Assorted hypotheses on the science-humanities divide.

Reading the comments on my post and Chad's post about the different societal attitudes towards humanities and arts and math and science (especially in terms of what "basic" knowledge a well-educated person ought to have), I get the feeling that some interesting assumptions are at play. Since I don't want to put words in anyone's mouth, I'm just going to lay out some of the hypotheses that have occurred to me as I've read through these discussions:

  1. Math and science are objectively harder (and/or require greater intelligence to learn) than humanities and arts.
  2. While math and science do not require greater intelligence to learn than humanities and arts, the people who are really good at math and science tend also to learn a lot about humanities and arts, while the people who are really good at humanities and arts tend not to learn a lot about math and science.
  3. Something about humanities (maybe that postmodernist stuff?) interferes with the ability of people who are good at humanities and arts to really grok what science is about (which, obviously, undercuts their ability to get a basic grounding in the sciences).
  4. The amount of brain-labor required to get a "basic grounding" in math and science is much greater than the amount of brain-labor required to get a "basic grounding" in humanities and arts.
  5. What would count as a "basic grounding" in math and science is many more levels of complexity removed from current work in science than what would count as a "basic grounding" in humanities and arts is from current work in humanities and arts.
  6. The humanities and arts lack rigor and/or operate in a sphere where "there are no wrong answers".
  7. Most people see the connections between their lives and what is being taught in humanities and arts better than they see the connections between their lives and what is being taught in math and science.
  8. All this talk of "basic grounding" and "well-educated people" is a trick to fill classes which are mostly useful in keeping the people teaching them employed.

I'm probably forgetting some. Feel free to chime in with others (or to elaborate on or modify any of these) in the comments. Also, let's all keep in mind that hypotheses without data to support them need not force anyone's assent.

With so many people coming at the initial question -- why does it seem like so many intellectuals are OK knowing a lot less about math and science when they'd be embarrassed to acknowledge the same level of ignorance about humanities and arts? -- from so many different starting assumptions, it's no wonder that there's not broad agreement about what can be done about this, or about the extent to which it's really a problem.

Myself, I'm inclined to think that almost everyone can learn more than he thinks he can (not just in depth but also in range), given inviting materials or a good teacher. And I'm not inclined to get into a debate about which kinds of competencies people need more at this particular moment in history, this particular political era, this particular set of economic conditions. The best reason to learn something is that learning it is a fun thing to do with your brain. Learning math and science can make your brain just as happy as learning humanities and arts, so who wouldn't want to be an intellectual omnivore?

More like this

One more hypothesis: Grounding in humanities and the arts has traditionally been a marker of social status. Those who have the leisure time to study things things must be "better" than those who must devote themselves to "useful" work like digging ditches or curing cancer.

So naturally in the academy it's embarrassing to not be well-grounded in humanities and arts, but not so embarrassing to be ignorant of science -- just as it's not embarrassing to say you don't know how to change the oil in your car.

One of my pet peeves is that science majors are required to take the exact same history, literature, art, etc., class as the majors in the various fields, but the opposite doesn't apply. (At least in the schools I'm familiar with). It does seem odd that people are actually proud of limited knowledge. I'll admit to not knowing a lot about literature, but I wouldn't say I'm proud of that fact (in fact, I think it is a big hole in my education). Commentary point by point... for what it's worth.

1. Which is why there are "botany for poets" and "rocks for jocks" classes.
2. Which is why there aren't the corresponding "Interpreting Literature for Literalists" or the equivalent of the non-majors courses in humanities and arts, etc. (Why aren't there corresponding non-majors courses in the "non-technical" fields?)
3. I can tell you that I have trouble groking "deep meaning" in literature and art? Is that because I'm a scientist or am I a scientist because I don't deal with the humanities and arts very well.
4. I would think it would take less grey matter to effectively deal with the sciences. After all, we're restricted to the facts with limited interpretation. The humanities and arts seem to have limitless interpretation. :-)
5. That would surprise me, but then humanities and the arts often do.
6. One of the reason why Dave Barry suggested you major in humanities and arts....
7. Count me as one of the few with the opposite view, but I'm admittedly biased towards science. Other than entertainment and social commentary, where are the connections between the humanities and the arts and everyday life? (Oops, I guess communicating effectively would be a good connection.)
8. I'd much rather deal with people that have seen a bit more of life than the lab, but I'd also like to deal with people that have seen a bit more of the the lab.... And the second group is significantly larger than the former.

