Medical Researcher Rediscovers Integration 473
parallel_prankster writes "I find this paper very amusing. From the abstract: 'To develop a mathematical model for the determination of total areas under curves from various metabolic studies.' 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.). Apparently this is called 'Tai's Model.'"
So how is a 16 year old report news? (Score:3, Interesting)
And he needs a computer to do it for curves (Score:4, Interesting)
While boat-builders use Simpson's rule on hull surfaces to estimate the displacement...with a slide rule and a sharp pencil.
Oh, but they're trained in Union apprenticeship programs and so could not *possibly* be as bright or talented or well-trained as a Doctor who went to University. And see? This Doctor has a publication! He must deserve 10X the salary of a boat builder.
Number of citations... (Score:2, Interesting)
The first link is even more amusing than the paper itself. Look at the number of citations the paper received!!! I mean, WTF???
No calculus? (Score:5, Interesting)
I don't know what kind of academic curriculum a student could choose these days that would permit them to pursue a career in medical research without ever having learned basic calculus at SOME point. I mean, when I was in high school, having taken AP Calculus AB was more or less a requirement for applying to almost any reasonably competitive four-year university. How do you enter a pre-med program without even knowing what an integral or derivative is? It seems completely implausible to me, given how competitive these programs have become. Moreover, that this author somehow thought it novel to estimate the area under a curve via trapezoidal approximation is not nearly as bewildering as the fact that they should have had the basic research skills to find that their "discovery" amounted to something that is regularly taught to high school kids. To me, that's the real scandal--that someone who can write a journal article doesn't know or care to look for prior research.
And 40 papers reference this one. (Score:5, Interesting)
About 40 papers supposedly reference this one.
Of course, I can't read them, because they're behind a paywall. The rights to the paper are owned by the American Diabetes Association, which supports something called the "Washington DC Principles for Free Access to Science" [dcprinciples.org]. This is a lobbying group against free access to scientific publications. They've been fighting open publication since 1994. Here's their latest output, opposition to the Federal Research Public Access Act, which would force all Government-funded research papers onto public servers.
Re:This is actually more impressive than it sounds (Score:4, Interesting)
Apparently most slashdotters do math on a daily basis. I can't recall the last time I needed to do integrals - in fact, if you had asked me 5 minutes ago how to calculate the area under a curve, I would have needed a trip to google/wolfram to look it up.
Can't really fault someone who isn't doing it on a daily basis for not knowing the "obvious" answer.
Re:So how is a 16 year old report news? (Score:4, Interesting)
>>His hubris must be punished by way of an Internet meme.
Tai me up?
Tai your shoelaces?
Could probably do something with Tai meaning "Red Snapper" in Japanese, or "Wife" in Chinese, but that might be a bit too highbrow for an internet meme.
In any event, it's not hubris to get excited about something you invented that you didn't know existed before. It's ignorance. I once explained to a CS professor this method I'd found for finding the greatest common divisor of two integers, and he cut me off by saying that Euclid had figured it out 2300 years ago. :p
Re:This is actually more impressive than it sounds (Score:5, Interesting)
There is a great short story by Jorge Luis Borges, called "Pierre Menard, Author of Don Quixote," wherein the titular character sets out of to write Don Quixote. The fact that Don Quixote was written by Miguel de Cervantes centuries ago is irrelevant. Pierre Menard does not try to copy Cervantes' work, and in fact he avoids reading it to make sure that it does not affect his own authorship. Instead, Menard goes out and makes it so that his combined life experiences inspire him to write a creative work, pulled out of his own imagination, that just so happens to conform, word-for-word, to the original text of Don Quixote. He is not the first to write it, but neither is he plagiarizing. He completes his masterpiece shortly before his death, and it goes largely unnoticed....
The story goes into a critical review of the piece and claims that due to the author's particular circumstances, it is artistically superior to the original Don Quixote.
This reminds me of that.
Re:No calculus? (Score:5, Interesting)
The scary part is this sentence:
"Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin".
Re:Ugh (Score:5, Interesting)
Actually, from the abstract this looks like a moderately interesting paper. Also note that the slashdot summary is (as often the case) wrong. You can't solve the problem the paper is referring to with integral calculus.
