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Medical Researcher Rediscovers Integration
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.'"
ABSTRACT:
Method for dissipation of influenza symptoms through prolong dietary restriction versus current methods of hypercaloric intake treatment of cold virus carriers.
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First, does anyone have a link to the actual article? TFS only seems to include an abstract. Second, this was published in 1994. Third, while it may simply seem that the author is rediscovering integration, the field of numerical integration is actually a rather rich one. It's all well and good to say "take an antiderivate and evaluate at the endpoints", but for a function that is found experimentally this is essentially nonsense. While the submitter here claims that this article is simply rediscovering the trapezoid rule, there's actually no such evidence given in the Abstract--algorithms for determining how big of rectangles/trapezoids/etc to use in your calculations is actually an active area of research (albeit usually for the multidimensional case) and it is possible that this researcher did actually discover a better algorithm for deciding how to do the numerical approximations.
Really it should be under idle, it's just the fact that the dude forgot all about calculus and went back and remade the approximate method of integration. His hubris must be punished by way of an Internet meme.
Eat sleep die
Nothing spoils the joy of having an original idea more than discovering it's actually a basic concept of another discipline.
Given that this is highschool - level math, I'd say "reinventing" it primarily shows a shocking lack of education (for a doctor).
Or evidence of having cheated his way through school like well over half of premeds [citation needed].
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.
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". 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.
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.
I don't believe in time. It's a grand conspiracy designed to sell watches.
No better way to learn than to discover it yourself. You'll never forget Euclid's algorithm, but I have to look it up every time.
It's like that joke: what is 2+2?
Engineering student: (punching into a calculator) 4.000000000001
Math student: (after five months) I don't know, but I can prove it converges.
Premed: (immediately, from memory) The Gettysburg Address!
You may laught at this, but you find the same thing in all fields. Programming language designers are writing papers on decades old language features, user interface researchers are getting lots of citations for decades old ideas or gimmicks from scifi movies, and theoretical computer science authors are woefully ignorant of statistics and machine learning. Mathematicians and physicists aren't immune either.
Even if he isn't, the failure is on the journal for not properly reviewing the paper. If it's purportedly a mathematical paper (as in, the title starts with, "A Mathematical Model for....") then perhaps a mathematician should look at it.
I don't believe in time. It's a grand conspiracy designed to sell watches.
...he reinvented integration...
"Reinvented" is putting it a bit strongly, at least from the abstract of the paper (I, shockingly, don't have access to the Diabetes Care journal to see the full extent of the "discovery"). As well as I can gather, he noticed the area of a curve can be approximated by making a bunch of rectangles underneath it, and that you can be "clever" and add a triangle above the rectangles to get an even better answer. That's not even close to reinventing integration. To be honest, it's not even integration in a formal sense; no idea of limits seems to be used, for instance, or boundedness, infinite sums, or infimums/supremums.
Did he, say, find the fundamental theorem of calculus and derivatives, along with a few formulae like the binomial theorem which gives the usual power rule? Is he able to compute some integrals symbolically? If so, I'd be impressed. But, and without being able to read the article itself, he seems like a guy who got tired of counting cells on graph paper and noticed he could do a little better by drawing trapezoids.
Because you are too lazy to add it?
Diabetes Care February 1994 vol. 17 no. 2 152-154
That this study was stating the obvious was also noted 16 years ago. Unfortunately, often these follow up comments are very hard to find. Seeing all these comments, the article perhaps should have been pulled.
Diabetes Care. 1994 Oct;17(10):1223-4; author reply 1225-6. Comments on Tai's mathematic model. Wolever TM. Comment on: * Diabetes Care. 1994 Feb;17(2):152-4. PMID: 7821151
Diabetes Care. 1994 Oct;17(10):1224-5; author reply 1225-7. Tai's formula is the trapezoidal rule. Monaco JH, Anderson RL. Comment on: * Diabetes Care. 1994 Feb;17(2):152-4. PMID: 7677819
Diabetes Care. 1994 Oct;17(10):1225. Modeling metabolic curves. Shannon AG, Owens DR. Comment on: * Diabetes Care. 1994 Feb;17(2):152-4. PMID: 7821152
Diabetes Care. 1994 Oct;17(10):1223; author reply 1225-6. Determination of the area under a curve. Bender R. Comment on: * Diabetes Care. 1994 Feb;17(2):152-4. PMID: 7821150
Tai's article was printed in February of 1994. An author comment printed in the October 1994 issue is titled "Tai's formula is the trapezoidal rule." I don't have full text access to either, but the title of the followup is not encouraging.
