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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.'"
No, Tai.
This Article 1. doi: 10.2337/diacare.17.2.152 Diabetes Care February 1994 vol. 17 no. 2 152-154
We were all warned a long time ago that MS products sucked, remember the Magic 8 Ball said, "Outlook not so good"
Simpson did it!
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.
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.
The first link is even more amusing than the paper itself. Look at the number of citations the paper received!!! I mean, WTF???
Nothing spoils the joy of having an original idea more than discovering it's actually a basic concept of another discipline.
Tai's model is obviously doing well its field, it has 38 citations with the last being in 2010.
Did it ever occur to anyone that the author is nothing more than a publication troll, seeing what exactly he can get away with? It's possible that the joke's on the journal, not the author.
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.
Life scientists don't get the same calculus we get as engineers.
This summer I helped a MD discover that factorials yield largish integers. At first I thought he was mocking me but it turned out that he really was serious.
Turns out that MD's are ordinary mortals after all.
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.
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.
Things that are ridiculous about this paper:
1) The man names the method after himself. I can see the smug look on his face when he figured out how to integrate, and decided to name his newfound discovery after himself. That's a big no no in science.
2) It's been cited 137 times since it was published. Most recently in June. That means that there has been ~137 people that cited it without seeing that it's just an integral.
3) It completely reaffirms the whole stereotype of the premedical student memorizing everything they need to get into medicine but understanding nothing.
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.
One of the papers that cites Tai's: http://www.lexjansen.com/wuss/2004/posters/c_post_the_sas_calculations_.pdf It includes a formula Tai 'invented' (quotes in the paper) and acknowledges that it is the trapezoid rule. I can't find Tai's full paper of course, but this article shows that Tai frighteningly might have been serious about his discovery, but also that at least some MDs took calculus.
As a physics grad student, I TA a LOT of life-science, pre-med students for introductory physics. In these courses, calculus is not necessary. Considering how horrific an average student performs when confronted a problem requiring more than 3 lines of algebra manipulations, I would not be surprised if there's a statistic somewhere more than half of MDs cannot do first-year college level math. I also tutored people taking the MCAT, again, calculus not necessary.
The only possible interpretation of any research whatever in the 'social sciences' is: some do, some don't
This isn't about not knowing the answer, this is about not knowing an answer might exist.
I would never blame anybody not to know details about stuff not within his field.
The catch phrase being "details". You should however be smart enough, to accept that you don't know everything and that it is no shame to ask a professional.
It's not like medical researchers do the statistical analysis of their data themselves on a regular basis.
All I ask for is the ability to identify what kind of problem it is you have and then start asking or reading.
It is even more sad, this went through review and got published.
While I'm already ranting, try asking a doctor what he thinks of amateurs (read: not a doctor) meddling in their field.
got a published article with a lot of citations in a high impact factor journal.
I'm sure he gives a shit what you think about it.
"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."
I haven't done any calculus in XY years but I guarantee you if someone asked "how do I figure out the area under a curve" I'd eventually answer "Calculus", at least before I wrote a medical journal about it and submit it for peer review. I mean he quotes the first chapter of my old calculus book almost exactly: "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."
Sorry but this dr deserves to be shot, next thing he'll be figuring out how to measure the sides of a triangle given then lengths of the other two sides.
my karma will be here long after I'm gone
Because you are too lazy to add it?
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.
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.
Though a very valid comment (Simpson's Rule would be better), note that you may not be able to apply Simpson's Rule here directly. The basic form of Simpson's Rule needs evenly spaced sample points, which might not be the case for experimental results.
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...
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
Correction: They do NOT win Nobel Prices.
They win fake prices set up by banks, names to be confused with real nobel prices, in an effort to leech on the publicity of the real nobel prices and somehow legitimize economics as a science.
HI O WISE PRINCE. WHT TOOK U SO DAM LONG?
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.
Neither, apparently, did he. For the record, it isn't.
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.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Wait, what?... When did integration require you to have a 'formula' for the function?...
Or rather to put it in another way; a data set as in the measurements from a lab test do translate into a function (for the points where we have data) and if we decide on how to interpolate between values we have a function which is continuous. So yeah, the slashdot item is spot on and you're probably in the same category as dr. Tai.
- These characters were randomly selected.
Without a formula, you CAN'T do integration, and must rely on a numerical technique. What he's 'invented' here is the trapezoidal rule.
You are aware that the trapezoidal rule is simply an approximation technique for a definite integral, right? QED it is integration via a numerical technique.
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.
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.
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It is not only that they don't understand mathematics. They also learn from their teachers that mathematical models are useless, and distrust anybody that uses math on their research.
Rethinking email
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.
.... 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..."
An integral requires that you know a formula that describes the curve.
Not if you're using numerical methods it doesn't.
I've abandoned my search for truth; now I'm just looking for some useful delusions.
To apply the rule for a polynomial term - "add one to the exponent of x, then divide by the new exponent",
Of course if you're talking about a numerical approximation to an integral it's different. But that isn't what rve said.
What rve said is irrelevant.
Before that rule existed, before the Fundamental Theorem of Calculus existed, "Tai's Method" was the way integration was done. And of course "Tai's Method" taken to the limit of zero-width trapezoids was fundamental to proving the Fundamental Theorem of Calculus.
Of course with non-zero width trapezoids it is merely an approximation... for a continuous function. For a function defined by discreet data points, and assuming you're linearly interpolating between data points, then this is as good as it gets.
Either way, the point is, this is anything but new or novel. It is how integrals were calculated literally hundreds of years ago, and it was never forgotten, at least not by anyone who took and remembers Calc I.
The enemies of Democracy are
I should add that it's a very difficult problem to solve. In general, people need a lot of specialised knowledge to make a valuable contribution to a specific field. Acquiring the same level of knowledge of multiple fields would take many years. That said, it's always worth spending time with people outside your own discipline. Richard Hamming, for example, claimed that he always had lunch with the physicists or chemists in his group, rather than with other mathematicians, and often provided or gained new insights into problems by approaching them from an unusual direction.
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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).
You'd be surprise how many academic papers cite other papers based on keyword matching and one-line sentence citations only.
Actually, some of the folks I know who worked early NASA efforts (Mercury-Apollo) did exactly this [weighing graph paper] as a means of integrating functions. Indeed, the graph paper they used was spec'd to have uniform density to within a specified tolerance - so that variations in thickness, etc. didn't affect the integral.