Let me say at once, the tentative and
rather speculative ideas I am presenting here are not
intended to answer the question of what time is, in an
ontological sense. I am interested in how the thinking mind
might come to have a concept of time. This
concept has been a problem from the beginning of Western
philosophy. It was implicit in the irreconcilable conflict
between Parmenides' notion of an eternal, changeless world of
being and Heraclitus' unceasing flux. The history of modern
science, and especially biology - as Stephen Gould so
convincingly argues - manifests the dichotomy expressed by
the contrasting metaphors of "Time's arrow and Time's
cycle", which he took as title for his book. As Gould
remarks:
"We often try to cram our complex
world into the confines of what human reason can grasp,
by collapsing the hyperspace of true conceptual
complexity into a single line, and then labeling the ends
of the line with names construed as polar opposites
..."2
What human reason grasps, it grasps by
conceptualizing, and then relating the results in its
thinking. I therefore want to change Gould's statement and
say, it is the hyperspace of experience that we collapse into
our concepts. In this sense, knowledge is always our own
construction.
Jean Piaget has shown us that it is more
fruitful to ask how we construct the notions and conceptual
schemes that enable us to deal with the experiential world
than to engage in the ultimately undecidable metaphysical
debates about the nature of reality.
As you all know, Piaget developed a theory
of cognition that is in many ways compatible with Kant's
approach to reason. But he vigorously opposed Kant's notion
that the ideas of space and time are given a priori.
Consequently, he developed a model to show the possibility of
constructing a concept of time that is neither innate nor, as
evolutionary epistemologists claim, predicated on adaptation
to a universe presumed to be temporal in itself.
The section on time in Piaget's fundamental
work, La construction du réel chez l'enfant, ends
with two important conclusions:
L'enfant, devenant capable d'évoquer
des souvenirs non liés à la perception directe,
parvient par cela même à les situer dans un temps qui
englobe toute l'histoire de son univers.*
and
... la durée propre est situe par
rapport à celle des choses, ce qui rend possible à la
fois l'ordination des moments du temps et leur mesure en
relation avec les point de repère extérieurs.**3
In his inimitable way, Piaget showed in
this section of the book, how he developed these conclusions
by minutely observing his children, Laurent and Jacqueline.
As in all construction of conceptual models, Piaget begins by
observing cognizing organisms and then conjectures and
analyzes their experiences. This is necessarily speculative
and at best hypothetical. First, because in each and every
one of us, rational reflection begins much later than the
construction of the first basic schemes that enabled us
somehow to order and provisionally systematize experience and
observations. Second, because when we eventually begin to
reflect upon conceptual operations, we are already well
accustomed to the use of language and its metaphors. Even the
most meticulous scientist cannot be aware of all the
implications of the words he or she uses in an analysis.
Common expressions such as "history" and
"duration" implicitly involve the notion of continuity,
and we therefore tend to think of time as a flow. It
is an image we tacitly accepted when we first heard it said
that "time goes by" or "le temps
passe"; and the image persists regardless of whether
we visualize time as an arrow or as a cycle.
I believe, that the image of time moving
and "going by" is misleading. What goes by are our
experiences.
We know that while we are experiencing one
thing, we cannot experience another. Experiences, therefore,
are manifestly sequential. But they do not move like boats
floating down a river. There is no moving substrate that
carries them along. Each one is superseded by another - just
as are the words when you are reading or, indeed, listening
to me now. There are no intervals filled with the flowing of
time. Some items are retained in memory, others not. If there
are gaps in retrospect, we know that they were filled with
other experiences, or sleep.
A conceptual model of the operations that
generate a particular piece of knowledge must not take any
image for granted. I repeat - I am focusing on knowing,
not on the metaphysical question of what things are.
From my point of view, the passages I have
quoted from Piaget provide an excellent description of the
general process, but they do not cover certain details. There
is one point which, although Piaget touches upon it in the
context of "object permanence" (1937, p.75), I have
not found explained anywhere in his writings: it is the
construction of the kind of continuity that is
implicit in concepts such as history, duration, and flow.
All authors I have read agree that the
relation of continuity is a crucial component of the concept
of time. It, too, must be analyzed in terms of sensorimotor
experience, mental operations performed with this material,
and reflective abstraction from these operations.
The model I am proposing uses elements
which, although not those actually used by Piaget, could be
seen as compatible with his. My conceptual analyses are built
on the presupposition that, because experience is inherently
sequential, abstract concepts begin with a reflection upon
sequences constituted by moments of attention.
