Tue 5 Aug 2008
Thanks to Wick Sloane ‘76 for pointing out this column by Chad Orzel ‘93(who also blogs at Uncertain Principles).
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 an undergraduate at Williams College, 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 I didn’t feel I had 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.
Read the whole thing. But isn’t it a universal truth that people who know a lot about thing X look down on people who don’t? Given that fact, can you guess what a physicist like Orzel is going to say next? I can!
But the avoidance of math and science is a common and accepted part of many core curricula, and this attitude gets 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.
They can’t. This is surprising?
The right answer is not to make the college students who don’t like art/music or math/physics take those classes. The right answer is to give students the freedom to choose.
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.
If Orzel thinks thats better knowledge of math would have avoided the current financial crisis, then he knows even less about finance than he knows about music.
27 Responses to “Innumeracy”
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August 5th, 2008 at 9:51 am | Reply
In my opinion, true intellect is not about what you know. It’s about curiosity and the desire to learn.
And if Orzel’s colleagues are looking at him “sideways”, I would bet that it isn’t because he doesn’t “know Beethoven from Bach”, but more about his unwillingness to join into a conversation on which he isn’t an expert; to ask questions, to show the humility, and interest necessary, to learn from others, whether it be art, math, science or plumbing.
Being able to admit what we don’t know, and to learn from those who do, should be a trait that we nurture for a lifetime. And to measure ourselves, and others, by level of learned knowledge, is ignorant and pompous, and the sign of a true bore. Unfortunately, it is behavior more often exhibited by those who consider themselves the ‘well-educated elite’.
Orzel can argue all he wants, as to which subjects are the most important, which have the most “consequences for society”…but the true worry lies elsewhere. If our schools are producing professors and academics who readily attach “intellectual stigma” to those who confuse “Darwin with Dawkins” or “Bach with Beethoven”, and who go so far as to take their measure of each other in this way, then we are failing at the most important level…that of nurturing and encouraging, curiosity and humility, not just in the students, but in the educators as well.
August 5th, 2008 at 9:59 am | Reply
How is an 18 year old entering college supposed to know what he ought to study when he does not yet know much about the various subjects that are on offer? A basic set of arts and music (and math and science!) requirements would help to ensure that they gain initial exposure to a wide range of subjects before they have to decide.
And is it really so ridiculous to state that better numeracy among the American population would have made them a little bit more careful about entering into stupid loans?
It seems almost certain that a large number of Americans lacked even the basic cognitive skills to understand what they were getting into; they should have been disqualified from credit card and mortgage applications based on intellectual deficiencies.
Basically, David, I think you overestimate the abilities of both 18 year olds and people in general.
August 5th, 2008 at 11:13 am | Reply
In reading Ronit’s comment, I realize that my comment is based more on Orzel’s article, than on David’s argument, but it still boils down to the same thing for me…that of nurturing curiosity, and engagement, at all levels of society.
And exhibiting this kind of curiosity and engagement is a responsibility we should all take on, whether it be in the classroom or the workplace, by the teacher or the student, the person getting the loan or giving it…heck, we would all be a little better off if it was shown more fully in the voting booth and the Oval Office.
August 5th, 2008 at 11:29 am | Reply
Wick,
You should not give up on classical music without trying new music. Elliott Carter, Ameirca’s leading living composser now clebrating his 100th year, recently explained that he came to new music because as a teenager he hated classical music. He hapened to have an understanding neighbor who lived near him in Manhattan, an insurance executive named Charles Ives, who also did some far out composing. Ives told young Carter he knew some music he would like. There was no NYC orchestra doing new music. But, Serge Kousesvitzky had been appointed conductor of the Boston Symphony in 1924 and brought new music to NYC 3 or 4 times a year. Ives started taking his young mentor to these concerts and for Carter it was love at first sight. More than 80 years later Carter is still keeping up the fight against traditional music. They did a whole all Carter week at this year’s Festival Of Contemporary Music at Tanglewood.(10 concerts in 5 days) There is more to music than Bethoven and Bach just as there is more to literature than Milton.
It might be that you will like new music. Especailly since 12 tone music has interesting mathematical patterns.
August 5th, 2008 at 11:58 am | Reply
I don’t get the vaguely prickish and snide comments sniping about what seems to be a pretty good larger point or Orzel’s argument. Oh yeah, wait. Kane posted this. I do get it.
dcat
August 5th, 2008 at 12:26 pm | Reply
Derek,
In all fairness, don’t you think Orzel’s argument would have a lot more merit if it didn’t paint a picture of a “prickish” and “snide” attitude within the educational environment?
