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The mathefication is not just an academic thing. The real world is becoming more quantitative. Some examples:
(1) Major League Baseball has (slowly ... with a lot of resistance) started paying attention to statistics *much* more when evaluating players. The key here isn't just that people are paying attention to things like batting average. They have *always* done that. The key is that people are starting to try to correlate different things with winning. So, the modern baseball stats-head mostly doesn't care about batting average.
The stats are easily available to someone with a *solid* high school math education. The point, however, is that even baseball is getting much more quantitative than it historically has.
(2) Drug Design. More and more companies are trying to design drugs using computer models (not just physics/chemistry simulators). This requires *lots* of math beyond what a normal PhD chemist would know.
(3) Quantitative supply chain management. Think about what Wal-Mart does. Very mathy. Wasn't done by anyone 30 years ago.
(4) Wall Street Trading. I'd say that today if you don't have a very heavy math background, you basically *can't* trade stocks/bonds/etc on Wall Street today. There may be some exceptions, but the field is much more quantitative than 30 years ago. Read up on LTCM (which went down in flames!) for more details.
(5) SQM (Statistical Quality Control), used by many manufacturing companies, is a mathematical approach to quality control.
So it isn't just academia. A lot more jobs have gotten quantitative in the last 30 years.
Which sorta makes things like TERC even more scary.
Wednesday, April 30, 2008
Mark Roulo on the mathefication of the universe
"What I've seen in academia is that the various disciplines seem to 'complexifiy' themselves, either by becoming 'theoretical,' in the case of language-based disciplines, or by becoming 'mathified,' in the case of the social sciences."
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While I agree with Mark's overall point, I want to add some details.
I think it's a misnomer to say that the actual *trading* of stock or bonds requres a math background. No, traders are still salesmen. They require a different skill entirely: the ability to convince someone of a bad idea repeatedly.
But *trading* is not really where it's at on Wall Street. Mostly, there aren't traders. There are computer models and programs that trade. And those models are writen by "quants" and those quants came from phds in math or physics. The lowest down folks came from undergrad degrees in math or physics, but usually, that's just a lousy entry level job.
There are a whole host of other banking jobs that require math skills, too. Understanding future markets requires some pretty sophisticated statistical mechanics (a field in physics) or fluid dynamics background. Any risk management job does because you need to understand these models and a bunch of statistics well enough to understand what's going on.
So what level of math are we talking about? Well, to create the models for quantitative supply chain management, you need to have gotten at least a solid engineering math background. That is, you could have been a CS or EE engineer, or a math person, or a physicist and learned enough math. Mostly, you're just learning about Markov chains, eigenvalue problems, linear programming. These are things you'd learn in an upper division engineering math class (where it was done in the engineering class, and you'd have to grasp it well enough to adapt it to later applications), or you'd learn it in a discrete math class.
That means you had to have gotten through multivariable calculus, differential equations, linear algebra, and at least some discrete math, and hopefully, at least one upper division advanced math application class to really understand these things.
Students who aren't in math, science, or engineering simply ARE NOT going to take those courses.
Actually, this ties into the comments on the "the deathless meme of the high performing school", too.
The reason for the mathification of the social sciences is precisely because the top Americans realized it was easier to be the best math/science geek in a social science department than it was to be a mediocre math geek in a math or physics department.
They were looking for problems to solve. It was easier to go into a field where there was no real mathematical competition and start solving problems there than it was to go head to head against better and brighter and more capable students and professors in the science and math fields. Can't get into a top ten grad school in math? Might as well do econ! Can't get into a top ten grad school in physics? Might as well do investment banking!
As more and more foreign students push American students out of the pure sciences and math, those kids realize that they can apply their talents to places where they are the biggest fish. So even though they were 2nd rate physicists compared to the Asians and Eastern bloc grad students, they weren't the 2nd rate economists, psychologists, bankers, etc. They became engineers, too.
The reason for such high falutin' mathematics used in baseball today is because it's a lot more fun to go work for the Oakland A's when you can't get that discrete math professorship.
So, the irony is that more fields are becoming influence by math BECAUSE of our own failures to teach it well, to compete on the major math and science playing fields.
"The reason for such high falutin' mathematics used in baseball today is because it's a lot more fun to go work for the Oakland A's when you can't get that discrete math professorship."
Except that this wouldn't matter if the math didn't *work*. My point is that lots of areas of non-academic businesses are getting more mathy. Typically this is because the companies that do so gain a competetive advantage over those that don't. The 'more math in business' may be enabled by people who can't get math professorships, but it isn't *caused* by more failed academic careers.
[And, as nearly as I can tell, most of the SABERMetrics community is not made up of PhDs who couldn't find work. The stats they use *are* pretty simple. It is just that the stats are a lot better than the few that baseball has traditionally tracked.]
-Mark Roulo
"I think it's a misnomer to say that the actual *trading* of stock or bonds requres a math background. No, traders are still salesmen. They require a different skill entirely: the ability to convince someone of a bad idea repeatedly.
But *trading* is not really where it's at on Wall Street. Mostly, there aren't traders. There are computer models and programs that trade. And those models are writen by "quants" and those quants came from phds in math or physics."