The idea to characterize events by
sequences of static situations, like the single frames of a
film, was formulated by Silvio Ceccato at the Cybernetics
Center in Milan in the 1950s, while we were working on a
project to make the meaning of verbs accessible to a
computer.4 Only
recently did I discover that Henri Bergson, half a century
earlier, had already written: "The mechanism of our
ordinary knowledge is of a cinematographical kind."5. Later, however, he said
that this was "a habit of thinking and perceiving that
needed to be broken".6
To explain the notion of duration, he shifted to
the example of a tune. Although the sounds of the notes are
separate, he said, the continuity (and, by implication,
duration) arises because each is modified by the preceding
one.7
In a tune, there is, indeed, a connection
constructed with the help of the successive interaction and
modification of sounds. But this is an empirical abstraction
from the recurrence of individual notes and it functions in
the manner of links in a chain. I would call it sensorimotor
connection, because it does not bestow continuity on
other notes or other elements. It links changes and creates a
succession. Piaget describes this in the context of
experiments with moving objects (Piaget, 1969, p. 67)8. Although this provides
suitable material for the construction of a concept of time,
it does not itself involve that concept.9
What I am pursuing is, I think, close to
what the mathematician William Rowan Hamilton called
"pure time" and described as:
... distinguished on the one hand from
all actual Outward Chronology (or collections of recorded
events and phenomenal marks and measures), and on the
other hand from all Dynamical Science (or reasonings and
results from the notion of cause and effect).
(Hamilton, Mathematical Papers,
3:7)
The frame metaphor of cinematography helps
to illuminate a relation that remains implicit in the
patterns of change such as musical tunes. In a succession of
separate frames, connections between two or more frames are
not given. They may be suggested by the quality of
their content and thus give rise to an empirical abstraction.
But such an abstraction merely links a specific succession of
static frames, such as successive individual sounds that
compose a tune. The frames are static, and only an active
mind can supply a relational concept beyond the simple
succession.
A further act of reflection is needed to
separate the pattern of connectedness from the specific
material, so that it may become available as a general
concept of continuity and duration.
Piaget indeed mentioned the need of such an
act of reflective abstraction in a passage in which he
explained how an object finally acquires its
"permanence":
En effet, par le fait même qu'il entre
dans le système des représentations et des relations
abstraites ou indirectes, l'objet acquiert, pour la
conscience du sujet, un nouveau et ultime degré de
liberté: il est conû comme demeurant identiqué lui
même quels que soient ses déplacements invisibles ou la
complexité des écrans qui le masquent.***
(1937, p.75)
It is the ability to re-present the object
to oneself when it is not actually available in the
perceptual field, that leads to the conception of a
maintained identity. Piaget provides an important hint when
he locates the origin of this ability in the child's
experience of a moving object that is temporarily hidden by a
screen. In that situation, the child tracks the object
visually, continues the tracking motion of her eyes when the
object disappears behind a visual obstacle, and picks it up
again when it reappears. This has been demonstrated
experimentally and it shows that the connection between the
object before and after its disappearance is provided by the
continuous motion the child carries out with her eyes. But
this, too, is still a sensorimotor continuity. It is not
unlike the continuity of a tune, where the preceding notes,
because they continue to reverberate, are linked to the
following ones.
In the construction of permanence, it is
essential that the object, when it is perceived again,
is taken to be the self-same individual as before - not
merely an object that happens to be like the former
one.
Such an individual identity is often
tacitly assumed when there are no sensorimotor elements, such
as visual tracking, or the reverberation of a sound, to
provide an experiential continuity. In these cases it is a
purely conceptual construction, and the use of language tends
to obscure it. The word "same" in English (and
"le même" in French) is a case in point. If
we say to our friend Tom: "You are wearing the same
shirt Jack is wearing," we are speaking of two shirts;
if we say: "You are wearing the same shirt you wore
yesterday," we have only one shirt in mind.
In Piaget's terms, both instances could be
described as assimilation. The results, however, are
different, and the difference opens the path to two divergent
conceptual constructions. In the first case, Tom and Jack may
or may not both be in our visual field. It is irrelevant,
because the judgment of sameness is based on the comparison
of two separate sensory impressions which, in themselves,
entail no permanence. We merely have to be able to re-present
to ourselves the former shirt when we see the second. Indeed,
this re-presentation can serve as prototype of a class, if we
meet other people with shirts that we find "the
same" with regard to the characteristics we have
retained from the earlier experience.
