Discussion Overview
The discussion revolves around the properties of a function measuring "error," specifically a non-symmetric error function denoted as e(x,y). Participants explore the implications of its non-normative characteristics in the context of comparing positions and orientations of a drill.
Discussion Character
- Exploratory, Conceptual clarification, Debate/contested
Main Points Raised
- One participant introduces a non-symmetric error function e(x,y) and questions its suitability as a measure of error.
- Another participant suggests that the appropriateness of the function depends on the intended application, noting that boundedness does not necessarily require norm properties.
- A different participant expresses concern about the measure's effectiveness given its non-symmetry, seeking clarification on what constitutes a "good" measure.
- Further clarification reveals that x and y represent elements of SE(3), related to the positions and orientations of a drill.
- One participant proposes that asymmetry in the error measure may be acceptable, citing practical examples where certain errors (e.g., "drill too low") could be significantly worse than others (e.g., "drill too high").
Areas of Agreement / Disagreement
Participants do not reach a consensus on whether the non-symmetric error function is a good measure, with differing opinions on the implications of its properties and the context of its application.
Contextual Notes
The discussion highlights the need for clarity on the definitions of "good" in the context of error measurement and the specific applications being considered.