I don't think it's necessarily about the value of the coursework, or the difficulty.

Rather, it's that the humanities tend to provide a sort of shared background for people to discuss when they meet- even if you've never met someone before, chances are they've got an opinion on classical music, or that they've seen That Hot New TV Show.

And likewise, discussions on the arts tend to be open to interpretation- what you like (and why) can be used to convey something about how you see yourself. The basic structure of scientific theories is a bit too cut and dry for that, partly because the most widely known work is usually also widely accepted. (Imagine the conversation: "Gravity? Hooyah!")

There are exceptions, of course- in particular, people absolutely need to understand some basic science in order to understand policy and make rational choices. And truth be told, I've had some fantastic conversations with people from the arts and humanities who wanted to learn more about science.

The trick is that we discuss specific examples that catch their attention, and build on that interest. It also helps that in the domain of government and policy, there's room for inquiry and interpretation, rather than handing someone a list of basic facts about the world as we understand it.

Another hypothesis that occurs to me is the following: The decision to pursue a career as a scholar in the humanities is regarded by society as so impractical -- hence, bizarre and ridiculous -- that young people making that decision defensively cultivate an attitude of disdain toward more "practical" (and socially valued) subjects like mathematics and the sciences. By the time they realize how much they have missed out on, they probably believe it is too late to become genuinely literate in those subjects.

Personally, I don't think that there are any sharp divided between any particular area of inquiry - they bleed into each other without any clear boundary. But, here are three thoughts to at least ponder:

(1) It is easier to see how the humanities can play a role in the sciences. Math used logic, but logic isn't all mathematical. The theoretical side of evolutionary biology is indistinguishable from the philosophy of biology, but if you read Lolita in a literature class, it is not immediately apparent that Nabokov study of butterflies influenced his novel.

(2) When we are taught as children that reading is a worthwhile activity, we are generally given story books, that is, literature. From an early age, reading is for many of us associated with more fiction books, while science and math are school subjects, that is, work. Thus, people are generally more inclined to pick up literature (humanities) than math and science for their non-work reading, and so science people tend to have a broader knowledge of the humanities.

(3) Historically, the sciences grew out of the humanities - philosophy and natural theology. Perhaps the academy has inherited a mindset where the humanities are prior to the sciences - you can't be a natural philosopher without being a philosopher, but you can be a philosopher without being a natural philosopher. This doesn't work directly for math, but since math and science are often seen as being closely related, the same attitude carries over into mathematics.

For the first commenter: The notion of an over-educated scientist socially standing shoulder to shoulder with a ditch digger in some kind of git-r-done club of people who do practical work vs the elitist, upper-class dilettante loafers in the humanities (and presumably their welfare queen allies) locked in a never ending battle of good vs evil is really hilarious. Only a elite, highly educated academic could seriously entertain such a notion.

As for the topic generally: it really speaks to the elitism in the hard sciences that everyone from the "science side" is more than happy (either implicitly or explicitly) to lump the soft sciences in with fine arts and literature without batting an eye. It's also rather ironic that many people on the "science side" of this debate seem to have no problem with trotting out tired cliches, culture war bugaboos, and fourth hand anecdotes to shore up their, frankly childish, arguments regarding the irrelevancy of the humanities.

