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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.'"
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.
t
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.
Tai's model is obviously doing well its field, it has 38 citations with the last being in 2010.
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.
>>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
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.
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.
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.
The really scary bit is the 137 citations that Google Scholar reports for this paper. (Link to the Canadianized version of Google Scholar)
In any event, it's not hubris to get excited about something you invented that you didn't know existed before. It's ignorance.
The two are not mutually exclusive. Going so far as to publish a paper describing something he is expected to have learned in high school or at least in college is over the top.
Its pretty bad that the peer review didn't catch it either...
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.
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.
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!
Brilliant. So an American high school student watches the bullets fall from his friends clip as he fires on a random teacher, and thinks "I shall call it Gravity, yo."
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
That's the difference between software "engineering" and any other form of engineering. Maybe in another 200 years programmers will be there, civil and electrical disciplines have had a fair head start.
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.
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.
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
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.
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..."
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
And this is how MATH should be taught.
Maybe some bits can and should be taught that way, but the body of knowledge in mathematics is too large to try and teach any significant portion that way. It's taken humanity many lifetimes to discover what we know, one person doesn't have that long. 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. Discovery is about the need to know and understand and the drive to sate that need. It's hard to teach those qualities when someone wants everything laid out for them.
As for the quadratic equation, well applications for that are as numerous as applications of algebra. I would give examples but as you've stated your willful ignorance already I suspect that examples wouldn't have helped you in school either. I sense a lot of finger pointing in your tirade. I'm curious why you feel that way when so many others have gone on from the same educational systems (or even foreign ones that are even more hard-line/drill based) to figure things out and make great discoveries.
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.
Sapere aude!
> 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
* The Underground History of American Education
http://www.johntaylorgatto.com/chapters/index.htm