jedbrown

Plagiarism, at its most fundamental level, is a lie. It is the taking of works or ideas of others and passing them off as your own, either directly or indirectly. The misdeed itself is in the lie, the “I created this” when it is known to be untrue.

However, that lie isn’t being told to the original victim. It’s a lie about the victim, claiming that they didn’t create it or their contributions didn’t matter, but it’s not a lie to them. Instead, it’s a lie to the audience, which is the second victim and the actual target of the con.

> Under settled Board law, numerous practices employers may engage in using new surveillance and management technologies are already unlawful. In cases involving employer observation of open protected concerted activity and public union activity like picketing or handbilling, the Board has recognized that “pictorial recordkeeping tends to create fear among employees of future reprisals.”10 The Board accordingly balances an employer’s justification for surveillance “against the tendency of that conduct to interfere with employees’ right to engage in concerted activity.”11 In that context, “the Board has long held that absent proper justification, the photographing of employees engaged in protected concerted activities violates the Act because it has a tendency to intimidate.”12

It is perhaps worth noting that mathematicians at all three of the above stages of mathematical development can still make formal mistakes in their mathematical writing. However, the nature of these mistakes tends to be rather different, depending on what stage one is at:

1. Mathematicians at the pre-rigorous stage of development often make formal errors because they are unable to understand how the rigorous mathematical formalism actually works, and are instead applying formal rules or heuristics blindly. It can often be quite difficult for such mathematicians to appreciate and correct these errors even when those errors are explicitly pointed out to them.

2. Mathematicians at the rigorous stage of development can still make formal errors because they have not yet perfected their formal understanding, or are unable to perform enough “sanity checks” against intuition or other rules of thumb to catch, say, a sign error, or a failure to correctly verify a crucial hypothesis in a tool. However, such errors can usually be detected (and often repaired) once they are pointed out to them.

3. Mathematicians at the post-rigorous stage of development are not infallible, and are still capable of making formal errors in their writing. But this is often because they no longer need the formalism in order to perform high-level mathematical reasoning, and are actually proceeding largely through intuition, which is then translated (possibly incorrectly) into formal mathematical language.

The distinction between the three types of errors can lead to the phenomenon (which can often be quite puzzling to readers at earlier stages of mathematical development) of a mathematical argument by a post-rigorous mathematician which locally contains a number of typos and other formal errors, but is globally quite sound, with the local errors propagating for a while before being cancelled out by other local errors. (In contrast, when unchecked by a solid intuition, once an error is introduced in an argument by a pre-rigorous or rigorous mathematician, it is possible for the error to propagate out of control until one is left with complete nonsense at the end of the argument.)