The Innumeracy of Intellectuals

I know nothing about art or music.

OK, that’s not entirely true– I know a little bit here and there. I just have no systematic knowledge of art or music (by which I mean fine art and classical music). I don’t know Beethoven from Bach, Renaissance from Romantics. I’m not even sure those are both art terms.

Despite the sterling reputation of the department, I never took an Art History class when I was at Williams, nor did I take any music classes. They weren’t specifically required, and I was a physics major– my schedule was full of math and science classes, and between that and the boozing, I didn’t have time for six hours a week of looking at slides. It’s a significant gap in my education.

Given my line of work, this is occasionally… it doesn’t rise to the level of a liability, but it’s awkward. I’m a professor at a liberal arts college, putting me solidly in the “Intellectual” class, and there’s a background assumption that anyone with as much education as I have will know something about history and philosophy and literature and art and classical music. I read enough to have literature covered, even if my knowledge is a little patchy, and I took enough classes in college to have a rough grasp of history and philosophy, but art and music are hopeless. When those subjects come up in conversation, I just smile and nod and change the topic as soon as possible. On those occasions when I’m forced to admit my ignorance (or, worse yet, the fact that I don’t even like classical music), my colleagues tend to look a little sideways at me, and I can feel myself drop slightly in their estimation. Not knowing anything about those subjects makes me less of an Intellectual to most people in the academy.

I was reminded of this by a recent Republic of T post, which puts into stark relief what is missing from that list of background assumptions: math and science.

Intellectuals and academics are just assumed to have some background knowledge of the arts, and not knowing those things can count against you. Ignorance of math and science is no obstacle, though. I have seen tenured professors of the humanities say– in public faculty discussions, no less– “I’m just no good at math,” without a trace of shame. There is absolutely no expectation that Intellectuals know even basic math.

Ignorance of math can even be a source of a perverse sort of pride– the bit of Terrance’s post that reminded me of this is a call-back to an earlier post in which he relates his troubles with math, and how he exploited a loophole in his college rules to graduate without passing algebra. I’m not going to blockquote it, lest I take things out of context, but to me that anecdote reads as more proud than shameful– less “I’m not good at math” and more “I’m clever enough to circumvent the rules.”

It’s not entirely without shame, of course. In the paragraph immediately after the algebra anecdote, he gets a little defensive:

Or is it worth considering that perhaps not everyone can “do” algebra, trig or calculus? Is it worth considering that perhaps there are even some smart people who aren’t great at math and/or science?… [A]re we to force every peg, round or square, into that hole at the expense of forcing students, who may be gifted in other equally important subjects, to dropout after a long series of demoralizing failures?

This is the exact same chippiness I hear from Physics majors who are annoyed at having to take liberal arts classes in order to graduate. The only difference is that Terrance can expect to get a sympathetic hearing from much of the academy, where the grousing of Physics majors is written off as whining by nerds who badly need to expand their narrow minds.

I don’t mean to pick on Terrance, here– for all I know, he’s also against mandatory liberal arts instruction for science majors. He’s a very good writer whose blog I enjoy, and he’s obviously a smart guy. But it’s precisely because he’s a good writer and a smart guy that his comments get my back up.

I’m not exaggerating when I say that I think the lack of respect for math and science is one of the largest unacknowledged problems in today’s society. And it starts in the academy– somehow, we have moved to a place where people can consider themselves educated while remaining ignorant of remarkably basic facts of math and science. If I admit an ignorance of art or music, I get sideways looks, but if I argue for taking a stronger line on math and science requirements, I’m being unreasonable. The arts are essential, but Math Is Hard, and I just need to accept that not everybody can handle it.

This has real consequences for society, and not just in the usual “without math, we won’t be able to maintain our technical edge, and the Chinese will crush us in a few years” sense. You don’t need to look past the front section of the paper– our economy is teetering because people can’t hack the math needed to understand how big a loan they can afford. 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. And that state of affairs has come about in no small part because the people running the academy these days have no personal appreciation of math, and thus no qualms about coddling innumeracy.

I’m not entirely sure what to do about it, alas. I half want to start calling bullshit on this– to return the sideways looks when colleagues in the humanities and social sciences confess ignorance of science. I want to get in people’s faces when they off-handedly dismiss math and science, in the same way that they get in people’s faces for comments that hint at racial or gender insensitivity. I suspect that all this would accomplish is to get me a reputation as “That asshole who won’t shut up about math,” though, and people will stop inviting me to parties.

Sadly, I don’t know what other solution there is. It simply should not be acceptable for people who are ignorant of math and science to consider themselves Intellectuals. Somehow, we need to move away from where we are and toward a place where confusing Darwin with Dirac carries the same intellectual stigma as confusing Bach with Beethoven or Rembrandt with Reubens.

Comments

  1. #1 TomS
    July 26, 2008

    You may be interested to hear that the anti-math sentiment has been around for a long time. I came across this in the writings of Galen, about the 2nd century AD, so don’t blame it on “modern times”:

    For truly on countless occasions throughout my life I have had this experience: persons for a time talk pleasantly with me because of my work among the sick, in which they think me very well trained, but when they learn later on that I am also trained in mathematics, they avoid me for the most part and are no longer at all glad to be with me.

    Book X, chapter 14
    volume 2, page 502
    Margaret Tallmadge May
    Galen on the Usefulness of the Parts of the Body
    Ithaca, New York: Cornell U. Press, 1968

  2. #2 Michael Anes
    July 26, 2008

    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…

  3. #3 Joe Shelby
    July 26, 2008

    Hear Hear, though I went to a liberal arts school (JMU) for a science major (Physics, though I gave up after DiffEQ and switched to CS). In fact, the reason I did so was that I was already reasonably good at history and very musically educated thanks to my parents and didn’t want to give that up.

    Though it’s not “math is hard” stuff that depresses me so much as “school’s over, so i don’t need nor want to learn or discuss anything academic again”, which is what i often find myself surrounded by. I embraced an attitude of continual learning (hence, reading scienceblogs.com), so I find the lack of curiosity in people today, even “smart” people, to be rather sad.

  4. #4 Joe Shelby
    July 26, 2008

    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.

  5. #5 Jonathan Vos Post
    July 26, 2008

    In such encounters, I sometimes say something like this.

    With all due respect, you and I disagree on the purpose of Mathematics. I believe that the primary purpose of Mathematics is not its use as a tool — for which tool you seem to have no interest or necessity to use. No, I believe that the primary purpose of Mathematics is Enlightenment. This includes self-enlightenment.

    I agree with you that a day without beautiful music, or wonderful art, or a meaningful philosophical idea, or a good book, or the glory of Nature is a wasted day. I am sorry, therefore, that you have silent, idea-free, plotless, un-natural days without Mathematics.

    It is hard for an illiterate adult to learn to read, but shame often forces them. It is not too late for you to overcome your Math Disability. There are those on this very campus who could cure you, had you the courage to go to them for help.

    Death to “The Two Cultures” hypothesis of C. P. Snow.

    If “the unexamined life is not worth living” — then pity the people who do not examine the mathenmatical structure of their own lives, and the greater reality beyond.

  6. #6 phisrow
    July 26, 2008

    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.

  7. #7 onymous
    July 26, 2008

    the same intellectual stigma as confusing Bach with Beethoven or Rembrandt with Reubens

    Reubens are sandwiches and Rembrandt is some sort of tooth-whitening system. There should be a huge stigma associated with confusing those!

  8. #8 JSS
    July 26, 2008

    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.

  9. #9 PuckishOne
    July 26, 2008

    @ #4, Joe Shelby: This is exactly what happened to my husband and I whilst applying for our home loan. A mysterious $25,000 “account” turned up, as well as income neither of us was actually earning. We called the finance guy on it, and both he and our realtors shrugged it off and said, “Well, that’s the way it’s done.” We refused to continue unless the numbers reflected reality. Neither of us are scientists or particularly well-versed in math beyond algebra…but Chad’s correct in saying that it’s a simple – a willful – ignorance of arithmetic (although that’s just one part of the problem, IMO). If your income is $X per month, and you sign up for a house payment that could be $X+100 per month, it doesn’t take a math genius to see how quickly this can get ugly.

  10. #10 6EQUJ5
    July 26, 2008

    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.

  11. #11 Thiago
    July 26, 2008

    Nice Post!
    I suppose you’re talking mainly about the situation in the US… but, as a physics student in Brazil (so please, excuse my mistakes, and feel free to correct me), I can tell you it happens here too, all over South America, actually. Couple of friends of mine say it happens in Europe too (at least in France, Sokal, back me up on this one…)
    Anyway, even if innumeracy has nothing to do with the mortgage crisis thing, it does with a lot of other stuff… Who else is tired of crap like “Evolution is highly unlikely, thus it’s wrong” (yeah, like all species just popping out of the blue is so much more probable…), or “The Second Law forbids Evolution, entropy always increases”? Who hasn’t seen politicians, journalists, intelectuals, misuse (or deliberatly abuse) statistics and get away with it?

  12. #12 Karl
    July 26, 2008

    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.

  13. #13 Jonathan Vos Post
    July 26, 2008

    Part of the intellectual stigma of confusing Bach with Beethoven is that one does not have the systematic understanding to incorporate later music, such as (sticking to the Killer B’s) Brahms, Berliotz, Bernstein, Beatles, or the Beastie Boys.

