It is worse than not understanding differential equations.

The N's generally don't even understand arithmetic.

Same goes, by the way, for 'E' people and 'F' people... referencing ECONOMICS.

Like Cruz Bustamante telling everyone that gas prices are too high and the way to fix this is to nationalize -- er, state-ize the gas business. He's an 'F', with absolutely no clue how the powers operate that control his very life.

Joe, M. Simon I suppose that you both think that the fallout from the anecdote was 'accidental', or is 'that's all there is'?

Even if the Mathematician of your story was well-grounded he probably lacked compassion. Rockhard 'facts' tend to obscure charitable thoughts. Not that Ms. CrapArtist couldn't win an argument with Mr. StoneCold, but if we're discussing who appears to be winning the ArroganceAward?

I can wrap myself around equations, and I also am capable of stating a proposition and supporting arguments using the Scholastic method. I am no Crap Artist. Do I defy the odds, or am I just an 'accident'?

Deal with PALE GAS = Death. The first is the worst.

CRAP! I left out some Periods. The periods reoccur between the elements on the left side of the equation. Damn! I hate myself when I make mistakes... :o)

I am a soil scientist / geo-chemist by training (undergrad degree in geology), and as I see it, both ends of the spectrum have a problem.

Many scientifically trained people have been trapped within a certain reductionist thinking that was at one point at least in part dictated by the limited computational power available. Such mechanistic, reductionist thinking has generally served us quite well at doing things like keeping aeroplanes from falling out of the sky at inconvenient moments.

It is, however, rather inadequate for understanding /living/ systems -- agriculture being my preferred example.

On the non-science/math end of things, the problem is much worse than described in 'Two Cultures.' Not only do they lack basic maths knowledge and have no understanding of scientific method ... the tenets of logic and reason are also a foreign language.

Not only can you not have a logical, rational discussion with such people, but more often than not they reject the very concepts of logic and rationality. No wonder, then, and arguments with such people rapidly descend into uni-dirctional ad hominem attacks and tu quoque evasions.

I was not always that way. My chemical engineer father correctly said of my mother that she gets befuddled by anything more technically complex than a marble. She, however, could more than hold her own in discussions and arguments with my dad and his colleagues because she could construct a rationally tight and logical argument, bringing many non-scientific factors to bear quite effectively.

Of the two cultures, one is logical, and the other is not. Even though mathematics is a /sub-set/ of logic, it (by itself) is an incomplete descriptions of the divide.

Having a discussion with someone who does not understand the difference between precision and accuracy; between inference and implication; between association and causality; or even between celebrity and importance ... is not very productive, and isn't even fun.

Bart Hall Thank you for adding some common sense and humor to an otherwise dry discussion! LOL.

I also have seen both sides of this equation: I'm a writer and liberal arts type, but studied enough physics, calculus and other math/science to understand scientists and engineers when they speak (not to do anything they do, but enough to ask questions and understand, to some extent, the answers). My father was a civil engineer (yeah, I know EE's, give it a rest) who had a separate degree in mathematics, and I had engineering and math drilled into me as a child.

With that as preface, let me say this: I have found scientists and engineers to be much more precise thinkers, but sometimes too precise, and as someone said above, reductionist. That is, they are often extremely confident on extremely small points. They seem less confident discussing things like I am doing right now, things like tendencies which have all sorts of unstated caveats ... the techies want their caveats.

And I have found liberal arts types mostly are the opposite -- they under-estimate their epistemology, and yet conversely are too quick to abstract general principles out from concrete matters they simply don't understand.

There are dangers on both sides ... but I'm not splitting the difference. I have found engineers and scientists are usually far more rigorous in their thinking.

However, particularly, they have this limitation: They often seem to be unaware of how their training has conditioned their worldview.

I recall one engineer I interviewed who simply refused to abstract any general principles at all from a production maintenance system he had developed -- insisting that every parameter he had stated had to be in place or the whole thing didn't work and there was nothing more to be learned from it than that.

He also seemed genuinely pissed off when I suggested that he must have applied some abstract principles for creating his system; otherwise, he wouldn't have been able to do it. He simply didn't understand the limits of his point of view, which is something a philosopher would.

