Re: Page and line penalties

[Joe Neeman]

On Fri, 7 Apr 2006 20:00, Han-Wen Nienhuys wrote:
> Joe Neeman wrote:
> > On Fri, 7 Apr 2006 16:31, Werner LEMBERG wrote:
> >> TeX has exactly the same problem.
> >
> > Does TeX allow the user to arbitrarily assign penalties for inserting a
> > line break at the end of any word?
>
> Yes, I'm certain. See ch. 14 of the TeXbook (you can download that book,
> btw). In fact our use of the value 10000 was taken from Knuth's example,
> who takes 10000 to mean "infinity".
Thanks -- Werner has sent me a copy of that chapter. I will read it next week.

>
> > OK, so the solution will always have a certain level of instability. Just
> > to put some idea of scale on my previous example graphs, it's possible
> > that LilyPond will be tossing up between using 5 systems and using 10
> > systems. 5 systems provides much better spacing but 10 systems has less
> > penalties. The total badness is _slightly_ less for 5 systems so Lily
> > goes with that.
>
> I think this is perfectly reasonable, at least if you're trying to fill
> out pages. 5 systems=1 page, 10 systems=2 pages.

I wasn't thinking in terms of filling out pages. The point is that, 
independent of page breaks, you might have a situation where F(5 lines) < F(6 
lines) < F(7 lines) < F(8 lines) < F(9 lines) but F(10 lines) is between F(5) 
and F(6). Just because the line break penalties happen to add up strangely.

I don't think TeX has to deal with this problem because each paragraph is 
self-contained. In LilyPond, every line affects every other line. (This is 
just an initial reaction. It might change after I read the TeXbook.) 
Therefore penalties in TeX cause less instability than penalties in LilyPond. 
Or at least they only cause local instability.