Everything from ascot-ed and monocled patricians, to post-modern mandarins, to smug artsy conformists, a rouges gallery of stereotypes and cartoons presented as if it were actual evidence. But I guess what do you expect from a bunch of nerds who have no knowledge of real life. (See? It's such an easy game to play.)

Yes, of course science saves lives and makes life better, but the actual business of living, 90% of the lifespan of the overwhelming majority of humans is dominated by subjects connected to the realm of humanities. The internet is the product of science and engineering (and massive government/tax-payer funded research), but in the end it's merely a vehicle for people to conduct their lives and maybe (or maybe not) enrich their lives. Science certainly can save your life, but the humanities make it worth living.

The humanities IS civilization and civilization is the sciences' natural habitat. Science is in fact inconceivable without the humanities.

I think the issue is less "basic grounding" as a scientist might think of it, and more the knowledge needed to pursue a casual interest in the field. When pursued rigorously, I'd expect that both the humanities and the sciences are very difficult and very interesting. But at the level of casual-but-intelligent conversation, it's a lot easier to gain a "working knowledge" of classical music because you don't need to learn music theory to talk about a concert or CD. Likewise, you can casually explore art or literature in a useful/enjoyable manner without reading textbooks on their basic principles.

Compare that to topics like nuclear energy or genetics, or other science topics which might interest an outsider. If you don't know some basic theory of physics or biology, or if you don't have a mathematical mindset, it's a lot harder to learn something interesting or converse intelligently about these topics. The barrier to entry is a lot higher in science, and the learning curve a lot steeper before you get to the original motivating topic.

This is true even in the University. As a science student, I had no trouble taking classes on jazz and rock music without basic music theory, and a course on the Middle East without political theory. Undoubtedly I gained a much less rich understanding, but I was able to learn something about topics which interested me immediately. How many classes on "current events" topics like nanotechnology are available to students without Physics 101?

Another model I don't see reflected here--math and science people may think significantly differently than arts and humanities people. Especially for PhD level academics, who represent the very tail of the distribution curve for having a certain world-view, comments from the other side of the divide just sound irrelevant. Someone who has spent their whole life learning to think in mathematical terms may tend to look at literature in mathematical terms too. If the cup is full, there is no room for more tea.

By whomever1 (not verified) on 27 Jul 2008 #permalink

I suspect there's a historical influence at work here.

The idea that a scientist should be knowledgeable about the sciences and the humanities can probably be traced back to the notion of the polymath during the Renaissance, and an early 20th century version of this idea, the Renaissance Man. The educated person of the Renaissance was expected to be knowledgeable about all of the important ideas of the day (covering both the sciences and humanities); the Renaissance Man of today is defined as one achieving expert level proficiency in a wide variety of fields.

However, since the amount of knowledge today is far greater than several hundred years ago, this ideal has become virtually impossible. As suggested in the Wikipedia polymath article, it has become such that anyone attempting to achieve this ideal may be looked down upon; especially as evidenced in the expression "jack of all trades, master of none". Perhaps this is the viewpoint held by humanists.

However, the cultural asymmetry between scientists and humanists concerning what should be the basic knowledge of an educated person, is probably epistemological. Scientists believe the world should be understood via the sense organs (i.e., empiricism); humanists believe the world should be experienced via emotions (i.e., Romanticism). Given Romanticism was a reaction against empiricism, it's perhaps not suprising that (traditional) humanists would hold a somewhat anti-science view.

So the noted asymmetry between scientists and humanists probably has something to do with the history of the polymath scientist and the Romantic humanist. Depending on degree of adherence to historical traditions (and perhaps in conjunction with age), remnants of this history may still exist at an institutional and/or individual level.

By Tony Jeremiah (not verified) on 27 Jul 2008 #permalink

The humanities and arts lack rigor and/or operate in a sphere where "there are no wrong answers".

