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George, yes, the piece of Roberto's you mentioned that I was referring to in the traffic cop remark is the Reducer. [I'm perfectly happy to continue from MAB Overview & Glossary to Prince to here, and I admit to being a bit curious where we'll wind up next. I enjoy these 'far-ranging' conversations.] The relevant part of your comment/question was: 
'What is a ''traffic cop piece'' of Joyce? It could be a good one. In some languages overseas they call those deliberate bumps all the way across the road ''lying-down policemen'' loosely translated.'

I think the traffic-cop piece acts in a similar manner to the reducer, which limits all pieces to a 1-square move, if next to them. But I would give it an area effect, since that's what we've been talking about. I'd suggest a 'zone of influence' that extends 2-3 squares [cubes, tesseracts...] and slows pieces. How does it slow them? 

First, let's consider an 'infinite' slider; on the standard chess board [8x8], it actually moves only 1-7 squares. So call its movement 'allowance' 7. As it moves across the board, it expends 1 from its allowance to enter each empty square. When it does not have enough allowance left to move one more square, it must stop. We can define more powerful pieces as having a larger allowance, maybe 10 for a queen, say. Now we can define some pieces in terms of movement allowances.
 
Our traffic cop piece would work very simply, by increasing the cost to enter squares in its zone. For the first square entered, it costs the basic 1, plus 1 additional. For the second square, the basic 1, plus 2 additional. For a third square in the zone, it's 1 + 3, and so on. We can also define a 'bender' piece, that works similarly, but pulls a piece 1 square toward itself for each square that piece moves in the bender's zone of influence. This is 'point gravity' chess. Just thinking about how pieces might move through a bunch of these gravity points with a handful of movement points can cause thoughts of 'gravitational slingshots' where pieces travel farther than their movement allowance, 'black holes' which cannot be escaped from because they're too big and powerful, and severe headaches. 

Since we're on a page of Roberto's, I'll mention one piece he uses, the battery. The battery augments the power of a piece it's next to. So it would increase the range of the cop and the bender, thus allowing the creation of the effects mentioned at the end of the last paragraph. But I don't think this discussion is actually appropriate to Roberto's Altair page, so I'll continue it in the Philosophy thread. Roberto's stuff rocks; it shouldn't be taken over, other than marginally, by a discussion that is only peripherally related to Altair. I worked in the reducer and traffic cop, and added a possibly new, certainly rare, piece along with another of Roberto's pieces, so he's getting equal time. ;-) [He deserves at least that! Hope to see that name show up again as an author of something.] 

But before I leave, I have to correct one small thing. George, you said:
'Two-path Rook being attributed to Witham in Joyce's present instigating comments is already invented long ago shows Pritchard 'ECV'' All I did was attribute the use of the word 'planar' to C Witham, which Witham used to describe hook-rooks, a different thing than the planar pieces of Prince.