@John_Baez
@Sophie_Libkind
@Robert_Figura

John wrote in 19.
>"This is a perfectly self-consistent viewpoint."

It seems you forgot something here.

That is Puzzle 57 reads:
>Puzzle 57. Which tasks could take longer, without changing the answer to Puzzle 56?..

and
>Puzzle 56. What is the minimum amount of time it takes to get from state 10 to state 50?

But seven months is not the minimum time it takes to get from state 10 to state 50. Please see again comment 15.

John wrote:
>That's not really what I meant, but it's what I should have meant. One reason is that Jared Summers, an official expert on PERT charts, answered my puzzles in the way that's consistent with this correction.

He gave the same answer as me for the second variant (see comment 15). This seems indeed to be the official reading of PERT charts -at least I understood it in the same way (I recently also needed to look a bit at those organization tools jobwise and I understand that he his not very happy with having to deal with PERT charts and the like, too bad that he couldn't avoid being recruited).

But as I said in 15. there exist also processes, where your initial interpretation makes also sense. An example can be found in the italian haute couture production. It's given as one example of how certain social conditions arise in this book. I bought the book as a present and got to look only briefly into it, but if I remember correctly it describes how the production of some haute couture items is put up for a kind of auction: those who sew fastest and cheapest (while keeping haute couture quality) will be paid for the sewn product the others not. At least it seems they are allowed to sell their later-or partly unfinished product on some secondary market, but I dont know how this will go together in future with the new IP tendencies in fashion.