An abacus is a digital device, but it's not a binary digital device obviously.
> Since it is very common for an abacus to have 5 beads per pole
These are "bi-quinary" abacuses that have two rows of beads, the bottom row is 0-4 and the top row is either 0 or 5.
Computers weren't always binary, though. https://en.wikipedia.org/wiki/ENIAC - looks like it was decimal based as it was electronically (with tubes) working like an adding machine.
> A good example among analog controllers is the Atari one that had a variable capacitor and the capacitance was measured to infer its position. Although the measurement is digital, the controller, yes, was analog.
An abacus allows you to slide beads along a rod. Similar to your example of an analog controller, the device itself is analog but the measurement is digital. The traditional way to use an abacus is to slide beads from one end to the other with beads on one end counting as 1-5 (or multiples of 5, or so on). But you don't have to use it like that. You could use just 1 bead on each rod to represent a value from 0 to 5 with its position along the rod, or even a value from 0 to 100 with its position. Heck, you could use two beads on the rod to represent a range using their positions. Using this logic, an abacus is analog but the traditional way of interpreting them is digital.
One could argue that fingers are analog in the same way as abacus beads or electronic signal voltages in "digital" circuits. Yes, the traditional way to count on your fingers is to count each finger held up as a value of 1 and then add up the number of fingers to get the represented value, but fingers can be anywhere between entirely up and entirely down. You could hold a finger halfway up and count it as 0.5.
If you feel that argument falls under remark 3, I think you have some options:
1) Resolve the conflict between your example of an analog controller in remark 2 and your refusal to consider interpreting an analog signal/state as a discrete value as digital (as expressed in remark 3).
2) Accept that trying to fit everything in the real world into strict definitions is a fool's errand. Definitions are essentially simplified models that allow us to represent some aspect of the real world, but they can never entirely encapsulate the nature of the real world (the map is not the territory).
Let's stick with option 1 because it's more practical than philosophical (although, exploring option 2 may help you cope with life better in the long run). You can go with option 1 by simply dropping remark 3 entirely and accepting that a device can be analog in its physical form and digital in an interpretation.
Alternately, you can accept that the context affects which model best describes an abacus/fingers/electronic signal because your interpretation defines what the values represent. That is, the abacus has no representation of "internal values" -- it doesn't care if the beads are supposed to be 1's, 5's, fractions, or space ships. What each bead represents lies entirely in the person looking at the beads, not the abacus.
An example in that line of thought: the computer engineer designing a chip has to face the reality that electronic signals are analogue so he can design a chip that functions properly. In his context of work, the chip is analogue. The software engineer who uses that chip needs to know very little about the underlying hardware and is able to model its behavior as entirely digital. In his context of work, the chip is digital.
An abacus is a digital device, but it's not a binary digital device obviously.
> Since it is very common for an abacus to have 5 beads per pole
These are "bi-quinary" abacuses that have two rows of beads, the bottom row is 0-4 and the top row is either 0 or 5.
Computers weren't always binary, though. https://en.wikipedia.org/wiki/ENIAC - looks like it was decimal based as it was electronically (with tubes) working like an adding machine.
> A good example among analog controllers is the Atari one that had a variable capacitor and the capacitance was measured to infer its position. Although the measurement is digital, the controller, yes, was analog.
An abacus allows you to slide beads along a rod. Similar to your example of an analog controller, the device itself is analog but the measurement is digital. The traditional way to use an abacus is to slide beads from one end to the other with beads on one end counting as 1-5 (or multiples of 5, or so on). But you don't have to use it like that. You could use just 1 bead on each rod to represent a value from 0 to 5 with its position along the rod, or even a value from 0 to 100 with its position. Heck, you could use two beads on the rod to represent a range using their positions. Using this logic, an abacus is analog but the traditional way of interpreting them is digital.
One could argue that fingers are analog in the same way as abacus beads or electronic signal voltages in "digital" circuits. Yes, the traditional way to count on your fingers is to count each finger held up as a value of 1 and then add up the number of fingers to get the represented value, but fingers can be anywhere between entirely up and entirely down. You could hold a finger halfway up and count it as 0.5.
If you feel that argument falls under remark 3, I think you have some options:
1) Resolve the conflict between your example of an analog controller in remark 2 and your refusal to consider interpreting an analog signal/state as a discrete value as digital (as expressed in remark 3).
2) Accept that trying to fit everything in the real world into strict definitions is a fool's errand. Definitions are essentially simplified models that allow us to represent some aspect of the real world, but they can never entirely encapsulate the nature of the real world (the map is not the territory).
Let's stick with option 1 because it's more practical than philosophical (although, exploring option 2 may help you cope with life better in the long run). You can go with option 1 by simply dropping remark 3 entirely and accepting that a device can be analog in its physical form and digital in an interpretation.
Alternately, you can accept that the context affects which model best describes an abacus/fingers/electronic signal because your interpretation defines what the values represent. That is, the abacus has no representation of "internal values" -- it doesn't care if the beads are supposed to be 1's, 5's, fractions, or space ships. What each bead represents lies entirely in the person looking at the beads, not the abacus.
An example in that line of thought: the computer engineer designing a chip has to face the reality that electronic signals are analogue so he can design a chip that functions properly. In his context of work, the chip is analogue. The software engineer who uses that chip needs to know very little about the underlying hardware and is able to model its behavior as entirely digital. In his context of work, the chip is digital.