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The Innumeracy of Intellectuals (2008)

101 points| Thrymr | 13 years ago |scienceblogs.com

98 comments

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[+] cperciva|13 years ago|reply
I don't mind the innumeracy of so many liberal arts intellectuals... as long as they stick to liberal arts. Alas, they do not.

A short time ago, I was involved in debate over instituting a new affirmative action program at my university. "We're failing this group terribly! We must do something about this!" came the rallying cry.

I responded with university admissions statistics, high school graduation statistics, and census statistics, showing that the largest reason behind our apparent lack of members of that group was that we were an urban institution which drew students mostly from the local area, and members of that group lived mostly in rural areas where the population as a whole tended to attend more rural institutions. (Canada has far more of a trend towards attending "nearby" post-secondary institutions than the US does.)

I was accused of trying to confuse the issue "by introducing numbers and percentages", and the admissions policy was adopted.

[+] Homunculiheaded|13 years ago|reply
As someone with a BA in English and wrapping up an MS in Computer Science, I really think anyone who considers themselves an "intellectual" should know both the theory of probability and Foucault. I'll be the first to agree that probability will land you more jobs, but from a purely intellectual angle I woulds say these have equally helped me undertand the world around me.

I've been in rooms of really smart technical people who have a child-like understanding of social and cultural issues that effect them (discussion about gender on HN can be a great example of this). At the same time I've been in rooms of extremely well read humanists who cringe at any attempt to understand the world through mathematical models. Both of these groups exhibit a clear intellectual poverty that limits their overall understanding of the world.

The worst part isn't merely that each group has such ignorance of the other's domain, but that each will proudly defend this ignorance. The "enjoy working at starbucks" and "buzzes like a fridge" comments are equally anti-intellectual. The first thing that needs to change is this attitude.

[+] simonsarris|13 years ago|reply
Is there a good reason to think this is not either a curious outlier or strawman? Is that situation alone actually good reason to demand people "stick to the liberal arts"? Or is there something else here among your reasoning?

For the record, I have a degree in CS and Philosophy, so its awfully tough to "stick to the liberal arts".

[+] pfedor|13 years ago|reply
Your point may be true, but this is not a good example, since the question discussed was of political nature, and even very smart people will ignore whatever evidence contradicts their political choices. That your argument was ignored had nothing to do with the innumeracy of the faculty members, and everything with them being liberals. If the room had been full of Google engineers, the outcome of the discussion wouldn't have been any different. (Although obviously they wouldn't use the phrase "confuse the issue by introducing numbers and percentages.")
[+] _delirium|13 years ago|reply
This is a bit of a curious post. I'm not sure the antidote to people being proud of ignorance in science/math (which is a problem) is to be proud of ignorance in the humanities (which is also a problem). I mean, if you'd rather go boozing than read Bertrand Russell, that's a choice you're free to make, but I wouldn't be proud of it. I guess I don't know much about the history of classical music myself, but mostly because one can't study everything, and it isn't currently near the top of my reading list (though the fact that both Douglas Hofstadter and David Cope constantly mention J.S. Bach makes it somewhat relevant to my AI interests).

I also don't generally think as scientists we can afford to be ignorant of the humanities in general, though many people can afford to ignore parts. There is a lot of physics that suffers from "bad metaphysics" precisely because of its practitioners reinventing metaphysics, in the guise of "interpretations" of physics, when they are unaware of obvious problems that arise, which even a small amount of reading would've made them aware of. And there's a lot of work in artificial intelligence that makes more sense with a humanities background.

Oddly this seems to be a recent phenomenon. Early 20th century physicists were very well-read in philosophy, and their interpretations are accordingly sophisticated and rarely run into novice problems. Same with mathematicians; it's hard to even separate whether someone like Frege was a mathematician or philosopher. Some is unavoidable due to increasing specialization, but if anything that would seem to call for more humility, not extra arrogance that we know how to solve the philosophical problems that we don't time to study in as much depth as Einstein/Planck/Bohr/etc. did...

I'd trace some of it (on both sides) to a general academic tendency to want to rationalize why the fields you didn't specialize in and don't know about aren't that important to know about. There's an only half-joke that academics always want to reduce every field to their own: to an economist everything is analyzable with economic tools, to a sociologist everything is culture, to a physicist everything is physics and its minor epiphenomena, to a philosopher everything is philosophy plus implementation details, to a dynamical systems theorist everything is just instantiations of dynamical systems, etc.

[+] krakensden|13 years ago|reply
> This is a bit of a curious post. I'm not sure the antidote to people being proud of ignorance in science/math (which is a problem) is to be proud of ignorance in the humanities (which is also a problem).

