Gears of war: When mechanical analog computers ruled the waves
arstechnica.com
arstechnica.com
Physical machines have varying levels of tolerance, and this impacts the accuracy of calculations in just the same way as a truncated number in a digital system reduces accuracy.
It was a lot more interesting to read about the pros and cons of digital vs analog computers with respect to maintenance, reprogrammability, energy use, and reliability. It's a pity there wasn't a similarly in-depth account of the precision of each system.
I suppose it's forgivable that the author didn't think of these things but they should have run their technical article past a subject expert before publishing it. This isn't a nitpick, they screwed up the core concept of their article!
> there wasn't a similarly in-depth account of the precision of each system
That's because digital circuits won the "precision wars" so spectacularly that there was no need for comparison. On a digital computer, you can just keep adding bits to your datatype, doubling your precision with each bit, until you are happy. Bits cost almost nothing today (and very little 30 years ago) so you use as many as you need. If you underestimate how many you need, that's a planning problem, not a limitation of the digital technique. Meanwhile, the price of increasing the precision of an analog computer (mechanical, electrical, or fluidic) shoots up dramatically after a few decimal places and goes to infinity after a few more. That is a limitation of the analog technique.
Here's a fun demo of how the digital nature of a circuit grants it complete noise immunity (within tolerances), unlike any analog circuit that could ever be built:
Before a digital circuit can process a signal, it must first be quantized, an inherently analog process. Your digital data is only as good as your analog signal, plus inherent quantization noise[1]. In addition, any mixed-signal IC represents a design compromise between digital and analog constraints.
Any signal processing system is inherently limited by the SNR of its source signal. There is no point in building a more accurate converter than the noisiest component of your input data. In fact, when metrologists are trying achieve the maximum accuracy in their measurements, it is not uncommon to leave a test circuit on for days at a time, in order to reach a thermal equilibrium to minimize the seebeck effect[2].
And when engineers to need to make the most accurate of measurements, what do they turn to? Analog circuits. The world's most accurate voltage reference, the Kelvin-Varley Divider, dates back to the late 19th century[3]. For a modern example of a precision reference, see Jim William's excellent white paper, "Quantifying Silence"[4].
[1] http://en.wikipedia.org/wiki/Quantization_(signal_processing...
[2] http://www.keithley.com/knowledgecenter/knowledgecenter_pdf/...
[3] http://en.wikipedia.org/wiki/Kelvin%E2%80%93Varley_divider
[4] http://cds.linear.com/docs/en/application-note/an124f.pdf
Yes, you are limited by your measurement, but you are so limited when operating entirely within the analog domain as well. Therefore it makes sense to make your measurements as accurate as possible, quantize once, and be done with it. Keeping it in the analog domain merely allows more points for noise to enter the picture.
> There are no least significant digits dropped, and answers are continuous rather than dependent on “for-next” clock-driven computing cycles.
Even if the article had talked about improving accuracy by skipping the digitizing step for gyroscopes, wind vanes, etc, his claim would not have been credible. It's not terribly difficult to digitize mechanical motion to the subatomic level (AFM is from the '80s) and many modern data sources (ring-laser gyroscopes, information acquired from remote ships and satellites) could not be coupled to the mechanical computer in a way that could be expected to beat digitization error.
A GPS chip likely has something to gain from correlating in front of the analog front end but a firing computer does not. You pay a fixed cost to go in and out of a digital representation, but with analog you keep paying for each calculation and, given that one of these firing computers weighed 3000lbs, I expect that this application saw digitization errors that were tiny next to calculation errors.
Thanks for being thorough, but I see your post as a tangental point rather than as a counterargument.
https://www.youtube.com/watch?v=s1i-dnAH9Y4
edit: This video is the same footage featured throughout the article, in fact.
I can kinda get my head around slow moving ships being tracked by a mechanical computer, but the Russian ZSU-23-4 Shilka self propelled anti-aircraft artillery vehicle used an electro mechanical gun aiming computer in the 60s and 70s.
A mechanical computer that can track a supersonic rapidly manoeuvring jet aircraft by radar, and adjust the aim of its guns quickly enough and accurately enough to score hits. It's amazing what can be achieved.
This line of one commercial just blew my mind: 'the less they know, the safer they are' ...can a security oriented company actually get away with saying that?!