We're always reminded love and hate aren't black or white, but shades of grey. There's a continuum between those two poles. I don't disagree, but that's not the whole story, either: I think there are at least three of these axes, and possibly more.

### Axis 1, Direction: Love vs. Hate

This is probably the easiest to explain, especially since most of us already have a good feel for it. We're used to thinking in these terms. I used to believe that this range could be easily mapped onto, say, the integers, but after thinking about the next two axes, I'm not so sure.

### Axis 2, Intensity: Indifference vs. Obsession

The first axis tells us whether your feelings for someone (or something) are positive or negative. That is, they give a direction. This second axis shows how strongly you feel that way. In pseudomathematical terms, this adds a magnitude to your love/hate direction.

While it's a convenient shorthand, I don't think that you can really model this using vectors. If we look at the emotions we see in ourselves and others, and plot those along the two axes we've described so far, we might see a triangle:

```         Indifference
/\
/  \
/    \
/      \
Hate     /        \     Love
/          \
/            \
/              \
/________________\
Obsession
```

An odd feature of extreme Obsession is that it's difficult to tell whether the original feeling was love or hate. Obsession seems to push out the original positive or negative emotion, and just fill it with a wild intensity. Acting like an emotional Möbius Strip, we get something that looks more like a diamond:

```         Indifference
/\
/  \
/    \
/      \
Hate <        > Love
\      /
\    /
\  /
\/
Obsession
```

(As an aside, I almost described this axis as being between obsession and apathy, instead of indifference. I concluded that apathy is more a result of indifference, and that indifference is a more diametric opposite to obsession.

### Axis 3, Importance: Trivial vs. Vital

While this isn't necessarily an axis of emotions themselves, it's an obvious attribute to consider when reflecting on emotions and how they affect our lives. There seems to be two components to this: objective and subjective. When these two perceptions of an emotional matter disagree, it can cause problems. Examples include everything from a teenager's first big heartache to more serious neuroses and psychoses.

I haven't decided whether these two are really a separate axis or not. It probably falls back to the deep question of whether there is an objective reality at all, or if everything is subjective, since that's (by definition) the only way we can experience the world.