[Юмор] Оказывается метод трапеций и прямоугольников...


Не сдержался, запостил сюда, а не в юмор. Мудрые модераторы, поступайте как хотите...
Medical researcher discovers integration, gets 75 citations
(Note: this post is `just for fun;’ no premeds, doctors, researchers, or nobel laureates were meant to be offended in the writing of this post.)
The bane of many American physics grad students is teaching introductory physics to premed students. Due to the nature of med school admissions, one ends up with classrooms full of students who cannot afford to get anything less than an A+++ if they hope to make it to (Ivy League) Med School. Further, due to the nature of medicine, these students also approach physics as something that’s meant to be memorized by rote. Note to premeds: every time you ask your TA what the relevant formula is so that you can memorize it, you kill a fraction of that poor grad student’s soul.
Not all premeds are like this. In fact, it may be true that most aren’t. But it sure needles the hell out of grad students when they have to teach those that are. It’s no surprise then, that there’s an uneasy tension between doctors and physicists.
So you’ll have to excuse me when I stuck out my tongue and blew a big raspberry to the medical community after I heard about the following paper:
A mathematical model for the determination of total area under glucose tolerance and other metabolic curves. M.M. Tai. Diabetes Care, Vol 17, Issue 2 152-154
(Try removing the phrase “glucose tolerance and other metabolic” if you find that title daunting.) I encourage you to take a quick look at the abstract, whose stated objective is this:
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.
Hint! If you replace phrases like “curves from metabolic studies” with just “curves,” then you’ll note that Dr. Tai rediscovered the rectangle method of approximating an integral. (Actually, Dr. Tai rediscovered the trapezoidal rule.) To top it all off, Dr. Tai decided to name this “Tai’s Model” and the medical community cited this paper 75 times.
It’s highly possible that I’m just an overly smug physicist, but I still find this especially amusing. No—it’s not an early April Fool’s gag. Nor does the abstract hint at any specialization of the basic mathematical tool (summing the areas of rectangles) beyond what is familar to any high school calculus student. Doesn’t second semester calculus start with estimating the areas under curves by drawing rectangles on graph paper?
Okay, you might argue that unlike physicists, not everyone in the world takes calculus. Fine—but if you’re a scientific researcher dealing with numbers and data, I should hope that you’ve had a complete high school mathematics curriculum. Isn’t calculus required for med school, anyway?
What I find really interesting is that the abstract notes that the Tai Model is significantly more accurate than other `widely applied’ methods. What could these other `widely applied’ methods have possibly been?
I don’t mean to pick on Dr. Tai, especially since I only have access to the paper’s abstract. In fact, it’s perhaps a credit that s/he rediscovered the rectangle/trapezoidal method. Further and more seriously, this paper is perhaps an important example of the importance of interdisciplinary communication.
My more reasonable friends claim that this abstract isn’t really as amusing as I make it out to be. And to be sure, they’re right.
Murray Gell-Mann developed the “eight-fold way” to explain the spectrum of hadrons in the 1960s. It wasn’t until after he’d developed this formalism that he discussed his model with mathematicians, who then told him that he’d rediscovered group (representation) theory. This ushered ina new era in the history of particle physics where symmetry became our guiding light and group theory became a necessary tool for any particle theorist. Though, to be fair, in the 1960s group theory—unlike calculus—wasn’t something that physicists were expected to take during high school.
Anyway, the lesson here? It doesn’t hurt to keep in contact with your friends that are outside your professional field. Once in a while they might be able to tell you something useful.



прикольно, что статья 1994 года. видимо тогда не было гугла и некуда было вбить "calculate area under the curve"


Мне вот неделю назад человек совершено не связный с МГУ прислала ссылку на эту же статью, учитывая что сама заметка трехлетней давности то что, кто-то где-то подбросил говна на вентилятор?
Though, to be fair, in the 1960s group theory—unlike calculus—wasn’t something that physicists were expected to take during high school.
Как-то странно в контекст того, что физики уже должны бы были вполне быть знакомы с теорий групп (Группа Гейзенберг, Преобразования Лоренца) разве нет?


Прикольно, что на нее до сих пор ссылаются...


Честно говоря, далеко не все физики понимают теорию групп. Отдельного общего курса алгебры у нас нет, теория групп преподается на линале... К группам преобразований многие относится как просто к неким формулам перехода от одной системы к другой, не выделяя ее теоретико-группового смысла.
Я сам теорию групп не использую вообще... Хотя при желании мог бы ее приятнуть в одну статью (как раз этого года но зачем?.. И так все клево получилось.


теорию групп
когда в физике это пошло косяком это в то время даже называлось (из серии физики шутят) групповым сумасшествием в физике
PS в юмор для истории перепости :) а то ищи потом в архиве




Как-то странно в контекст того, что физики уже должны бы были вполне быть знакомы с теорий групп
У физиков проблема математизации тоже встаёт регулярно. Не так жестоко, но тоже временами остро.
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