I realize that what you're talking about above is a reference book, but my question was: why a reference book instead of a text book? To some degree, you answered this question by saying:
Texts are boring and stupid and useless
This may be true of all of the texts you've come across, but it isn't true for all texts. Moreover, I'm not sure why you think the same things aren't true of reference books.
The main problem with reference books is that you can't use them to learn anything from. The examples you cite acknowledge this. On the other hand, anything you can do with a reference book, you can do with a sufficiently voluminous textbook.
In addition, your second example also points out a failing of a reference
book model. Important concepts are often defined differently in different
works, and the theorems presented depend upon the definitions given. (The
dichotomy is usually "easy definitions => hard proofs, hard definitions
=> easy proofs") Choosing definitions and theorems willy-nilly from
different text books is a recipe for disaster. Similarly, using an
online reference book to get a definition may or may not give you the
definition you need. With a textbook style, you can (ideally) see which
versions of the theorems result from the given definitions.
But perhaps our visions aren't so far apart after all... What I envision
is something like Mathworld, but with the individual nodes about 1-4 pages
in length. Ideally, they'd be about the length that can be covered in
one 50-minute lecture, covering perhaps an important definition and its
consequences. Further, the nodes would be arranged in an acyclic tree,
and ordered by dependencies. This way, if you're interested in learning
about the solution to the heat equation, you can go to that section,
and quickly find out which sections you need to read (solutions of second
order ODEs with constant coefficients, separation of variables, Fourier
series, etc.) to understand the material of that section. In addition,
after reading a section, you could be given a set of sections which you
are now able to understand. Something like the Technology help viewer
in Freeciv is what I've got in mind, only much larger, of course.
This type of system can be used as a reference book (provided a
searchable index is kept), or as a basis for a text book for a course.
The dependency information should make it easy to plan a course, and
the granularity of the sections should make it easily extensible.
Finally, I'll note that you appear to argue for my position in the second
paragraph. You write:
some [professors] might say, "If I can write this up very well, adding
interesting examples, illustrations, and applications then someone
who is looking this up might become more interested in this topic
and in mathematics in general."
I agree that this could generate some high quality submissions. However,
what you're describing here is a textbook, not a reference book. There's
no way to incorporate a lot of examples, illustrations and applications
into a reference book without turning it into a textbook.
"Die, spork user! And burn in fiery torment!" -- Handy, the Handpuppet of Doom
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