False Blocks

[Annah]

Dear Dave,
Hello
I am having some trouble understanding False Blocks. Mainly, the distinction between regular blocks and false blocks when words such as 'immediately before' and 'immediately preceding' are used.

On page 17 an example depicting the usage of blocks states:
'Y is tutored during the hour immediately before Z is tutored.'

On page 47 the example states: 'Each Rock classic is immediately preceded on the CD by a new composition.' In the explanation it further states that the rule does not state that the two variables are in block formation and describes the above statement as a conditional statement.

The word 'before' being a synonym for the word 'preceding' enables me to use the latter in place of the former in the example on page 17. It would then read as: 'Y is tutored in the hour immediately preceding the hour during which Z is tutored.'

This is not a conditional statement. Nor is there a statement which states that Z is tutored after Y. But we gauge as much from the conditional block created.
In the example on pg.47 however, similar wording reads to a conditional statement. What is the difference between the two?

Thank you.

[Dave Killoran]

Hi Anna,

Thanks for the question--it is a very good one!

The difference diagram in these two situations results from the number of each type of variable available in each instance. For example, if you have a game where there are six distinct variables--R, S, T, W, Y, Z, for example--any block rule such "Y is tutored during the hour immediately before Z is tutored" would be a constant. That is, YZ would always occur because there is only one Y, and only one Z.

Now, consider how the environment changes if you have, say, a variable group of N, N, N, N, R, and R. If you are presented with a rule such as "Each rock classic is immediately preceded by a new composition," you can see how NR needs to occur when R is present, leading to the representation on page 47. I tried to get that point across by referencing the presence of multiple Ns and Rs, but I'll add a sidenote on that page in the next reprint that expands on this point so it is as clear as possible.

Also, the second rule is conditional (the first is as well, but the second is probably easier to see as conditional). The word "each" at the beginning of the second rule--that connects the block to the idea that "each" time this thing occurs, another thing will occur, turning it into a conditional relationship.

Also, for other readers of this thread, the page references in the original question are for an older version of the LGB. In the newest version (released last month), the concepts referenced are on now pages 41 and 81.

Please let me know if that helps clear up this tricky issue, and many thanks for the great question!

[Annah]

Dear Dave,

Thank you very much for your prompt reply. I had a vague hunch that the difference between the two might lie in the difference between variable sets but was not entirely certain. The concept is very clear now Thank you for explaining it in such a coherent and thorough manner, and most importantly, thank you for making yourself available to answer questions.

[Dave Killoran]

Great, glad I could help! I'm always happy to answer questions about the book, and I find the feedback extremely useful. Please let me know if you have any other questions going forward.

Thanks!

[T9909]

Does this mean a no block is seen with limited variables? So two variables 7 spaces?

[Shannon Parker]

Does this mean a no block is seen with limited variables? So two variables 7 spaces?

A not block is when something cannot happen. For instance if there were variables P and S, and S could not occur directly after P, then you would have a not block of PS (block with a diagonal line through it).

I am not sure if this answers your question.
Shannon

[T9909]

Thank you for the quick reply.

I'm referring to the example that was originally given in the post. Do we only see not blocks in games where there are only two variables, but 7 spaces? So for example, N must precede R, and since there are only two variables we know this will always be a not block? If the game says there are 7 variables (a, b, c, d, e, f,g ,h) and 7 spaces, and A must precede C, will that be a block or not block?

I think I'm overthinking the terms, specifically conditional and not conditional and that's where the confusion lies.

Thank you!!

[Jonathan Evans]

Hi, T9909,

In fact this would be a block (not a not block)! Just to clarify, let's consider two examples:

• Example A
  
  Seven items, A B C D E F G, are being put into order, first through seventh. The following restrictions apply.
  
  Example B
  
  Seven birds, two bluejays (B) and five cardinals (C), are being put into order, first through seventh. The following restrictions apply.

In Example A, if we know that D precedes G, we can make a [DG] block. There's only one D. There's only one G. If we know D comes before G, then we've got a [DG] block; we've accounted for both of them.

In Example B, if we know that every B is followed by a C, we do not have a [BC] block. This is because while it is true that every B is followed by a C, it is not true that every C is preceded by a B. We have five Cs and only two Bs. Thus, the correct way to represent this clue is as follows:

• B [BC]

This kind of situation is possible when there are repeating variables.

[T9909]

Perfect!

So just to clarify the language for the first example it will always be DG and not DG or GD because the rule explicitly states D comes before G.

And in situations where there are repeating variables then a not block would exist like in example B?

[Adam Tyson]

Sounds like you've got it, T9909! In the first case we can make an absolute block because we know about something that always happens, but in the second case we can only make a conditional block because we only know that something happens when something else also happens. It's not always, but only when another thing occurs.

Thinking of not-blocks now, what if in Jonathan's first example the rule was "B is not immediately before F"? In that case, we would have a BF not-block, or BF, and that would indicate that B followed immediately by F can NEVER happen.

In the second example, we might have a rule that says "at least one of the bluejays is not immediately preceded by a cardinal". Could we come up with a not-block there, like CB? I wouldn't, because the other bluejay COULD be preceded by a cardinal. Instead of using blocks in that situation, I would try to find another way to show that. How could it be that one of those bluejays is not preceded by a cardinal? Only two options that I can think of, and that is that either one of the bluejays is first, or else the two bluejays are consecutive, or both. That is what I would diagram - the positive inference from that rule ("B1 or BB) - rather than trying to create a useful conditional representation for the rule as presented. The latter would look very awkward, I think: B CBmin 1 time. Ugh!

As Shannon said, a not block is used to indicate that something is impossible. If that's what your rule creates, and the not block is the best way to show it for you, then use it! Just be careful that you aren't showing something to be impossible when it actually is possible, but might just be limited in some way.