Textbooks

Feature ideas

• Extensive cross-referencing. Full text search is not a substitute for good indexing and referencing. I should be able to find the definition of a term, the statement of a theorem, or a particular example or homework problem, with just a quick search. I suggest a contextual index: tag terms that belong in the index, much as you would in a LaTeX document, but have the indexer be context-aware, so that the index entry for the Dominated Convergence Theorem looks something like this:
  • dominated convergence theorem. Definition, section 3.2. See examples 3.2.4, 3.2.7, 3.2.8, problems 3.17 - 3.24. See also monotone convergence theorem.

  with hyperlinks to everything, of course. (Presumably a viewer could offer popups showing the example excerpts and such.)

• Full text search taking advantage of the cross-referencing.

• Hyperlinked notation. Advanced books tend to define all sorts of notation for convergence in distribution, expectation with respect to certain measures, sigma algebras, etc. etc. If we offer a mechanism to define math macros – e.g. I could define \convd for convergence in distribution – we could have the system automatically hyperlink the use of these symbols to their definition, or some sort of notation table. This might mean using a custom language for math, instead of LaTeX syntax.

• Embedded code in R or whatever relevant language, with output included, in the style of R Markdown. Tools for including values from code in text, so code can be used to derive values used in the text.

• Hyperlinked code, in the style of the Racket documentation, in which each function call is automatically linked to the function documentation, as well as being syntax-highlighted.

• Domain-specific languages and tools for things like drawing causal diagrams, generating probability tables, generating boilerplate code for certain tasks, etc.

  • Penrose is a very interesting approach to declarative diagram generation: instead of something like TiKZ, where you must manually specify lines and points and arrows, Penrose lets you define domain-specific specification languages, such as a language for declaring vectors and vector spaces and their relationships. A constrained optimization algorithm then applies a user-defined style to the relationships to decide how to draw them. You can hence provide multiple representations for the same diagram.

• Explorable interactive text, like Tangle or Idyll, so problems and examples can be defined to let the user play with input values and see the results. (This might be tricky to implement; if values are calculated in embedded R, how do we implement that in-browser when the user manipulates the values?)

• Automatic cross-referencing, in the style of LaTeX’s \ref or \cleveref. Maybe the indexer could take advantage of this information in some clever way, or the reference target could include a back-reference in the margin pointing to the sections that reference it.

• Built-in plotting and diagram drawing, via R or TikZ (or whatever favored languages you might have – should be extensible).

• Automatic bibliography management via something imitating BibTeX. (Naturally, there should be back-references to where references are used.)

• Good ways of writing proofs, in the style of Lamport’s 21st Century Proof. (See Writing proofs.)

Technology

See also Scientific typesetting.

LaTeX isn’t suited for the Web. Pollen is an extensible option, given enough willingness to write Racket; Sphinx could perhaps be adapted with enough hacking. MathBook XML is interesting, but I’m not enthused about writing in XML; worth investigating to see whether it’s capable of supporting the features I want, since perhaps writing XML is preferable to reinventing an entire system from scratch.

Examples

• Immersive Linear Algebra, which uses JavaScript-based interactive animations for pretty much every figure in the book. There’s also good use of hyperlinking and cross-referencing: definitions of common terms appear as pop-ups upon hovering over the terms, and referenced equations have both links to context and popups giving the equation itself, so you don’t have to flip back and forth between pages just to see the equation. The book isn’t yet complete, and I think needs some editing and improvement, but the implementation is innovative.

• Quantum Country, an introduction to quantum computing with beautiful design and embedded spaced repetition quizzes that follow up with you after several days to quiz you again. In a companion essay, “How can we develop transformative tools for thought?”, the authors discuss the motivation for spaced repetition and show data suggesting that readers get dramatically more out of the book through engaging with the quizzes repeatedly. They also discuss ideas such as executable books and why nobody seems to be investing in new media for thought.

• Mechanical Watch, an example of how interactive visualizations can be used to make very complicated things very clear.