(PDF) https://www.ngs.noaa.gov/PUBS_LIB/GeoCenter_USA1.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.
The original paper was immediately followed (i.e. in the same issue) by two corrective articles, one titled "Tai's Formula Is the Trapezoidal Rule". So why did they publish it at all? This page discusses that question:
..and links to this, which talks about how wheels are reinvented all the time.
Funny anecdote, serves as a reminder to not take all academic literature as gospel.
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"?
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."
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)
The instruction videos alone are worth the visit. Geekery of the first order.
there's a remarkable feature of these old videos, they're so easy to follow. No matter the topic, analog gear-computers, car mechanics, wave principles & radio .. it's always fun yet quite precise. We've lost something here.
I was mulling the comment here a few days ago pointing out Heinlein's prescient depiction of networked computers, and thinking that the hard part would be having mechanical computers pick up the phone and sending electromagnetic pulses down the line. Perhaps pecking at telegraph keys ...
A analog device for performing Fourier analysis.
The other is the fucking fantastic Bay Model, a 1:1000 physical model of the San Francisco Bay: https://en.wikipedia.org/wiki/U.S._Army_Corps_of_Engineers_B...
It was built in the 1950s to study the effects of various plans, including one proposal to divert all incoming rivers to "productive" use. It was eventually made obsolete by computer simulation, but it's still there. I bring a lot of my nerdy out-of-town visitors there; it's amazing to walk around on a 2-acre simulation.
In the front right corner, in a structure that resembles a large cupboard with a transparent front, stands a Rube Goldberg collection of tubes, tanks, valves, pumps and sluices. You could think of it as a hydraulic computer. Water flows through a series of clear pipes, mimicking the way that money flows through the economy. It lets you see (literally) what would happen if you lower tax rates or increase the money supply or whatever; just open a valve here or pull a lever there and the machine sloshes away, showing in real time how the water levels rise and fall in various tanks representing the growth in personal savings, tax revenue, and so on.
“It’s a network of dynamic feedback loops,” Strogatz further writes. “In this sense the Phillips machine foreshadowed one of the most central challenges in science today: the quest to decipher and control the complex, interconnected systems that pervade our lives.”
I wonder how did they deal with thermal expansion. Maybe instead of using water at room temp they heated it to something higher and then a thermostat took care of it? But it still would be very hard to distribute heat evenly.
The part that reads bogus to me is the fractions of a mm, water meniscus is sensitive to contamination and diameter, its "always" been easier to measure liquid masses to higher sig figs than to measure liquid volumes, I suspect the journalist filter turned mg into mm or the precision scale produced repeatable results equivalent to fractions of a mm in the container. The only solution I can come up with that would work in that era would be something weirdly optical involving mirrors and multiple floats.
I vaguely remember a quarter century ago in a chemistry lab placing a beaker of distilled room temp water in a very nice precision scale as a demonstration while the instructor had us calculate how long it would take the inch or so of water to evaporate based on the slowly decreasing mass, and the result during a dry winter was somewhere around a month. The room must have been sealed and 100% humidity because small fractions of a mm in height would represent in a very hand wavy way around a minute of evaporation if represented as time in normal winter lab air. I also wonder how volume of water changes as CO2 is absorbed or emitted by the water, even the smallest gas bubble could mess up fraction of a mm measurements.
>The U.S. Army Corps of Engineers Bay Model is a working hydraulic scale model of the San Francisco Bay and Sacramento-San Joaquin River Delta System. While the Bay Model is still operational, it is no longer used for scientific research but is instead open to the public alongside educational exhibits about Bay hydrology. The model is located in the Bay Model Visitor Center at 2100 Bridgeway Blvd. in Sausalito, California.
Here is an interesting demo:
* "Thou shalt not make a machine in the likeness of a human mind."
Customer: the phone complains memory is full.
Rep: ok there is probably a memory leak.
Customer: no, it cannot be leaking since it is full!