I don't think you really mean ignorance in the humanities, you mean ignorance in philosophy. Being able to distinguish all the various cantatas of Bach is the most trivial of trivialities. More broadly, I suspect talking about "the humanities" as a category is worse than useless, because you get passionate defenses of literacy in reply to weeping and moaning over the sad state of modern dance.

Talk about literacy, philosophy, history. Talk about theater and dance. Talk about visual art and music. Talk about rhetoric and economics.

[+] crusso|13 years ago|reply
Early 20th century physicists were very well-read in philosophy

Philosophy's usefulness to Science died off in the early 20th century for a reason.

Richard Dawkins and Neil deGrasse Tyson commented upon this very issue in their Poetry of Science talk. Very insightful:

http://www.youtube.com/watch?v=9RExQFZzHXQ&feature=playe...

[+] ced|13 years ago|reply
There is a lot of physics that suffers from "bad metaphysics" precisely because of its practitioners reinventing metaphysics, in the guise of "interpretations" of physics, when they are unaware of obvious problems that arise, which even a small amount of reading would've made them aware of.

Could you give examples? I'm not sure what you're referring to.

[+] kafkaesque|13 years ago|reply
Oddly this seems to be a recent phenomenon. Early 20th century physicists were very well-read in philosophy, and their interpretations are accordingly sophisticated and rarely run into novice problems. Same with mathematicians; it's hard to even separate whether someone like Frege was a mathematician or philosopher.

Bertrand Russell and Frege are part of philosophy of science, a relatively recent period in philosophy.

It is widely accepted that philosophy of science was initiated by Immanuel Kant (late 18th century) in the Western world, and since then, philosophers have been trying to give solutions to some of the problems he first posed.

What's more, most of the Western world at the end of the 18th century underwent a period called Enlightenment. This meant, all of a sudden, there was a huge emphasis on science and empiricism throughout all parts of society (Academia included, of course).

Before that, 'philosophy of science' was known as (observations on) natural history, and then the term 'natural philosophy' was created.

Thus, since mathematics is the language of science, this is why you can't/couldn't tell whether a philosopher of science was a mathematician or a philosopher.

Even nowadays, most programmes (my own research covers Canada and major American universities) only offer philosophy of science courses, but many do not explicitly state 'philosophy of science'. I know this because I almost majored in philosophy, but I specifically wanted to go away from this branch and instead wanted to specialize in pre-Socratic philosophy, but there were no programmes dedicated to this.

As for my personal opinion on students/teachers of science vs. arts, I feel many science students lack an appreciation of philosophy and how much it did for the sciences in its early years. Most science majors shove philosophy with the rest of the arts, but, as an arts major, philosophy is the hardest arts subject and can be equally demanding as a physics course, because it is the only subject which requires an extremely rigorous knowledge of science and arts. And there are simply very few people who hold such knowledge. Philosophy is the ultimate interdisciplinary subject where in a given class, you can talk about the laws of speed and light, 18th century subtexts vis-à-vis slavery, and biology (the growth process of plants and trees).

[+] neutronicus|13 years ago|reply
In Physics, the general feeling is that "philosophical interpretation" is simply out of the scope of our work. I think this derives mainly from the intensity and ultimate futility of the disagreements over the interpretation of quantum mechanics in the early 20th century. It's seen as a waste of time and a seed of acrimony that we're better off not indulging in as a field.
[+] dinkumthinkum|13 years ago|reply
I think this misses the point a little bit though. I believe he acknowledges that that is probably not a good thing but he is trying to point out the phenomenon of it being "acceptable" to well-trained in humanities but be prideful of not knowing mathematics but the reverse is considered strange.
[+] Tichy|13 years ago|reply
Isn't the difference that you can do practical stuff with maths, but not really with literature and art (except, granted, create more literature and art, which might be the only jobs left in the future)?

Perhaps knowing maths is a bit like having dirty fingernails from doing manual labor. A certain class of people is proud of not having to do manual labor, and hence they take pride in their clean and long fingernails. Others will despise them and value "real work" higher.

[+] vegas|13 years ago|reply
Chad Orzel isn't glamourizing his lack of systematic knowledge, merely acknowledging it in a forthright and fairly humble manner. I'd argue that he's trying to avoid coming off as and arrogant physics/math nerd.

In fact, here is direct textual evidence contradicting your caricaturization:

"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 give you an F in Reading, and a B in Rhetoric. I concur entirely that the lack of intellectual breadth amongst both technical and non-technical academics is quite obnoxious, and I'd argue that the rather pointlessly competitive nature of academic subfield is a holdover from when academics were basically young courtiers trying to secure themselves a nice sinecure. Sometimes this energy can produce great things, I'd venture that at this point we are just making the remarkable research discoveries that are largely just waiting around for some humble systematic work, further away.

