6 ms·

If they had a plot of the function in a digital format that could be printed what stopped them from doing numerical integration?

• nestorD 8y ago
  It was not invented yet, the "Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves" paper came out in 1994... https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/ https://fliptomato.wordpress.com/2007/03/19/medical-research...
  • auxym 8y ago
    Before following your link, I was getting all ready to point you to Wikipedia's page on Simpson's rule (invented sometime in the 18th century). Funny anecdote, serves as a reminder to not take all academic literature as gospel.
  • konschubert 8y ago
    I hope that's a joke. The most basic numeric integration method is so simple I don't think it needed to be invented.
    • atleta 8y ago
      It's not. It's serious and sad. I remember a news article from a few months ago that exactly mentioned (and made fun) of this paper.
      • vanderZwan 8y ago
        It's a good example of why multidisciplinary research is essential though
    • tomxor 8y ago
      > The most basic numeric integration method is so simple I don't think it needed to be invented. Exactly, the individual who came up with that paper shows a complete lack of imagination, not merely ignorance - how someone (scientist or not) lacks the ability to see the likelihood of such a simple method having been discovered before is quite puzzling to me... This happens to be closely related to what I was doing recently: implementing a very simple little tool to integrate raw data, (I don't know calculus well at all) but here is my thought process (and probably most peoples): 1. I just want basic integration of raw data, something simple no interpolation at this stage. 2. hmm just draw a polyline through the points - how do I find the area it outlines (figure that bit out quickly it's just basic trig then some simplification, all very intuitive). 3. Ok that's how I find the area, I wonder what this is called it's too simple to not have been discovered hundreds of years ago... goes and does some searching to find matching definition. ... What kind of person gets to step 3 and marvels at their re-invention of the trapezoidal rule and goes straight to publishing a paper? How is it they are "doing science"?
      • ams6110 8y ago
        And how is it that the paper got reviewed and accepted for publication without somebody pointing out the obvious? As a 1980s high school student my first thought of how I'd find the area under a curve with a computer was basically to pick random points and see if they were above or below the curve. At the time I had about one year of exposure to Apple II basic. My math teacher said "yeah that's the Monte Carlo technique."
        • deleted 8y ago
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  • gumby 8y ago
    When I was learning to use a chromatograph (barely a decade ago) the textbook still suggested the "plate stacking method" to figure out the AUC (area under the curve): basically see how many rectangles fit under the curve.
  • yesenadam 8y ago
    Original paper, which appeared in Diabetes Care. https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf Reading it, it's quite hard to believe it wasn't a joke, but it doesn't seem to be. It thanks R. Kuc of Yale (a professor of electrical engineering) for his expert review. Google Scholar says it has 336 citations, most of which appear to be non-ironic[0]. The original paper was immediately followed (i.e. in the same issue) by two corrective articles[1], one titled "Tai's Formula Is the Trapezoidal Rule". So why did they publish it at all? This page discusses that question: https://academia.stackexchange.com/questions/9602/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper https://academia.stackexchange.com/questions/9602/rediscover... ..and links to this, which talks about how wheels are reinvented all the time. https://academia.stackexchange.com/questions/7360/how-common-is-it-to-inadvertently-reinvent-the-wheel-in-academia https://academia.stackexchange.com/questions/7360/how-common... [0] http://scholar.google.com/scholar?cites=18129095207210817294&as_sdt=2005&sciodt=0,5&hl=en http://scholar.google.com/scholar?cites=18129095207210817294... [1] http://libgen.io/scimag/ads.php?doi=10.2337%2Fdiacare.17.10.1233b http://libgen.io/scimag/ads.php?doi=10.2337%2Fdiacare.17.10....
  • deleted 8y ago
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• VLM 8y ago
  The user interface of scissors and scale is much faster than the human/computer user interface for numerical integration after fitting a smoothed curve to the measured data. The human scissor operator, in theory, can exercise far better judgment at throwing out invalid data points than an algorithm, when fitting curves. (When I was measuring datapoint 15 I know I was distracted, no surprise its an outlier, I can safely disregard it completely, etc)
  • greggyb 8y ago
    I think the concomitant risk is that a human scissor operator can also apply bias, sometimes unconsciously.