    The underlying premise of Academe is not just Enlightenment, as I’ve said. Enlightenment can be religious or secular; indeed, the secular University was a much later invention than the University itself.

    The underlying premise of Academe is that knowledge is built upon knowledge, in a structure, an architecture, a web, call it what you will.

    Not knowing the difference between Rembrandt and Reubens leaves you without an armamentarium to appreciate, to take examples (restricted to the Pirates’ Arrrrgggghhhh) from major American artists alone:

    Born before 1800:
    William Rush (1756-1833), sculptor

    Born 1800-1809:
    Peter Rindisbacher (1806-1834), watercolorist, illustrator

    Born 1810-1819:
    Peter F. Rothermel (1817-1895), painter

    Born 1820-1829:
    William Henry Rinehart (1825-1874), sculptor

    Born 1840-1849:
    Albert Pinkham Ryder (1847-1917), painter
    Jacob Riis (1849-1914), photographer

    Born 1850-1859:
    Theodore Robinson (1852-1896), painter

    Born 1860-1869:
    Frederick Remington (1861-1909), painter, sculptor, illustrator
    Frank Rinehart (1861-1928), photographer, illustrator
    Robert Reid (1862-1929), painter and muralist
    Charles Marion Russell (1864-1926), painter, sculptor
    Edward Willis Redfield (1869-1965), painter

    Born 1870-1879:
    Granville Redmond (1871-1935), painter

    Born 1880-1889:
    Morgan Russell (1886-1953), painter

    Born 1890-1899:
    Man Ray (1890-1976), photographer, dadaist
    Abraham Rattner (1893-1978), painter
    Norman Rockwell (1894-1978), painter, illustrator

    Born 1900-1909:
    Mark Rothko (1903-1970), painter
    George Rickey (1907-2002), sculptor
    Theodore Roszak (1907-1981), sculptor, painter

    Born 1910-1919:
    Ad Reinhardt (1913-1967), painter
    Milton Resnick (1917-2004), painter

    Born 1920-1929:
    Ray Harryhausen (born 1920) stop-motion animator, sculptor
    Roy Lichtenstein (1923-1997), painter, sculptor, printmaker
    … what a minim, I’ve slipped to first names, not being able to resist Ray Harryhausen while San Diego Comic-Con is happenning. Back to last names now…
    Larry Rivers (1923-2002), painter
    Robert Rauschenberg (1925-2008), all media

    Born 1930-1939:
    Faith Ringgold (born 1930), painter and fabric artist
    Robert Ryman (born 1930), painter
    James Rosenquist (born 1933), painter and muralist, printmaker
    Yvonne Rainer (born 1934), performance artist, choreographer, dancer
    Dorothea Rockburne (born 1934), painter
    Mel Ramos (born 1935), painter
    Edward Ruscha (born 1937), painter, printmaker, photographer, conceptual artist

    Born 1940-1949:
    Barbara Rossi (born 1940), painter
    Bob Ross (1942-1995), painter, television artist
    Martha Rosler (born 1943), video, photo-text, installation, performance art
    Richard Rappaport (born 1944) painter
    Allen Ruppersberg (born 1944), conceptual artist, installation artist
    Peter Reginato (born 1945), sculptor
    Susan Rothenberg (born 1945), painter, printmaker

    Born 1950-1959:
    Archie Rand (born 1950), painter, muralist
    Jack Reilly (born 1950), painter

    Born 1960-1969:
    Jason Rhoades (1965-2006), installation artist

    Point taken?

    What good is History, your colleagues might agree, without History of Art, History of Music, History of Philosophy, History of Literature? Once they stipulate to that, point out that there is immense value in including History of Astronomy, History of Biology (Darwin versus Dirac being a Category error), History of Chemistry, History of Earth Sciences, History of Mathematics, History of Physics…

    It was because there were such gaping holes in my knowledge of History that I had to build my own textbook online. Hence my “Timeline” pages of magicdragon.com

    In any decade, and century, any millennium, who are the smart creative people that we would want to talk to, given a time machine and a babelfish? Don’t you place Science Fiction in your personal History of Literature? Wasn’t Albert Einstein, to Time Magazine, the Man of the Century?

    I rest my case. The witness may now step down.

  14. #14 Uncle Al
    July 26, 2008

    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.

  15. #15 chris
    July 26, 2008

    Just to follow along on the mortgage issue, I think it is a combination. Both the lenders and the borrowers need to be accountable. When we applied for our current loan, about 3 years ago, we asked for about $190,000, which we had calculated as the high end of what we could afford. We were offered $310,000 on some sort of interest-only ARM package. Luckily, we were prepared and knew that was a bad idea, but it never should have been brought up. We turned it down, obviously.

    My wife has a double major in Business Accounting and Computer Science, and mine is in History, so we make a good pair. She is actually fairly weak in the arts, and never took history in HS (she was in band and always got excused, although she did get to march in the Rose Parade playing the bass drum). I can do basic math calculations and I understand most basic science concepts. We’ve already mapped out who’s going to help the kids with which homework.

    As for your post, I couldn’t agree more that all subjects must be understood at at least the introductory level. I do find math “hard” but that doesn’t mean I shouldn’t try. I got a D in Calculus as a Senior in HS, but I tried and I do recall some of it. If you are interested in more exposure to art and music, try watching “Little Einsteins” on the Disney channel. Each episode features an artist and a composer of the day. They incorporate a phrase of music and scenes from the artist’s work into the story. Today it was Van Gogh and Beethoven’s Fifth. Seems silly, but I did hear my three year old son later in the sandbox humming da-da-da-dum, da-da-da-dummm, so it does sink in.

  16. #16 Colin
    July 26, 2008

    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?

  17. #17 Jennifer Ouellette
    July 26, 2008

    I think this is a very valid point, and I say that as one of the liberal arts types who loathed and avoided all math as much as possible…. until I became a science writer specializing in physics. A bona fide liberal arts education should include some rudimentary basics in math and science. Full Stop. Period. We don’t all have to excel at things outside our specialties, but that’s no excuse not to TRY. We should at least understand a few basic concepts, some of the history, and why the major milestones are significant. It is much a part of our rich cultural heritage as art and music.

    I exploited loopholes and let myself off the hook for far too long, and hate to see others making that same mistake. I’ll never be a math whiz, and that’s okay. But I get why it’s important, and why things like calculus are a significant achievement.

  18. #18 Terrance
    July 26, 2008

    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!

  19. #19 Jonathan Vos Post
    July 26, 2008

    #19: “math-related learning disorder” is exactly right.

    I see two clusters of comments. One says that liberal arts intellectuals SHOULD know some Math, Physics, and their history and major players. One says that some people have not been ABLE to learn Math and Science.

    These are both true. These need to be combined into one approach.

    It is not enough just to TRY. Would the Art History professor tell a blind student to just try and see? Would the Music History professor tell a deaf student to just try and hear?

    Of course not.

    Hence, by analogy, a Math or Physics professor should not tell a student with Dyscalculia to just try and “do the Math.”

    Step one in dealing with a disability is to put the person first. Treat every student — and every innumerate liberal arts intellectual — with respect and compassion, and without condescension.

    Step two is to get that person and their family and support group to acknowledge that there is a problem.

    Step three is to assess the problem. Informally, and then formally.

    Step four is to collectively come up with a plan to treat the disability.

    The prejudices of individuals and communities against people with disabilities is the handicap. The disability itself is not a handicap.

    That’s why I wrote, #5: “It is hard for an illiterate adult to learn to read, but shame often forces them. It is not too late for you to overcome your Math Disability. There are those on this very campus who could cure you, had you the courage to go to them for help.”

    There should be no shame involved, for the Math, Science, Engineering, Technology people who have an Arts and Humanities deficiency, nor for the Arts and Humanities people who have a Math, Science, Engineering, Technology deficiency.

    The university is partly for research. It is partly for teaching. It is partly for profit. It is partly for fun. But the overall function is Enlightenment, and that can be a blessing and a cure.

  20. #20 Chad Orzel
    July 26, 2008

    Colin: 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.

    That’s an excellent point, and I think it is part of the problem. I can think of a few non-science professors whose classes I left thinking “Well, that was a crock of shit…” but that was more contempt than incomprehension. I didn’t leave the class thinking I hadn’t understood the subject, I left the class thinking that the whole thing was kind of pointless.

    I’ve left more than a few math classes feeling that I didn’t have the foggiest idea what the class had been about. For that matter, there are areas of physics that I never really grasped, thanks in large part to bad teaching.

    I think this does have a lot to do with the problem. I also think, to answer phisrow in #6, that there’s an element of academic politics– scientists and engineers are a little more likely to hunker down in their labs and focus on research to the exclusion of all else, so colleges and universities end up being run largely by humanities faculty. If the people setting instituional priorities aren’t getting input from scientists, it’s not that surprising that science gets shorter shrift in curricular decisions.

    Terrance: 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.

    Glad to hear it– I thought I was getting a little rant-y toward the end, and it might’ve come off badly.

    I’m really pleasantly surprised at how much quality discussion this has generated, on a Saturday no less. A nice Saturday, at least in our part of the world, so I’m going to sit outside and read– I may have more to say later.

