drafting "'Yes, and—' Requires the Possibility of 'No, Because—'"

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+# "Yes, and—" Requires the Possibility of "No, Because—"
+
+Scott Garrabrant [gives a number of examples to illustrate a principle that "Yes Requires the Possibility of No"](https://www.lesswrong.com/posts/G5TwJ9BGxcgh5DsmQ/yes-requires-the-possibility-of-no). We can understand the principle in terms of information theory. Consider the answer to a yes-or-no question as a binary random variable. The "amount of information" associated with a random variable is quantified by the [entropy](https://en.wikipedia.org/wiki/Entropy_(information_theory)), the expected value of the negative logarithm of the probability of the outcome. If we know in advance of asking that the answer to the question will always be Yes, then the entropy is −P(Yes)·log(P(Yes)) − P(No)·log(P(No)) = −1·log(1) − 0·log(0) = 0.[^undefined-convention] If you already knew what the answer would be, then the answer contains no information; you didn't learn anything new by asking.
+
+[^undefined-convention]: I'm glossing over a technical subtlety here by assuming—pretending?—that 0·log(0) = 0, when log(0) is actually undefined. But it's the correct thing to pretend, because the linear factor $p$ goes to zero faster than $\log p$ can go to negative infinity. Formally: $\lim_{p \to 0^+} p \log(p) = \lim_{p \to 0^+} \frac{\log(p)}{1/p} = \lim_{p \to 0^+} \frac{1/p}{-1/p^2} = 0$
+
+----
+
+Practioners of [improvisational comedy](https://en.wikipedia.org/wiki/Improvisational_theatre) have a principle of "Yes, and": when an actor [offers](https://improwiki.com/en/wiki/improv/offer) an element of the scene being portrayed, their fellow actors are supposed to accept the proposal as the reality of the scene ("Yes"), and respond with their own complementary proposal ("and").
+
+The practice of "Yes, and" is important for maintaining momentum while building out a coherent reality for the audience. If one actor opens the scene with, "Surrender, Agent Stone, or I'll shoot these hostages!"—establishing a scene in which they're playing an armed villain being confronted by an Agent Stone—it wouldn't do for their partner to reply, "That's not my name, you don't have a gun, and there are no hostages." That would halt the momentum and confuse the audience. Better for the second actor to say, "Go ahead and shoot, Dr. Skull! You'll find that my double agent on your team has stolen your bullets"—accepting the premise, and adding new elements to the scene (the villain's name and the double agent).
+
+Notice a subtlety: the Agent Stone _character_ isn't "Yes, and"-ing the Dr. Skull _character's_ demand to surrender. Rather, the second actor is "Yes, and"-ing the first actor's worldbuilding efforts. The actors must cooperate in constructing a shared reality, even if their characters are in conflict. ["Blocking"](https://improwiki.com/en/wiki/improv/blocking) your partner's offers kills the vibe, and with it, the scene. No one wants to watch two people [arguing back-and-forth about what reality is](https://www.lesswrong.com/posts/yr4pSJweTnF6QDHHC/comment-on-four-layers-of-intellectual-conversation).
+
+----
+
+Proponents of [collaborative truthseeking](https://www.lesswrong.com/posts/ckwzjbfHTCdPs2Y4J/collaborative-truth-seeking) think that many discussions benefit from a more "open" or "interpretive" mode in which participants are expected to be curious about each other's models. Collaborative truthseeking does not discourage disagreement as such, but prioritizes productive ways to express disagreement: paraphrasing your interlocutor's views and relating them to your own is preferred to flatly contradicting them.