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.


19 Responses to “Medical researcher discovers integration, gets 75 citations”

  1. 1 Bee

    🙂 Very amusing

    I remember some while ago I met a former classmate in the subway who had chosen to study economics. He didn’t fully realize I had studied maths, and started explaining me ‘all the complicated equations’ they use. Like, they use (ooh-ooh) functions. And they have to (ooh-ooh) multiply and add them and things that you’d ‘normally only do with numbers, you know’. When he told me they even have functions (ooh-ooh) that depend on more than one ‘thing’ (I believe he meant variable) I totally lost it. Luckily I had to leave next stop. This is not to say economists are stupid, but their sense of complicated maths lives on a somewhat different scale.



  2. 2 David S-D

    What a fantastic post — this is hilarious! How on earth did you find this?

  3. As a smug physicist myself, I did find this funny, but I can’t help thinking that this post makes us look worse than them. It has a slight tone of “what’s wrong with these cripples? Why don’t they just walk?” I’m sure you can find plenty of physicists saying spectacularly naive things about medicine or economics, so let he who is without sin, etc. Your point about the importance of interdisciplinary communication is a good one, but I fear such communication will remain the exception in the current academic climate.

  4. I couldn’t access the actual paper, but the abstract was enough. This is hilarious.

  5. 5 andy.s

    You should submit a paper which explains Simpson’s method. They’ll probably think you’re a wizard.

  6. 6 Alejandro Rivero

    On the other hand, I am very fond of a friend, an historian, who independently discovered the algorithm to do multiplications by hand. Really, he had forgotten the trick after years of computers, calculators and first-digit approximations, and when at age 30 he found it, he urgently called me to ask if the method of decomposing 26354*336=((26354*3)*100)+((26354*3)*10)+(26354*6)*1 was known.

  7. Dear Flip Tomato,
    just to enrich the post.
    Disclaimer: I am a PhD Student in Plant Biology with little knowledge of numbers. However, as soon as I saw the title of the article I thought, Is he talking about integration? I despise medics, they think they are the most perfect living beings on earth, but they are as normal as you and me. Anyway, I want to add some data to enrich this debate.
    Let’s talk about the article first. It was published in 1994 in a Journal with an impact factor of 7’8 (the eleventh out of 84 in its category). That means that it was reviewed and approved for publication by top medics, people that did not have time (or capacity) to check if someone thought that before.
    Ironically, or not, this paper has been cited 75 times, a good number, but certainly low for such an important journal, this proves that at least 75 (supposed to be) scientists didn’t know about integration approximation. Neither do I, but I can see a book from my desk entitled basic physics for life scientists that widely covers the subject.
    However, I have to defend scientific community. If you look carefully, you can see in PubMed that this article had four responses:
    Unfortunately, I do not have access to the responses, but their titles are self-explanatory:
    Determination of the area under a curve.
    Comments on Tai’s mathematic model.
    Tai’s formula is the trapezoidal rule.
    Modeling metabolic curves.
    Therefore, I suppose that the authors of the responses were aware of the mistake of Mr. Tai and tried to put things in order. This is a proof that scientific community is auto-regulated and does not rely on false assumptions.
    The discussion now is the criterion those 75 scientists used to ignore the responses an continue to use Mr. Tai “model”, but that is another story.
    Great post, and great blog. Kudos!

  8. 8 katm

    Hmmm… It took me one read through of the title to wonder why was so revolutionary about the article. It gave me a good laugh this morning. For some reason a line from M*A*S*H comes to mind. Hawkeye talking to Burns when he found a pot of KimChi thinking it was a land mine. “My God man! You’ve struck cole-slaw”. Don’t ask me why…

    As a former pre-med student (I came to my senses and went to grad school to get a degree in psychology) your description of the way pre-med students think about physics classes is spot on. I’m sure my class killed a large portion of the professor’s (a full professor, none the less) soul. Then again, after teaching pre-meds for many years (He taught intro physics to the NEOUCOM students (an accelerated undergrad/med school curriculum) for god only knows how many years) he might not even had a soul. I didn’t get excited about my physics classes until we started studying light and sound, which I saw as directly applicable to my interest in perception.