  21. #21 Ryan Lanham
    July 26, 2008

    Define “well-rounded”? What a stupid discussion. No one is well-rounded–name the most well-rounded person you know. Now name five key areas where that person hasn’t a clue. So now what?

    Why don’t you focus on the fact that choice is what matters…not selling your particular brand of knowledge. If people want biology, they’ll get it. If they want math, they’ll get it. If they want art…etc. I notice as I drive down the street we have more grocery stores than science labs and more churches than art businesses. So, enough with the social engineering already…

  22. #22 John Novak
    July 26, 2008

    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.

  23. #23 HennepinCountyLawyer
    July 26, 2008

    Based on my own experience, and on the people I know–ranging from math majors to the “I don’t get math” types–I think there is a broader range of “built-in” ability in math than in other subjects. Back in college I remember there was a subset of math majors to whom math came very easily. They did the least work of anyone on campus, less even than the people who were just getting by in the humanities. (I also know a couple of brilliant math types who finished their bachelor’s degree at the age of 18.) Other math majors struggled like most of us on campus.

    I think math is the extreme case of this, but the same phenomenon exists with other subjects. A fair number of people, when they first encounter the types of reasoning lawyers do, react either: “Huh?” or “Well, yeah, that’s obvious, what’s the big deal.” I found law school fairly easy (and a lot boring), but I know someone from high school who spent half a semester in law school and gave up. He then got a master’s degree in statistics!

    One other point: arts departments tend to have courses specifically targeted to nonmajors. Maybe it’s different at larger schools, but at my college there was a Rocks for Jocks course and a Physics for Poets, but nothing like that in math. Especially to the extent the problem is the math needed for citizenship and functioning in society, we ought to be doing more math education outside the major track.

    (There may be a trend towards this at the elementary and secondary levels. My kids’ math classes started introducing statistical concepts, bit by bit, in grade school, which I heartily applaud.)

    Of course, when I am appointed Ruler of the Galaxy, I’m going to get rid of all the college “distribution requirements.” I think we should resurrect the minor, and require everyone to have a minor in a subject that doesn’t resemble their major. I.e., physics majors can minor in art history or sociology but not math or chemistry.

  24. #24 my one cent
    July 26, 2008

    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.

  25. #25 Luna_the_cat
    July 26, 2008

    @Ryan, #21 — When I go to the grocery store, I regularly run across situations where a 250g can of something is £0.84, and a 500g can of the same substance is £1.72 — and people are buying the bigger can, because they think they are getting a better deal. Innumeracy impacts on people in multiple ways from big to small, but it almost always hurts. It’s not just a “don’t be a snob” problem — people are somehow making it out of an educational system in a state to be consistently ripped off by con artists, and that is just flat out wrong. And there is this cultural thing that, because it’s math, it’s ok to be stupid — and really, that is just flat out wrong, too!

    Not knowing when Beethoven lived isn’t going to net you a bigger grocery bill, or an unpayable mortgage, or a life-insurance policy that sucks away more money than anyone could ever under any circumstances get from it. There is a difference in “real harm” which results, see?

  26. #26 blf
    July 26, 2008

    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.

  27. #27 Luna_the_cat
    July 26, 2008

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

    That was john novak @ #22. And — if you give someone $10 for a $9.88 purchase, you get a dime and two pennies back. If you give someone $10.13 for a $9.88 purchase, you get $0.25 back — a single quarter. Less shrapnel in your pocket after the purchase. (I do that too, this is why I get it.)

  28. #28 Frederick Ross
    July 26, 2008

    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.

  29. #29 blf
    July 26, 2008

    Oh blast, that’s right, this blog puts the taglines at the top, so yes, my bad, I did credit the post to the wrong person. Apologies.

    I also overlooked that the post was using USAian currency, which has a 25¢ coin. The euro (€), perhaps to its credit, does not; however, that does mean 0.25€ can be a lot of shrapnel (some of which must be copper). Of course, 0.24€ clearly isn’t any better. So I was quite puzzled. A more rational amount to fork over would be 10.08€, giving 0.20€, which (assuming the change is two 0.10€ coins) is the least amount of non-copper shrapnel (it’s the copper stuff which I find the most annoying). But in thinking about it, 13 is an odd typo for 08, so that should have clewed me in. Yes, I do get it (and sometimes do similar), but got my currencies/coinages confused.

  30. #30 Mike Kozlowski
    July 26, 2008

    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.

  31. #31 Paul Burnett
    July 26, 2008

    My dear wife is a psychologist (and a classical pianist) – her hardest classes by far were anything involving mathematics, particularly statistics. On the other hand I have no idea how to “do” math – the answer to most math problems is instantly intuitively obvious to me, but I can’t explain how I got there. Needless to say, we drove our kids nuts at homework time – neither one of us could help them very much.

  32. #32 John Novak
    July 26, 2008

    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.

  33. #33 Chad Orzel
    July 26, 2008

    Frederick Ross: 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.

    Yes and no.
    If a student were to come in and start playing a violin concerto as a biergarten polka, that would almost certainly be seen as wrong. If an acknowledged professional performer or compser were to do the same thing, I wouldn’t be surprised to see it hailed as a brilliantly trenchant commentary on what it means to be a work of music, or some such.

    That’s how it looks from well outside the field, anyway.

    Mike Kozlowski: 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.

    Again, I’d say yes and no.
    I would agree that the effort I needed to put in to get a B+ in a math or science class was significantly greater than the effort required to get the same grade in a humanities class.

    I’m not sure there’s as much difference in the amount of effort/talent required to excel in the two disciplines, though. I know I couldn’t do what my colleagues in the humanities do– there’s a manner of thinking required to do real literary scholarship or art history that’s as foreign to me as math is to them. I can’t even really get my head around half-assed genre fiction lit-crit on the Internet.

    I agree that it takes certain habits of mind to really understand math and science, but the same is true of scholarship in the humanities and social sciences. The difference is, we’re conditioned to think of the mindset required for non-science scholarship as within the reach of all students, while science is alien and difficult.

    And, of course, it’s easier to fake non-science scholarship– see the infamous Sokal incident. Or, for that matter, my undergrad transcript.

  34. #34 Chad Orzel
    July 26, 2008

    John Novak: 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.

    That would be interesting.
    I’m not sure how to answer that, though– I know there are a couple of humanities bloggers who read this at least occasionally, maybe one of them will weigh in.

  35. #35 Shawn
    July 27, 2008

    If a student were to come in and start playing a violin concerto as a biergarten polka, that would almost certainly be seen as wrong. If an acknowledged professional performer or compser were to do the same thing, I wouldn’t be surprised to see it hailed as a brilliantly trenchant commentary on what it means to be a work of music, or some such.

    That’s how it looks from well outside the field, anyway.

    That’s because you’re talking out your ass about an area of knowledge you admit to being largely ignorant of.

  36. #36 Kurt
    July 27, 2008

    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.

  37. #37 CButterb
    July 27, 2008

    If a student were to come in and start playing a violin concerto as a biergarten polka, that would almost certainly be seen as wrong. If an acknowledged professional performer or compser were to do the same thing, I wouldn’t be surprised to see it hailed as a brilliantly trenchant commentary on what it means to be a work of music, or some such.

    That’s how it looks from well outside the field, anyway.

    In addition to what Shawn said, you’re equivocating. Assuming this assertion about the bad performance being hailed as brilliant satire or whatever is correct (it isn’t), the satire would only be recognizable as satire if the performance is obviously wrong in some objective way. What would be “correct” or “good” would be the satire, which is a new work, and not the piece itself, so Frederick’s objection still stands.

    At any rate, a beginner’s-level ear for the distinctive features of various eras and composers is fairly easy to come by: a few Wikipedia articles will give you some historical context, and CDs no doubt abound at your local library. There’s even some enjoyable performances on YouTube.

  38. #38 CButterb
    July 27, 2008

    The italic tag should have ended after “anyway.” Sorry.

  39. #39 D
    July 27, 2008

    Some observations:

    – Some mathematical subjects (like probability, calculus, abstract algebra, statistics) are far removed from the sorts of things human brains have evolved to be good at.

    – Scientific results routinely challenge folk physics or folk biology in a way and to an extent that readings of Freud don’t challenge folk psychology or sociology.

    – We’ve evolved to construct and understand narrative. By contrast even the Wittens doing string theory are in the position of having to figure out crazy hard math using brains that can’t multiply three digit numbers without paper or calculators.

    – I don’t think factors like the above do anything like fully explain the asymmetries you’ve noted, but they’re an important part of why chemistry professors can read Weber and Marx but sociology professors don’t understand even the basics of how different electrophilic substitution reactions differ.

    Now my point: I think scientists intuitively grok that understanding general relativity is harder than understanding Tolstoy just as well as non-scientists do. I doubt more than 1% of the population is capable of the latter, while anyone at college who has the time can at least read Anna Karenina. And yes, anyone with an ear can understand intuitively the beauty of a Beethoven symphony while very significantly fewer can understand how Cantor’s proof works.

    Now of course gloating about this openly is declasse, but opining piously about laypeople not caring about science is an acceptable substitute.

  40. #40 Luna_the_cat
    July 27, 2008

    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”!

  41. #41 Chad Orzel
    July 27, 2008

    In addition to what Shawn said, you’re equivocating.

