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Comment by toolslive | Hacker News Reader

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.

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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

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.

Let's face it, that had that lab set up from before and didn't want to update it :D

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.

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://news.ycombinator.com/item?id=16032930

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

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-research...

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.

I hope that's a joke. The most basic numeric integration method is so simple I don't think it needed to be invented.

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.

It's a good example of why multidisciplinary research is essential though

> 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"?

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."

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.

Original paper, which appeared in Diabetes Care.

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/rediscover...

..and links to this, which talks about how wheels are reinvented all the time.

https://academia.stackexchange.com/questions/7360/how-common...

[0] http://scholar.google.com/scholar?cites=18129095207210817294...

[1] http://libgen.io/scimag/ads.php?doi=10.2337%2Fdiacare.17.10....

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)

I think the concomitant risk is that a human scissor operator can also apply bias, sometimes unconsciously.

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

I don't have actual numbers but it's pretty uniform.

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.

You could always use a stack of paper to average out the error.

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