## Medical Researcher Rediscovers Integration 473

Posted
by
timothy

from the it's-all-mathy dept.

from the it's-all-mathy dept.

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.'"*
## Newton? Leibniz? (Score:2)

No, Tai.

## So how is a 16 year old report news? (Score:3, Interesting)

## Re: (Score:2, Funny)

Well, to be fair to the poster, the blog entry regarding the paper is only under 4 years old (March 2007)

## Re:So how is a 16 year old report news? (Score:5, Insightful)

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.

## 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:So how is a 16 year old report news? (Score:5, Insightful)

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.

## Re: (Score:3)

And this is how MATH should be taught. Lead people to discover the truths. When they discover it for themselves, it is memorable, and the sign of true enlightenment, rather than education.

We should be enlightening our children not educating them. Education is just "indoctrination" to scholarly principles, the recitation of useless facts without understanding or passion.

I still have no idea what a quadratic formula is used for. Don't bother telling me, because I don't care at this point. I learned it long ag

## Re: (Score:3, Insightful)

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 q

## 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]

## Re: (Score:3, Insightful)

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...

## Re: (Score:3)

Tai: So as you can see I used this method to calculate the surface underneath the graph, and as you can clearly see the results show that....

Fellow MD1: Wait, what method? That looks pretty sciency!

Fellow MD2: Cool method, did you think of it yourself?

Tai: Huh, I just calculated the surface underneath the graph, it's basic calculus you know?

Fellow MD1: Calculus schmalculus, did you think of publishing your method

Fellow MD2: Yeah you should totally publis

## Re: (Score:3)

Education is not the same as enlightenment.

The sad thing is, he probably had some level of Calculus in school, and probably memorized the formulas and rules, did the math and answered the questions and got a passing grade, all without understanding. Education doesn't require understanding, it is just indoctrination of scholarly principles.

Don't blame him for the error, blame the system that allowed it to happen.

## Re: (Score:3)

The hubris is in publishing it without doing any research first.

What's really piteous is that the reviewers didn't catch it.

## Re:So how is a 16 year old report news? (Score:4, Informative)

The really scary bit is the 137 citations that Google Scholar reports for this paper. (Link to the Canadianized version of Google Scholar [google.ca])

## 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: (Score:3)

And this doesn't help the people trying to fight the stigma that biology isn't a 'hard science'.The problem isn't that biology isn't a "hard science" (although some branches are pretty soft), the problem is that most MDs aren't real scientists. Ask any biology grad student what it's like to teach pre-meds and you'll get an earful. It's difficult for me to take the profession seriously any more; my employer and I combined are paying $700 per month in case I get sick and need to be treated by some overpaid

## Re: (Score:3, Funny)

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."

## Re: (Score:3)

You do not need to see the bullets. That's impossible. Instead only try to realize the truth. There are no bullets. Then you'll see, it's not the bullets that need to move, it is only the idea of where they are aren't.

## Re: (Score:3)

you assume he knew calculus before he started. In terms of relevance to us today, I see this kind of thing all the time in computing - why bother using the standard mechanism of performing a task when tyou can reinvent the wheel all over again. From the innumerable number of programming languages, to open source projects, to just my co-worker making up his own string class (gah!!)

Sometimes I wonder if its a lack of education (or more likely experience), or just bone-headed stubborness to understand anything

## Re:So how is a 16 year old report news? (Score:4, Insightful)

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.

## 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???

## Re:Number of citations... (Score:5, Informative)

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

## 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: (Score:3)

## Re: (Score:2)

Not only that, but the mathematical technique he describes is centuries old!

## Re:So how is a 16 year old report news? (Score:5, Informative)

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

## Re:So how is a 16 year old report news? (Score:5, Informative)

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.

## 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.

## 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.

## Re: (Score:3, Insightful)

reinventedintegration, not just learned how to solve a couple of integrals, right?It says something sad about the state of interdisciplinary communication that this was considered worthy of publication, but if you think it reflects poorly on his intelligence, you're missing the point.

## Re:And he needs a computer to do it for curves (Score:5, Insightful)

Given that this is highschool - level math, I'd say "reinventing" it primarily shows a shocking lack of education (for a doctor).