    It was the “Yes and no” that gave me away, wasn’t it?

    I wasn’t entirely serious with that comment. I didn’t think it would be taken quite so personally.

  42. #42 D
    July 27, 2008

    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?

  43. #43 D
    July 27, 2008

    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. #44 Roman Werpachowski
    July 27, 2008

    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.

  45. #45 Chris Crawford
    July 27, 2008

    I was trained as a physicist and I work in software. My experience is that the two cultures problem is reversed in this field: the great majority of computer people know far too little about the arts & humanities. It is striking to compare European computer people with American computer people. The Europeans have a greater appreciation of artistic issues than the Americans. While this is of no value in computer science, when it comes to making software that normal human beings can use and enjoy, the Europeans are well ahead of the Americans.

  46. #46 puzzled
    July 27, 2008

    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.

  47. #47 Chad Orzel
    July 27, 2008

    I don’t mean to absolve financial companies from all fault in the mortgage mess– predatory practices by lenders definitely played a big role.

    But that stuff only works because the people they’re lending to aren’t good at math. It takes two to write a bad loan– one person to put up money that they’re unlikely to get back, and one to take money that they’re unlikely to be able to pay back.

    When we took out the mortgage for our house, we got a big stack of government-mandated forms that clearly spelled out the terms of the loan, the repayment schedule, and the manner in which the money was to be paid back. All the information you need to avoid deception is there, provided, of course, that you’re comfortable enough with numbers to understand that information.

  48. #48 bigTom
    July 27, 2008

    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 amenable to being forced to follow existing learning paradigms.

  49. #49 Roman Werpachowski
    July 27, 2008

    “But that stuff only works because the people they’re lending to aren’t good at math.”

    And lie to themselves. Some mortgages work like a bet on your future earnings increasing (you pay less now and more later). You may understand numbers, but if you make unrealistic assumptions about your future income, you’ll be in trouble.

  50. #50 Roman Werpachowski
    July 27, 2008

    “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 had the same problem (though I’m not sure if I would cruise through Berkeley — but I managed to finish my theoretical physics PhD). The only time when I got excited about mathematics was when it was really a deep concept (like, construction of real numbers) or it was a result which I needed to progress in my research. I think that showing a lot of applications would help people learn maths. But to show applications, you must use some knowledge from outside mathematics, which may be a problem for mathematicians teaching people.

    Mathematics, unfortunately, has certain unavoidable dryness. Our minds are not adapted too well to studying mathematics. Following a theorem in detail is always a conscious effort. Some people say that “theorem is intuitive”, but this is learned intuition. You get the intuition needed to make learning maths less cumbersome from… learning maths. No matter how you want to climb from the Dead Sea of ignorance to the Mount Everest of calculus, you still need to rise these almost 9000 metres.

  51. #51 Chris Crawford
    July 27, 2008

    I’d like to take a contrarian stance here and suggest that it might be more constructive for science/engineering people to focus on their own deficiencies than to bemoan the deficiencies of arts/humanities people. You can’t DO anything about THEIR problems — but you CAN do something about YOUR problems. I think that science/engineering people can all benefit from a deeper appreciation of the arts & humanities. I don’t mean that you should be able to quote Shakespeare. Instead, I am suggesting that every member of our society can benefit from a better appreciation of history and the human condition. The illustrative topic discussed here is the mortgage crisis — would it have happened if more citizens were numerate? And in fact I’ll add global warming as a good example of a problem that wouldn’t be so serious if more people were scientifically literate. But let’s tackle some REALLY serious screwups. How about Iraq? Do you really think Americans would have gotten themselves into this screwup had they had a better appreciation of history — history of wars, history of insurgencies, history of the Middle East, etc? The same thing goes for our reaction to terrorism in general. Many of our efforts here are misguided; would we not have done a better job if we had a better understanding of the social forces that generate terrorists? Certainly anybody who thinks that “If we kick them in the butt hard enough, they’ll knuckle under” needs a lot more education in the humanities!

    I agree that innumeracy is a problem, but I recommend that science/engineering people concentrate on the problems that they can do something about.

  52. #52 Jonathan Vos Post
    July 27, 2008

    #48, “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.”

    Exactly!

    Excerpt from Dr. John Shindler’s class
    “EDSE 415: Classroom Management in the Secondary School”
    (Wednesdays, 4:20-8:00 p.m.)
    Revised draft of Mon 12 May 2008

    Journal Entry #1

    Bring to mind a student that you seem to have particular difficulty in understanding and/or relating to, then one for whom you seem to have a natural affinity. Do you think Cognitive/Learning Style has something to do with how well you relate to each of these students? If so, what implications does that have for your teaching?

    Sensory modality was apparently the key. I deduced that Jerry was a Tactile Learner (as are roughly 10% of students, with roughly 45% being Visual and 30% being Auditory).

    I built a lesson plan around Tactile Learning. See (for details) the
    roughly 30-page lesson plan prepared for EDSE 401 (Prof. Nick Doom). The entire class, and, indeed, all 6 sections (periods) that I taught used this lesson plan. Every student had the opportunity to cut out shapes from papers that I photocopied, fold them correctly, and glue them into their form as Platonic Solids — the 5 regular polyhedra (identical regular polygons for faces, every face in the solid the same, every corner the same).

    These 5 shapes were known since prehistory (stones carved into these 5 shapes have been uncovered in prehistoric digs in Scotland), albeit ascribed to Plato in naive texts. The students would color these as they wished, and number the faces so that they could be used a polyhedral dice in the related lesson plan on Data Analysis, Probability, and Statistics (to CAHSEE standards). The tactile students in particular, and almost every other student, was engaged, absorbed, and happy in building these shapes. Many asked to do more than the one assigned. They were proud of their accomplishments, and opened up considerably to the notion that Math (which they hated) could include fun activities and beautiful objects.

  53. #53 whomever1
    July 27, 2008

    I went to an interesting master’s project show at the USC –damn–I forget the exact name of the school–but it was their school of computer gaming arts. I’m imagining this would be an area where a balance between the two cultures would be desirable.

  54. #54 thoughtcounts Z
    July 27, 2008

    My coauthor just wrote a post on the “I’m just no good at math” refrain that scientists and mathematicians hear so often. We both totally agree with what you’re saying here — the strong social bias towards the humanities and away from the sciences as a way to be “intellectual” is really silly.

    Obviously there are some limitations on what’s appropriate behavior, but I think it’s good to be a little taken aback when someone is flippant about their lack of science knowledge. We should make a habit of using scientific terms and naming famous names without stopping to explain what we’re referring to. The only way to change social norms is to start contributing to the new norm we’d rather see.

  55. #55 Roman Werpachowski
    July 27, 2008

    “We should make a habit of using scientific terms and naming famous names without stopping to explain what we’re referring to.”

    I don’t think acting like a prick (OK, only a little) is going to achieve anything.

  56. #56 Pierce R. Butler
    July 27, 2008

    Somewhere Noam Chomsky has a great line about how politicians wouldn’t be able to get away with most of their monetary shell games if the people who follow sports would apply any part of their (considerable) ability to work with game stats to the national budget.

  57. #57 Johan Larson
    July 27, 2008

    I just have no systematic knowledge of art or music (by which I mean fine art and classical music).

    You know, it wouldn’t be hard to fix that. A course each in music appreciation and art history would get you the lay of the land in both fields. If you found yourself intrigued, there’s plenty more out there. And if not, you could say with a clear conscience that you tried the stuff and didn’t like it.

    Don’t be surprised if you don’t. Both fine art and classical music went off in weird directions during the twentieth century, spending far more attention than they should have on inside-the-academy status games while neglecting (or mocking!) their audiences. It is not an accident that most painters, sculptors, and classical composers you are likely to have heard of predate WW-I.

  58. #58 Eric Lund
    July 27, 2008

    I agree that there has been too much forgiveness about “educated” people seeing nothing wrong with knowing no mathematics, as opposed to art/music/literature/etc. And you are entirely correct about the economic crisis being caused by people who either did not understand the arithmetic of the mortgage or who allowed their greed to overcome their mathematical good sense.

    I’ve noticed one exception to this emphasis on humanities over science, at least in this country: Many people are proud of knowing only one language. I’m not talking only about the decline of Latin and Greek, either; many people never even try to learn a second modern language. Since most Americans are native speakers of the primary international language of business and science (English), there is no impetus to learn anything else. Clearly this is not true of countries with official languages other than English, with the result that scientists from everywhere else are better at English than I am at French, Russian, Hindi, Chinese, etc. It’s too easy to take English for granted. Granted, it is hard for most adults to learn a new language, but that doesn’t excuse failing to try.

    As for other humanities fields, I have something of a background in classical music, but I am as hopeless as you are when it comes to art history. There seems to be some sort of code in the poses of the people in the paintings which is the guide to their interpretation, but since I never learned the code I don’t pick up those messages. Nobody has ever explained to me why knowing that code is useful for anything other than interpreting these paintings.