[+] unknown|13 years ago|reply

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[+] barrkel|13 years ago|reply
The problem is that mathematics and the sciences are useful, while the humanities are largely about social signalling. One may be proud to be ignorant of mathematics precisely because it is useful; being ignorant of it indicates you have sufficient wealth in other areas that you don't need to get your hands dirty, as it were. And on the other hand, being ignorant of something like classical music is looked down upon precisely because it marks you out as not a member of the group.
[+] aamar|13 years ago|reply
But there are reams of math and many fields of science (astronomy, paleontology) that have no practical utility. It's quite easy to find this sort of material in any university, in books, etc.

While I won't directly take on your social signaling claim, there are some humanities which have clear utility (while also functioning as social signals), for example knowing the precise meaning and usage of a large set of words. People in the academy are not disdained for having this practical facility.

An adjusted version of your claim: I think that in some countries (including the U.S.) math & hard science are tarnished through their association with poorly-protected and therefore indifferently remunerated professions, such as accounting, pharmacology, and engineering. Most educated people I encounter would, all things being equal, like to be good at math, but some let themselves off a little easy. Trying and being bad at history would make you dumber than a lawyer, which feels okay; trying and being bad at algebra makes you dumber than an accountant, which is humiliating--so better not to try.

[+] dmhdlr|13 years ago|reply
Among the Western public this might be true. But among intellectuals the bigger prejudice is that numbers are "hard." I certainly find them to be so, and have felt like this since high school algebra.

At root it seems to be an epistemological problem, complicated in higher learning by over-specialization in all disciplines.

[+] zeteo|13 years ago|reply
Precisely. Maybe the best way to make math "cool" is to reclaim for it that status of "completely useless but fun knowledge" that Hardy was so proud about in his Apology.
[+] jdleesmiller|13 years ago|reply
A related anecdote: I saw mathematician Andrew Dilnot [1] at a Mathematica users conference a couple years ago, and he asked the audience how many times the size of the world economy had doubled since 1900, given that it had grown at about 5% per year. The audience guesses were in the 2-4 range, but he pointed out that the rule of 72 gives 110/(72/5) ~= 7.6. "Don't feel bad," he said, "last week I gave this talk to the council of European finance ministers, and they did no better!" (I may not have remembered the numbers exactly, but they were something like that.)

[1] http://en.wikipedia.org/wiki/Andrew_Dilnot

[+] Locke1689|13 years ago|reply
Your calculation is way off. You forget that the rule of 72 is how long it takes for the money to double. Thus, the final calculation is 2^7.6 which is, as any good computer scientist knows, a little less than 256
[+] evincarofautumn|13 years ago|reply
Perhaps the sciences are just harder to pretend to care about. I don’t mean that derisively—it’s just that the arts are very approachable because you don’t need to understand everything in order to appreciate it.

I’m a designer at heart, but my work is firmly in the hard sciences. I’m excited about what I do, and it shows. That’s what gets people interested—ferocity, passion.

You have to be able to describe your work in accessible terms, so that other people can appreciate it without having to understand it in depth. Not all people want to understand everything—it’s hard work. Work that we hackers can take for granted because, by our nature, we enjoy it.

[+] _delirium|13 years ago|reply
That's probably true for some parts of science, but I think the general public pays at least as much attention to science as to art, when something catches its attention. How many people who don't know the first thing about particle physics were tweeting about the Higgs Boson? Probably more than the number who tweet about Damien Hirst! Astronomers are good at getting public attention and cultivating a sense of "astronomy appreciation" among laypeople as well.
[+] dkarl|13 years ago|reply
Perhaps the sciences are just harder to pretend to care about. I don’t mean that derisively—it’s just that the arts are very approachable because you don’t need to understand everything in order to appreciate it.

Your second statement is the core issue; pretense has nothing to do with it. The sciences are harder to care about because reaping the rewards of science requires reaching a minimal level of competence.

In art or literature teachers are happy to pass students who never really grasp the basics of how literature is constructed and interpreted. They only demand one thing: that you put enough effort into studying basic critical techniques that you learn to imitate them somewhat. Even that is subordinate to their main hope, which is that you see something in a work of art or literature that inspires a new perspective about something in your life or in the world.

A literature class built around those standards is a valuable and enriching experience, and it can even be valuable and enriching for someone really competent who shares the same classroom with people who aren't.

How could that be accomplished in math or science? If you only require that the students engage with the experience of investigating math or science, and you don't require that they develop competence at applying scientific knowledge, then the students will develop appreciation for the field and perhaps some good will and appreciation for people who are competent, but they won't learn anything useful they can apply in their own lives. They won't learn to read popular science articles intelligently. They won't gain a better understanding of their own health. The only positive outcome is that they might believe that scientists are okay people after all and not scary soulless monsters. (A lot of people in academia would consider that a negative outcome anyway.)