That's a hypothesis? I'd call it a given. :-)

Okay, okay, seriously. I wonder how much assessment plays into it. In my experience, it's pretty easy to bullshit an essay for a lit class (otherwise I'da flunked), and pretty hard to bullshit an answer on a calculus test (which I did flunk).

Furthermore, there are great essays and horrible ones, but sorting out the middle of the pack is hard. As a consequence, I think a lot of grading in the humanities is either pretty forgiving (that how mine skewed when I taught writing), or if the grading is more strict, it just strikes the students as capricious--unless the instructor does a damn near heroic job of explaining what separates bad from good writing. And I say "damn near heroic" because if the instructor actually knows what separates bad from good writing, and can articulate that so that undergrads can get it, she is probably doing something more lucrative than teaching intro humanities courses. (Feel free to argue otherwise, though.)

So my take is that humanities courses are in general more bullshittable than science and math courses. That was my experience as an undergrad, it's the impression I get from talking with undergrads now, and it has also been my experience as an instructor for both kinds of courses.

That doesn't mean that the humanities and arts actually are less rigorous, necessarily, but that's the reputation they have. Whether that rep seeps up to the faculty from the students or vice versa is another question.

Math and science (particularly math) are a different kind of activity than humanities. It would be interesting to see if anyone has does a study to see what areas of the brain are engaged when solving equations and which areas are engaged in reading a novel. I'd wager something that they are different parts of the brain.

Not that one is better in any moral sense than the other, just that they are not equivalent because they are different activities that require different specific types of focus.

And the point is well taken about the bar for having an intelligent discussion about science or math is higher. I'm a musician. I talk with people who aren't musicians about music all the time. There's never the idea that they are unqualified to talk about music because they aren't musicians.

That isn't true for science. If you don't have a science or math background, and particularly, again, in math, if your skills aren't current, you cannot carry on intelligent conversation.

Same for computer science. If you have never done any programming, you simply cannot engage in any kind of intelligent discussion about programming.

The sh*t really goes out of control for a subject such as global warming. It's an important public topic these days, but truthfully, the majority of the public does not understand the basic mechanisms by which the average global temperature rises and falls because they don't have the science background for it.

So in the public debate it becomes a moral issue, or an economic issue, or a political issue, when really, it's a science problem.

The same is true, by the way, for economics. Most people don't have a background in economic theory, and therefore cannot discuss the economics of our country with a high level of intelligence. It really hampers the debate.

So you end up with issues which should be decided based on the scientific research and evidence being batted around in the media as if they were moral or political issues.

The reality is that certain scientific processes are happening to the climate of the Earth, and the effects they have are not determined by opinion polls.

But the way we deal with the issue in society is by gauging the public opinion, then proposing political solutions (at the risk of being viewed as immoral if we don't take political action).

All this to try to handle a science problem.

Why? Because people don't have the background in science and therefore cannot accurately grasp the problems or propose effective solutions hat would be obvious if they knew the science.

No wonder scientists get frustrated with how science issues get handled in the public debate.

Politicians, of course, want to avoid looking ignorant, so shifting the discussion to a moral or political one is to their advantage. If that fails, they can vilify the scientists. Some good old character assassination can go along way towards eliminating a few pesky scientists. And since the public doesn't understand the science, it does no good for the scientists to point out that they are only the messengers, not the source of the problems.

Result: people create more hot air arguing about morals and politics, while no effective action is taken because what is needed are scientific solutions, but the public doesn't understand the science.

I'm not leaving much wriggle room for the humanities types (of which I myself am one).

There really is no excuse for being ignorant.We have to give our kids better math and science skills.

More economic theory and some civics wouldn't be bad ideas either.

Raising a nation that doesn't grasp the science it needs to survive, doesn't grasp the economics it needs to prosper, and doesn't know the civics necessary to maintain a democracy is not a recipe that is going to lead anywhere good for this country.

We need to fix that.

And it is not the scientists fault that the the system is broken.