    I can give you a reason for knowing a little bit of Bach: he championed even-tempered tuning of instruments. If you have a good ear, you may notice that the major third in pre-18th century music is a bit flat by modern standards, because the 5/4 ratio they used is a bit smaller than the 2^(1/3) required by even-tempered tuning. Almost all western music since The Well-Tempered Clavier, whether classical or popular, melodic or atonal, is based on Bach’s work. Of course, I haven’t explained why you, as somebody who doesn’t perform it, need to know anything more recent about classical music–a large part of why I do is because I played clarinet in high school and undergraduate symphonic bands.

  59. #59 Roman Werpachowski
    July 27, 2008

    @Johan Larson

    “It is not an accident that most painters, sculptors, and classical composers you are likely to have heard of predate WW-I.”

    I think that the reason is quite simple: WW-I happened only ca 90 years ago ;-)

  60. #60 thm
    July 27, 2008

    I’m a bit late to this discussion, but my perspective on this changed after reading Paul Fussell’s Class. The liberal arts educational viewpoint, and all the traditions of being an intellectual and being a part of academia, were developed when elite universities were primarily for the elite. They were infused with, and promulgated, the values of the upper classes. The upper classes, Fussell explains, value fine art and music and literature precisely because they offer little practical benefit. Pure mathematics might be fine, but anything that hints at accounting or engineering or laboratory work is far too crass for the upper classes.

    Which is, in part, why I’d never make it in the upper class; I relish a hands-on approach to life.

  61. #61 Roman Werpachowski
    July 27, 2008

    @thm

    You’ve just disappeared the whole world of folk music, which inspired such classis masters like Chopin or Shostakovich.

  62. #62 Chad Orzel
    July 27, 2008

    Chris Crawford: I’d like to take a contrarian stance here and suggest that it might be more constructive for science/engineering people to focus on their own deficiencies than to bemoan the deficiencies of arts/humanities people. You can’t DO anything about THEIR problems — but you CAN do something about YOUR problems.

    That’s an unexpected argument…
    So, the next time a European starts complaining about American foreign policy, or human rights violations, I should tell them to focus on their own deficiencies, and not worry about things that they can’t fix?

    I’m sure that’ll be fun. Productive, too.

    Johan Larson: A course each in music appreciation and art history would get you the lay of the land in both fields. If you found yourself intrigued, there’s plenty more out there. And if not, you could say with a clear conscience that you tried the stuff and didn’t like it.

    In principle, yes.
    In practice, my time is a finite resource, and it’s about to get a lot more finite. The chances of me actually doing such a thing are pretty slim.

    If I had the free time needed to take classes in other subjects, I’d go for group theory, which would be of more concrete benefit to me.

    Kate’s been listening to lecture courses on tape during her commutes, which might be a more attractive option. If I could listen to more than ten minutes of an audiobook without falling asleep, that is.

  63. #63 Roman Werpachowski
    July 27, 2008

    “So, the next time a European starts complaining about American foreign policy, or human rights violations, I should tell them to focus on their own deficiencies, and not worry about things that they can’t fix?”

    I don’t think this is a good analogy. Your not knowing anything about Mozart and Bach does not hurt anyone else but you.

  64. #64 krf
    July 27, 2008

    Just a quick note that the Science-Humanities “snobbery” works in both directions. As a music & psychology double major, I’ve had my share of science types assuming I wasn’t smart enough to major in a “hard science.” I heard a panel talk in which a Dean of Research at a large public university mused that social science majors were those who couldn’t “make it” in the sciences. When the audience boo-ed he commented, “Well that’s what happened to the social science majors I know.”

    As for a relationship between the arts & the sciences, the more I learned about music theory, the more mathematical it seemed to be. For me it is the structured order behind Bach, Mozart, and U2.

  65. #65 CCPhysicist
    July 27, 2008

    I agree 100%, but ignorance need not be bliss.

    One solution would be self study. We used a book by Gombrich in my hum class decades ago, and it struck me as fairly readable at the time. A bit of Googling suggests it was called “The Story of Art”. Probably available really cheap at a college book store, since it is a textbook and you don’t need the latest edition.

    I don’t know whether it was the book or the teacher, but I still knew important parts of it decades later when talking about Hockney’s book “Secret Knowledge” with a local artist. (Where it was supremely evident that I knew more about art than he knew about physics.) You might find this second book makes an interesting read specifically for the connection between physics and art at a liberal arts college.

  66. #66 Chris Crawford
    July 27, 2008

    Once again, I’m going to play the devil’s advocate here. This time, I’m going to address the problem of whether science & engineering people really know as much about the arts & humanities as they should. So far, the only discussion I have read concerns the fine arts. But there’s a lot more to the arts & humanities than the fine arts. So let me pose a few rhetorical questions from those fields. Answer them to your own satisfaction; then ask yourself, “Do I know more about the arts & humanities than most of them know about math?”

    Why wasn’t Luther burned at the stake?
    What’s the difference between a proximate cause and an ultimate cause?
    What was Rousseau’s intellectual contribution to the principles of American democracy?
    Name a teaching shared by Buddha and Christ that was NOT shared by Mohammed.
    What’s the incidence of matriarchy in human history?
    How has Confucianism hindered Chinese society?
    What’s the relationship between the language that you use and the way you think?
    Name the two biggest differences between classical Athenian democracy and American democracy.
    Why is it almost a certainty that Iraq will not enjoy a genuine democracy in our lifetimes?
    Name three wars in which the victor would NOT have been better off had the war never been fought.
    What can we learn about feminism from The Merchant of Venice?
    Why is linguistic prescriptivism a stupid idea?
    What is the basic fact of Chinese history that guarantees that the modern rise of China will be geopolitically very stressful?

    I realize that this set of questions is not fair, and it does not span the vector space of relevant knowledge from the arts & humanities. It proves nothing. I offer it as food for thought only.

  67. #67 thoughtcounts Z
    July 27, 2008

    @Roman, and the conversation in general:

    I want to clarify something — I don’t think anyone’s really advocating that scientists should know nothing about the humanities. A well-rounded person should know some history and philosophy and literature, and so on. It’s probably unrealistic to expect widespread appreciation of operas, or something, but some basic grounding in the humanities should be expected.

    At the same time, some basic knowledge in math and science should be expected for everyone. Even a “humanities person” should understand the difference between a mean and a median, or why statistical studies should have a large sample size. We shouldn’t have to constantly explain what a “theory” really is. Everyone should know why Marie Curie, Niels Bohr, Alan Turing, and Leonhard Euler are famous. That’s what I meant by terminology and names. That sort of level, nothing outlandish. Educated people routinely refer to Tchaikovsky or Rousseau or Herodotus, and they’re not expected to volunteer a fifteen minute intro lesson.

  68. #68 rjb
    July 27, 2008

    About the only interesting thing I can add is that there are people in the humanities who are trying to bring a more “scientific” worldview to their disciplines. One example is Jonathan Gottschall, who has actually co-written a book with David Sloan Wilson on literary criticism using evolutionary principles. This is an interesting approach, but I haven’t read it. I am intrigued by it, though, and being an evolutionary biologist, I may pick it up and give it a read some day.

  69. #69 Chris Crawford
    July 27, 2008

    What, exactly, constitutes the minimum level of appreciation of one of these “uber-fields”? Our correspondent ‘thoughtcounts Z’ suggests that, for science & engineering, it’s the ability to recognize such names as Marie Curie, Neils Bohr, Alan Turing, or Leonard Euler. But there’s a tricky problem of subjectivity here: what seems simple and obvious to us on OUR side of the fence may not be so simple and obvious on THEIR side of the fence. Let’s put it this way: what are comparable levels of knowledge in the two ‘uber-fields’? Is recognizing Curie, Bohr, Turing, and Euler comparable to recognizing Tchaikovsky, Rousseau, and Herodotus? Or are the science names more obscure than the arts names? Who decides what’s more or less obscure? Is there any way any of us can make that decision objectively? How do we know our assessment isn’t grossly biased?

  70. #70 Malcolm
    July 27, 2008

    To see how serious this situation is, just look at the current debate over evolution vs. ID. If the general population of the US had a halfway decent grounding in biology, the Discovery Institute would have been laughed out of town.

  71. #71 M Fiddler
    July 27, 2008

    It seems to me that whatever we learn is a response to uncertainty… so if I choose to learn math or literature or art history or lego engineering, I must have been (or be)uncertain about something for which those bodies of ideas and information are likely to reduce my uncertainty itch. Or at least I thought they would.

    So, doesn’t the discussion (I tend to save ‘arguments’ for the trivialities of faculty meetings and cheaters at the poker tables)of the innumeracy (or in-art-imacy)of intellectuals start with what it is we/they are uncertain about it in the first place. And if we’re not uncertain about the nature of humanity or the nature of the cosmos or the nature of nature or the nature of… as the reason to wonder about things, then we’re inevitably going to perpetuate the sort of sniping that our host of Uncertain Principles describes. None of these uncertainties have been satisfactorily alleviated by any single discipline or line of inquiry, at least as far as I know.

    If for a moment I thought the questions that keep me busy in genetics were more important than the ones that keep me, or my neighbors, busy in music or chemistry, I’d end up in the same squabble and miss the point of it all… or have I already done that?

  72. #72 thoughtcounts Z
    July 27, 2008

    @Chris Crawford: You make a good point. It’s hard to tell exactly where the line of equivalence falls here. I think the best we can do is try to push things closer to optimal than they are now.