Actually, I was trying to refer to the folks who were making the models. Today these do tend to be PhD math/physics types. 30 years ago almost nobody traded that way. So ... early 1970s you can trade based on gut feel (or whatever) and need reasonably good sales skills. Today, mathy people decide what trades to make and different sales folks talk the other side into going along with it (except that I think it is more complicated than that ... the key point I was trying to make was that Wall Street mostly didn't employ the math geeks 30+ years ago and today pretty much all the trading systems are designed and run by them. Wall Street didn't bring in the math geeks because we had a bunch laying around. It brought them in because the trading systems they designed tended to make more money than the older, less-mathy approaches. Once things started in that direction, things got more-and-more mathy).
-Mark Roulo
SABREmetrics is pretty far from "math" or even modern statistics. It works, but it's not rocket science. There's a lot more out there now, though, that they do do. (Like mathematicians who try to prove why total runs scored is a good estimator of winning one's division)
Of course math WORKS--but a tiny tiny improvement by math is enough for nearly all industries. The competitive advantage is because most companies methods are simply dreadful. This is true in nearly every engineering process out there, and 1 year in any company will give you over a dozen examples of how inside the company or their clients genereally sees the need to make any real improvements, because currently "it's good enough". Have you looked at the reality of how little math was in most industries? My husband was in econometrics, and in companies that did retail price optimization. Their models WERE CRAP! Most of the people working on those models didn't even bother to realize when their matrix was singular, or when they were trying to invert a singular matrix. These folks had phds and claimed to have done something important, but the truth was they were implementing the most basic of models, if they were implementing anything right at all. And yet, it made grocers money. Why? Because grocers were so old fashioned they used CONSTANT MARKUP. That meant that when they got a better deal on something, THEY DIDNT TAKE ADVANTAGE OF IT, but lowered their selling price below the market equilibrium.
--The 'more math in business' may be enabled by people who can't get math professorships, but it isn't *caused* by more failed academic careers.
Are you sure? Math was always providing a competitive advantage--why NOW does it appear in so many industries? Because of the greater surplus of people versed in math. Yes, math working is a necessary condition, but not sufficient, if you have no mathematicians. You can see that as a benefit--look! higher ed is working! or you could see that as an interesting example of how we're not really utilitizing those people well.
Linguistics -- voice onset time!
Another factor behind the advance of maths is most likely the advance of computers and of easily available statistical databases. The computing power available in my cellphone is probably more than the computing power available in a university computer science lab in the 1960s. And of course the Internet gives fast access to new datasets, and the WWW makes it far easier to find those datasets.
So manipulating data is far cheaper and faster. It's quite plausible that the elasticity of demand for statistical analysis compared to cost is greater than 1l.
My son's school district used INVESTIGATIONS IN NUMBER, DATA & SPACE (there's no such animal in textbooks as TERC) for K-4 when he was in elementary school. He seemed to thrive with it quite nicely. He's a h.s. freshman who finished algebra in 8th grade, geometry in two trimesters this year, and seems well-positioned to continue as far as he chooses to go in mathematics. And that was without any particular help from me other than my willingness to play the math games he brought home and begged me to engage in with him when he was little.
That doesn't prove that the curriculum is a panacea, but it isn't quite the disaster the math warriors need to claim it is.
But then, this isn't REALLY about textbooks, is it, Mark? It's about politics. And that's what's even MORE scary.
"..but it isn't quite the disaster the math warriors need to claim it is."
I guess "disaster" is saved for a 100% failure rate.
"It's about politics. And that's what's even MORE scary."
The politics card so soon?
"My son's school district used INVESTIGATIONS IN NUMBER, DATA & SPACE (there's no such animal in textbooks as TERC) for K-4 when he was in elementary school. He seemed to thrive with it quite nicely. He's a h.s. freshman who finished algebra in 8th grade, geometry in two trimesters this year, and seems well-positioned to continue as far as he chooses to go in mathematics. And that was without any particular help from me other than my willingness to play the math games he brought home and begged me to engage in with him when he was little.
That doesn't prove that the curriculum is a panacea, but it isn't quite the disaster the math warriors need to claim it is."
Please, please, please tell me that you are trying to say something other than, "I can point to one success story using TERC, therefore TERC isn't a disaster." Please.
[NOTE: For brevity, TERC is often used for "Investigations in ...", just like Singapore Math (or occasionally SM) is used for "Primary Mathematics", which is the formal title of the Singapore Math textbooks.]
I doubt that you will find anyone here suggesting that the failure rate of *any* math program with reasonably widespread adoption is 100%. What you will find is the belief that some curricula are much more likely to track kids out of a STEM career.
"But then, this isn't REALLY about textbooks, is it, Mark? It's about politics."
No, for math it really *IS* about textbooks. And teacher training. And other things related to the question, "Are the kids learning math." It does eventually become political in the broader math wars context (just like the "how best to teach children to read" is political ... and I don't know why that is the case, either), but here it is all about the math.
I suspect that the political makeup (at least as traditionally measured: liberal vs. conservative, democrat vs republican) here is not quite as conservative/republican as you might guess. Catherine's husband, for example, was part of a history curriculum project that got raked over the coals by the "hard right" (Catherine, you can provide details?).
-Mark Roulo
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