly with the substance of your post.

I do dislike the implication in this quote "our economy is teetering because people can't hack the math needed to understand how big a loan they can afford" that somehow the economic problems brought about by subprime loans are the fault of the people taking out the loans. The problem was in the rapacious taking of huge sums of cash in a speculative market that saw no bounds; the packaging of overvalued paper instruments, the lack of income verification of any kind, etc. This American Life had a great piece on the mortgage banking crisis.

This is not to say some basic numeracy would have helped folks with balooning APRs, but in many cases these finer points were deliberately obscured or misrepresented. Finally, is it really not smart to take advantage of the booming market and move your family into a large house, apparently risk-free?

Whatever the case, I do not believe the end consumer bears the lion's share of responsibility...

# 4 | Joe Shelby | July 26, 2008 10:15 AM

The problem was in the rapacious taking of huge sums of cash in a speculative market that saw no bounds

partially, but there was also the lack of accountability at the lower levels, which encouraged them to inflate incomes on forms for approval above. Bob Cringely over at PBS wrote that he actually applied for a loan, and when the final paperwork came back for him to sign, his "income" on the form was double what he originally submitted. When he pointed it out (he actually *read* the document; most don't), the chap on the phone replied "do you want the loan or not?".

THAT kind of irresponsibility is what got the normal people in trouble, feeding the problem up into the speculators you mention which started killing the banks - it all had to go together.

# 6 | phisrow | July 26, 2008 10:42 AM

Your post is entirely correct. I am very curious, though, as to the reason why things would be so. Is there a contingent historical reason of some flavor, or does it have something to do with the subjects themselves?

Off hand, I can't think of any terribly compelling explanations that fall into either camp; but there must be some sort of reason behind it.

# 8 | JSS | July 26, 2008 11:16 AM

Arts major here. Here's some advice: stop distinguishing between high and low culture, and I think you'll feel less self-conscious about your knowledge of art and music. Then you can start lecturing the condescending pricks about how irrelevant their aesthetic preferences are as an indication of intellectual capital.

As far as your comment about intellectuals is concerned, I agree that being ignorant of math and science is unacceptable. Unfortunately, the university isn't a great environment for learning everything that we should learn.

Yeah, you usually have to take some required courses, but a first year biology course isn't going to teach you everything you should know about science, and by the time you've chosen your major it becomes more difficult to justify natural science and math electives (or humanities and social science electives if you're a science major).

So, it's the responsibility of the individual to continue their learning in their own time.

# 10 | 6EQUJ5 | July 26, 2008 11:20 AM

Anciently, the liberal arts were grammar, rhetoric, logic, geometry, arithmetic, music, and astronomy. The music of the time was rather simple, and it included the mechanics of making music, which related physics, mathematics, sound, and timing together. The seven liberal arts were considered necessary for the education of a freeman (a citizen).

If someone could not reason his way through arithmetic, geometry, logic, and astronomy, he would be considered an uneducated lout.

# 12 | Karl | July 26, 2008 11:48 AM

I want to comment as a person with a Liberal Arts education, MS in math, and 15 years experience teaching math. First, the problem that most people have with math, even if we only consider that to be through first year algebra, is that the people who taught them arithmetic taught them how to use the traditional algorithms without any understanding of why those algorithms work. They never developed any number sense. Most people, especially any one who is intelligent enough to have a PhD in any field, would be able to understand algebra with just a few (?) properly taught lessons. In fact, I would be happy to demonstrate that to anyone who is willing to try.
On the other hand, I think that there is a vast, significant, qualitative difference in the kind of thinking that goes on in being good at math and being good in Arts and Literature. Math is objective, there are right answers. Art and literature are subjective, there are no right answers, only interpretations. (I am ignoring music here because I think that there is a required, innate physical ability - an ear). Because I got a Liberal education, I took an Art History class. The prime example that I remember from that is an explanation of Michelangelo's Sistine Chapel. It was said (this was around 1960) that he made wonderful use of light and dark, and very little color - and how wonderful that was. Since the cleaning of the ceiling in 1994, the entire explanation has had to be changed.
That is just an example of subjectivity.
My main point: anyone on your faculty can become numerate. They only need a little good instruction. Arithmetic is not hard. It is Arithmetic instruction that makes it seem hard. It is a lack of understanding of the meaning of the symbols, and the reasons why the algoritms work that makes it hard.

