One area of current interest is the application of semiotic morphisms to
information visualization. It is relatively straightforward to use principles
of algebraic semiotics to critique given representations, but more challenging
to contemplate the generation of appropriate representations. See the online
paper *Scientific Visualization and Semiotic
Morphisms* for more detail.

The cognitive linguists Fauconnier and Turner [4] have studied the "blending" of conceptual representations, and in particular, of metaphors, using diagrams like that below, where the four dashed lines should be arrows that point upwards, representing semiotic morphisms (but note that the diagrams in [4] are actually upside down from this):

B / \ / \ I1 I2 \ / \ / GA

So called "*oxymorons*" (like "military intelligence") are a form
of humor in which there are two different blends, one of which is in some
sense self contradictory; the tension between the two meanings and the
paradoxical nature of one of them gives rise to a pleasant feeling called
"humor" in many humans (see the oxymoron
list). More precisely, it seems that *re*-blending creates this
feeling, for reasons that can be given an evolutionary bases. It also seems
that blends play a key role in many kinds of humor.

An amazing fact about the human mind is that we do a lot of our everyday reasoning using metaphors (which are semiotic morphisms) and blends of metaphors, rather than anything that could be recognized as formal logic. (This recent finding of cognitive science, or more specifically, cognitive linguistics, is discussed in more detail, for example, in [18] and [4].) Thus blends play an important role not just in humor, but in many kinds of practical reasoning, including legal and moral reasoning, as shown in many case studies.

We have developed a rigorous, systematic theory of blends, based on the
rather esoteric branch of mathematics called "category theory," and more
specifically, on the category^{2} of sign systems with semiotic morphisms,
which is actually an "order enriched category," because it is enriched with a
priority ordering on the morphisms. Category theory suggests that the right
definition of blend is characterized by the "optimality" or "universal"
property of "pushouts" (which must be in some sense "lax" because of the
ordering); see [B] for details. The
diagram above is called a **pushout diagram** in category theory - see the
discussion in Appendix B (page 30ff) of [B].

Empirical work will be useful for learning more about the orderings on
representations, thus providing better foundations for measuring the adequacy
of a given representation for a given task. More optimistically, given sign
systems *S1, S2*, where *S1* contains abstract forms of the
information to be conveyed, we would like to generate (preferably
automatically) a semiotic morphism *M : S1 -> S2* that adequately
represents signs from *S1* in the system *S2*. For example, if
*S1* contains instructions for repairing some piece of equipment, and
*S2* is a non-color graphics screen with a speech chip, then the problem
is to generate instructional material that uses those particular capabilities
most effectively for that task.

Another interesting direction for future research is *dynamic* sign
systems; in a sense, the theory is already done, it is only necessary to
replace ordinary algebraic specifications with hidden algebraic
specifications (which are specifically designed to handle dynamics - see [D]) in the mathematical framework given in [B]; some further discussion of this appears
on page 23 of [B]. It will also be
important to do some case studies using these notions. (Note added April
2004: Some case studies may be found in [D].)

Our approach proposes a language for describing perceived regularities of
certain kinds; it does *not* assert that real entities corresponding to
such descriptions actually exist, or that best possible descriptions exist for
any given phenomenon, that is, it does *not* take a "realist" (i.e.,
Platonic) view of signs and representations. William Burroughs famously said
"language is a virus." Updating this in light of Bakhtin's heteroglossia, we
might say that *language is a plague of competing viruses*. Thus we
should not expect to find formal modernist order in this realm, but rather
multiple species of interacting chaotic evolution^{3}; what order there is may be found in our
multiple, partial descriptions.

19 October 1996

Revised 27 February 2000, and further edited in May of 2000 and 2002. Additional minor edits in April 2004.