Mike has zeroed in on the same issue that most interested me as I read the
start of the discussion of LBE and the New and Old Intro chapters .... the
relation of 'horizontal' expansion and 'vertical' development. I see this
as connected closely with the issue of contradictions as motivating force,
and with Don's very generative initial question: why would anyone feel
uncomfortable with the status quo? i.e. how do expansive cycles get started?
A lot of us I am sure have been thinking about these issues under various
guises for a long time. I started in the 70s with a notion I called
'slippage' ... the inevitably imperfect match between any abstract category
and any actual material "instance" of the category. Yrjo makes a
wonderfully related point about moving beyond the logicist notion of
abstraction as common properties, which requires a reduced view of
something (seen only in terms of its having these particular properties and
ignoring all else about it), and his 'dialectical' notion of the abstract
as a part-that-is-to-be-functionally-placed-in-a-larger-whole. (Something
that would be called 'extraction' perhaps if it referred only to material
constituents rather than to functional or logical ones.) Slippage
guarantees that we are always faced with the work of, and usually some
dilemma in, reconciling categorial abstractions, of the kind that abound in
verbal language (and are imitated in some kinds of visual representations,
like diagrams; and in symbolic languages that derive from natural language,
like mathematics), with concrete instances. The instances almost fit, don't
quite fit, the slop over the neat edges, they sit on the fence, they fit in
ways that are not canonical ...
Perhaps the same thing can be said of practices, of typical action routines
in repeatable kinds of activities, that are 'abstract' in the sense that we
tend to try to do the same thing in different circumstances. Similar
circumstances, but again the same problem: a typology of situation types
also always fails to quite fit. So we are constantly trying to deploy a
repertory of relatively fixed schemas for action in new concrete situations
where what we are trying do either can't quite be done, given the specific
affordances of this situation, or does quite have the desired effects, or
has unintended side-effects ... and so leads us to improvisation, to
bricolage, to adaptation, to getting stuck, to getting frustrated, and
maybe angry .... or to trying something innovative, or bizarre, or
dangerous, or just untried, or not fully thought out. And perhaps
serendipitous.
My first example and paradigm for slippage was watching a choreographer
create a dance on the dancers. He came with the music in his head (played
on tape or by a pianist for the dancers), and with a plan in his head, even
with some steps, some movements, in the classical ballet repertory (a
relatively fixed vocabulary), and a sense of how he wanted the next section
to look. These were abstract imaginations, they sought to realize in actual
physical dancers on a real floor idealized types of movement. And
frequently they did not work, anatomically (some sequences of idealized
movements could not anatomically flow smoothly into one another),
technically (in terms of these dancers skills), or stylistically (they
imagined right, they danced wrong). So he would improvise, sometimes as
problem-solving, to get close to a fixed ideal or goal by another route,
but often also as creative response: he would see in the 'wrong' concrete
result of his imagined abstract 'right' movement sequence something that
suggested to him an entirely unexpected possibility ... something he had
not considered before, and he would try that, and it might then shift the
whole direction of his project and goals for that section of the dance.
Here was learning, here was development (vertical) that only happened
because of the slippage between ideal and real, abstract type and concrete
token; the contradiction, one might say, between abstract and concrete ...
that, in the context of the larger activity system (classical ballet
conventions, traditions of the roles of choreographer and dancer, the
histories of these individuals, the choreographic project for some dance
company, etc.) provided a pivot and a spur, a resource for change.
One can generalize this case semiotically. A simple second example to spur
the generalization. A phoneme is an abstract unit of phonological
distinctiveness in spoken language; it identifies just what criterial
properties a sound must have to make a syllable sound like one word of a
language rather than another (possible) word: like pot rather than pat, or
bat rather than pat. It's is like an ideal ballet position, minimally
distinctive from some other position, rather than some muddy in-between.