Maybe I am misunderstanding, but when Orzel describes an atmosphere in which professors look down at each other based on what they do or don’t have within their arsenal of intellectual knowledge, how well they can converse on the differences between Bach and Beethoven, and Darwin and Dawkins…all within the same conversation…then how can they expect to nurture the basic curiosity needed to learn in the first place?
I am all for accomplishing and encouraging a better education, one that places importance on each and every subject, including numeracy. But when it is accompanied by an attitude, and petty argument, that one subject may be more important than the other, then it ‘bites itself in the ass’ in the effort.
August 5th, 2008 at 12:36 pm | Reply
Soph Mom –
So why shoot the messenger? If Chad is describing what he sees as reality, why take it out on Chad for an argument that I’m not convinced is wrong, Dave’s mockery notwithstanding?
dcat
August 5th, 2008 at 12:45 pm | Reply
You pampered, materialist, self-indulgent, emotionally immature, immediate gratification driven, improvident, fundamentally selfish boomers and post-boomers may not be able to discipline yourselves concerning the level of your personal or the nation’s debt or savings, but those who went through the denials and other tribulations of the Great Depression and WWII generally have had a lot less trouble than you with such a simple calculus and its application, irrespective of the nature of their intellectual training or its lack. Grow up!
August 5th, 2008 at 12:51 pm | Reply
Well…I will agree that the more interesting argument is to be had on Orzel’s article, rather than David’s argument.
David, I don’t want to start a DK bashing, as you have had quite a lot of that lately, and because I have seen you make some real effort at listening to all the bloggers criticisms, but IMHO, it would be better if you posted the full article, and then made your comment separately. It would be more fair to the original writer and would make for a much more dynamic discussion in the long run.
It would also avoid a lot of confusion and misappropriated statements. For example, it is hard to know what you wrote vs. what Chad wrote, and if Wick contributed anything at all, to the above post. I have seen this confusion happen on numerous threads.
August 5th, 2008 at 1:08 pm | Reply
Over 50 years ago, when Biology, Chemistry, Physics, Geology, and the contributions of Boole were not at the current stage, I fulfilled my Lab Quad requirements with Psych 1-2, Botany 3-4, and Phil Hastings marvelous course, The History and Method of Science.
This course laid out the timeline and key events of the development of the Scientific Method. It was an outlook that could be applied to the courses taken on the other side of the campus including the two specifics in the article: The learning of the math of reading music and its historical path with Barrow/Shainman, and the perspective, volume, color, and ‘golden mean’ of the slides being presented in darkened rooms by the Blessed Trinity.
In a spotted career which included having to ‘sell’ the use of analytic programming and multi-variant research for business decision-making, I found Hasting’s course had provided me with insights into human motivation and even human fears about things abstract.
I would hope that, as Sophmon writes, ‘curiosity and the desire to learn’ have not become so compartmentalized that the offerings from both sides of the campus are an either/or proposition.
Hopefully, the importance of a well-rounded education at the undergraduate level is a part of the liberal arts college mission.
I feel sorry for Chad Orzel ‘93 when he states with I am imagining is a mix of pride and candor “I know nothing about art or music”. It seems he missed a great opportunity!
I even agree with dkane of his sum-up, but see it this way (thanks to Phil Hastings) : the understanding of the math is not the same as the hope in the numbers.
August 5th, 2008 at 5:16 pm | Reply
Frank: why did the generation of Americans that lived through the Depression (at least the bourgeois and higher classes of said generation) get into so much trouble in the first place?
Partly, it’s because they were even worse at calculating risk/reward ratios or understanding the danger of leverage. If Americans are innumerate now, they were positively retarded then.
Americans in the 1920s were perhaps the most naive and foolish bunch of patsies and suckers in the history of capitalism, at least since the South Sea Bubble. They took part enthusiastically in the greatest speculative boom this country has ever seen – and the inevitable collapse of said boom still dwarfs any problems that subsequent generations have caused. Even the housing bubble looks relatively modest compared to it. America lost a decade to stagnation and poverty because the populace had gone through a temporary bout of mass delusion and short-sighted selfishness. Like many participants in the housing bubble, they believed they could easily make money without having to do any work for it.
If they did learn any lessons, as you claim, from the Depression, then they learned those lessons at a ruinous cost to themselves and the nation.
