5 ms·

In the 1980s people in chemistry labs that needed to find the area beneath a curve used to print/plot the curve, cut out the area and weigh it. This worked quit

In the 1980s people in chemistry labs that needed to find the area beneath a curve used to print/plot the curve, cut out the area and weigh it. This worked quite well as they had accurate scales.

gugagore 8y ago
Ha! Very interesting. And the density of paper was uniform enough? Or maybe they used a different material?
- std_throwawayay 8y ago
  I don't have actual numbers but it's pretty uniform.
- toolslive 8y ago
  I'm not sure if they ever did a scientific study on this, but you can choose your accuracy by playing with the scale of the plot.
- vanderZwan 8y ago
  You could always use a stack of paper to average out the error.
_Microft 8y ago
There was one experiment in physics lab course (undergraduate level) just ten years ago in which we also had to integrate like this. Not because we lacked better methods but to have experienced that it can be done this way.
- konschubert 8y ago
  Let's face it, that had that lab set up from before and didn't want to update it :D
  - _Microft 8y ago
    I think it would actually have been easier to use current equipment than maintaining older but it was really about doing the work manually. Imagine it like having to learn to do mental arithmetics before being allowed to use a calculator. And so we got to write lists with data points or plot them with an X-Y plotter instead of automated collection of measurements. We hated it at times (noting a single value every 5 minutes is way more annoying that it might sound! The interval is too long to keep one busy and too short to do something meaningful in between) but in retrospect was the right way to learn to do experiments, in my opinion.
bno1 8y ago
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"?
niftich 8y ago
This reminds me of how the geographical center of the US was once found by balancing a cardboard cutout [1]; an accompanying document then explains the limitations and caveats of this method and of other methods which produce different results, while musing about the discrepancy between the ambiguity of the ask and the public's expectations of producing a clear and reproducible answer. [1] (PDF) https://www.ngs.noaa.gov/PUBS_LIB/GeoCenter_USA1.pdf https://www.ngs.noaa.gov/PUBS_LIB/GeoCenter_USA1.pdf
jaclaz 8y ago
More generally, there was a dedicated instrument to calculate areas of a map or drawing, the planimeter, widely used before the advent of (affordable) computing: https://en.wikipedia.org/wiki/Planimeter https://en.wikipedia.org/wiki/Planimeter https://news.ycombinator.com/item?id=16032930 https://news.ycombinator.com/item?id=16032930

In the 1980s people in chemistry labs that needed to find the area beneath a curve used to print/plot the curve, cut out the area and weigh it. This worked quite well as they had accurate scales.

gugagore 8y ago

Ha! Very interesting. And the density of paper was uniform enough? Or maybe they used a different material?

std_throwawayay 8y ago
I don't have actual numbers but it's pretty uniform.
toolslive 8y ago
I'm not sure if they ever did a scientific study on this, but you can choose your accuracy by playing with the scale of the plot.
vanderZwan 8y ago
You could always use a stack of paper to average out the error.

_Microft 8y ago

There was one experiment in physics lab course (undergraduate level) just ten years ago in which we also had to integrate like this. Not because we lacked better methods but to have experienced that it can be done this way.

konschubert 8y ago
Let's face it, that had that lab set up from before and didn't want to update it :D
- _Microft 8y ago
  I think it would actually have been easier to use current equipment than maintaining older but it was really about doing the work manually. Imagine it like having to learn to do mental arithmetics before being allowed to use a calculator. And so we got to write lists with data points or plot them with an X-Y plotter instead of automated collection of measurements. We hated it at times (noting a single value every 5 minutes is way more annoying that it might sound! The interval is too long to keep one busy and too short to do something meaningful in between) but in retrospect was the right way to learn to do experiments, in my opinion.

bno1 8y ago

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"?

niftich 8y ago

This reminds me of how the geographical center of the US was once found by balancing a cardboard cutout [1]; an accompanying document then explains the limitations and caveats of this method and of other methods which produce different results, while musing about the discrepancy between the ambiguity of the ask and the public's expectations of producing a clear and reproducible answer. [1] (PDF) https://www.ngs.noaa.gov/PUBS_LIB/GeoCenter_USA1.pdf https://www.ngs.noaa.gov/PUBS_LIB/GeoCenter_USA1.pdf

jaclaz 8y ago

More generally, there was a dedicated instrument to calculate areas of a map or drawing, the planimeter, widely used before the advent of (affordable) computing: https://en.wikipedia.org/wiki/Planimeter https://en.wikipedia.org/wiki/Planimeter https://news.ycombinator.com/item?id=16032930 https://news.ycombinator.com/item?id=16032930