The curve that the paper is talking about is an experimental result, not a formula. All you have are the experimental samples from the curve. Without a formula, you CAN'T do integration, and must rely on a numerical technique. What he's 'invented' here is the trapezoidal rule. He'd do even better with something like Simpson's rule, but that might be impossible to apply if the sample points are not evenly spaced. Similar problems occur for the various Runge-Kutta methods.
Although the numerical technique that claims to be invented here is indeed a basic numerical technique, the paper is interesting for pointing out that the even cruder numerical techniques that have been used before are overestimating the curve area, and that is an interesting result.
Re:I am not surprise... (Score:5, Interesting)
We hated that. As it turned out, the faculty's supposition was correct. The majority of students could not write a simple declaratory sentence, much less a coherent paragraph. Grading them was a nightmare, especially the premeds who would cry and moan over 1 or 2 points. Try as we might, I doubt that we taught them a whole lot (either English or Molecular Biology)
Then at least some of them went to Medical School.
But medicine these days is a really a long, drawn out vocational school. There is very little 'Science' and even less 'Humanity'. It is memorize and practice. To a large degree this is unavoidable - there is a huge volume of baseline knowledge to acquire in a relatively short period of time. But given that the premedical experience is likewise short on science and humanities, your average physician really does not have the broad educational experience that many folks assume they do.
Calculus? That's some form of kidney stone, right?
Re:No surprise (Score:4, Interesting)
When our son was clearly guessing at the answer, we we simply walked through it. It went like this:
Dad: What is water made of?
Son: Hydrogen and Oxygen.
Dad: What is Hydrogen and Oxygen made of?
Son: Atoms?
Dad: What makes atoms weigh something?
Son: Gravity.
Dad: What is gravity?
Son: The force that pulls matter together.
Dad: OK, what happens what are you doing to the ice when you melt it?
Son: Making it hotter.
Dad: So, what happens to the atoms?
Son: The move faster?
Dad: And?
Son: They take up more space?
Dad: And?
Son: B, its weight stays the same!
This is not how math and science are normally taught. Normally, the same information is taught as "If you freeze water it's weight doesn't change. Remember that." If your lucky it is "If you freeze matter, its weight doesn't change. Remember that."
Yes, we could have just had him memorize the trivia, but instead we helped him "Rediscover" that mass doesn't change weight when you heat it.
The fact that a public school would just have him memorize the fact is one of the reasons we home school.
Re:And (Score:5, Interesting)
Actually the headline should say 'Slashdotter Rediscovers Paper from 1994 '
exactly... it's been a running gag in the biology department of our university probably ever since it came out back then
Re:Damning Followup (Score:4, Interesting)
Apart from the one you mentioned there's R Bender, "Determination of the area under a curve." and T M Wolever, "Comments on Tai's mathematic model.".
In my experience, an article has to be pretty damn bad to get any kind of commentary against it, but three? That basically means it's just as crazy as we think it is.
And sure, numerical integration is a rich field, but real advances in numerical integration aren't published in "Diabetes Care".
Doesn't have to be a math journal, physics or comp sci could be just as plausible, but a medical journal? Not really.
Re:No no no no, you didn't RTFA (Score:2, Interesting)
Integral is the limit of area as the size of the rectangles (and thus error) approaches zero. It uses this method as a starting point.
It isn't, and it isn't. It's typically taught in high school during introduction to calculus.
That said, reinventing calculus is no small feat, and certainly not worthy of mockery. Dr. Tai simply lacks education, which is something that should be addressed in med student curriculum.
Re:No no no no, you didn't RTFA (Score:5, Interesting)
TRWTF, IMHO, is that Tai's article is cited almost 40 times. I'd like to think it was meant as an April Fool's joke and got published too soon (in February).
Re:So how is a 16 year old report news? (Score:5, Interesting)
I peeked at one or two of the articles citing this paper:
"The glucose and insulin responses to the OGTT were analyzed by calculating the area under the curve (AUC). The AUCs for glucose (AUCglucose) and insulin (AUCinsulin) were determined according to the Tai procedure for the metabolic curves (25)."