And I can recall, during a game of trivial pursuit, a physicist who seemed genuinely surprised when I kept taking science questions instead of literature or history. He asked me why, and I told him, "Because there's a lot more history and literature than science."

On the other hand, I've had fellow writers brag about their lack of mathematics skills and then turn around and make all sorts of economics pronouncements. I once tried to explain to a friend that when people use resources, that creates demand, which raises the price, which creates more resources. She said no,the resources get all used up and then there are no more. She simply couldn't get the idea of time in her economic system, or that people might go and find resources to meet demand.

On another occasion, I had a friend who insisted that an electron had no mass and simply would not be convinced otherwise, until the above physicist friend later brought it up and disabused him of the notion. He said, as I recall, "Are you the guy who said an electron has no mass?" Pretty funny.

Finally, to not leave me out of this general swinging at everyone's thinking, I was once sitting around explaining to a couple of electrical engineers that I didn't understand electricity. What's the problem, one asked.

Well, electricity is a flow of electrons, right? Yup, they are answered. I continued, then how come there isn't a big pile of electrons at the end of the wire? Won't the wire eventually run out of electrons? What happens to all those electronless atoms?

They had a good laugh, which was the point.

I just want to clarify this point. It seems to me that tech types want their caveats and their parameters defined clearly or it doesn't count as thinking. I dunno. I could be wrong on this. But I've seen more than one engineer or scientist simply murmur, "this is BS" or tune out when things become less defined and murky.

"It seems to me that tech types want their caveats and their parameters defined clearly or it doesn't count as thinking. I dunno. I could be wrong on this. But I've seen more than one engineer or scientist simply murmur, "this is BS" or tune out when things become less defined and murky."

I don't know that this is really any sort of flaw in their thinking. A reluctance to engage in over-hasty generalizations, and a willingness to acknowledge the limitations of one's reasoning (by issuing caveats and so forth), strike me as nothing more than proper scientific practice. I know that many biologists, geologists and others who have to deal with highly complex systems like to sneer at "reductionism," but the truth is that nearly everything we know in science today has been arrived at by the reductionist method.

Complex (or, if you prefer, "emergent") phenomena certainly do arise all the time that cannot be scientifically treated by reducing them to lower order concepts, but this is so mainly because of the practical limitations imposed on us by physical reality, rather than being ruled out by some deep physical principle along the lines of Heisenberg's uncertainty principle.* That we cannot predict the weather a month from now isn't due to any laws of Newtonian physics, but because we are unable to acquire enough data to enough accuracy to do so - in theory, some extremely advanced alien race might possess such capabilities. Similar things hold true for most biological and geological phenomena.

Even in those cases in which practical limitations bar us from working at the lowest possible conceptual level, we can usually impose some rigor on our investigations by resorting to statistical techniques, and this is true not just in fields like statistical mechanics, but also for biology, economics, psychology and a lot of other areas that are often held to be immune to "reductionism." That we are dealing with statistical phenomena does not preclude us from thinking carefully and rigorously about whatever it is we are interested in, so to a great extent, those who spend their time bashing "reductionism" are expending their energies on a straw man. In fact, I suspect that the real target of their anger isn't "reductionism", but the utilization of mathematical techniques, perhaps because so many of them would prefer to engage in the literary equivalent of hand-waving, if only they could get away with it.

To summarize, I don't think that there are good grounds for apportioning any of the blame to the scientific/technical types. To do so is to engage in the sort of bogus "even-handedness" that newspapers are all too often guilty of. Not all views deserve to be taken equally seriously, and those who refuse to utilize the tools of mathematics in thinking about the world around them shouldn't expect anything but condescension from those who are numerate. Talk about "holistic" or "emergent" properties is a lot more convincing coming from someone who has demonstrated sophisticated mathematical skill in the past than it does from the average artsy or literary intellectual, and even then one has a right to ask for evidence that nothing in the mathematical armory suffices.

*Few people seem to realize just what the uncertainty principle implies: it does NOT mean that we live in a "non-deterministic" universe, as the evolution of any system's wavefunction remains perfectly deterministic even in light of it. Quantum mechanics is every bit as deterministic a theory as Newtonian mechanics, and Heisenberg's principle is only a statement about the probability distributions of pairs of observables in a system - albeit, an extremely important statement at that.

