6 ms·

>>> Don’t speed and efficiency make up the entire set of practical uses for digital computing? A couple more uses: First is "noise immunity:" The fact that you

>>> Don’t speed and efficiency make up the entire set of practical uses for digital computing? A couple more uses: First is "noise immunity:" The fact that you can perform a computation twice and get the same answer, and chain multiple processing steps together with no degradation. Though to be fair this includes digital computation by pencil and paper. Second, complex operations that simply can't be conceptualized in the analog domain.

dahart 3y ago
You’re totally right about chaining and repeated computations, however I think it’s possible to do this with analog machines as well by factoring in threshold in and precision tolerances. Digital floating point has precision limits too, they’re just a different kind (I’m referring to rounding, for example). I know that’s not at all what you meant about noise, I’m just saying the bigger picture is that both digital and analog computation has limited precision, and both can have increased precision and can meet specific tolerances by adding more wires. Typical fp32 and especially fp64 has way higher precision than a typical single analog signal, but that doesn’t mean that very high precision with analog isn’t possible, it just means we don’t often do it. The fundamental differences might be less black and white than you or the gp imagine.
- corethree 3y ago
  >I think it’s possible to do this with analog machines as well by factoring in threshold in and precision tolerances. With enough compositions even the smallest tolerances will add up. This presents a scaling problem in analog electronics. With the miniaturization of electronics into nano scale components this noise is even more prevalent. Additionally the way a transistor works it's just easier to use these things in saturation mode. And one more thing. Yes precision can be "equivalent" but exactness is not. An analog computer cannot represent the value 1 consistently. It essentially can never be precise. There will always be noise on the voltage. A digital computer has finite precision but it has exact finite precision.. so it can represent the exact integer 1. And you can increase precision arbitrarily by using more bytes up to the point where you use up all available bytes in memory. You don't technically have to use the default floating point values which have limited size. With an analog computer you cannot do this at all.
  - dahart 3y ago
    > With enough compositions even the smallest tolerances will add up. This is true of digital floating point too, chained compositions lose precision. > A digital computer has finite precision but it has exact finite precision.. so it can represent the exact integer 1. I’m not sure what you mean here exactly. Most real numbers cannot be represented exactly, and the idea of an exact number in digital integers and/or floating point still comes with a tolerance range. It’s only possible to have an exact number by construction or a-priori knowledge, but not in general and especially not when processing input data. It is possible to have an “exact” analog number, within a tolerance range. > With an analog computer you cannot do this at all. That’s incorrect. It’s true a single analog signal has noise and not incredible precision / resolution. That’s not a limitation of analog computing in general, it’s a limitation of choosing to use a single signal. You don’t have to use only a single signal. If you used, say, one analog signal per decimal digit, you can have as much practical precision as you can afford digits/signals. Then it becomes a bit more “digital” but the math doesn’t need to be implemented using gate logic. Digital lines also have analog noise, we just threshold and abstract it away. The line between digital and analog is always there but you can move it. It is possible with analog circuitry to quantize a signal and/or interpret and have an analog ‘repeater’ that will rectify the signal into the interpreted value, correcting for line noise. This way it’s possible to do some amount of integer math without introducing noise into the result. This isn’t common or particularly practical, but it does help clarify what analog and digital really mean. Hey you’re right about these being common issues, and about the typical advantages of digital logic, you’re just overstating the limitations and fundamental differences between digital and analog, and making assumptions about where that line is being drawn without considering all possibilities.
    - analog31 3y ago
      A good exercise is to look at the "eye diagram" of something like an Ethernet or USB signal. Google will return plenty of hits, but here's one: https://www.testandmeasurementtips.com/basics-eye-diagrams/ https://www.testandmeasurementtips.com/basics-eye-diagrams/ Thought of as an analog signal, it looks like a mess. In fact, you don't know if it's an analog or digital signal from the picture alone. What makes it a digital signal is a convention for interpreting it as a discrete sequence of symbols. The convention is designed so that under reasonable conditions, the interpretation is unambiguous. "Noise" is ill defined by itself. It means an unwanted fluctuation of a signal. If the digital signal is correctly transmitted and received, it is noise free, regardless of what it looks like on an oscilloscope. On the other hand, "analog" doesn't just mean any continuous electrical signal. It means that a signal represents a quantity, such as temperature or acoustic pressure. It can't be noise free. If thresholds are applied to define discrete values of the quantity, then it's not analog any more. There is a profound amount of confusion about this, so I'm sympathetic. I dabble in some audio electronics, and there are endless debates about whether Class-D amplifiers are "digital" or not. They are certainly marketed as digital. ;-) The vagaries of floating point arithmetic, the possibility of errors in digital systems, and whether anything physical represents a real number, are interesting but basically sideshows.

