Safe extensions and the 3x3 invasion

I just read about walls in Bruce Wilcox's Sector fights. There is a lot more in there, but I just have to share a few juicy concepts.

The largest safe extension is equal to the height of your wall. Extend to the 3rd line.

So, here is a completely made up position that illustrates the concept:


If you count from the top edge of the board, the black wall is 6 tall, or you can say it reaches the 6th line. The white wall reaches the 5th line. The safe extension is the same number of spaces away from the wall (on the 3rd line). So white can jump out 5 spaces (a "four space jump") and Black can jump 6. The theory is that the height of the wall helps insure the area can't be invaded. I haven't played one of these big extensions and seen it work, but I am trusting it is true.
It matches up with the proverb, "From a 1 stone base jump two, from 2 stones jump three".


And here is the piece that got the "aha" from me. Why do you see an extension from a single 4-4 stone to the middle of the side? I have seen this and it looked like a lone stone out hoping to claim some territory. Why does this make sense?


Take a look at the picture below - this is the same board after a 3-3 invasion by white. Count up how far away that lone stone is from the wall (consider it to be on the third line from the left). AHA! :)


Lastly, I'll do a little plug for Go Dojo - Bruce talks about a LOT more than just this in his section on walls. Among other things he covers diagonal walls, walls with missing stones, jumping walls and how to destroy the effectiveness of opponents walls. Good stuff!