Throughout his or her tortured existence, a mathematical physicist has two mortal enemies. These enemies are battled constantly, strike at any moment, and can merely wound or actually kill vast swaths of calculations. Here is one:
2
and here is the other:
-
Yes, they are small. But they are mighty. It is their tiny stature that often leads to their deadly effectiveness -- for they are sneaky. And they must be controlled. If one appears in the wrong place, or disappears from the right place, it spawns errors in every subsequent expression until its victory over the theorist is immortalized in publication.
OK, so, big deal, a few "-" here and there can't be that hard to keep track of, even if one does tend to juggle several in the head at once during a calculation, right? How many are we talking about? I just did a search through my notes at Deferential Geometry... There are currently 2,277 "-" living there.
=:-o
Sure, some of these are hyphens so they don't count. But still, that's a lot of potential evil, lurking. The odds of 2,277 irascible "-" all being in the right place at the right time... well, it saddens me to think about how small (or even negative?) that probability is.
So I'm offering a bounty!
$100 to the first person to find three initial appearances (or disappearances ) of a malicious "-" at Deferential Geometry.
The restrictions:
1) You have to correctly identify the root cause, where a mistaken sign first occurs -- its dependents don't count.
2) It has to be an actual mistake, not due to a difference of opinion or convention.
3) A mistake in a note tagged with a "0" is only worth half, since those are often rough or incomplete calculations.
Please post a comment here if you think you've spotted one or several of the enemy. (Describe the note and the erroneous expression in it.) If it's a mistake, you get the credit for finding it first even if you weren't sure about it. The victor will be heralded and sent $100 from me via paypal.
A suggestion: If you have to argue to make your case, you're probably wasting time. Out of 2,277 signs, I'm sure I just plain dropped some in calculations. But feel free to ask.
Once this bounty is claimed, we'll talk about the 2,428 2's...