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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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  1. isomorphismes posted this