In the second case, however, we regard the
shirt, as Piaget says, as demeurant identiqué lui
même, that is, as the self-same individual that we
encountered before. This individual identity has to be
stretched and preserved throughout the interval between our
first perception of the shirt and the perception we are
assimilating to it now. For us, this interval between the two
perceptions was filled with a succession of other experiences
(perhaps even a night's sleep). Hence there is no
sensorimotor continuity whatever. The shirt's preservation of
identity, therefore, extends through a domain outside
the field of our experience. I have elsewhere suggested that
the creation of this domain eventually serves as foundation
for what we think of as "being" and what
philosophers call ontological reality.8
Here, however, we are concerned with the
concept of time, and in this context I want to stress that,
although the imaginary domain where objects can preserve
their individual identities provides the opportunity for the
construction of time, it does not by itself constitute it. An
additional operation has to be carried out, and I return to
the example of the shirt to explain it.
When we assimilate Tom's shirt to the one
we saw him wear yesterday, we attribute individual identity
to it and assume that it is the self-same shirt. The
assumption may of course be wrong. Tom might reply that he
has half a dozen of these shirts. This would compel us to
conceive of a class instead of an identity. But if our
assumption of identity is not contradicted, we have to think
of a single shirt, one and the same individual that has a
continuous connection with the one we saw yesterday. Yet, we
have no continuous sensorimotor elements to warrant such a
connection, and therefore have to construct it as a
continuity outside our own field of experience. We
have to think of it as a link that is separate but, as it
were, parallel to the succession of experiences we have had
in the interval between the two shirt-perceptions. We
remember the succession of our actual experiences as
continuous and having a sequential order, and we can now
project the pattern of sequentiality on the imaginary line
that preserved the shirt's individual identity. By this
projection we generate a sequentiality without events, an abstracted
flow. This is what Hamilton called "pure time".
In fact, he gave an excellent description of this operation
of projection:
"... we form the nearest
approach to the idea of time when we think of one
order as the mental basis of another, and consider the
latter arrangement, which in this view resembles the
course of events, as reducible to a mental dependence on
the former arrangement which corresponds to the course of
time.10
Wittgenstein, incidentally, expressed the
same idea in his earliest work, the Tractatus
logico-philosophicus, which he wrote during the First
World War and which, although he later discarded parts of it,
contains a great many valuable intuitions. He there wrote:
"The description of the temporal sequence of events is
only possible if we support ourselves on another
process."11
Let me end by emphasizing once more that
what I have presented here in no way contradicts Piaget's
expositions. It is nothing but a slight amplification which,
in my view, strengthens his position against Kant's a
priori and highlights his account of the construction of
reality.
Acknowledgment
My thinking was greatly expanded by reading
Thomas L. Hankins' wonderfully lucid analysis of Hamilton's
ideas (Note 10).
Notes
2. Gould, S.J. (1987) Time's arrow,
time's cycle. Cambridge, Massachusetts: Harvard
Universioty Press; p.191.
3. Piaget, J. (1937) La construction du
réel chez l'enfant. Neuchâtel,
Delachaux et Niestlé; p.306.
4. We used this method successfully in many
semantic analyses, but Ceccato did not publish it until much
later; Ceccato, S. & Zonta, B., Linguaggio,
consapevolezza, pensiero. Milan: Feltrinelli, 1980.
5. Bergson, H. (1907) L'évolution
créatrice,
6. Bergson, H. (1938) La pensée et le
mouvement.
7. Bergson, H. (1889) Essai sur les
données immédiates de la conscience.
8. Piaget, J. (1969) The child's
conception of time. (Translation: A.J.Pomerans), New
York: Basic Books. (Original: Le développement de la
notion de temps chez l'enfant. Paris: P.U.F., 1927)
9. See my "Notes on the concept of
change" in Cahiers de la Fondation Archives Jean
Piaget, No.13 (91-96). Geneva: Fondation Archives Jean
Piaget, 1993
10. Hamilton, W.R. Manuscript in Trinity
College, Dublin; Box VI, 21 April 1832. Quoted in Thomas
L.Hankins, "Algebra as pure time: William Rowan Hamilton
and the foundations of algebra" in P.K.Machamer &
R.G.Turnbull (Eds.), Motion and time, space and matter
(Ch.12), Ohio State University Press, 1976.
11. Wittgenstein, L. (1933) Tractatus
logico-philosophicus. London: Kegan Paul, Trench, Trubner
& Co. (revsd reprint,1933), §6.3611.
* As the child becomes able to recall
memories unrelated to direct perceptiion, it succeeds in this
way to situate them in a time that comprises the entire
history of its universe.
** ... the child's own duration is placed
in relation to the duration of things, which makes possible
at once the ordering of moments of time and their measurement
in relation to external reference points.
*** Indeed, by the very fact that it enters
into the system of representations and abstract, or indirect,
relations, the object acquires an ultimate degree of freedom
in th subject's consciousness: It is now conceived as
remaining identical in spite of all its displacements and the
complexity of the screens that mask it.
