Tuesday, April 19, 2016
"Calculus is so last century"? Hardly!
Two months ago a WSJ op-ed ('Calculus Is So Last Century') by Tianhul Michael Li caught the eyes of many mathematicians as well as physicists (and I can assure you, many space and solar physicists). In it Li basically argued that calculus is primarily of the last century as it "is the handmaiden of physics - invented by Newton to explain planetary and projectile motion."
"While its place at the core of math education may have made sense for Cold War adversaries engaged in a missile and space race, 'Minute Man' and 'Apollo' no longer occupy the same prominent role in national security and prosperity they once did."
Which makes one wonder what alternative universe and planet this guy is living on? Surely not the one that I'm on!
A feature story in Saturday's NY Times, for example, expatiated on the latest developments including "hypersonic targeted warheads" not only under development by the U.S. but China and Russia as well. The U.S. has a non-nuclear version but the take is that the Russians and Chinese are developing nuclear warheads- independent of missiles- that can be hurled into space then come down on an enemy with little or no warning time. This is in contrast to Cold War ICBMs that general gave about 30 minutes advance notice, unless launched by submarines)
Most alarming is the drive by a number of nations, including the U.S., China and Russia, to develop low yield nukes which - as the article put it- could make their use much more likely than the "mutually assured destruction" (MAD) model of the past allowed. Indeed, the Russian already have a military posture firmly in place that permits the use of tactical nukes (with 10- 25 kt warheads) in the event that NATO forces overwhelm Russian positions in Eastern Europe. (And cruise missiles are also being outfitted with low yield nukes.)
The current U.S. proposal to "modernize" its nuclear warheads is also seen as possibly destabilizing the existing system and rousing the Chinese and Russians to action in their own warhead development.
Far from national security having switched away from H-bomb Cold War worries, we are evidently entering a new era wherein nuclear "swords of Damocles" literally hang over our collective heads, in the form of targeted hypersonic warheads, or even nuclear-armed satellites,
None of these systems will use linear algebra (the math Li mainly advocates teaching) to reach their targets, but plain old brute differential calculus, of a form I described in earlier blog posts, e.g. from May 6, 2013 (the rocket problem).
Surely then, Calculus isn't passé if it is still central to the ultimate form of nullifying any national security or 'prosperity': nuclear war,
Meanwhile, in fields as diverse as astrophysics, astronomy, quantum mechanics and plasma physics - not to mention climate science - differential calculus is as critical as ever. While it is true algorithms and numerical simulations, models have been developed in all these fields, it is also true that differential calculus underscores that development and continued tweaking of those models depends on the actual math, not just crunching numbers into numerical or statistical data sets.
Li is correct when he asks at the outset 'Can you remember the last time you did calculus?' But that question could also be asked about linear algebra or finite mathematics, or a course in multivariate statistics. The point is that any form of advanced learned in high school or college will fall by the wayside if it is not used in some way later on, irrespective of how it was taught.
Li argues that he isn't saying calculus shouldn't be taught, as it is "great mental training" which is most gracious of him. But if nuclear warheads are going to be set off in detached form and land on my head, I'd be curious as to the math underlying the dynamics. I don't want to just read about it in the NY Times.
Where I do agree with him more, is when he criticizes the "single drive toward calculus in high school and college" which "displaces other topics more important for today's economy and society". These include "statistics, linear algebra and algorithmic thinking" (such as revealed in finite math.)
I concur because I've always been skeptical of the high school AP Calculus curricula and whether students are really of sufficient mental maturity that the courses serve any useful purpose (apart from the usual academic 'feather' in the cap to expand their choice of college). And I never saw the reason for pre-med students to be taking calculus. In each case then, perhaps some finite math course or statistics would better serve these populations as opposed to differential and integral calculus.
Calculus then, ought to be here to stay, certainly for most college math and science majors and perhaps even some others (e.g. Philosophy) interested in exploring the role of quantum mechanics in modern expositions, say involving quantum nonlocality and entanglement.