And, let’s not forget, it took the government to bail them out. Without FDR’s massive expansion of federal spending and entitlements, and the beneficial economic effects of a World War, I don’t see any way in which these supposedly hardworking and industrious people would have pulled themselves out of the hole they had dug.
August 5th, 2008 at 5:50 pm | Reply
Ronit, I think most people agree that the New Deal made things worse. It took WWII to bail us out of the New Deal, which had paralyzed the money supply during the preceeding decade.
August 5th, 2008 at 6:40 pm | Reply
Aidan,
wait, what? most people agree on what?
August 5th, 2008 at 7:17 pm | Reply
Before we digress even further into a discussion of early 20th century economics, I will point out another eph link to this article’s sentiment: Brent Yorgey’s excellent math blog, the Mathless Traveled, featured a post on Lockhart’s Lament. The essay decries requiring math in curricula while teaching in a manner that sucks the art out of it in favor of rote progress towards making people more “numerable,” as Ronit introduced me to the word.
Lockhart’s essay begins:
August 5th, 2008 at 7:31 pm | Reply
1) Aiden’s assertion about “most people” thinking the Depression worse is simply wrong. Amity Shlaes made that argument, and I did not find it entirely convincing. And she is not a historian, but rather a writer for the Wall Street Journal.
2) Frank: Are you unfamiliar with the deficit spending of Ronald Reagan? Not a boomer.
dcat
August 5th, 2008 at 11:03 pm | Reply
Aidan: From a macro standpoint, how is deficit spending on welfare and entitlement any different from deficit spending on arms and armament?
Jonathan: I didn’t use the word “numerable”
August 5th, 2008 at 11:18 pm | Reply
I should note that the debate around the New Deal is really a bit of a distraction, as are our modern debates about fiscal policy. The real economic power of government comes from its ability to create money.
More than the New Deal, the government actions, or really inactions, that prolonged the Depression include: orthodox clinging to the gold standard, the rigid non-interventionist stances of the Fed and Treasury under Coolidge and Hoover, and the confusion of nominal interest rates with real interest rates – basically, they raised the (apparently low) nominal interest rates even as prices were falling, leading to a deflationary shock that wiped out farmers and businesses.
Many of these errors were committed by people at the Treasury and the Federal Reserve long before FDR came to power, and they exacerbated the worst impact of the Crash.
Perhaps FDR’s greatest contribution was the creation of a muscular SEC, FDIC, and Fed; for all that we might carp at them now, their presence has done much to moderate the course of subsequent booms and busts. He also took the US off the gold standard as soon as he came to power, which helped to spark economic growth in the pre-war period of 1933-1938 (real GDP bottomed out in 1932, which shows the “New Deal made it worse” theory to be complete nonsense).
EDIT: For GDP figures during the pre-war decade, here’s a chart from the St. Louis Fed – http://research.stlouisfed.org/fred2/fredgraph?&chart_type=line&graph_id=0&category_id=&recession_bars=On&width=630&height=378&bgcolor=%23B3CDE7&txtcolor=%23000000&preserve_ratio=true&&s_1=1&s1id=GDPCA&s1transformation=lin&s1scale=Left&s1range=Custom&s1cosd=1929-01-01&s1coed=1939-01-01&s1line_color=%230000FF
August 6th, 2008 at 12:10 am | Reply
Oh man, that was a very dumb mistake.
“Innumerate”. So new a word to me I probably should have checked Ronit’s post before quoting him.
August 6th, 2008 at 12:56 am | Reply
At first I thought responding would be of interest to a dialogue on the question of art or music, or to the turn towards the current financial crisis which leads us to examine why we refer to an education when within a crisis people capitulate their conversation to a diatribe about the chaos in their personal lives.
I listened to the comments and wondered about the mental and spiritual state of our commentators. I came here to Williams for an education within a forest with an experience to behold a lifetime. I revel in the fact that I await my classes this fall. Yet I hear numerous statements that have much emotional investment.
There was a gentleman who commented on Elliott Carter. I like Mr. Carter. Unfortunately he wrote very few works. I enjoy playing Bach and Bethoven besides other luminary characters who have given us much to learn from.
And then I went further down the comments lists to Mr. Uible to hear his disparaging comments on #8. We have an intellectual and personal disconnect with this conversation. You have my best wishes Mr. Uible and heartfelt interests in resolving our dispute with life.
We all miss opportunities when we reflect upon our choices made. This is fine. It is in how we have capitalized upon them. I learn this every day.