There's a problem that is being missed:

"It's more than that," I said. "It is fundamental. People of type N cannot argue science or technology with people of type M."
-- "Why?"
"Because they always lose."
-- "Are you sure?"
"Yes," I said. "They lose even when they are right."

Jay wouldn't have made a post and we wouldn't be discussing this as a problem except for the fact that when it comes to policy debates, it is the converse that is true. When it comes to policy debates it is more apt to say "they win even when they are wrong."

That's because their is a flip side of the coin to the woeful science knowledge of Liberal Arts majors. I, by the way, am speaking as a Liberal Arts major. I am fairly confident on a wide range of "Liberal Arts" and "Social Science" related topics. I have a fair understanding of economics and some science. But my grasp of mathmatics is lacking (I'm really good at the basic add, subtract, multiply and divide stuff - I have, in the past, been able to beat-the-calculator. I mean by that someone gives a long number string to be multiplied or divided by another complex number, and at my best I have been able to produce the answer faster than someone can pick up a calculator, hit the on button, enter the numbers, and get the total. Though I'm rusty now). Anything beyond simple algebra is beyond me, though.

However, science majors often lack a facility with words that is very helpful in winning arguments on the grounds that matter in policy debates. Sure, they can thwart Lib Arts folks by their own standards - as in the example. But did the sociologist leave the conversation convinced of anything about the issue at hand? The physisict "counted coup" in the exchange by his standards, but what is the state of nuclear energy in America today?

All those examples Jay mentions in the posts of his he quotes from later in the essay prove that - sure, science/math types can "win" by meaningless standards when it comes to a mathmatical proof that x is a "ponzi scheme" or global warming worries are overbloan and the like. But these wins are empty and meaningless from the standpoint of public policy because the void Lib Arts majors have in mathmatical and scientific background knowledge that Science majors lament is easily matched by the void in rhetorical skill and intellectual debate (as opposed to what we may as well call "scientific debate") that exists in science majors as opposed to their counterparts in the Liberal Arts who have developed a greater skill with words and persuasion.

So our Science Major types come to the conclusion that the "problem" is that the rest of us are bad at math. But the real problem is that they are bad at words. They need to learn how better to impart what they know, in a manner that is persuasive in public policy debates, to the rest of us rather than expect everyone to become a science and math wiz.

Now, we Lib Arts types do have something to learn, too. It isn't necessarily physics formulas on nuclear decay, though. We need to learn better to differentiate between quality science when we hear it and the quackery that often is passes as science in the pages of, say, the NYT.

But till the Scientists rectify their own void, they'll be grousing over beers over what public policy on scientific issues is.

NO. The real problems are that most scientific types can't grasp the fact that understanding the human condition is not amenable to their methods, AND that the non-scientific types do not have, or even know about, the tools that can drive reality to a sustainable change, even if they KNOW what the problems are. The inablity to bridge this chasm of thought is the real tragedy.

If reason prevailed, the trains would run on time, but it would be a lot more boring... and less human.

Contradiction?

"The real problems are that most scientific types can't grasp the fact that understanding the human condition is not amenable to their methods"

I thought their methods were largely devoted to understanding the human condition. Is that even possible anyway?

This article touches on some of the bad philosophy debates as well as the lack of accountability in the liberal arts. Bad ideas kill just as much as bad science.

Back in college, I had a good laugh at all my engineering friends who whined and bitched about those silly three page papers they had to write once a year. Of course, I couldn't even begin to understand what they studied everyday. Perhaps education has become too specialized, too in-bred, and Summers' ideas about the necessary melding of disciplines will energize both fields. The inbred liberal arts is how we got post-modernism!

This thread has perhaps focused too much on arguments. We need to look at the whole question of conclusions, as well as the cost, magnitude and type of error.

There are a /lot/ of bad decisions out there, many of them tangled up in the precision--accuracy question I mentioned earlier. Approximately right is a lot better than precisely wrong.

Errors tend to fall into three broad categories.

ERRORS OF FACT -- everybody makes 'em. Recognise it, admit it, correct it, move on. No big deal.

