Ask HN: Is the Abacus a Digital Device? | Hacker News Reader

Ask HN: Is the Abacus a Digital Device?

2 pointsmarcodiego2 comments

I usually define a digital device as "a device where internal values are represented in a discrete form" while an analog device is "a device where internal values are represented in a continuous form".

By these definitions I'm rarely concerned if the device is electronic, mechanical, biological (counting with fingers) or even imaginary. Also, by these same definitions, an abacus is clearly a digital device since internally, its values a represented in a discrete form. Unfortunately, there are conflicting (reasonably common or trustworthy) sources that disagree with me.

Usually, such sources are based of the fact that the abacus is not electronic or other considerations regarding its operation but not taking internal representation of values into account.

So, I'd like to question the HN crowd definitions, sources and (to a much lesser extent) opinions about this question. Is the abacus a digital device?

Remark 1: Since it is very common for an abacus to have 5 beads per pole (specially mimicking a counting method using the fingers of a hand), the abacus is probably (the most) classical example of a digital device: it literally mimics digitos (fingers in latin).

Remark 2: Also, I don't want to consider the common opinion among gamers that call a CD as an analog device when it is clearly digital, or controller with joysticks as analog because the mimic very close continuous states. 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. Modern ones are not analog, they're fully digital.

Remark 3: I don't want tô fall into irrelevant technicalities like saying "an analog TV could be considered digital since it can have buttons in discrete" states, actually you're just choose analog values from a small set. Argument about electric charge in semiconductors ignoring thresholds fall in this same category.

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.

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