# 14 | Uncle Al | July 26, 2008 12:21 PM

Everything in the Arts is simultaneously true and untrue. Do you think Beethoven was competent? John Cage. Rembrandt? Jackson "Jack the Dripper" Pollack. A lecturer at Harvard then Yale wrote his Novel and was denied tenure. Critical analysis of Love Story was granted tenure. (Eric Segal was a font of unconscionable crap, e.g., Homer's Iliad: The Song and Shield of Memory). Above all, the Arts disdain rigorous craft.

Euler's equation, e^[i(pi)] = -1, inescapably unites algebra and analytic geometry. Reality is not a peer vote.

# 16 | Colin | July 26, 2008 1:00 PM

I did a fair bit of arts at Williams (well, literature and music) squeezed in around physics. Overall, I couldn't agree more with your general outlook in this post, and I'd encourage you to take arts-oriented Intellectuals to task every time they dismiss math and science as inessential parts of a well-rounded thinker.

But just to be provocative, let me suggest a reason for this asymmetry. What if the real problem is that people in the arts are just better at teaching their fields than people in math and science? We've all had the experience of terrible math/science teachers who can barely communicate with their students, let alone convey the beauty of their fields. And while we've probably all had bad arts teachers too, I'd be willing to bet that in most cases they were still a lot better than the worst math/science teachers.

Can you name an arts teacher who left you thoroughly confused and alienated about the entire subject? Probably not -- but ask the question about math or physics or chemistry, and the answer is probably yes.

So when otherwise well-educated people scoff at math and science, how much responsibility do their former math and science teachers bear for turning them off to those subjects?

# 18 | Terrance | July 26, 2008 1:17 PM

Wow. I appreciate the thoughtful response to a post I must admit I didn't put a great deal of thought into writing. I don't feel "picked on" in the slightest, and I appreciate hearing about it from a different perspective.

When I stopped and thought about it, I realized we have a similar divide in our house. My husband's an MD, and got an undergraduate degree in organic (I think) chemistry. He comes from a family of engineers and MBAs, and grew up in a household where his parents required him to read something like 30 pages of "hard science" on a regular (nightly or weekly, I can't remember) basis. When I told him the story about my graduating from college, his eyes got very wide and he said "Never tell that story to my parents."

(I should add that because of my untreated A.D.D., I "crashed and burned" in my second year of college. Afterward, I had to go part time, because I couldn't handle a full course load. So, it took my seven years to finish my undergrad. When I heard what my graduation adviser said, I envisioned myself never finishing at all; something which was pretty likely, given that I was still without a diagnosis or treatment, and wasn't likely to get either at that time.)

I our house, I'm the closest thing to a expert on art, music & popular culture (though my husband, who played french horn in high school, has a better knowledge of classical music than I do.). On those subjects, my husband usually draws a blank and I have to fill him in. He does the same on subjects were I come up short.

One thing I didn't mention in the previous posts that probably had some impact on my experience in school is that I lived for most of my life with Attention Deficit Disorder that went undiagnosed and untreated until my mid 30s. I suspect that, with its attendant problems with focus and attention to detail probably played a part in my difficulties with math and science. Since getting treatment for that, I've experience improved focus, and I can't help wondering if I might have had less trouble with an earlier diagnosis. (I was never hyperactive, but am the "inattentive type," which means I was never disruptive enough to get a diagnosis when I was in school. Instead of disrupting the class, I was the quiet, distracted daydreamer.

It's never been diagnosed but I suspect my A.D.D. may be accompanied by a math-related learning disorder. The difficulties I still experience in that regard seem to follow some particular patterns.