But you can never utter a phoneme. You can only utter a phone, an actual
complex acoustical sound. It may have the criterial properties of the
correct ideal phoneme (or close enough), but it always also has other sound
properties that are NOT specified as criterial. For example it may betray
your 'accent', or the state of your anxiety. When you put phones together,
it is not JUST their phonemic properties that matter, it is also these
'accidental' properties ... and so a set of phonemic instructions, like an
ideally imagined sequence of ballet movements, will always eventually lead
you into trouble, into unexpected awkwardnesses that arise because
accidental properties always necessarily accompany criterial properties.
The systemness of language, or ballet, tells us how to negotiate the
combinations of criterial properties, but to actually speak (or synthesize
realistic language on a computer) you have to also deal with the
accompanying accidental properties and what happens to them in combination.
(Imagine synthesized speech in which the phonemes are perfect, but each
vowel betrays a different inconsistent 'accent'.)
There are a lot of complications in more fully developing the argument, but
the point again is just that slippage is inevitable and slippage between
abstract schemas and concrete actions-in-situations is one 'motor' of
development/expansion. I don't know if I would call it a 'contradiction' in
the classic dialectical sense, but it certainly has the same function. Or
can have.
I see slippage as horizontal. A case where this is a little clearer might
be the integration of verbal and visual representations, or more generally
the simple fact that you can never make meaning with just one semiotic
resource (just with the linguistic system, say) ... because the signifiers
are material, and they alway have other properties in addition to the ones
required by, say, the linguistic system. In print, the 'text' is the same
whatever font we type it in, but we must type it in some font, and fonts
carry meaning in a visual-typographical semiotic system, meaning that
overflows the textual meaning in the narrowest sense. You can't realize
linguistic signs in no medium, and every medium has properties that are
supernumerary with respect to the criterial properties that minimally
distinguish one linguistic sign from another. When we cross the boundary,
horizontally, from spoken language to writing, we get into trouble, we face
choices and dilemmas we could not have anticipated, we make new conventions
and choices, we make new kinds of mistakes ... and we never look at
language the same way again.
And here is the vertical ... the integration horizontally across the
boundaries between typical schemas and actually situated actions, which is
always also that between one set of differences that make a difference and
another, which also is the simplest case of horizontal connection across
distinct situation-types or cultural meaning systems, impels us toward
unanticipatable dilemmas, whose resolution CAN represent vertical
development. It does represent vertical development, I think, when the
connections are not just viable, nor even just sustainable and repeatable,
but when they are truly 'synthetic' -- that is the new expanded, or
extended system of practices (the joint or hybrid system) provides us with
a _multiplied_ system of resources. By this I mean that in the new context
(say of writing), the old resources of spoken language are changed too ...
because, in Yrjo's terms, which are also those of structuralist semiotics,
the old parts are now systematically and functionally integrated into a
new, larger, higher-dimensional whole. The new joint system. If this system
is for us a productive resource, then we have developed in terms I would be
willing to call vertical.
Finally, on the matter of sequence. For me, what matters for vertical
development is not strictness of sequence, but rather the existence of a
'ratchet' effect as some people call it, or of irreversibility. This has
two sides to it, well known in both developmental theory and complex system
dynamics. First, once a new synthesis is achieved, all the components are
transformed (relationally, and so in how they can mean and how we use them)
and so while performance can degrade, you can never go back again to the
status ante quo. Second, you can't take shortcuts. In order to get to later
dynamical regimes of the system, you must first pass through various
intermediate ones. This is not to say that all paths are identical, or that
there are not in real systems a lot of interacting developments that can
have different phase relations to one another (uneven development). So
there is not a fixed sequence, especially not one in terms of details.
There is not even true equifinality, only at most equi-functionality ... we
don't all wind up the same, but we can all in our different ways manage.
So, I share Mike's sense that there is a dialectical relationship between
horizontal expansion and vertical development; that it is the
contradictions, or at least the concrete messiness, of living across
difference, that impels development toward adaptive complexity.
---------------------------
JAY L. LEMKE
PROFESSOR OF EDUCATION
CITY UNIVERSITY OF NEW YORK
JLLBC@CUNYVM.CUNY.EDU
<http://academic.brooklyn.cuny.edu/education/jlemke/index.htm>
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