What an excellently well written paper! It does all the basics right - describes it's objective, the domain of the problem, a quick example (Rush hour) to nudge some intuition toward the reader, before going on to prove undecidability. It even tackles the decidability of another "should-obviously-work" (Bounded braid) idea that the author had (turns out to be decidable).
Also, I wonder if most programmers have unknowingly built a ton of Braid intuition because of the way the time reversal tree matches the way we model the undo tree in $EDITOR.
I completely agree. Percentiles are a very unintuitive way of thinking for this sort of data. It's really easy to know how much one made last year, but it takes a while to figure out what percentile one's income was in. Differences in Percentile vs differences in Income is even harder.
I felt strongly about this the moment I read the article on NYTimes - I reproduced the data set to the best extent I could and actually went about plotting against absolute income:
That's a far more intuitive chart, that a lot of us will understand better. I also graphed how much these children actually go on to earn against absolute income. I compared these results in a blog post - http://unside.t4you.in/data/intuitive-axes/
Also, I wonder if most programmers have unknowingly built a ton of Braid intuition because of the way the time reversal tree matches the way we model the undo tree in $EDITOR.