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.
A. They cut out the plot and weigh the piece of paper. Then compare this with the weight of a piece of paper of known area.
There's a great ancient method for estimating curves that we used to use all the time in instrumental analysis.
You now have the area under the curve!
It's a lot quicker and easier than most other methods for estimating the area if you are dealing with a complex curve. Of course now that computers are used to gather the data instead of strip charts it's even easier for the computer to just add up the magnitude of all the data points and multiply by some constant to get a decent estimate.
Sapere aude!
Theory: All odd numbers above 1 are prime.
Proofs by discipline:
Philosopher: 3 is prime, 5 is prime, 7 is prime, therefore by induction all odd numbers are prime.
Physicist: 3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime...
Computer Scientist: 3 is prime, 3 is prime, 3 is prime, 3 is prime, 3 is prime...
Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime...
Statistician: In the same of odd numbers: 3, 5, 11, 13, and 29 they are all prime so all odd number are prime.
Artist: 1 is prime, 2 is prime, 3 is prime, 4 is prime...
That's OK, when I was a grad student in Molecular and Cell Biology, we of course had to TA the 100 level intro course which, of course, was on the pre med track. The faculty was on this kick that college students could not express themselves so they decided that all of the tests were to be exposition style. Sentences and paragraphs and the like.
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?
Faster! Faster! Faster would be better!
So... what's the story?
Actually the headline should say 'Slashdotter Rediscovers Paper from 1994 '
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
researchers will tend to insist that what they have handed over is raw data because they have (or a research associate, or Excel! has) only performed a few simple transformations on it and, that being many months ago, probably have forgotten the fact. one can either keep performing extra (unpaid and unasked for) analyses showing that this distribution verges on the impossible (and risk not be asked for help in future) or shut up and get cited and allow your reputation to grow
having said that, the same is true for many scientific practitioners and, indeed, the majority of published journal papers - the peer review generally doesn't extend to a competent mathematical practitioner (still less frequently a statistician) and most academics do not appear to consider that anything beyond their (often high school- or graduate-level) understanding of mathematics is required, after all (like the paper concerned here) building on previously published and highly cited work of little worth is all that's required for a career
This isn't as stupid as it sounds, because up to the 1980s spectrometers and chromatographs had pen-and-paper plotters, not personal computers for data recording. Numerical integration would've been a waste of time without a computer.
You subscribe to the common (and completely erroneous) delusion that doctors make a lot of money. While sure it might sound great to say your income is 400k a year as a specialist, and completely ignore the 10+ years of school it took to get there, the student loans, and since medicine is not really a career you can work your way through, that's 10 years of no income too. THEN give half of it to the government in taxes. THEN give half of THAT to the insurance companies for liability insurance. THEN pay for all your supplies. And then you can afford a modest lifestyle.
Love,
A physician.
Seven puppies were harmed during the making of this post.
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).
A successful API design takes a mixture of software design and pedagogy.
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
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'.
The story is one of the problem of overspecialisation. This is a very good example, because it's a very basic principle in mathematics that someone sufficiently advanced in the field of medicine to be publishing research papers. It's a problem all over academia, however. Pick up a journal from a distantly related field and you'll be pretty much guaranteed to see a paper inventing or discovering something that everyone in your field has known about for decades.
I am TheRaven on Soylent News
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.
Starships were meant to fly, Hands up and touch the sky - Nicky Minaj
My revolutionary method involves drawing the graph on a piece of paper, sticking it on the wall and throwing darts at it with your eyes closed.
I think you just rediscovered the Monte Carlo method.
Doctors tend to complain that they can only afford a "modest lifestyle" but tend not to understand what they have is generally well above "modest."
.... 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..."