Respond at most as much as the original

By dkl9, written 2024-159, revised 2024-159 (0 revisions)

An honest, direct response to a claim serves to explain and correct differences from exact relevant truth. If the claim is roughly in the right direction, the response only has to make some small corrections. If the claim is a confused mess, or is based around lies, the response must, at least in effect, deny all the lies, then introduce what is true.

Intuitively, the truth, the original statement, and the response are high-dimensional vectors, respectively x, s, and r = x - s. By the law of cosines, |r| = sqrt(|x|² + |s|² - 2 |x| |s| cos(θ)), with θ the angle between truth and statement. The response is longer than just stating the truth from a state of zero knowledge iff |r| > |x| iff |s|² - 2 |x| |s| cos(θ) > 0 iff |s| > 2 |x| cos(θ). If a statement s is about as complex as the truth x which it targets, i.e. |s| ≈ |x|, then that inequality holds iff θ > τ / 6, i.e. for any substantially confused or misleading statements.

A response to fix a claim getting longer than the claim itself has two main explanations. Perhaps the response is verbose compared to its target. Or the claim is a confused, lying mess, and, to be efficient, you should give up on fixing it directly. Instead, find and reference, or write yourself, a more accurate answer to the original inquiry, ignoring the wrong answer.