I could give an example in joystick controllers. It requires more than two inputs in any direction. You can use fuzzy logic which gets rid of law of non-contradiction and law of excluded middle and allows half presses on electric keyboard which mimics the piano key hitting a string with the variable force you use to press it.
So while digital can't exactly mimic the analog in that same manner, it can do a decent job trying to cover it.
Classical logic, however, is dualistic and uses only a bivalence logic (bi = two and valence = value) so the way they get around it is by using two or multiple propositions creating a pseudo-multi-valued logic (speed/force and direction).

There are other issues including Russell's paradox but computers run on them. I think the "true/false" duality actually hides two other choices (maybe "stop/go") but it is workable just doesn't seem fully accurate. A corollary may be that polarities/opposites don't actually exist except as an epistemological framework that inaccurately captures what happens (xx > xy chromosomes etc).

Of course, polarity itself is limiting, at it only offers two possibilities, rather than many others. — Josh Alfred

A dichotomy is formally defined as that which is "jointly exhaustive and mutually exclusive". So a polarity is the successful reduction of some set of possibilities or pluralities to a dialectic relationship, or unity of opposites.

The whole point is to eliminate as many free variables as possible to arrive at the central structure of some symmetry breaking. It is the basic way that metaphysics has always reasoned.

Which gets me thinking that there must be something other than polarity with which to conceptualize decisions and dialect. — Josh Alfred

Well something further must ground a polarity as all the free possibility that gets cleanly divided by the laws of thought. To arrive at the bivalent Law of the excluded middle, one must have some the many lesser notions of categorisation that got discarded along the way.

Peircean logic added this third thing in the form of the notion of vagueness - that to which the bivalent Principle of Contradiction fails to apply.

So there you have a starting point in a uniform confusion. Everything going off in all directions without structure or pattern. And then this field of vagueness is what must develop into its mutually opposing polar limits.

So take some metaphysical dyad like the discrete~continuous, or chance~necessity. As paired bounds on possibility, the discrete and the continuous are categories that both directly oppose each other, and jointly make all more intermediate grades of connectedness or disconnectedness rather subsidiary.

All grades of connection and disconnection are either more towards one pole or the other. And it would only be precisely in the middle that things might turn vague as everything becomes neither the one, nor the other, in any counterfactual way.

Same with chance and necessity. In being exactly opposed - defined in terms of being absolutely unalike in character - they bound all other lesser intermediate states. And this all the lesser intermediates states can be measured in terms of how far they sit towards one or other pole of the single metaphysical spectrum.

So polarity was the general metaphysical trick to discover what might be the natural, self-defining, measures of reality. It was what paved the way for the development of science by tying the notion of metaphysical quality to that of methodological quantification.

To return to mathematics for a moment, polarity first becomes significant when we develop the relational number line out of the natural number line. The relational number line, the line of the negative and positive numbers, is sometimes (confusingly) referred to as the "integer" line; I prefer the term "relational", because it more accurately captures what is important and interesting about this particular number line.

Whereas a natural number is the name of a set, by adding a polarity to the number, we transform it into a quantitive relation. In the context of the "relational" number line, the relation is obviously to 0; -2 points to the value which is 2 less than 0. In any other arithmetical operation, the relation -2 points to the number which is 2 less than the preceding number; so, 0 - 2 = -2, but 5 - 2 = 3.

A dichotomy is formally defined as that which is "jointly exhaustive and mutually exclusive" — apokrisis

This form of duality presents a serious problem - a dilemma which, much to our disappointment, isn't a false dichotomy fallacy.

The only reasonable response is a counterdilemma à la Protagoras' paradox (of the court).

For instance, in re the notorious trolley problem.

The dilemma: Either you kill an innocent person or you let 5 people die. Bad, very bad!

Counterdilemma: Either you save an innocent person or you save 5 people. Not bad, not bad at all!

My example isn't one in which the options are both mutually exclusive and jointly exhaustive, but you get the idea.

Can I take this opportunity to remind contributors that this is a mathematical page, and we are discussing polarity in the purely mathematical sense?