(3) Historically, the sciences grew out of the humanities - philosophy and natural theology. Perhaps the academy has inherited a mindset where the humanities are prior to the sciences - you can't be a natural philosopher without being a philosopher, but you can be a philosopher without being a natural philosopher. This doesn't work directly for math, but since math and science are often seen as being closely related, the same attitude carries over into mathematics.

Banging rocks together created Fire and edged tools.

Ok, that's a snide response, but to be serious (And less insulting) "Banging rocks" is the basis of scientific inquiry: Characterization (Rocks that can be knapped into edges, vs. those that can't), Hypothesis (What happens if I hit this rock at this angle?) , Experiment (whack), and peer review (Hey Bob, try this!)

While philosophy may have settled the finer points and set into language a standardized system of observation, experimentation, prediction and review that makes up modern science, that doesn't necessarily mean that philosophy necessarily has any more intrinsic merit than banging rocks together. Short of a system to actually test or falsify those predictions put forth by philosophy, there's nothing that can separate useful information from lovely, elegant, plausible fictions.

I think John Wilkins had some good points about the role of the humanities as a check and balance on the human influence on science, both in the way the experimenter influences data or interprets it. I think much of the reason philosophy continues to exist separately from science is because complex systems like individuals and societies are so hard to pick apart with the sort of scientific rigor applied to stars and atoms. If the scientists are banging rocks at the foot of the mountain, and philosophers are speculating about it's composition, it's origins, and the dwarves pulling gold and rubies from it's deepest mines, philosophy certainly appears more productive. But in the end, schools of philosophical thought become hypothesis to be proven or not. Without the scientific endeavor, the composition of granite formed over millions of years be tectonic pressures is the equal of the pillar of God and home of the King Under The Mountain.

The theoretical side of evolutionary biology is indistinguishable from the philosophy of biology, isn't. Theories are empirically testable.

Another model I don't see reflected here--math and science people may think significantly differently than arts and humanities people.

I've always thought this, but I didn't know anybody else out there also did. It's definitely an idea that should be looked into further.

And whoever suggested Literature for Literalists: if only! I would have signed up for a course like that.

Just a quick comment. It seems to be something coming up over and over again is a point along the lines of "It's easier for nonexperts to have discussions in the arts and humanities than in the sciences because of reasons x,y and z". I agree this is true. But this is not necessarily because the arts are more "accessible" and the sciences are "technical". If we gave school children books about biology, physics and maths (for example), instead of fictional books, we'd probably see more math and science conversations happen casually in everyday life. I'm not saying this is how it "should" be. I loved picture books and fairy tales as a kid. But it still shows that a "dislike" for the sciences is cultural. There's lots of science, math and technology to talk about all the time (not just how to take a derivative), but since that's "hard" or "technical" people don't talk about it as readily.

Disclaimer: the arts and humanities are great, and should be discussed as much as possible :)

In North America, having a Physics degree is like having magic powers. Math is arcane. I think innumeracy and scientific illiteracy are attitude problems, leftovers from simpler times when only "smart people" needed numbers. I find this far more aggravating than the idiot Arts/Science culture wars.

In many liberal arts colleges, science majors spend 25 to 30 hours a week in class and lab, while their humanities peers spend 12 to 15 hours a week in classroom settings for the same amount of credit. Science and humanities majors have similar amounts of reading and writing to do outside the classroom. I suspect that this disparity primes future scientists to develop superiority complexes.

As an undergrad at a small liberal arts school, I majored in biology and minored in English. I found that two very different types of thinking were required for the two disciplines. In biology, I based my analyses on observations/experimental results, as well as published literature. I used my scientific intuition and creativity primarily to direct pilot studies, rather than to come to conclusions about results. In English, I was encouraged to base my analyses of literature both on the literature and my own personal identity poliitics/experience. I was rewarded with good grades when I pushed the envelope and developed analyses that were new/exciting/somewhat-out-there/substantiated by a fairly biased reading of the text. I know that many of my friends, who were also bridging the divide, felt the same dichotomy in thought patterns. The distinction between the two types of thinking seems pretty obvious now. In science we use blind observations, well-designed experiments, and statistics to avoid subjectivity. However, since personal experience is the essence of subjectivity and any interaction with the fine arts is a personal experience, the study of the fine arts must be highly subjective as well.