    Why do I think they’re not optimal? I think we can get a good sense of what I’m talking about by looking at Jeopardy! questions. If you’re asked a literature question, you’re generally asked something like to name a non-title character in The Tempest or to recognize the plot of Crime and Punishment. Occasionally for science questions you need to know some science history trivia. Maybe you need to know what an ion is. The real insult comes from the math questions, which are usually things like calculating the area of a triangle. The percentage of humanities questions that are answerable with a good recollection of high school is much, much lower than the percentage of math/science questions answerable with the same background. This is because it’s assumed that, if you’re well-educated, you’ve gone beyond the standard high school curriculum in the humanities. The same assumption is not made about the sciences.

    I agree that there’s a debate to be had about exactly how much knowledge of others’ fields should be required, and another debate to be had about how we should compare amounts of knowledge in different fields. But I think it’s clear that, wherever we are, it’s not yet ideal — and I think it’s also clear in which direction we need to push.

  73. #73 Chris Crawford
    July 27, 2008

    What, exactly, constitutes the minimum level of appreciation of one of these “uber-fields”? Our correspondent ‘thoughtcounts Z’ suggests that, for science & engineering, it’s the ability to recognize such names as Marie Curie, Neils Bohr, Alan Turing, or Leonard Euler. But there’s a tricky problem of subjectivity here: what seems simple and obvious to us on OUR side of the fence may not be so simple and obvious on THEIR side of the fence. Let’s put it this way: what are comparable levels of knowledge in the two ‘uber-fields’? Is recognizing Curie, Bohr, Turing, and Euler comparable to recognizing Tchaikovsky, Rousseau, and Herodotus? Or are the science names more obscure than the arts names? Who decides what’s more or less obscure? Is there any way any of us can make that decision objectively? How do we know our assessment isn’t grossly biased?

  74. #74 Chris Crawford
    July 28, 2008

    First, sorry everybody, for the double-post. I posted the original and walked away; when I came back the website informed me that the post had timed out and I had to re-post. Shoot the programmer!

    thoughtCountsZ, you may have a good criterion there in the notion of high school competency in all fields as a basis for objective comparison. If we assume a basic college-track high school course, then everybody would be familiar with math up to but not including calculus; and simple biology, chemistry, and physics. On the humanities side, we’d have basic history of Western civilization plus a smidge of economics, sociology, and/or political science.

    I think we can reasonably guess that very few arts & humanities people remember their trig, Newton’s Laws, or the notion of chemical equilibrium. On the other hand, I’m willing to guess that most science & engineering people remember who Charlemagne was, what Luther did, the law of supply and demand, and what the First Amendment says. So on that basis, I think we can conclude that, yes, the A&H people have more makeup work to do than the S&E people.

  75. #75 Paul Murray
    July 28, 2008

    Last time there was this level of antiintellectialism in the west was during the 50’s. You know what fixed it? Sputnik. People would look up and see that little dot that the russions put in the sky, and realise that maybe math and science are worthwhile after all.

  76. #76 Jonathan
    July 28, 2008

    I’m an English professor, and I’d like to register some disagreement with the widely presumed innumeracy and proud scientific ignorance of humanists. I was an avid reader of Martin Gardner’s Scientific American columns as a child and still enjoy recreational mathematics and reading widely in science. (Orzel’s comment about “Darwin and Dirac” let alliterative consistency exceed wisdom, as I can tell you with some assurance that no imaginable humanist would fail to know who Darwin was, even if they couldn’t reliably identify Dirac, which wouldn’t, I think, be likely.) My dissertation director studied electrical engineering at MIT before graduate school, and Hugh Kenner, who was a prominent critic in my field, wrote a book on Buckminster Fuller. A small sample, but the rest of the comments seem unafraid of generalizing from impressionistic evidence

    I also like science fiction, and I apologize for those humanists who’ve looked down* on you for that and the comic books.

    *Even perhaps, for liking the wrong kind of SF: Heinlein, Niven, Pournelle, and other heroes of that slide rule. (You’re safe with Lem.)

  77. #77 Pseudonym
    July 28, 2008

    Paul Murray:

    Last time there was this level of antiintellectialism in the west was during the 50’s. You know what fixed it? Sputnik. People would look up and see that little dot that the russions put in the sky, and realise that maybe math and science are worthwhile after all.

    The problem is that it seems to have been replaced by the idea that this is all that maths and science are good for.

    This didn’t happen in a vacuum, though. In the second half of the 20th century, pretty much everything in the developed world became “managerialised” (to coin a word). Political leaders are no longer providers of vision, they are managers of resources. Universities are no longer institutes of higher learning, they are glorified vocational training centres, with emphasis on research that promotes the agendas of those who provide the funding. And academics themselves are increasingly beholden to those who provide grants. Australia has even done away with tenure.

    In such an environment, Sputnik-like areas of research, whose courses have jobs at the end of them and whose research projects fit with areas of focus important to the policies of the government and industry partners, tend to be encouraged and promoted. More “general education”-type areas (e.g. English literature) tend to be overlooked or shunned. Sometimes, whole departments have had to shut down. Perhaps unsurprisingly, it’s precisely the humanities areas which would normally be critical of the change in climate (e.g. political science, philosophy) which seem to be targeted, leading some to suggest more sinister motives.

    You could also interpret a recent resurgence of woo-woo and denialism as being part of a backlash against this change in culture which seems to make the world a more sterile and less vibrant place to live in. Might promoting the humanities be a good antidote to this? I don’t know, but it’s a fascinating idea.

    The upshot of all this is that if there is an undercurrent of resentment amongst academics in the humanities, it’s probably not entirely undeserved, though it’s arguably mistargeted. It’s not the science academics which are the problem, but external forces.

  78. #78 Pseudonym
    July 28, 2008

    Oh, something I said which might be misinterpreted.

    Universities are no longer institutes of higher learning, they are glorified vocational training centres, with emphasis on research that promotes the agendas of those who provide the funding. And academics themselves are increasingly beholden to those who provide grants.

    I don’t mean by this that academics are generally corrupt, and will sell themselves out for a dollar. I mean that dollars influence the topics that are studied, not the results obtained.

    If people with grant money want rockets built, researchers will be more likely to study how to build rockets.

  79. #79 Wilson
    July 28, 2008

    With regards to math learning/teaching, one of the most hopeful books I’ve read on the subject is “The Myth of Ability” by John Mighton. I highly recommend it.

    Mighton did poorly at math in grade school and early university, but went on to get a Ph.D. in math (knot and graph theory).

    His belief, unlike that of many who have commented above, is that anyone can do math, if it’s taught correctly. Some may need to be taught a little more slowly or in smaller steps than others, but anyone can learn it. (Hence the title of his book – he believes that innate mathematical disability is, largely, a myth – at least for normal brains undamaged by disease or other damage.)

    Not one to rest on theory, he founded a program in Toronto called Junior Undiscovered Math Prodigies (JUMP), to teach math to grade-school kids that had been ‘diagnosed’ by their teachers as unable to learn math.

    Turned out they were wrong. With results reminiscent of those from the movie Stand and Deliver, but with fractions instead of calculus (?), he got the job done. It was actually the JUMP program that taught him that anyone can learn math, and that math-ability (and disability) is a myth.

    It’s an inspiring read, plus the book includes a several units from the JUMP program, showing how to teach various concepts at the grade- and high school levels.

    I’m not affiliated with the book or Mighton or the JUMP program at all. I saw the book mentioned somewhere – can’t remember where now – borrowed it from the library and liked it so much I bought my own copy (rare for me – not buying a book, per se but buying one I’ve already gotten from the library).

    Has anyone else run into this program and seen it work (or, for that matter, seen it fail)?

  80. #80 deadpost
    July 28, 2008

    Government should subsidize math majors and university students studying science.
    Enough with the arts funding. We don’t need governments funding a guy to do a sculpture of a dot on the wall or a naked woman with 2 heads chewing on a ballet slipper or something.

  81. #81 E
    July 28, 2008

    As a full-blown humanities PhD student in Islamic Studies, I’m a little shocked by some of some of these assertions about the ignorance of humanities people in general. I am a dedicated reader of science magazines and blogs. I found math hard, and still do, but have never taken that to mean that I don’t have a responsibility to understand the major scientific understandings that underpin our civilization. If you don’t understand these things you don’t understand the world that we live in, making any deep understanding of the humanities rather difficult. Does this make my appreciation for classical music more or less valuable or pretentious?

    I find that one of the most relatable aspects of Islamic civilization for students and friends is the history of Islamic Science. Far from seeming affronted by the suggestion that they should be interested in such things, people in my experience seem very much able to appreciate the history of science. Likewise, I have had many positive experiences with science students who take classes in the humanities. They are frequently a breath of fresh air, bringing a needed dose of reality to the classroom. The academy would lose something by not bringing different types of students together for exchanges of views that are shaped by their various fields. Fostering narrow specialization is not what we are supposed to be about!

  82. #82 ElizabethP
    July 28, 2008

    Interesting post. Until my mid-20’s, I had very little interest in math or science. I didn’t seem to have a great aptitude for learning them in school so I sort of tuned them out. I was good at foreign languages and all of the humanities, as well as music, so that is where I concentrated my efforts. I went to grad school in the humanities.

