What does "but one" mean here?

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NewHopeR

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And what does "in our neck of the woods" mean here?

Context:

The progress of the human race in understanding the universe has established a small corner of order in an
increasingly disordered universe. If you remember every word in this book, your memory will have recorded
about two million pieces of information: the order in your brain will have increased by about two million units.
However, while you have been reading the book, you will have converted at least a thousand calories of
ordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air around
you by convection and sweat. This will increase the disorder of the universe by about twenty million million
million million units – or about ten million million million times the increase in order in your brain – and that’s if
you remember everything in this book. In the next chapter but one I will try to increase the order in our neck of
the woods
a little further by explaining how people are trying to fit together the partial theories I have described
to form a complete unified theory that would cover everything in the universe.
 
The chapter after next. If you are currently reading chapter 1, then you will find that information in chapter 3.
 
The chapter after next. If you are currently reading chapter 1, then you will find that information in chapter 3.

I've never heard the phrase 'but one' used like this. Is this common usage in the UK?
 
It's fairly common in BrE, in my opinion.
 
It's fairly common in BrE, in my opinion.
This is getting uncomfortably close to 'second [to] last' thread. :) (It's interesting that while 'second last' and 'second to last' are both acceptable in Br Eng, the 'to' is not optional in 'next to last'*.)

b

PS * Here my brain jumped a groove [and if you didn't use vinyl, or even shellac, records that metaphor won't mean much to you!]. I was thinking of the expression 'last but one'.
 
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