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Math

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Andrius Kulikauskas

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See: Math

Another key concept for me is the idea of an "unmarked opposite" vs. a "marked opposite".

  • We can have what is beyond a system be identified with an opposite within the system. For example, a blank sheet of paper can be noted by the empty set. The empty set is opposite to nonempty sets. And there is a sense in which the empty set is preferred, is central. Or we can have the identity element of a group which expresses no action at all. Similarly, good can be distinguished from bad by claiming that God is good, where God is what is beyond the system. So here in this sense I say that good is the marked opposite, the one identified with what is beyond the system.
  • Also, in a different sense, in a system, a marked opposite is when you have two opposites (choices) that are clearly distinguished and one is the default (thus preferred) because it is unmarked, whereas the other one is marked to distinguish it and thus secondary. For example, 1 and -1. 1 is unmarked and -1 is marked (and it actually has an extra mark). And they are clearly distinct: -1 x -1 = 1 whereas 1 x 1 = 1.
  • Finally, we can have "unmarked opposites" where two choices are distinct but otherwise not distinguishable. They have yet to be marked. For example, the two square roots of -1. One will imagined clockwise, the other counterclockwise, perhaps. But which is which doesn't matter. Only when we name them using + and -, only when we attribute such a prejudice to them, do we lose touch with their original indistinguishability, thus ending up with i and -i, forgetting that -i is no less basic than +i.

So I'm very interested where such dualities and opposites come up in math.

Opposites


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Puslapis paskutinį kartą pakeistas 2016 birželio 19 d., 14:06
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