  9. 9 nobodyreally

    Nice post, made me laugh! There’s at least one future medic who will definitely not write that kind of paper though 😉

  10. 10 some geezer

    this one made me chuckle, reminds me of the time I discovered that the diagonal of a square was root 2 times its side in a chemistry lesson in 1988.


    You should send it to “bad science” on the guardian, that guy is a medic, a bit of a smug one about medics doing good maths.

  11. 11 robert

    A Cambridge pure mathematician points out that (a+b)^2=a^2+b^2+2ab: the Hardy-Weinberg (and you could hardly have two more impressive names than these) Equilibrium provides the foundation for quantitative genetics. Pascal abandoned math for more spiritual pursuits, until he fell victim to a terrible toothache (a potentially life threatening condition back in those days): his thoughts turned to the cycloid and, a couple of Pt 1b ‘maths for Nat Sci’ integrations later, the pain was gone. Such is the stuff of interdisciplinary badinage. However, given chest pains, a troubling twinge or a disconcerting lump; who are you gonna call? Ed Witten or one of these sub-numerate A+++ guys? Google Simpson’s rule + medical to see how things are progressing. Much as I respect Witten, and theoretical physicists in general, I would go for the money-grubbing and barely numerate sawbones.

  12. Robert, I’ve misconveyed part of my point. The issue isn’t that one should ask Ed Witten to diagnose an ailment. The `Tai Model’ is a little different. The paper isn’t about medicine but rather about dealing with data. I would expect that someone dealing with data (e.g. someone doing medical research related to… what was it, glucose curves?) should have familiarity in the relevant mathematical tools (e.g. calculus).

    That’s different from diagnosing suspicious lump where a background in statistics and calculus are not relevant compared to an encyclopedic knowledge of medicine. Someone dealing with controlled experiments is a scientist as well as a medic, and [most] scientists should know the basic mathematics to deal with data.

    It’s not that a physicist was teasing a doctor because the doctor doesn’t know string theory; it’s that person A is teasing person B for re-inventing the wheel within a domain of knowledge for which (I claim) person B should be responsible.

  13. 13 curious

    “Though, to be fair, in the 1960s group theory—unlike calculus—wasn’t something that physicists were expected to take during high school.”

    You’re kidding, right? Tell me you didn’t take group theory in high school..


    This is ofcourse the reflection of the real situation in our high school and predegree level teaching.Serious subjects like maths,physics ,chemistry are taught in our schools in the worst possible manner .Both teachers and students are running after marks and grades.The most pathetic situation is that the science students who integrate ,integrate and integrate for years actually dont know actually what integration is! I have talked about this to many science graduates who have passed with very high grades but their response was terrific that they all didnt know what integration is!But they know how to integrate a function if it is in the standard form given in text books.The main reason for this kind of shameful outputs from our students is the system of evaluating students.If our evalation system is giving importants to understanding than mugging up facts,atleast those who work in the field of science ,will be compelled to be aware of the basics of science.

  15. 15 Clucky

    > I don’t mean to pick on Dr. Tai

    Why not?

    > In fact, it’s perhaps a credit that s/he rediscovered the rectangle/trapezoidal method.

    Yes it is. I don’t make fun of him for his discovery. However, the fact that he thought he result was publishable shows (1) his extreme ignorance of mathematics, and (2) the fact that he did not make the slightest effort to check whether his discovery was anything new. And the fact that the journal published it shows that their review process is pretty worthless.

    You noted that physicists might say silly things about medicine. True, and there is nothing wrong with that. But if they try to publish their thoughts on medicine in an academic journal, then we should hold them to higher standards. At least, we should expect them to check with someone who knows something about medicine to see if their thoughts are at all worthwhile. And we would expect any journal they submit to, to hold them to these standards as well.

    > My more reasonable friends claim that this abstract isn’t really as amusing as I make it out to be.

    I don’t know about “amusing”, but it reflects *very* poorly both on Dr. Tai and the journal.

  16. Great post. I needed a goog laugh. Thank you.

  17. 17 lilliethomas

    well it is very common to find some extra ordinary peoples when you are travelling,the same concept on physics like you are describing here was represented to me by a person travelling in local train.and after looking their expression and the deep knowledge i am willing to go to local rain rarely.and wish to god that this type of accident never happen again. these type of persons press you to suicide.anyway it doesn’t mean that you did anything wrong,you did justice with the subject.not like him.
    i enjoyed.
    back pain exercises

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