These days, as a Ph.D. student in the biological sciences at R1 research institute, I think that my graduate school experience is in many ways far easier than the experience of humanities grad students in the same institute. Hours of training and research experience as an undergraduate left me well prepared to succeed in my discipline. I will almost certainly graduate sooner than my fellow humanities Ph.D. students and will be better paid while I'm here. There is more structure and predictability in my research (lab work, field work, and tons of writing). In some ways, the tables have turned since college. It's clear to me that humanities PhDs must be both exceptionaly intelligent and persistent to acheive their graduate degrees. And I bet that their PhD ordeal lead them to develop a superiority complex too! (Hell, how could anyone survive 7 years of grad school without one?)

I have never seen this "divide" as anything but an unfortunate set of stereotypes a few people hold. I don't think there's any inherent dichotomy between so-called humanities people and sciences people. It's like the East coast/West coast thing-- kind of non-existent except for the crazies who keep it alive. Better stuff to get your blood pressure up about, I think.

My sister is a psych major leaning more towards sociology lately, and she has some weird complex about that field being "useless," which is ridiculous. I'm trying to tease her out of that mindset because I don't think it's good for her self-esteem to think her interests are unrealistic or worthless. For Sis, it may be more of an Asian "pragmatism" thing than whatever forces you guys are talking about.

It may be worthy of note that a person can be very well-versed in the fine arts without having much knowledge of the European masters.

Random: my advisor did his undergrad in English literature before pursuing graduate work in biochemistry. He's pretty friggin' smart.

Hi Shawn:

"As for the topic generally: it really speaks to the elitism in the hard sciences that everyone from the "science side" is more than happy (either implicitly or explicitly) to lump the soft sciences in with fine arts and literature without batting an eye."

Talk about lumping.

Left_Wing_Fox - No, you're missing my point about the history and philosophy of science. My point is that, historically, the sciences grew out of philosophy. The basic method that you spelled out was developed out of trends that appeared within philosophy in the late Middle Ages and Renaissance, and codified and made popular by folks like Francis Bacon and Rene Descartes. This was long before the sciences as we know them existed, that is, before anything like a humanities/science divide was even conceivable.

I'm really not sure what the connection between philosophy and banging rocks together is.

outlier - I know of no tactful way of putting this, but no, you're factually wrong. Take, for example, Daniel Dennett's Darwin's Dangerous Idea, Ernst Mayr and Richard Dawkins' popular works, and journal articles dealing with, say, cladistic vs. phenetic approaches to biological systematics. There as no significant differences in their general approach and methodology. Once you get to the highly theoretical side of biology, you really cannot tell the difference.

@ both of you who responded to my previous post- I'm curious to know what you think philosophy is, what its purpose is, and what it works to accomplish. I think I have a very different sense of philosophy's task, and clarifying that might help to resolve some of these disputes.

To sum up my view in short, philosophy deals with clarifying the boundaries and interrelationships of our conceptual categories; drawing out assumptions and implications of our beliefs; and evaluating whether those beliefs are justified, internally logically consistent, and consistent with our other beliefs.

This is hard. On the one hand, I think that the level of discussion (and therefore the required background) usually had by "scientists" is no higher than the level of discussion (and background) had by "humanists," that is, people who have spent years studying it; this leads to a diminishment of humanists' accomplishments -- "You just read all day, how hard can that be?" sort of thing.
On the other hand, science doesn't permeate day-to-day life the way certain aspects of humanities do; that is, everyone has to read something every day, even if it's just the memo from a boss, and it's quite likely that the typical day will include music (even if it's something that individual hates), because most stores & a large-though-not-majority number of workplaces often have music. No, these are The Humanities, but they are much more exposure to elements of the humanities than the sciences ever get. (I'm basically trying to restate Josh's point).