ERRORS OF CIRCUMSTANCE -- perfectly good decision undone by something truly unpredictable. A hailstorm wipe out a broccoli crop. Expect them. Allow for them. Create enough margin to absorb them.

ERRORS OF APPROACH -- Doing a great job of climbing the ladder, except it's leaning against the wrong building. These are killers, chief of which is probably the assumption of linearity in a non-linear (ie living) system. Pouring money into 'anti-poverty' programs is a great example.

The core issue, especially with errors of approach, is that in living systems cause and effect are almost always separated in both time and space.

Money poured into 'anti-poverty' programs was especially targeted towards women without a man around. There was even an incentive to kick the man out. A generation later the prisons are full of angry confused young men raised in the absence of a father.

High power statistical analysis (and I mean that in the mathematical sense) is needed to determine differences in complex systems where the downside of being wrong is considerable. Most people have woefully incorrect (not just inadequate)understandings of what statistics are and can do.

Nowhere is statistical ignorance so costly as in the field of economics. I challenge anyone to show me a real (as in requiring calculus) statistics course in any economics department in the country.

We have precision out the wazoo in economics, but our accuracy sucks and nobody even bothers to run the statistical analysis that might help determine which are the most dangerous errors of approach.

As a society we have far more power than wisdom, and it is starting to bite us in the ass.

Unfortunately, those who attempt to apply logic, consistency and statistics to the issues of the day all too often have their arguments dismissed as "an artefact of homophobic racist patriarchal hegemony intended to maintain imperialist constructs of a decadent culture in a post-modern world where they no longer apply."

Or any number of similar statements from be-tweeded intellectuals who never once have had to make payroll, work on commission, or evacuate the wounded. In other words, people who don't have to live or die (literally or figuratively) by the consequences of their decisions.

I'll suggest that in some areas, there are legitimate places for the humanists to push back; there are ways in which traditional descriptions of complex systems begins to break down - I've talked about tame and wicked problems, and much of what Joe talks about as 4th Generation thinking is an attempt to look at things which haven't been managed well in a reductionist way.

Doesn't mean that airline pilots can get away without math...just that there is a point where the boundary bewteen the two worlds is becoming somewhat less defined.

A.L.

I'd like to add another category of errors: Errors of Omission, whether conscious or not, where facts, circumstances, or approaches are ignored in order to arrive at a comfortable conclusion.

IB Bill, I have a somewhat different riff on your statement:

I just want to clarify this point. It seems to me that tech types want their caveats and their parameters defined clearly or it doesn't count as thinking. I dunno. I could be wrong on this. But I've seen more than one engineer or scientist simply murmur, "this is BS" or tune out when things become less defined and murky

I am an engineer by training, but I work now in a corporate research lab as a liason to various product and development groups. I help define research agendas based on the needs identified by the product groups and emerging areas of study in academia and other research labs. While I can understand and talk about the research and its goals, often I'm not really qualified to conduct the research itself. I find this is something of an advantage - when you are defining an aggressive research goal, you cannot simply get a bunch of experts in a room and get them to apply what they know - you need to get them in a room and half forget what they know. You have to help them over the mental barriers against generalization and extrapolation in order to generate enthusiasm for the pursuit of technology which they can't just go back to their cubicles and crank out next quarter.

This extends to the business world as well - there is a reason why startup business plans (but not airplane blueprints) are written on cocktail napkins - it's the cocktails! Sometimes it takes a couple to loosen up all that concrete knowledge about products and markets and make a generalization or abstraction which leads to a new way of doing things.

Both the Mathematician and the Liberal Arts Major can glory in the wonders of Bach, Motzart, Beethoven, Brahms, or Lennon, but the Liberal Arts Major misses all the glories and wonders of that science offers, unless the display is decorated with flashy lights and a smoke machine.

Strangely enough, in my quest for a Master's in Applied Math, two things became obvious.

1) The progress of mathematics requires creativity and intuition along with a facility for applying lots of theorems. This may not be obvious to the layperson because the more intuition that is required to come to a conclusion, the more abstruse the material.

2) Mathematics is a useful, but not complete tool for understanding the world. It can't even explain itself!