## Re:And he needs a computer to do it for curves (Score:5, Insightful)

Or evidence of having cheated his way through school like well over half of premeds [citation needed].

## Re: (Score:3)

In US high schools you are not required to take calculus. Students going to college usually take it, but the rest prefer not to.

## Re: (Score:3)

Way too much of the practice of being a doctor involves calculus to let that slide.

Almost none of the practice of medicine requires calculus. Trust me, I'm a doctor. There's a lot of use for calculus in medical research, and in deeper understanding of physiology - but it has no bearing whatsoever on my daily work.

## Re:And he needs a computer to do it for curves (Score:4, Insightful)

...he

reinventedintegration..."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.

## Re: (Score:3)

Maybe the GP didn't care to type the word 'numeric', since it is obvious.Never underestimate a /.ers ability to fail to note the obvious when they are trying to be pedantic.

## Re: (Score:3, Informative)

This isn't integration. This is a numeric technique for estimating the area under the curve (the trapezoidal rule). This is a somewhat different branch of mathematics to integral calculus, which deals in the infinitesimal limits to provide exact results. You can't use integral calculus here, as there is no formula to integrate, only experimental results.

It looks like this area is indeed in need of some interdisciplinary communication: what they really need is for a statistician to come up with a robust form

## Re:And he needs a computer to do it for curves (Score:5, Insightful)

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.

## Re:And he needs a computer to do it for curves (Score:5, Insightful)

## Re: (Score:3, Interesting)

## Re:And he needs a computer to do it for curves (Score:4, Informative)

I don't think it's possible for you to be paying $200k in taxes with an income of $400k and deductions of $100k for insurance premiums and another positive amount for supplies. Assuming $50k in supplies, and living in California with a 9.3% state income tax, your total income tax burden (including self-employed SS/Medicare) is about $110k, not even close to $200k. That would make take-home, after-tax pay $140k. If you live in Florida with no state income tax, your take home pay is about $165k. If you can't get rich off of that over the course of your career, you are doing it wrong, simple as that. Marry someone who is better at handling money than you.

Maybe your doctor friends are so rich that you have lost track of what "modest lifestyle" means to most people vs you?

## Re: (Score:3)

## Physicists rediscover medicine: (Score:5, Funny)

ABSTRACT:

Method for dissipation of influenza symptoms through prolong dietary restriction versus current methods of hypercaloric intake treatment of cold virus carriers.

## Re:Physicists rediscover medicine: (Score:4, Insightful)

Method for dissipation of influenza symptoms through prolong dietary restriction versus current methods of hypercaloric intake treatment of cold virus carriers.If you can find a way of making that

Method, you could probably get a patent.and apparatus...## Re: (Score:3)

ABSTRACT:

Method for dissipation of influenza symptoms through prolong dietary restriction versus current methods of hypercaloric intake treatment of cold virus carriers.

CONCRETE:

Composite construction material composed of cement (commonly Portland cement) and other cementitious materials such as fly ash and slag cement, aggregate (generally a coarse aggregate made of gravels or crushed rocks such as limestone, or granite, plus a fine aggregate such as sand), water, and chemical admixtures.

## Not so simple... (Score:5, Insightful)

## Damning Followup (Score:5, Informative)

## Re:Damning Followup (Score:4, Interesting)

threefollow-up commentaries to that article in the same issue.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

anykind 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

medicaljournal? Not really.## Re: (Score:3, Funny)

First, let me assure you that this is not one of those shady pyramid schemes you've been hearing about. No sir. Our model is the trapezoid!

## This is actually more impressive than it sounds (Score:2)

What I think is most odd about this is that no-one in his peer review group noticed that this is actually relatively trivial calculus. My nephew has recently applied to study medicine in the university and I was more than

## Re:Google the topic? (Score:2)

## 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: (Score:3)

"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 quot

## 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 writeDon Quixote. The fact thatDon Quixotewas 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 ofDon 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: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.

## I hate it when that happens (Score:5, Insightful)

## Re:I hate it when that happens (Score:5, Funny)

I was gonna say the same thing until I read your post :(

## Re:I hate it when that happens (Score:5, Insightful)

Nothing spoils the joy of having an original idea more than discovering it's actually a basic concept of another discipline.