Then as I read further, the reference to Ronald Reagan as a deficit spender. Why Reagan inherited a Carter/Volker deficit amounting to interest rates that were raised from 6% to 21% and if you have any idea what that means to bonds and notes payable over time and what that means to an economy that needs to raise funds to service this, then you would understand why Reagan was such an individual that stated prior to his being shot at the hotel when he stated a week before that “I am up to my keesters with these banksters.” The rule of 7 should be well understood by economists, and when understood by his 8 year term, one should have no illusions as to the debt of the nation at the time.
There is a great deal of information to be sifted before one makes a declaration of party affiliation or upon taking a position.
Supporting a party is one thing, the truth another.
August 6th, 2008 at 1:06 am | Reply
Really Jonathan, don’t let that happen again…no mistakes on EB allowed. ;-)
Actually, I had never heard the word, so I looked it up in my Random House. Not there! Second try on the computer produced it. Of course, I knew it was legit if Ronit used it, but I was curious nonetheless. I (ahem) look up a lot of words. Frank, especially, comes out with some doozies.
Also…I enjoyed “Lockhart’s Lament”. His exuberance (on Math) is contagious. A creative teacher can make or break a subject…that’s for sure. I remember liking Geometry and Algebra in high school…and then got saddled with a Calculus teacher in college, so excruciatingly boring, that I dropped out.
So, to me, Lockhart’s concept of Math as art, makes sense. I know it links naturally to music as well.
If only there was more of an atmosphere amongst the academics of ’sharing’ knowledge, rather than arguing and competing. Then the missing puzzle pieces could be found…solidly linking the Arts and Sciences…doing away with (as Dick says) the ‘either/or’ proposition.
August 6th, 2008 at 1:11 am | Reply
Hey…The smile fell off the end of my winking emoticon!
Oh well, at least they aren’t big yellow ‘Jack-in-the-Box’ grinners anymore.
August 6th, 2008 at 1:14 am | Reply
Derek: Both Ronald and the equally responsible Tip were fiscal bums (from a governmental standpoint – I’m not familiar with their personal financial affairs), despite being pre-boomers.
August 6th, 2008 at 2:12 pm | Reply
Frank — right, so generational accusations are not useful, are they?
Broadband — The inheritance from Carter has little or nothing to do with the actual budgets that reagan put forward. And my argument was not one about party but rather a direct response to Frank’s generational assertions. read more closely before becoming too sanctimonious. If you want to argue modern American political history, let’s do. I’m comfortable with my cred on the issue. But how about not coming in like a scolding schoolmarm?
dcat
August 6th, 2008 at 4:44 pm | Reply
oh Ronit, you were kinda wrong about John Edwards…
August 6th, 2008 at 6:27 pm | Reply
Derek: No part of the human race is worthy of survival, but in my opinion immediate pre-boomers (those who were adults during the Great Depression and WWII) in general are less unworthy than boomers and post-boomers in general.
August 6th, 2008 at 7:34 pm | Reply
David Broadband,
Eliot Carter has compossed a large number of works. Have you been folowing his late career. More than half his work has been completed since he was 80. And most of his stuff is very difficult– complex works, things that take months to complete. There have been a half dozen in the last two years. A significant work was done by the BSO last fall. A wonderful one act opera was done at the Tanglewood Festival of Contemporaray Music two years ago. There is not much work of the young Carter, when he was still much under the influence of Ives. Carter did not come into his own until after World War II when what we now call New Music emerged after Boulez.
At the recent Festival of Contemporary Music there were 10 all Carter concerts. And they did not do everything. All 2 hour concerts. And as is the case with much new music lots of the pieces were very short, say 5 minutes. Carter is dificult to play especailly to play well enough to record.
It will take time to have an adequate number of Carter CDs. You will have to be patient. Some of the pieces at the recent Festival were a bit too difficult. And Levine got sick and couldn’t conduct some of the most dificult stuff and couldn’t be the pianist for others.
It is fortunate that Carter is still going at 100. If he had died at 75 he would be a much less important composer.
August 7th, 2008 at 12:49 am | Reply
Mr. Bass:
Thank you kindly for your thoughts about Eliot Carter. I have had the pleasure of his quartets and several of his string and symphonic pieces.
Though I have not heard nor had the opportunity to attend the Tanglewood Festival, I look forward, when possible, to inquire about his opus. I look forward to hearing him, as I had Ned Rorem.
Cordially,
DB