Oh, and I didn't intend to come off as dismissive of math and science. I actually have a great appreciation for them, considering the important role that they've played in my life. (Since getting treated for A.D.D., "Better living through chemistry," has become one of my mottoes.)

Great discussion!

# 22 | John Novak | July 26, 2008 3:22 PM

It's an old grievance, but one that still stings.

What makes the problem so large is that, of course, there's more than one problem. One is an absolutely undeniable (to me, at least) double standard, here. I would certainly be willing to go about my business, peacefully, not thinking too much less of people if they simply admitted that math is as much not their thing as art history is not mine. But there really are people out there-- I've met them-- who manage to hold the most amazing array of attitudes, all simultaneously.

My ability to make change in my head, the simple notion of giving someone $10.13 for a $9.88 purchase to reduce my coin count, for example, makes me a sorcerer. At the same time, I am regarded as barely capable (if that) of living a fulfilling life for not wanting to suffer through James Joyce. And simultaneously that, they seem to think the world owes them a math free existence, and have their opinions respected in discussions about science and engineering and technology policy.

That's a cocktail of attitudes I can't take lying down. It's one of the things I miss least about academia. (I miss it less than I do poverty, I think.)

There is also some element of truth to the notion of bad teaching, but I don't put it at the college level, I put it at the high school and grade school level. I had to bootstrap from, effectively, arithmetic to calculus in about two years in high school because my grade school teachers varied between mediocre and outright bad-- and the outright bad ones were very evidently terrified of the material themselves. And that fear does transfer to most students.

And mathematics is one of those subjects where, if you don't grasp the principles at one moment, you're just not going to get very much farther. A few bad teachers in a row at the grade school level, and you can end up disadvantages, if not crippled, for life.

That, and the more subjective nature of the arts and humanities, as opposed to math, engineering, and the sciences, make it easy to understand the natural tendency to slough it off. Have that happen long enough, and those who have sloughed it off rise to positions of authority and allow the sloughing off in a formal sense. And at that point, when you've got half the academy or more in that situation, it's a natural psychological and sociological trick to assign the blame to the subject rather than to yourself.

It's all quite understandable. It's also insufferable, and I once would have thought that people who pride themselves on living the examined life would realize this. Not so much, any more.

# 24 | my one cent | July 26, 2008 3:27 PM

Sorry to intrude on this very interesting discussion, but I have a story that might be relevant to this...

I am a physicist/astronomer by training, but I have an interest in some other subjects, including Mesoamerican archaeology. A few years ago, I attended a conference on the ancient Mayans, and heard a talk about the geometrical patterns in Mayan architecture.

The speaker was very good, and pointed out interesting relationships between the dimensions of rooms etc. and how they could help us infer how the buildings were laid. Of course, along the way he touched upon such points as "if a rectangular room is 3 units wide by 4 units long, then the distance between the corners is 5 units". I thought it was an interesting talk, although I wasn't totally convinced by all of his points.

However, I was completely shocked by the response of the (largely humanities-type) audience. They gave the guy a standing ovation with thunderous applause. At the time, I couldn't understand why the talk had grabbed the audience so strongly. I mean his points were interesting, but I didn't think his ideas were earth-shattering. Later, I realized that I was seeing this talk in a very different way from most of the audience.

To me, it was obvious that geometry could be used to describe Mayan monuments, after all, in physics we use math all the time to describe the real world. By contrast, I think many of the humanities-types roughly equated "math" with "magic", it is some obscure branch of knowledge that requires specialized training who are to be consulted only when absolutely necessary. Somehow, this talk shook that notion out of them. For some, it may have been the first time that they thought "geometry has relevance to things in my field", for others, they may have felt for the first time they could have access to the "mysteries" of mathematics. In either case, it seemed to have had a profound affect on them.

Perhaps there is a way to re-produce this mental shock in other contexts, and thereby help people understand why "math" is not "magic", but I have no idea how to do it.

# 26 | blf | July 26, 2008 4:55 PM

HennepinCountyLawyer@23, 10.13$ for a 9.88$ purchase? I assume 3 was mistyped for 2...

