Stimulants are an excellent short term solution. If you absolutely need to get work done tonight and can’t sleep amphetamine (i.e. Adderall) is a great solution. Indeed, there are a number of studies/experiments (including those the airforce relies on to give pilots amphetamines) backing up the fact that it improves the ability to get tasks done while sleep deprived.

Of course, if you are having long term sleep problems it will likely increase those problems.

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.