Now I know why people skip so many steps in their derivations, and just write stuff like "after some algebra, we find..."
This way, if you make a mistake, its only the final answer that's wrong, not 20 various intermediary steps along the way.
No, I am still not a competent 2 and minus sign finder.
Yes. I make mistakes.
I'd like to make this all fascinating and everything. But its really not. Its just me making dumb mistake after mistake in the very annoying details of this paper.
This was a pretty bad one though. Its especially annoying because its not totally obvious what the best fix is. From one point of view (that of me starting this part of the paper from the beginning) its obvious. But that involves changing the sign of like 30 equations. So I'm making the less aesthetically pleasing choice which involves changing just a few equations. But as I propogate these minus signs throughout the paper, I find doubt hiding in all sorts of corners that I thought I wouldn't have to visit anymore.
These are the moments that truly make you doubt your competence.
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