JSS@8, stop distinguishing between high and low culture: Hear, hear!

My own story about innumeracy was yonks ago in the States. One evening I went out to dine with two others (who were paying). I have no recollection of the bill's total, but the practice at the time was a tip of c.15%--and in this case, the waiting staff had definiately earned it. The other two started to struggle trying to calculate the 15%, holding a whispered discussion that, memory says, went on for several minutes. Finally I couldn't take it any more and asked "what's 10% of the total?"

"Tips are 15%."

"Yes. Humour me. What's 10%?"

"So-and-so much."

"Good. Remember that. Now, what's half of that?"

"So-and-such. Why?"

"Add it to the 10% you remembered."

"Huh?"

Probably sighing, "half of 10% is 5%. 5% added to 10% is 15%."

"Ahhh..."

One of the other people was a lawyer.

# 28 | Frederick Ross | July 26, 2008 5:42 PM

The following possibility occurred to me:

It's not that most academics have knowledge of art and music but not of math and science. It's that they have a pretension of knowledge of art and music but not of math and science.

They like the feeling going to concerts gives them, but start playing something besides the old warhorses and see who stays. I don't mean modern music, but anything that departs from the hundred or so symphonic pieces that are the cash cows of all major symphony orchestras.

I'm not willing to go on record ranting about painting, since I've spent many years playing and writing music, but have never produced a painting.

So perhaps we're looking at this backwards. Science and math can get federal funding on the grounds of "fund us or your economy/national security/etc. is toast." Classical music and the fine arts have had to create this pretentiousness in order to stay afloat.

I also object to the statements about no right and wrong answers in the humanities because they are subjective. If a student walks in and starts playing the opening of the Mendelssohn violin concerto like a biergarten polka as a serious attempt at rendering the piece, we can firmly tell him he is wrong. The criterion is empirical. If we study music as a means of expression from one person to another, we can cultivate awareness of how music acts upon us, and we can use that cultivation to decide between alternative performance practices. If we deny this, we also deny increasing body awareness in martial arts instructors, the growth of intuition about the structure of games in chess players, and the hunches and taste of mathematicians in choosing their problems, their structures, and their proof strategies. Academic rigor is the insistence on the highest achievable level of taste, not for pretension, but for the same reason a carpenter insists on the sharpness of his tools: you can cut deeper and faster and with less mishap.

Though it amuses me that someone trained as a mathematical physicist is standing up for rigor in the humanities.

# 30 | Mike Kozlowski | July 26, 2008 8:38 PM

Alternately, and entirely plausibly, maybe math and science REALLY ARE a lot harder than the humanities (certainly this is the position of most science types in humanities courses), and there's just not a large segment of the population that can be expected to ever understand them, and if you try to raise the "reasonably educated" bar to that level, it ends up being too exclusive to ever be a popular position.

I mean, I held up the opposite end of that argument against most of my biochem and engineering friends in college, because I hate snotty dismissiveness of the humanities... but there's no question that intro physics or calc 2 were harder than any class I took in the course of getting a history degree.

# 32 | John Novak | July 26, 2008 9:46 PM

Also, it occurs to me that it would be useful if someone could determine, honestly, whether the humanities professors feel the same sense of condescension among science and engineering professors.

# 36 | Kurt | July 27, 2008 1:06 AM

Math is hard. So is reading. I'm pretty sure that our brains have not been optimized for handling either one of these activities. It wasn't that long ago, in historical terms, that the majority of the population did not know how to read and write. The difference is that we have, as a society, made it a priority to eliminate illiteracy. If as much effort was put into eliminating innumeracy, I'm sure that we could make great strides against that as well.

# 38 | CButterb | July 27, 2008 4:26 AM

The italic tag should have ended after "anyway." Sorry.

