[cix_pkez]

While I found your comment funny, I could stand to be a bit more charitable. I think it's an interesting side point they're trying to make about analog computation, but to be accurate should maybe be written more like "A theoretical perfectly-machined set of gears could perform calculations to infinite precision."

[klodolph]

I don't know how to be charitable here, the side note is completely wrong, and I'm not sure what interesting point could be made here.

A theoretical perfectly-machined set of gears is a mathematical construction, not a physical construction. It seems reasonable to me that a mathematical construction could have infinite precision, but it is obvious that a physical device has limited precision. An analog computer is a physical device. We might as well pretend that a digital computer has infinite RAM and an infinitely fast CPU, if we are in the business of assuming that an analogue computer is infinitely precise.

In general you can make many of the same engineering tradeoffs with simple analogue computers. A cam wheel can encode a function, and by adjusting the size, manufacturing tolerances, and materials you can control the amount of error that the cam wheel gives you when calculating the function. Similarly, with a digital computer you can adjust the number of digits used to represent numbers, the size of lookup tables, the number of iteration for iterative methods, etc. and control the amount of precision a digital computer provides.

[cix_pkez]

I mean, you could definitely convince me that it's not an aside worth including in the article for the sake of staying on point.

I'll still take Ars at its worst over most general news sites' tech reporting at its best.

[gugagore]

If anyone is interested in this kind of model of computation that has infinite precision: https://en.m.wikipedia.org/wiki/Real_computation