Hacker News Reader

Comment by klodolph | Hacker News Reader

> When assembled precisely, analog computers can be much more accurate than digital computers on these types of questions.

Stopped reading here... whoever wrote the article is missing some critical pieces of the theory of how computers work or what computers are, as well as some basic understanding of how materials work. Mechanical computers are made with parts that have some finite tolerance in their manufacture as well as some measurable amount of flexibility in their parts and connections. Increasing the accuracy of analog computers requires developing new manufacturing techniques to reduce this error. On the other hand, making a digital computer more accurate just requires some extra memory and CPU time.

These analog machines are beautiful computers... but they are not more accurate than digital computers.

View on HN

Maybe they meant contemporary digital computers?

Although you're right, the claim that

> Because they use physical rather than digital inputs and outputs, they can represent curves and other geometric elements of calculations with an infinite level of resolution

is obviously bullshit, although the article does point this out:

> (though the precision of those calculations is based on how well their parts are machined, and loss from friction and slippage).

This is just a really roundabout way of not saying anything at all. "Analog computers can have infinite resolution, except for the fact that this is physically impossible." I could just as easily say, "I am a millionaire, except for the fact that I do not have that much money," or "My house is red, except for the fact that it is actually green, and no part is actually red, and I do not even have a house."

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."

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.

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.

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

I think the interesting question is are there scenarios where the practically achievable precision is good enough that the other benefits of analogue/mechanical results in a net win.

This is a point pondering hard about. Especially so, when we ourselves in the midst of programming with differentiable functions/programs approximated on digital computers.

One can see that one of the tools that will help us grapple with this question is rate distortion theory in general and quantization in particular.

Reply on news.ycombinator.com