I’m working on a longish post about **dichotomies**. It’s going to be about mathematical objects that can serve as metaphors to **think beyond binary opposition**.

In researching the article, I found the following in the Internet Encyclopedia:

According to Jacques Derrida,^{[citation needed]} meaning in the West is defined in terms of binary oppositions, **“a violent hierarchy”** where “one of the two terms governs the other.”

I don’t know if Derrida actually said that. But I can already think of a counterexample from mathematics.

The number **√−1** is logically equivalent to **−****√−1**. In other words **i** and **−i** are indistinguishable.

Doug Hofstadter was fond of making this point to us.

- Complex conjugation would work the same.
- Addition, subtraction, multiplication, and division would work the same.
- The anticlockwise direction in the complex plane is arbitrary. If the “southern”
**i** were the one we currently call **+i**, then we’d do things clockwise and everything would work out the same.
- So integration and differentiation would work the same as well.
- (On the other hand,
**−1** is not the same as **+1**. **−1** instantiates an “alternating” pattern whereas **+1** instantiates a “stay the same” pattern, under multiplication.)
- It’s like group theory. Say we’re talking about the group
**P₃**. *Any* of the atoms could be called “first”, “second”, or “third”. It wouldn’t matter.

What matters is the *structure*, the *relationships*, the *way* they do things. Neither is “worse”, “better”, “before”, “after”, or “dominated by” the others—they simply relate to each other in the **P₃** way.

So right there, you’ve got a binary opposition where **neither term governs the other**.

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