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## Medical Researcher Rediscovers Integration473

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.'"
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## Medical Researcher Rediscovers Integration

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

on Monday December 06, 2010 @03:24AM (#34457744)

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

on Monday December 06, 2010 @03:47AM (#34457854)

Because you are too lazy to add it?

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

by Anonymous Coward on Monday December 06, 2010 @03:51AM (#34457868)

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

• #### Damning Followup (Score:5, Informative)

on Monday December 06, 2010 @03:53AM (#34457874)
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." [nih.gov] I don't have full text access to either, but the title of the followup is not encouraging.
• #### Re:Not so simple... (Score:2, Informative)

on Monday December 06, 2010 @04:10AM (#34457940)
You are far too generous -- there was a comment on this paper in the next issue of the journal entitled Tai's formula is the trapezoidal rule [nih.gov]. There is nothing complicated or clever about it.
• #### Re:Next Paper .... Simpson's Rule (Score:4, Informative)

on Monday December 06, 2010 @04:16AM (#34457976)

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:And he needs a computer to do it for curves (Score:3, Informative)

on Monday December 06, 2010 @04:22AM (#34458006)

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 formula for this taking into account the errors.

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

on Monday December 06, 2010 @04:29AM (#34458026)

There's a great ancient method for estimating curves that we used to use all the time in instrumental analysis.

1. take a strip of paper that has a graph on it
2. cut out two pieces
1. the area under the curve that you want to measure
2. a rectangle a certain amount of units high and wide
3. weigh each piece of paper
4. multiply the height and width (in the units you are measuring) of the rectangular piece
5. divide that by the weight of the rectangular piece
6. multiply that by the weight of the curve piece

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:And (Score:5, Informative)

on Monday December 06, 2010 @05:19AM (#34458176) Journal

So... what's the story?

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

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

on Monday December 06, 2010 @05:28AM (#34458202) Homepage
in a word, yes, check out almost any medical stats methodology - it looks sort of right if you have only degree level maths but, eg, statisticians have pretty much given up on pointing out that treating binned averages of a population as raw data typically invalidates the method under consideration, rendering the results speculative at best.

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

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

on Monday December 06, 2010 @06:56AM (#34458484) Homepage
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.
• #### Re:No surprise (Score:1, Informative)

by Anonymous Coward on Monday December 06, 2010 @07:22AM (#34458578)

You're unlucky, water is one of the few substance than expands when it solidifies. Why ? It's something to do with thermodynamics and the the state diagram of water and the slope of the solidification/liquefaction curve. Second ice doesn't get hotter when you melt it, it
first get to 0 degree celsius then it melts while staying at that temperature during the melting process (both the ice and the water are at that same temperature).

• #### Re:No no no no, you didn't RTFA (Score:3, Informative)

on Monday December 06, 2010 @07:45AM (#34458680) Homepage Journal

I don't know if dr. Tai's technique was an important new development

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.

• #### Re:So how is a 16 year old report news? (Score:2, Informative)

on Monday December 06, 2010 @10:07AM (#34459838)

The shell casings eject from the breech. The bullets fly out of the barrel at high velocity. Anything dropping out of the magazine means you have a broken magazine.

Unless the 'shooter' is just manually cycling the gun, then the unfired bullets would come from the breech.

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

on Monday December 06, 2010 @11:18AM (#34460604) Homepage

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

on Monday December 06, 2010 @11:25AM (#34460672)

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?

We can found no scientific discipline, nor a healthy profession on the technical mistakes of the Department of Defense and IBM. -- Edsger Dijkstra

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