From Web Standards to Web
Combinatorics

Abstract:

Web "standards" have
become nonstandards, now led by implementors rather than architects.
When SVG and HTML were invented people asked "what would we like to be
able to do with the internet?" and then built to address such
vision. Now people ask "what, from a previous vision is expeditious and
inexpensive to implement? What can be cut without too many people
noticing?" It's time to move on. Let's forget about standards and build
web science and before we do that let's build the mathematics of that
science. Just as computer science needed graph theory as a mathematical
foundation, web science needs Web Combinatorics. Let's invent it!
Math has a long half-life; standards don't (except GIF).

Communication from speech to writing to printing to plain old HTML and SVG

Major shifts in communication:

- speech (oops)
- writing (oops x oops)
- printing press (jury is still out -- some setbacks)
- computer/internet -- even before Gopher people knew there would be a web

see Why SVG is going to be really BIG (2009) for background and elucidation

The Graphical Web: Motion, Meaning, Stories, Standards. Pictures for everyone.

Web standards -- what do we need to be able to do that we can't?

- flow into non-rectangles (break the rectilinear mold)
- text flow and warp
- have names of lakes stay inside the right country (magnets)
- knots and overpasses and biological drawings
- simplify replication
- declarative randomization
- collaboration (social networks)
- many big things
- zillions of tiny things
- trust them

Math is not usually mushy (however: fuzzy logic, near periphery of mathematics, society of human mathematicians)

Math can be applied to mushy things: biometrics, psychophysics, data mining, data visualization.

Combinatorics is a branch of
mathematics concerning the study of finite
or countable discrete structures. Aspects of combinatorics include
counting the structures of a given kind and size (enumerative
combinatorics), deciding when certain criteria can be met, and
constructing and analyzing objects meeting the criteria (as in
combinatorial designs and matroid theory), finding "largest",
"smallest", or "optimal" objects (extremal combinatorics and
combinatorial optimization), and studying combinatorial structures
arising in an algebraic context, or applying algebraic techniques to
combinatorial problems (algebraic combinatorics).

-- Source of definition: Wikipedia.

-- Source of definition: Wikipedia.

In web science, fields change. Over time words change in usage (and meaning).

Standards change. (graphic for gif, jpg, png, svg -- guess time frame -- graphic revealed -- hint )

If the calculus of integrals, derivatives and differential equations is the mathematics of physics and engineering,

and graph theory is the mathematics of computer science,

then what is the mathematics of web science?

Answer: ....

Web combinatorics:

- Topology and connectivity
- Packing and Divisions: constraints: gravitation and attraction, tables, tiles, css and rectangles versus "natural" shapes
- Perception, psychophysics, discriminability, illusion, accessibility, relations between geometry, behavior and meaning.
- Semantic combinatorics

combinatorial semantics, word meanings, cooccurrence/grammar, paradox, positional inference, glyph construction.

Examples:

- The world is made of vectors and tilings. Link.
- Animation for its own sake (Behavior comes later). Link
- Partitioning and packing (part of web geometry) Link
- Building with Constraints Link
- Tiling link
- Knots and diagrams link
- Travel and transition link
- Paradox link
- Visual Entendre (explanation) link
- Semantics geometry link
- Behavior link
- Community link
- Semantic combinatorics

Alternative answer: art