To illustrate the contrast, suppose I believe my spouse is cheating on me, and I think of Richard III and recognize the same feelings of anger and paranoia in Richard III's feelings towards his wife, and I gain a richer perspective on the possibility that my spouse is cheating on me. By mandatory general education standards, academia is willing to grant that I have successfully engaged with literature. It doesn't matter whether I understood Shakespeare's devices correctly or how many layers of meaning I penetrated. It doesn't even matter that I got Richard III and Othello mixed up. What matters is that my range and depth of understandings was enriched by my reading of the play. Most importantly, it doesn't matter whether my beliefs about my spouse's behavior are accurate or not. If I decide to trust my spouse, and four years and two children later I find out that my suspicions were founded all along, and two kids grow up with divorced mistrustful parents, then that is not a failure of my literary education.

In contrast to the literary example, if I read the CDC web site about MRSA and then read a web site that says all so-called infections are actually manifestations of nutritional imbalances, and then I decide it's perfectly appropriate to visit my grandmother in the hospital with an uncovered wound on my arm while she's recovering from surgery, then that's a complete failure of my science education, even though I engaged with writing about infection and enriched my range and depth of understandings about infection. Right answers may not be important to the process of doing science, but they are vital to reaping its rewards.

The difference is that art and literature fill the same role that Bertrand Russell described for philosophy (quote from a recent HN thread):

Philosophy is to be studied, not for the sake of any definite answers to its questions, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation....

This is the pragmatic approach to literature that colleges would like all graduates to appreciate. That means introductory literature classes can be enriching without demanding that everyone achieve any basic competence at literary analysis. Introductory science courses are useless unless the students achieve some basic level of competence. That means that mandatory science education is a very different proposition from mandatory art and literature courses. The minimum useful standard is much, much higher (unless the purpose of science education is merely to teach people to trust mainstream authorities.)

[+] hsmyers|13 years ago|reply
I was lucky enough to spend a fair amount of time in college with a senior citizen who was aiming for a fine arts degree in painting. As in most colleges, this does not require algebra which she thought was a shame as she had been home schooled and had a thorough background in mathematics as was expected of a young lady of her class and social standing. That 'woke' me up to the decline in education standards in the second half of the 20th century. Not only in this country but around the world. If you think I'm wrong, just compare the textbooks available now with what was available in say 1910! Would you even be allowed to use a text book by Hilbert? I doubt it. I will grant you that she was exceptional and typically excelled in any endeavor she chose---she was I believe the first American woman to be allowed a role on stage at the Abbey Theatre in Dublin as an example. Decline and Fall are us I guess...
[+] neutronicus|13 years ago|reply
You're comparing educational standards for the wealthy to educational standards for everyone.
[+] ColinWright|13 years ago|reply
[+] SagelyGuru|13 years ago|reply
Being an intellectual ought to be primarily a matter of attitude of respect towards knowledge of all kinds and, above all, a strong curiosity and interest in learning.

Thus what is particularly sad is not the fact that some subject or another is avoided and ignored by (intellectually) lazy people but that such people, proud of their ignorance, nowadays pass for intellectuals.

'My subject is more important than yours, so I am not going to waste time learning from you' is just a post-justification for being a dullard and a bigot.

[+] mangler|13 years ago|reply
Yeah, the next time you go to your local yoga class and the local bleached bimbo starts babbling on about quantum physics (for some reason, a favourite subject), ask them if they can solve a quadratic equation. Guess what, they can't. But that is not a reason to desist! The quantum physics banter lives on...

So, learn from these smart people. Fake it and bask in it!

[+] kingkawn|13 years ago|reply
There's also social signaling occurring when he includes boozing in his list of reasons he has chosen to remain ignorant of arts and music.
[+] pessimizer|13 years ago|reply
Case in point:

http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-...

I find it a bit sad how he thinks that people should be taught long division, which is what we have calculators for, but algebra is a step too far. The only reason I think people should be taught arithmetic is so that they understand algebra. After algebra, Calculus I for people who want to actually be knowledgeable about the world around them (No heavy series and no multivariate), and then I don't care what they do, because I trust that they understand how the world works.

Instead, Hacker suggests that we drill those future artists and writers on duplicating the functions of a calculator for 12 years, and then throw them into the voting booth. Bleah.

[+] rickmb|13 years ago|reply
"our economy is teetering because people can’t hack the math needed to understand how big a loan they can afford"

That is not so much caused by a lack of math as it is a surplus of delusional optimism. No amount of math will ever beat that. Not only is it a bad example, I can't think of any better examples, and apparently neither can the author.

It may be that my utter incompetence in math makes me less than objective, but I fail to see any convincing argument in the entire article.