Page 317 and page 278 LGB questions

[Stephanie Oswalt]

We recently received the following questions from a student. An instructor will respond below. Thanks!

1. Would you pls explain to me how/why the J X double-not arrow on p 217 of the LG Bible gets flipped around on p 218? This also happens further down the page 218 with K and W.


2. Would you pls clarify symbolizing for 1) J and H cannot be selected together (p278, LG Bible) and 3)W and X cannot be selected together (p 317, LG Bible). These two are symbolized differently, but I don't understand the difference in meaning between these two ways of describing the relationship between the variables.

Hope to hear from you soon!


With gratitude,


Leslie

[Jon Denning]

Thanks Leslie (and Stephanie) for the questions! Let me tackle these one at a time and see if we can't clear any confusion up

1. This is actually on pages 317-318 (for anyone out there reading this), and the answer is that double-arrows are reversible! That means that they can move left to right, or right to left, and be equally valid in either direction. So when one of the variables on the end of a double arrow is used again in another rule—that is, when a variable serves as the connecting piece—we show it in the middle of the chain with the two unique variables on the end. That way it's easy to determine if/how those two end pieces affect one another.

So when you see a rule like A B, and then another like C B, the B is the repeated variable and it will connect A and C. To show that connection though we want B in the middle of the chain, meaning we'd either want to reverse that first double-arrow diagram (B A) and then have C go to B, or we'd want to reverse the arrow between C and B
(B C) and keep the double-arrow the same as it was when we started:

C B A

A B C

Either is fine, but given that people tend to read from left to right (and thus better understand arrows that flow left to right), we tend to use the top illustration to show connections. And that's all we've done on 318: taken the original diagrams and flipped the order of the variables around the double-not arrow so the repeated term is the connecting piece.

2. Sure! This is explained on page 278, in fact. The block with the slash on 278 in a linear game would describe an impossible sequence. Namely, J can't be immediately before H. That's because linear games deal with order, and not selection (typically). Grouping game on the other hand are about selection, so a block like that with a slash in grouping would indicate two things that can't be chosen/placed together. It's fine to use a block for grouping, as long as you recognize that it means something different than it would in linear, however some people find that confusing or fail to make the distinction, so we also encourage the use of arrows in grouping: a double-not arrow means two things cannot occur together (cannot be selected together), so that's another way in grouping to show that relationship between variables. We use it again with W and X (and others like J and X) on 317 with grouping.

In short, blocks in linear are about order/sequences; blocks/arrows in grouping are about selections.

I hope that helps!