I used to feel that way, but now I don't. I've learned to take some comfort from the fact that if it's already a time-tested and useful idea, I can feel confident that I got it right.

In my own field, there's often as much as a ten year lag before some young upstart grad student comes along and proves that my ideas are bogus, and I hate the suspense.

## Doing well (Score:3, Insightful)

Tai's model is obviously doing well its field, it has 38 citations with the last being in 2010.

## Y'all just got Riemann-rolled (Score:3)

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.

## Re:Y'all just got Riemann-rolled (Score:5, Insightful)

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.

## Re: (Score:3)

Of course not. A mathematician might have a PhD, but we all know he's not a

doctor, and thus he's not a peer, and you need a peer topeer-review an article.## 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.

## 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: (Score:3)

And it becomes really, really scary when you realize that this is the level of calculus applied to life-saving techniques in medical science. It can probably explain a lot of medical failures made every year...

## Re: (Score:3)

I don't think many medial mishaps would be corrected by a better understanding of calculus.

See now, it may actually be that a better understanding of calculus would result in

moremedical mishaps. Here's why:Although I think getting surgeons to simply count the number of utensils on the bench before and after each operation would help quite a lot.

It may just be a fluke, but I and several of my classmates observed when we got to high school calc that the higher we got in math the more basic arithmetic and counting errors we made. If this phenomenon holds beyond our ridiculously small self-selected sample (which is a BIG if) then the medical profession may be doing us a big favor by keeping their calculus skills dull, thus keeping the

## 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

againstfree 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.## No surprise (Score:4, Insightful)

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.

## Re:No surprise (Score:4, Funny)

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!

## Or a varation on that (Score:5, Funny)

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...

## Re: (Score:3)

To be fair, I don't think high school courses usually cover numerical approximations to integration. At least here in the UK, our equivalent courses cover analytical integration of continuous functions in one variable, with just a brief covering of the principles behind integration (using the rectangular approximation, IIRC, along with the notion that as the width of the rectangles approach zero the error introduced disappears). But only the analytical approach is actually tested, so I wouldn't be surpris

## 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.

## Ugh (Score:3, Insightful)

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.

## 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.

## Numerical techniques work too (Score:3)

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 [wikipedia.org] for a definite integral, right? QED it is integration via a numerical technique.

## it's everywhere (Score:5, Insightful)

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.

## Re: (Score:3, Funny)

My sister, a librarian, was laughing when relating a story of software engineer explaining to them the concept of meta-data with respect to a library collection. He acted as if this was a concept well beyond their grasp. She finally moved the discussion along by saying "You mean it's like a card catalog, and the records are like the cards in the card catalog?"

## I am not surprise... (Score:3)

## 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?

## Said Researcher (Score:3)

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.

## Also in chemistry.... (Score:5, Funny)

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.

## Integration by paper (Score:5, Informative)

## Re: (Score:2, Funny)

Simpson did it!

## Re: (Score:2)

Doh!

## Re:Next Paper .... Simpson's Rule (Score:4, Informative)

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.

## Re:Next Paper .... Simpson's Rule (Score:5, Informative)

Because you are too lazy to add it?

## Re: (Score:3, Informative)

Neither, apparently, did he. For the record, it isn't.

Myrevolutionary method involves drawing the graph on a piece of paper, sticking it on the wall and throwing darts at it with your eyes closed.## Re:No no no no, you didn't RTFA (Score:5, Funny)

Myrevolutionary 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.

## Re:No no no no, you didn't RTFA (Score:4, Insightful)

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.

## Re:No no no no, you didn't RTFA (Score:4, Informative)

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.

## Re: (Score:3)

An integral requires that you know a formula that describes the curve.

Not if you're using numerical methods it doesn't.

## 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).

## Typical Status Quo (Score:3)

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.

## Re:And (Score:5, Informative)

So... what's the story?

Actually the headline should say 'Slashdotter Rediscovers Paper from 1994 '

## 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: (Score:3)

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.

## Re:And (Score:5, Interesting)

## 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: (Score:3)

## Re: (Score:3)

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.