Larry Wasserman has a recent post where he talks about the "p-value police". He makes an interesting point (all emphasis mine) (the premise in italics that I added, and his response below it):
The most common complaint is that physicists and journalists explain the meaning of a p-value incorrectly. For example, if the p-value is 0.000001 then we will see statements like “there is a 99.9999% confidence that the signal is real.” We then feel compelled to correct the statement: if there is no effect, then the chance of something as or more extreme is 0.000001.
Fair enough. But does it really matter? The big picture is: the evidence for the effect is overwhelming. Does it really matter if the wording is a bit misleading? I think we reinforce our image as pedants if we complain about this.
Which got me thinking -
Are there good examples of pedantry in TCS ? Such an example would consist of
- A claim that is commonly made in the popular press
- A standard correction that people insist on making
- The correct "big picture" that the claim does capture even while being imprecise.
where the claim is mathemtically wrong but "morally right" and the correction is technically correct but doesn't change the intuitive understanding.
To lead things off, my example would be:
- Claim - NP-complete problems take exponential time to solve
- Correction - No in fact we just don't know if they can be solved in polynomial time
- Big picture - NP-complete problems are HARD
Caution: I know there are many on this forum whose head will explode at the idea of claims that are wrong but "morally correct" :). Remember that these are statements targeted towards the public (where some degree of license can be permitted), rather than statements made in a research paper.