Flutterby™! : Rediscovering calculus 2011-01-05 00:42:39.69066+00

Rediscovering calculus

2011-01-05 00:42:39.69066+00 by Dan Lyke 10 comments

A mathematical model for the determination of total area under glucose tolerance and other metabolic curves. M M Tai.

OBJECTIVE--To develop a mathematical model for the determination of total areas under curves from various metabolic studies.
RESEARCH DESIGN AND METHODS--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. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method (less than +/- 0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin.

Yay! M M Tai has rediscovered the trapezoidal rule for approximating the integral!

The fun part? Google tells me that it's been cited by 136 other papers. That means a whole lot of doctors have apparently never heard of calculus.

Hat tip to J. J. Campanella.

peer reviewers for medical papers aspire to get paid (under the table) as patent examiners as well.

Eric, this suggests that the peer reviewers for medical papers are moonlighting as patent examiners.

I didn't go into this deeply, but I'll bet this thing was even peer reviewed. I wish I'd been able to get tenure that easily!!

I think you all missed the point. The article seems to prove that a Reimman Sum works even if the data are related to diabetes. Because, as you know, math may behave differently depending on the kind of data you are working with. Right?

#Comment Re: made: 2011-01-05 21:13:00.319867+00 by: m [edit history]

He has a whole lifetime of discoveries ahead of him. The various models of Simpson's rule. Monte Carlo integration. And best of all, determining the area under the curve by cutting the curve out and weighing it!

It seems to me that the problem with the Hellenistic scientists was that they didn't have printing. Knowlege might get handwritten onto a scroll, which might get copied to the Library of Alexandria or not. Or the scroll stored in a damp closet in Utrect might not survive as well as one in hot, dry Damascus. The knowlege was very fragile, in a physical sense. The other issue was their viewpoint on how the information was supposed to be used. Hero of Alexandria had pistons, rods, and steam boilers; everything he needed to build a reciprocating steam engine. So, why didn't he? I suspect a part of it was that a proper Greek gentleman didn't worry about pumping out mines or carrying heavy loads since they had slaves for that sort of thing.

DaveP, I think we go through a lot of such cycles. Small and large. The current maker and steampunk societies are having fun re-inventing things a previous generation relegated to mass Chindia production.

Science is often "forgotten" and rediscovered. I'm reading The Forgotten Revolution at the moment, which talks about all the stuff that was forgotten between the end of the Hellenistic Age and the Renaissance. Oy.

#Comment Re: calculus made: 2011-01-05 02:11:09.04918+00 by: papa0so

Whoa, this sure brings back memories... memories I'd rather not remember! Oh well, at least I passed my classes and earned my degree :D

#Comment Re: made: 2011-01-05 01:34:33.682799+00 by: meuon [edit history]

I remember (fondly) "inventing" the "bubble sort"... and you said somthing like: "Oh yeah, that's a bubble sort, you learn that first year in school.".