So your intent here is to diagnose the conceptual confusion that many people have with respect to infinity yes? And your thesis is that: people are confused about infinity because they think it has a unique referant while in fact positive and negative infinity are different?

I think you are on to something but it’s a little more complicated and that’s what gets people are confused. The problem is that in fact there are a number of different concepts we use the term infinity to describe which is why it so super confusing (and I bet there are more).

1. Virtual Points that are above or below all other values in an ordered ring (or their positive component) which we use as shorthand to write limits and reason about how they behave.

2. The background idea of the infinite as meaning something that is beyond all finite values (hence why a point at infinity is infinite).

3. The cardinality of sets which are bijectable with a proper subset of themselves, i.e., infinite. Even here there is an ambiguity between the sets with a given cardinality and the cardinal itself.

4. The notion of absolute mathematical infinity. If this concept makes sense it does have a single reference which is taken to be ‘larger’ (usually in the sense of cardinality) than any possible cardinal, i.e. the height of the true hierarchy of sets.

5. The metaphorical or theological notion of infinity as a way of describing something beyond human comprehension and/or without limits.

The fact that some of these notions do uniquely refer while others don’t is a part of the problem.

Interesting, but I think it’s the other end of the equation where the real problem lies: voting. Given the facts that

1) A surprisingly large fraction of the US population has tried hard drugs of one kind or another.

2) Even those who haven’t almost surely know people who have and seem to find it interesting/fascinating/etc.. not horrifying behavior that deserves prison time.

So why is it that people who would never dream of sending their friend who tried coke to prison or even the friend who sold that friend some of his stash how do we end up with draconian drug laws?

I don’t have an easy answer. I’m sure the overton window and a desire to signal that they themselves are not pro-drug or drug users is part of the answer. It’s like lowering the age of consent for sex. As long as the loudest voices arguing it should be legal for 40 year olds to sleep with 16 year olds are creeps few people will make that argument no matter how good.

But this doesn’t really seem like enough to explain the phenomena.