    Then I left grad school, disillusioned by many things about my chosen discipline (literature) and my particular department. I needed a job and had good GRE scores, so I became a GRE prep class teacher.

    So, that entailed teaching MATH – the GRE Quantitative section tests concepts from arithmetic and probability to algebra and geometry. It’s not higher math but it’s tricky; the test-makers know how to make the problems difficult even to “math-y” people. I had scored below the 99th percentile on the math part of the test but since my other 2 sections were 99th percentile, the company I work for gave me a pass on the math score…but obviously I still had to *teach* the math.

    I quickly taught myself everything I needed to know to teach the GRE class, and because I was motivated by fear of abject embarrassment in front of my students, I was a quick learner. A whole new world opened up to me. As an earlier poster put it, I had learned the algorithms of arithmetic and algebra without understanding why they work. After teaching this material for a while my understanding changed and I really did understand how it all fit together.

    I’m certainly no math whiz now, and I don’t understand anything about the math my husband does (he is a physics postdoc), but I do arithmetic in my head quickly and can lucidly explain arithmetic, algebra and basic geometry and relate one concept to another.

    I share my history with math to show other humanities types who feel like they “missed the window” with math, as I did, that it is actually possible to gain basic numeracy and in fact to be quite comfortable with math even as an adult after very little formal study as a younger person. I wish I had the time to dedicate to learning calculus and physics to the point where I could teach them.

    I also most heartily agree with the OP of the post, that basic mathematical and science knowledge should be in the possession of anyone who considers themselves an “intellectual”…but ALSO a basic knowledge of world/cultural history, art music, and literature. It’s a tall order, but I do feel that if someone like me can learn to teach math (at least a bit of math) in her late 20’s, then someone with no interest or aptitude for art or music can at least learn the difference between Beethoven and Brahms. Honestly, just reading a few Wikipedia articles on classical music and listening to some representative tracks from each era should get you up to speed for a cocktail party discussion touching on classical music – and it’s perfectly acceptable in most circles to admit ignorance of most 20th-century classical music, so you can stop at Stravinsky if you like…but if you can learn to discuss Schoenberg at least a little, you will impress many. :)

  83. #83 Roman Werpachowski
    July 28, 2008

    “Government should subsidize math majors and university students studying science.
    Enough with the arts funding. We don’t need governments funding a guy to do a sculpture of a dot on the wall or a naked woman with 2 heads chewing on a ballet slipper or something.”

    Meet your friends: http://archaeology.about.com/od/heritagemanagement/a/buddha.htm

  84. #84 Karl
    July 28, 2008

    It is interesting to come back two days later and see this line still going on. It seems to me that it has been hijacked. I thought that originally it was about why many people, including intelligent, PhD types, have trouble with arithmetic. (Please don’t start a string arguing about that, it’s not my point)
    My point is, after about 50 hours, and 70 comments (mine is #12), someone agreed with me. In #82, ElizabethP supported my explanation. I said: 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.
    She said: “I had learned the algorithms of arithmetic and algebra without understanding why they work. After teaching this material for a while my understanding changed and I really did understand how it all fit together….I do arithmetic in my head quickly and can lucidly explain arithmetic, algebra and basic geometry”
    That is, (almost) anyone should (would, if it were taught correctly) be able to understand enough arithmetic to be able to calculate MENTALLY how much change they should get back, whether one fraction is larger or smaller than another, whether the cost per unit is less for the bigger or smaller package, how much is 15% of their dinner bill, whether they can afford that mortgage, etc and etc.
    Whether sceiency types should have basic understanding of Art, Literature, Music, etc. is a different question.

  85. #85 Isabella
    July 28, 2008

    Though art is not one of the original seven liberal arts (music is), one who professes a belief in the liberal arts as an academic course of study, should know the basics of art, as well as math and science.
    Though math and science address our physical world, they outline the underlining structure. Art is all around is. Some designer who went to art school, designed the shoes I am wearing and well as this key board I am using. As with most thing, a basic understanding of the key periods of art, help us identify our current place in a larger historical dialog. Math and science are never cut from k-12 curriculum, art and music art. These two fields are the apex of human creation, began before an understanding of math and science or even language for that matter and are the first thing to go when a budget is mis-spent or lacking.
    As a sculpture instructor in a small liberal arts college, I am in a field where all these subject (except music… maybe) intersect. I find the lack of understanding of science a grievous oversight in our current crop of young minds. Students are taught that a theory is a flimsy opinion and not worth learning (or is this only in the south).
    I think one can not blame our economic crisis on a lack of understanding of math, this seems more like optimism to me. People taking out a mortgage and believing themselves capable of doing with out in order to pay it. They understand the numbers, they just ignore them.

  86. #86 rob
    July 29, 2008

    i think one of the major problems with mathematical ability today is the advent of the cheap portable calculator.

    for nearly three decades now, you don’t need to know what 2 plus 2 is. you simply plug the numbers into your calculator and out pops the answer.

    heck. if you have a personal computer, you don’t even need to know calc, diff-eq, algebra, linear algebra, statistics or how to plot a function. the computer will do it for you.

    the need for basic math understanding has declined as computer processing power has climbed–to the detriment of society.

    today many people can’t compute a 15% tip. engineers mess up unit conversions and cause the Mars Climate Orbiter to crash. people think it is an amazing coincidence that 2 people in a group of 23 have the same birthday.

  87. #87 Jonathan Vos Post
    July 30, 2008

    # 82 | ElizabethP: well said!

    It is never too late to achieve enlightenment, whether through Math, Literature, Music, Meditation, or whatever path you find yourself upon.

    And then one is so eager to share it…

  88. #88 K
    July 30, 2008

    I don’t think it’s actual contempt for maths – I think it’s fear of it. Maths is taught so badly at primary and secondary schools (elementary and high schools) that most of us see it as something strange and arcane that only people much cleverer than us can do, and that can never be picked up later in life. We’re made to feel stupid and inferior, and that is something that tends to make people defensive and angry and sometimes sneering.

    It has taken me 20 years to begin my real recovery from school. I know now that what I need is someone to relate mathematical concepts to practical applications so that I can deal with it before getting to the point where I can deal with it in more abstract terms – and that’s something that was never done at school after the very earliest years. I think that’s the key: we’re not taught that maths is all around us, in our shopping, our budgeting, our social arrangements, music, laying out gardens, cooking, etc. We’re taught maths as something separate from our everyday lives, something untethered to the practicalities, instead of something fundamental to them. I’m beginning to make my first steps in identifying the point at which maths became “hard” for me, when a string of numbers took on the power to take rational thought away from me and replace it with sheer stomach clenching panic. It was at some point after simple addition, subtraction, multiplication and division. So I need to go right back and weed out the sense memories of fear and get back to the mathematical basics. I have small nieces and nephews now – I’ll be damned if I’ll let them be hamstrung as I have been.

  89. #89 Orson Scott Card
    September 10, 2008

    Nobody expects that scientists should be able to DO art or music or even history. They only expect that they should be conversant with the PRODUCT of those who work in those fields.

    What is lacking in universities is “appreciation of” science and math courses, or “history of science and math for non-majors.” In short, survey courses.

    In BYU’s honors program in the late 1960s, I was lucky enough to be able to take a ‘structure of mathematics’ course that, without requiring us to DO math, introduced us to cutting edge (in those days) math topics so we knew what they were about. So we would know what was being referred to.

    Obviously, I can’t buy a set of CDs of Great Math and listen to them as background music. I can’t have Great Equations wallpaper – well, maybe I could, but I wouldn’t get it.

    Surrounding myself with math is difficult. But because of that survey course, and readings on my own since then (a biography of Srinivasa Ramanujan, for instance), I function toward math as I do towards art: completely incapable of even rudimentary accomplishment in the field, yet able to appreciate and even, at a certain level, understand what is going on.

    Science is even easier to handle this way than math. I’m no scientist – but I understand what scientific thought and method are, and I keep up – at least at the Scientific American and popularizing science book level. I am conversant enough to be able to recognize some bad science and false or unverifiable conclusions, for instance; I know when I’m being scammed with smoke and mirrors, or to recognize instances of bias in questionnaire-based studies.

    But I have regarded “literacy” (not “numeracy) in math and science to be a vital part of my overall education. Numeracy in math means you can do it (and of course I CAN do the basic high school stuff). But there is no reason why I should be able to DO calculus, since it is as irrelevant to my life and work as being able to DO engineering. There is every reason why I should know what calculus IS and what it’s used for and how it was developed – which is exactly the kind of thing I know about art and great music (i.e., music i can’t plunk out on my guitar).

    I actually DO drama – directing, writing, acting – and so I know that field the way mathematicians know math. I do not remotely believe that in order to be educated, all mathematicians should write and/or act in a play. That would be silly. But they should actually GO to an occasional play, just as I occasionally read survey-level articles ABOUT developments in math. I remain in the audience for mathematics. As mathematicians should put themselves in the audience for the arts.

  90. #90 Cora
    September 10, 2008

    In my MA-thesis (in English literature) there was a brief reference to the second law of thermodynamics. So I asked my supervisor, a wonderful teacher and published poet, whether I should include a footnote listing the three laws of thermodynamics or whether I could assume that this was common knowledge (which I would have assumed, if experience hadn’t taught me otherwise). My MA supervisor gave me a weird look and then said, “Put it in a footnote.”

