And yet, it's really important to learn math! One of the regular complaints heard from pre-med students is that they're forced to take some physics (which requires math) in order to get into med school. They complain they'll "never use it" or some other similar whine. But, here's an article, published in 1994 in the journal "Diabetes Care," a high-impact, peer-reviewed journal, where the author describes an incredible new way of calculating the area under curves (which she then names after herself!):
In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve.In other words, the so-called "trapezoid method," known well since the time of Isaac Newton, around 300 years earlier! This method is well documented in every calculus textbook out there, and yet this paper got published, and is cited (often!). While I think that having science literacy is an integral part of being a functioning member of an advanced human society, at a most basic level, a nice outcome of science literacy is that you (either as an "author" or a "reviewer") don't seem like a total moron!
Fortunately, many people responded to this article with nicer versions of "You moron!", but her indignant defense was, and I paraphrase, "I didn't know about this rule before, and I figured it out myself, so it's still original, and I can publish it!" While I commend her figuring it out (I really do!), original (i.e. publishable) research is not just something you figured out by yourself, it is something that no one else has figured out before! The "find out someone already did this" and "they figured this out 50 years ago" phases are an integral part of the scientific method, as described nicely in this rage comic from the Electron Cafe:
Wow - this post is great.
ReplyDeleteThe bottom half of the flowchart is amazingly accurate
Flexibility to vary your integration constants is not only good to relieving monotony, but can also save a lot of work, and reduce chance of error.
ReplyDeleteAs a representitive example, suppose you've integrated Navier-Stokes for viscous constant pressure gradient incompressible time independent flow, to find
u = -(G/2 mu) y^2 + C y + D
and want to match boundary value conditions at y = +h/-h (for fixed boundaries or shear flow as you please). You'll be much better off if you choose your constants to be
u = -(G/2 mu) y^2 + C y + D + G/(2 mu) h^2 +-h C
These adjusted constants automatically kill off the contributions at the boundaries.
That's a really good point!
DeleteAdding a function that generates arbitrary constants is an awesome idea; but I wonder if there are any math semi-literate readers who will accidentally add one whose output does not span the reals (sqrt, sin).
ReplyDeleteWhere did you find Tai's paper, and how did you manage to keep yourself from referencing Anne Elk while discussing it?
ReplyDelete