The humanities and arts lack rigor and/or operate in a sphere where "there are no wrong answers"

What bugged me more was when there was an answer that was deemed "correct" for a particular interpretation of what the artist or author was trying to convey.

Hypothesis: serious study of the sciences and of the humanities are approximately equally difficult, and both cultures feel similar alienation from each other (i.e. humanities types and science types, unless cross-trained tend to feel similar incomprehension of the other side).

However for outsiders of both (i.e. non-intellectuals), the humanities come across as more comprehensible (and BS-able), thus the prevailing attitude in society at large is more favorable towards the humanities, therefore making distaste for the sciences more socially expressible, whether you are an intellectual or not.

By Matthew L. (not verified) on 30 Jul 2008 #permalink

I am an engineer, and the educational system suited my interests well. But I could see how it was turning off most people.
Technical education in elementary school consisted mostly of arithmetic. Not math, arithmetic. It was boring and repetitive and lifeless and dull. It only got fun when we started having competitions at it around 4th grade and I found out I was good at it. I didn't get good at it because I liked it, I got to like it because I was good at it. Where does this leave the 50% of the students who were below average?
There wasn't a lot of science in elementary school. There was some, but not much. I think the feeling was that that would have to wait until we had the math for it.
Science really came in full force in high school. For the most part, engineering did not. They now have computer classes in high school, which weren't there when I was around, so I can't comment on them.

This was fine for me, because I was an honors student. I spent a tremendous amount of my spare time reading books on science, books on technology, and science fiction when I was growing up. I was also building flying model planes and flying model rockets and all sorts of gizmos. Furthermore, it was clear from a very young age that I wanted to be a technical person. On top of that, my father was an engineer and would talk to me about what he did.
But when I look at this education and ask myself, what would it have done for me without all this supplemental activity of mine on the side, and had I not been planning for technical future? Would I have seen any relevance in the math I was learning? Or the science for that matter? The answer is plainly no. And that is the answer I see reflected in the faces of most of the population when someone talks about technology.
Teaching Technology
The idea is that you have to know arithmetic to be able to handle math, you have to know math to be able to handle science, and you have to know science to be able to handle technology. And this idea is false. Yes, to do groundbreaking research in technology you need to be good and science and math, but most people can learn a lot about technology with neither, just using common sense.
And for someone who has no plans to do groundbreaking research of any kind, that is, most of the population, learning how things work is, unlike pure math or science, let alone arithmetic, potentially quite interesting.
Imagine if we taught gym the way we teach technical subjects. In K-12, students would do nothing but the basic movements, as calisthenics. Nothing would be done as coordinated teams and there would be no sports, on the belief that you weren't ready for sports until you had all the basic movements down. The focus would be on a few athletes who would actually do sports in college or in grad school to become professional athletes. Everyone else would be made to feel they had failed out of gym. I would predict that with such a program, most students would hate gym, and in fact hardly anyone would watch professional sports as adults. And that's what our current technical education program is doing to most people.
So we come to the million dollar puzzle: I think most people would be interested to know how the technology around them works, it is in society's overwhelming interest to have voters, consumers, and investors who know how things work, so why isn't K-12 teaching it to everybody?
A Technical Minor
Another thing that wasn't present in either of the universities I was at was the concept of a technical minor. It might be perfectly appropriate for someone majoring in, say, business or economics or law to want to get a minor in some technical discipline, or even in technology in general. This might already be done at teaching colleges (both the schools I went to were research institutions).
How Important is Arithmetic?