    On the other hand, I work as a translator for technical documents. All too often I find myself faced with texts that are nigh incomprehensible, not to mention riddled with grammar, punctuation and even basic spelling mistakes. These texts are written by engineers who are generally highly competent in their respective fields (there are some very incompetent ones, too, but that’s a different topic), yet are unable to form a sentence, write a coherent text or understand why it is necessary to write a brief introductory paragraph stating what the subject of the text. Some of them are even unable to use a spellchecker.

    Both lacks are unacceptable IMO. A professor of humanities should be able to recognize a fairly basic scientific concept such as the laws of thermodynamics, just as an engineer should be able to compose a readable text. Actually having read a work of fiction – any fiction – in the past fifteen years might help as well.

  91. #91 Dawn
    October 14, 2008

    I think that the basic problem is actually the *way* many of us are taught to “learn” from a very young age. In both humanities and sciences, we are essentially taught to memorize our way through school. Learning by way of rote memorization is not the best way to learn *at all* — no matter which field we are discussing. We should all be able to question, carefully analyze, and think our way through the problem at hand. If we were to actually look at the depth of understanding of most of the population, I think it would be pretty poor when it comes to arts, humanities, math, or science, equally. It may appear that people in general are better at humanities subjects than at math-related subjects just because they are able to read and regurgitate well (because of course that’s the way we were all taught!), not because they might actually understand it. In math and science, it is much more difficult to, well, bullshit.

  92. #92 Jonathan Vos Post
    October 14, 2008

    #91: I basically agree with Dawn. Not for the elite schools (such as Stuyvesant High School in New York City, where I went, and from which 100% of graduating seniors go to college) but for the mean and median schools. “In both humanities and sciences, we are essentially taught to memorize our way through school.”

    In my teaching (middle school, high school, community college, university) I see the sad results again and again. Students stumble through the written material, blinded as if by squid ink, haplessly seeking a buzzword that correlates with a multiple-choice question, and just put down whatever snippet seems vaguely connected.

    I see no critical thought, no depth of analysis, no comprehension. They’ve been mis-taught, and have practiced the wrong things.

    I discuss this with my fellow teachers, who are (except with AP students or in white suburban schools) crushed by the same circumstances. An Art teacher told me that she showed a slide of a painting to her class. It showed a human hand, with each finer a different color. “What do you think of this?” she asked. “Be creative.”

    “Uhhh,” said a student, “somebody stuck each finger in some paint?”

    I give self-contained homework assignments, because they always “lose” their textbooks in lockewrs, or “leave them at home.” Or I give a color laserprint article from the web, the hottst news, the day’s Nobel Prize press release, and ask questions EVERY ONE OF WHICH is directly answered in the text. Most of them cannot even find the sentence which precisely answers the question.

    When I require inference of any kind, they guess at random. Or worse. 10 multiple choice questions, 2 right.

    Again and again I step back from the subject and ask more basic metaphysical questions.

    “Are you in the real world? Or is this like in ‘The Matrix’ — just an illusion being fed into your brain? Are you a student, or just a butterfly dreaming that you’re a student.

    They enjoy these questions, because they can drop the idiotic parroting that they think school demands.

    “If I can’t save them,” I think, “then who can?”

    I feel that I’m on the front lines of civilization versus chaos.

    Chaos is winning. There is no exit strategy.

  93. #93 Pete Pango
    June 26, 2009

    It is depressing that so many people have little insight into the natural world, and I agree it is important that people have a good understanding of quantity and the aritmetic of quantity.

    But I am less convinced though that it is important to understand anything about (say) astrophysics or calculus.

    Most mathematicians don’t seem to understand that not only is mathematics quite difficult, it is also very tedious to many people. And that’s not just because they’re stupid or badly taught, it’s because it’s just not interesting. In the same way that many people find bellringing, sudoku (or crossword) puzzles, cricket, discussing the merits of cars, and many other activities dull, while others love them. No sir, patterns of prime numbers are, well, dull.

    But also the amount of mathematics required in most life is very, very small. Even working in engineering fields, one has to have understood “real” mathematics in the past, but it’s rare for most technical folk to do complications much more complex than arithmetic and some simple trigonometry. The computer does that!

    Yes, yes, everybody should have a good command of the basics and an appreciation of what can be done, but don’t try to force them to be interested!

  94. #94 Samantha Vimes
    August 6, 2010

    Don’t you think that *Darwin* stands out more to liberal arts majors than Bach to non-music majors? I mean, you bring up two fine art musicians, one Classical, one Romantic; and two painters from different periods. I know enough music and enough art not to get them confused, but I wouldn’t consider someone shamed for not being about to recognize which one did Prelude and Fugue in D Minor and which one did Ode to Joy.
    Darwin, however, created a huge paradigm shift in how we view life on Earth, to the point that he’s been villified by religious zealots. Anyone who couldn’t connect his name with the Origin of Species or theory of evolution by natural selection would be an ignoramous in my opinion.

  95. #95 jrkrideau
    February 22, 2011

    @21 HennepinCountyLawyer

    I have often thought that it was a lack of ability to learn mathe but I am now more of the opinion that much of the problem is as mentioned early, a lack of decent teaching, especially in the early grades and possibly extending into high school. I have a nephew who cannot really do anything useful in math due to a bad teacher (put-downs, insults etc) in Gr. 10 or 11 yet he reports having been able to handle chemistry equations at a high school level.

    I, also have been impressed with what I know of the JUMP (Junior Undiscovered Math Prodigies) program (http://www.jumpmath.org/about.htm) created by John Mighton an award-wining playwright with a PH.D in Mathematics.

    His thesis is that almost anyone — well children anyway?–can learn math with proper instruction. I don’t think the JUMP program has been formally and properly evaluated but preliminary evaluation work and testimonials make it look good.

  96. #96 Jerry Bishop
    May 22, 2011

    Where to begin without leading into a manifesto? I have been reading piles of material on irrationality, innumeracy and the like and must say I love the that there are enough people in both categories that books are written on them and blogs goon for years.

    For me it seems to be less about math and more about core abilities or interest in logic, reasoning, and perhaps an inability to grasp scales of things. I have sat through my share of cabinet meetings forced to endure painful presentations by learned intellectuals that abuse even the most basic rules of addition, ratios, fractions, and statistics in support of lazy reasoning, outcomes they must rationalize and more.

    It isn’t just math.

  97. #97 Lance
    July 30, 2011

    I think its merely a human tendency to weight attributes by your own scale.

    This is why if you poll most drivers, they are all, on average, better than average drivers.

    The guys who drive very fast on tight winding roads and value the skill to control the vehicle during 4 wheel power slides and heel-toe shifts rate them selves as great drivers because they consider the skills for high speed control, etc, as what CONSTITUTES being a “good” driver….

    …an they look at the doddering old lady in the wide brimmed hat, in their way, through the switch backs as a TERRIBLE driver, as that old lady OBVIOUSLY can’t make her car go as fast as THEY could, etc.

    Mean while, that same little old lady rates herself as a GREAT DRIVER, as she points out she always drives at no more than half the posted speed limit, maybe at a quarter of that if the road curves, stops at deer crossings altogether, and is very SAFE.

    They disagree of course, but they are both right, based on each’s scale.

    So, the math whiz has a scale with the weighting on the math side of things….math is obviously the stuff of the universe, etc…and the other elective crap is a waste of time unless you need to get laid, etc.

    The Liberal Arts major knows that its all about the words, and that math geeks are merely walking calculators with no soul…and that as long as you have enough math to tell if your paycheck is right, etc….you’re good to go.

    So, as every one is walking around with their OWN scale for weighing these things….

    …what the things REALLY weigh is subjective…albeit correct for THEM.

  98. #98 Collin
    September 1, 2011

    Considering that schools follow the money, it seems strange that people can monetize things like eating chocolate cereal and collecting Pokemon cards, but no one seems to have figured out how to monetize math and science.

  99. #99 Doug1943
    September 2, 2011

    What’s true is not new, and what’s new is not true.

    See here: http://en.wikipedia.org/wiki/The_Two_Cultures

  100. #100 Josh
    December 8, 2011

    I was trained as a classical pianist. I also majored in piano performance when I went to college. I was torn between majoring in physics or piano when I first went. I’m currently a software developer. I’m considering going back to get a degree in math so I can do more interesting software work.

    I don’t think the two cultures are mutually exclusive. In high school, I did math several years ahead of my peers. Simultaneously, I was winning state level piano competitions.

    Oddly enough, I think having artistic ability contributed to mathematical acuity. Believe it or not, being an artist requires a high degree of analytical ability (most “artists” don’t get this training to college and then it’s spotty at best.) I had a wonderful teacher. I was blessed with a teacher who trained me in analysis while developing my ability to intuit the correct solution to a musical “problem.”

    I’ve dabbled in some of the other humanities and I’ve even had a few bits of writing published. My analysis “meta-skill” has served me well regardless of what I’ve been working on. In my opinion, doing anything complicated at a high level pretty much requires the same meta-skills.

    Anyways, my point is that it irritates me when people artificially limit themselves and say “I’m not a math person” or “I’m not a humanities person.” Being able to work at the confluence of hard science and the humanities really does make you a better person.

    Truth is beauty and beauty truth…

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