# 40 | Luna_the_cat | July 27, 2008 9:25 AM

blf -- Yah. Thinking in Euros, it wouldn't make much sense. ;-)

D - but we're not talking about people not getting calculus, or Cantor's proof. We're talking about people who do not think of geometry as being related to buildings, who can't calculate a 15% tip, and who can't double the price of a can of tomatoes. Hark back to Prof. Orzel's statement "We're not talking about vector calculus or analytical geometry here-- we're mired in an economic crisis because millions of our citizens can't do arithmetic." That's about equivalent to people who can't read, but because it's math, it's seen as "ok"!

# 42 | D | July 27, 2008 11:01 AM

Luna:

1. I was commenting on the fact that in college, humanities students and professors know less biology or physics than scientists know music or literature. My point in this context was simply that a lot of this "two cultures" stuff is thinly disguised proxy for scientists primping and showing off, and that this is unbecoming. Ought implies can after all, and 'can' is a vastly more restrictive proposition when it comes to understanding college level math and science than it is with regards to college level lit-crit.

2. When it comes to the broader public (and surely claims of inability to multiply etc among the professoriate are wild exaggerations - the guy Prof. Orzel was criticizing said in the comments that he has learning disabilities) the analagous point holds though. Practically everyone can in fact read a newspaper or know where Iraq is if they care to. That simply isn't as true of knowing how to amortize, how demand curves work, what the uncertainties on a poll mean, or how type I and type II errors differ. For any given level of literacy and numeracy (and by extension the various literary and mathematical forms of knowledge) the former IS that much easier to acquire than the latter.

3. I call shenanigans on the equation you make between knowing how to read and knowing how to do "arithmetic." Just as most people can read words, most people can in fact read numbers in decimal notation :)

Calling the housing mess the outcome of an inability to add is wrongheaded - it's more like the inability of people to: understand complex financial instruments, grok compound interest and resist psychological temptations in the form of devilishly well crafted inducements to do silly things.

Can you tell me with a straight face that the skill-set required to know what a sum A of money at interest rate y --compounded at such and such rate over so many years given monthly payments of x -- results in is anything as easy to acquire as that involved in being able to read Huck Finn?

# 44 | Roman Werpachowski | July 27, 2008 12:21 PM

I second D. Come on, people: the guys who work on Wall Street got these things wrong. And they know their maths. It's not about not knowing maths, it's about being unable to resist your greed, it's about markets being unpredictable, it's about models breaking down and it's about buying stuff which know too little about to be able to value properly.

The whole market of mortgage-backed collateralized debt obligations was running on a very simple Gaussian copula model. A freshman math student can understand this model. Yet people spent billions of dollars based on the output of this model.

# 46 | puzzled | July 27, 2008 12:41 PM

I believe that not knowing artithmetic has nothing to do with people who got into trouble with their mortgages. Think about a person taking a $250,000 ARM who cannot figure out the payments. Couldn't he simply ask for the payment plan? Comparing a number on a printout with your monthly income does not require all that advanced math.

# 48 | bigTom | July 27, 2008 1:23 PM

The problem goes far beyond academics, and is worse in the general population. And it translates into politics, where campaign platforms don't have to add up. We have a serious and growing problem, where some level of understanding of mathematics, and basic dynamics of systems is needed to judge the difference between a sound policy and complete rubbish. And of course the need is not just stuff like the ability to make change, but to have some intuitive understanding of algebraic concepts. And the confidence to resist a clever loan sales pitch (this loan will be good for you...).

Speaking of learning of math. I think this goes to the heart of the societal problem. Especially in the lower grades our professional rewards system, rarely attracts those who have a real understanding of math, and the results are predictably poor. I think the problem is compounded by the multiplicity of learning/understanding styles among people. A teaching method that works well for one subset of the population can leave other subsets behind. Then there is the need to keep the subject interesting. This is especially difficult in traditional mathematics, where the most common approach is the theorem/lemma/corollary approach. For myself this is so boring, that I have never been able to get past a few pages of this, before I bog down because I can't remember what was covered on page one. (And I was one of those who cruised through calculus, and Berkeley Physics with straight A's and very little work needed). I'm not sure if we can come up with better teaching methodologies, but it is clear that their are many gifted minds, which are just not ame