I took astro-engineering in college. I've often found the main difference between the "hard" and "soft" majors was the willingness/ability to do math. Arithmatic is probably dull and difficult for everyone - the ability to calculate in quantities greater than the # of fingers on your hand is somewhat unnatural and needs to be drilled. However, the real divide in mathematical reasoning seems to develop during high-school algebra and calculus. Abstract manipulation of more complicated mathematical objects - equating one arrangement with another arrangment under a transformation, ect. Some people hate it and avoid it, and never develop the skills for learning it. Some people, myself included, either have an intuition for it, or can develop one after enough experience with it.

I remember taking a rather high level economics course - a game theory class. (Economics sort of straddling the boundary between "hard" and "soft". It can be mathematically rigorous, but all the intro classes that most business/humanities majors see are usually restricted to what can be described with only a trivial amount of it.) Many of the business and humanities majors followed it pretty well - up until the point where continuous probabilities were introduced and the math began getting a little intense. One of the students in class raised her hand and asked "Uhh - what does that stretched-S thingy do again?" They were fine with vaguely defined trend-lines and intercepts, but seemed to stall when rote formulas couldn't cut it in describing/navigating the situation.

Mathematical reasoning in general is a prerequisite for a broad class of subjects. Anything involving objective measures of the world and their interaction for starters.

In chemistry, it could be as simple as figuring out stochiometric ratios, or as complicated as working out the reaction rates. If you wanted to go a step further and ask *why*, for example, things reacted at this rate, you would have to be able to follow things like the kinetic theory of gasses and collision rates. You would need to reason about an abstract model of statistically moving particles.

In astro-engineering, you need to figure out how satellites will orbit. Even asking *how* things will orbit in a non-quantitative manner is somewhat incoherent. Figuring out how the satellite's orientation will evolve with time for objects with a certain mass distribution and rotation rate, subject to certain gravitational gradients also requires quantitative manipulation. Even describing the orientation of something to something else requires a set of angles at least. The distances, speeds, times and forces involved in orbital spaceflight are alien enough that you probably couldn't navigate from, say, Earth to the moon with a joystick on a strictly intuitive basis - probably why all our space-combat games are modelled after atmospheric flight.

Mathematical reasoning also seems to divide the programmers from non-programmers. Computer "language" (imperitively manipulating data-structures) requires a lot of mathematical reasoning. Formal logic is a branch of mathematics. When your logical operators are precisely defined, and your truth-variables layed out, then performing the operations in a strictly consistent manner is a mathematical process. In addition, I never really had much luck learning higher-level programming langugages in high school until I had something to program for - and what first got my foot in the door was needing to create and run numerical models.

So, in summary, if you want to be able to work with any of the "hard-science" disciplines, the key is learning math (abstract math starting with algebra and calculus specifically). After that, it's learning how to manipulate and visualize the quantities involved.

Bill wrote: The idea is that you have to know arithmetic to be able to handle math, you have to know math to be able to handle science, and you have to know science to be able to handle technology. And this idea is false. Yes, to do groundbreaking research in technology you need to be good and science and math, but most people can learn a lot about technology with neither, just using common sense.

I couldn't agree more. There seems to be an assumption that you must have the skills and education to actually DO research in order to understand how research is done and interpret the Big Picture results of that research. And I just can't help but think this is false. I am not a writer nor an artist, but I do have the skills to understand good writing. I can't create it, but I can appreciate and understand (and critique) it. Sciences should be treated the same way. Unfortunately, the gen ed course work that most folks get in high school and/or college throws people right into math or 'science' class, but does not give the option of 'science history' (the art history equivalent).

And that is one reason, in my option, why Science is seen as Difficult. Personally, I find Art incredibly Difficult, but I was able to take art history to at least get an appreciation for the craft. The option doesn't exist for Science.

Re: a Technical Minor. The Marine Option Program at the Univ of HI is one such minor. Most of the students who take that option are 'humanities' majors (journalism or English, etc), but who want enough 'science' background without the need to learn how to 'do' science. It's a great program.