DOI:10.1373/clinchem.2004.043109
http://dx.doi.org/10.1373/clinchem.2004.043109 [doi.org]
I wonder if this is sort of an inside joke now. Rather than saying we used the trapezoidal rule to approximate XYZ, everyone in the field now says "we used the Tai procedure". It sounds so much more 'official'. Remind me to reinvent the central limit theorem tomorrow.
And this doesn't help the people trying to fight the stigma that biology isn't a 'hard science'.
Re:And (Score:5, Interesting)
Re:This is actually more impressive than it sounds (Score:5, Interesting)
Concur. It is one of a number of devastating critiques by Borges of the various foibles of literary criticism itself - all told as very short delightful stories. "Pierre Menard" attacks the idea that examining the life of the author is necessary to evaluate a literary work -- that the work itself cannot stand on its own. He destroys the opposite extreme of literary criticism -- essentially the whole approach of deconstructionism - in "The Library of Babel" in which interpretations are read into works independent of any intended meaning of the authors (the books in the story are simply random combinations of symbols), and this was written in the late 1940s, 20 years before "deconstruction" was coined. Taken together he is defending the idea that books actually convey meaning themselves that a reader can apprehend.
And "Tlon, Uqbar, Orbus Tertius" is possible the most idea-dense work in the history of literature, it is a short story that plays with more concepts (with striking effect) than most "novels of ideas" (at the end of the 20th century the New York Times picked it as the greatest short story of the century). I am amused that the Wikipedia entry on the story (last time I checked) is longer than the story itself, but still fails to do justice to all the ideas presented.
Borges was easily the greatest writer of the 20th Century never to receive a Nobel Prize, and I would argue the greatest writer of the 20th Century, period.
Re:Number of citations... (Score:4, Interesting)
I would skim my girlfriend's Journal of the American Medical Association (JAMA) magazines occasionally and the studies people did in the same of science were appalling.
They'd make medical conclusions on best fit curves with regressions in the 0.5 range or populations of ~10-20 people. I understand the desire to move to a statistics based approach in medicine, but someone should teach medical researchers statistics. I've worked with engineers that have never had a stats course and they punch data into Excel. Get a curve fit with a ever no slight correlation and get all excited.
Compared to my boss who makes us explain every single outlier point, why it happened, and if possible collect new data if we can fix what went wrong.
Re:And (Score:4, Interesting)
.... this sounds so familiar... in the 1990's, one group inside Siemens discovered that contacts made of little carbon blocks can be used in CT scanners to transfer current and data from x-ray tube and detector (part of gantry that is moving around patient) to stationary part of gantry/scanner.
After proudly presenting that at internal meeting, one guy said: ".... but we have been using it for decades in trains.... for the same purpose..."
Re:And he needs a computer to do it for curves (Score:3, Interesting)
Re:So how is a 16 year old report news? (Score:4, Interesting)
So how do you estimate the error in your calculation due to differing density/thickness/weight throughout the paper? Do you cut up the paper into a thousand identical pieces and weigh each and determine the standard deviation? And then do you cut up multiple identical graph strips (and their inverses) to determine the errors in accuracy and precision in your scissors?
Yeah, pretty much. You'd be surprised at how accurate the method is, modern paper is actually remarkably uniform in composition so your error ends up lying mostly in your cutting technique.
It's not a perfect method but it ends up beating the pants off of most other methods of measuring the area under the curve, especially in how quick and easy it is to perform.
Re:So how is a 16 year old report news? (Score:4, Interesting)
> Rediscovering something can be really cool on a one off basis, but there isn't time to do that for the entire body of knowledge nor should we try.
I don't think anyone is arguing to try to teach the WHOLE domain of one field that way. We're talking about the _basics_. What is taught for today's Math is a total joke - kids aren't taught to think, just to mindless follow some "arcane formula". e.g. "Two weeks of content are stretched to semester length by masturbatory definitional runarounds." EVERYONE should read these two papers.
* A Mathematician's Lament
http://www.maa.org/devlin/LockhartsLament.pdf [maa.org]
* The Underground History of American Education
http://www.johntaylorgatto.com/chapters/index.htm [johntaylorgatto.com]