dahart 3y ago

You’re totally right about chaining and repeated computations, however I think it’s possible to do this with analog machines as well by factoring in threshold in and precision tolerances. Digital floating point has precision limits too, they’re just a different kind (I’m referring to rounding, for example). I know that’s not at all what you meant about noise, I’m just saying the bigger picture is that both digital and analog computation has limited precision, and both can have increased precision and can meet specific tolerances by adding more wires. Typical fp32 and especially fp64 has way higher precision than a typical single analog signal, but that doesn’t mean that very high precision with analog isn’t possible, it just means we don’t often do it. The fundamental differences might be less black and white than you or the gp imagine.

corethree 3y ago
>I think it’s possible to do this with analog machines as well by factoring in threshold in and precision tolerances. With enough compositions even the smallest tolerances will add up. This presents a scaling problem in analog electronics. With the miniaturization of electronics into nano scale components this noise is even more prevalent. Additionally the way a transistor works it's just easier to use these things in saturation mode. And one more thing. Yes precision can be "equivalent" but exactness is not. An analog computer cannot represent the value 1 consistently. It essentially can never be precise. There will always be noise on the voltage. A digital computer has finite precision but it has exact finite precision.. so it can represent the exact integer 1. And you can increase precision arbitrarily by using more bytes up to the point where you use up all available bytes in memory. You don't technically have to use the default floating point values which have limited size. With an analog computer you cannot do this at all.
- dahart 3y ago
  > With enough compositions even the smallest tolerances will add up. This is true of digital floating point too, chained compositions lose precision. > A digital computer has finite precision but it has exact finite precision.. so it can represent the exact integer 1. I’m not sure what you mean here exactly. Most real numbers cannot be represented exactly, and the idea of an exact number in digital integers and/or floating point still comes with a tolerance range. It’s only possible to have an exact number by construction or a-priori knowledge, but not in general and especially not when processing input data. It is possible to have an “exact” analog number, within a tolerance range. > With an analog computer you cannot do this at all. That’s incorrect. It’s true a single analog signal has noise and not incredible precision / resolution. That’s not a limitation of analog computing in general, it’s a limitation of choosing to use a single signal. You don’t have to use only a single signal. If you used, say, one analog signal per decimal digit, you can have as much practical precision as you can afford digits/signals. Then it becomes a bit more “digital” but the math doesn’t need to be implemented using gate logic. Digital lines also have analog noise, we just threshold and abstract it away. The line between digital and analog is always there but you can move it. It is possible with analog circuitry to quantize a signal and/or interpret and have an analog ‘repeater’ that will rectify the signal into the interpreted value, correcting for line noise. This way it’s possible to do some amount of integer math without introducing noise into the result. This isn’t common or particularly practical, but it does help clarify what analog and digital really mean. Hey you’re right about these being common issues, and about the typical advantages of digital logic, you’re just overstating the limitations and fundamental differences between digital and analog, and making assumptions about where that line is being drawn without considering all possibilities.
  - analog31 3y ago
    A good exercise is to look at the "eye diagram" of something like an Ethernet or USB signal. Google will return plenty of hits, but here's one: https://www.testandmeasurementtips.com/basics-eye-diagrams/ https://www.testandmeasurementtips.com/basics-eye-diagrams/ Thought of as an analog signal, it looks like a mess. In fact, you don't know if it's an analog or digital signal from the picture alone. What makes it a digital signal is a convention for interpreting it as a discrete sequence of symbols. The convention is designed so that under reasonable conditions, the interpretation is unambiguous. "Noise" is ill defined by itself. It means an unwanted fluctuation of a signal. If the digital signal is correctly transmitted and received, it is noise free, regardless of what it looks like on an oscilloscope. On the other hand, "analog" doesn't just mean any continuous electrical signal. It means that a signal represents a quantity, such as temperature or acoustic pressure. It can't be noise free. If thresholds are applied to define discrete values of the quantity, then it's not analog any more. There is a profound amount of confusion about this, so I'm sympathetic. I dabble in some audio electronics, and there are endless debates about whether Class-D amplifiers are "digital" or not. They are certainly marketed as digital. ;-) The vagaries of floating point arithmetic, the possibility of errors in digital systems, and whether anything physical represents a real number, are interesting but basically sideshows.