The goal of this article is to subsume the
concept of information under a more general header. One basic
notion which can be generally applied is the term "causality".
This concept is used in everyday language, in mythological thinking,
and in scientific languages as well. Therefore there exists some
chance to adopt it to the context of information, to extend it
toward our needs, and to explicate it more precisely. We think
it promising to look for information under this perspective, and
to work out the differences, similarities, and the particularities
of causality of information processes compared to physical ones.
The advantage of this perspective is the unfolding of larger range
of analysis than it is opened by physics. It allows for the inclusion
of different causal relations which cannot be viewed by the sciences.
Let us sketch the main argument: For human
beings it is essential to be able to understand the world, the
reason for understanding is the need for controlling the world,
the reason for controlling is the necessity for survival (although
one should not reduce human activity to this general goal). By
Kant the principle of causality is the a priori of how we talk
about this possibility of control (although we have to modify
its precise content). Cassirer taught us that the content of this
principle is not only applicable in physics, but in everyday modern
(and, as I see it, postmodern), and mythological thinking as well.
Nevertheless the understanding of the principle has changed considerable
over time. Here we will deal with the variations of the content
of causality during the history of physics, and we will look for
the difference and the implications of the causal principle between
the physical and informational processes.
Let us present a first, very general, definition of causality: Causality is the direct, concrete, and fundamental mediation of the connection between objects and processes, where one process (the cause) produces the other one (the effect) (Hˆrz: 208). In this definition causality is seen by Hˆrz as a property of the outer world, a property of things and objects, of objective reality.
It is not restricted to the physical world.
It may be applied to a mythical understanding of the world as
well, or to events of everyday life. Example: Sorcery by analogy
is a causal relationship: If one offers some cereals as a sacrifice
to a god his or her act is the cause for rain. There is a cause
(the sacrifice) and an effect (it is raining).
Causality in Classical Physics
Newton's (1643-1727) mechanical perception of the world was based on three principles (Vogel: 13):
From F = 0 follows the above principle of inertia.
Newton's classical mechanics used the concept
of causality in an elementary way: If a force is acting on a body,
by the principle of action the velocity of the body is changed
in a unique way. The body is accelerated proportionately to the
exerted force.
These principles - well known by the Latin
shortcut "actio est reactio" - imply the unique
determination of the effect on the basis of a known cause. Newton's
writings became the prototype for scientific reasoning
in the future. Newton's axioms nourished Laplace's (1749-1827)
fantasy about the omniscient scientist expressed by his "demon":
A demon who has the compete knowledge of the state of the world
in one single moment would be able to compute all future and past
states. The astronomers mind of the 18th century represents
an approximation to Laplace's demon.
Newton had felt intuitively the limitations
of the mechanical paradigm. He thought that God eventually had
to act directly to the solar system to keep it in order. This
way of interpretation was common for many scholars of those times.
Leibniz, Newton's competitor in being first in developing the
differential calculus, looked for other philosophical concepts
to explain everyday phenomena, in particular human beings, mind,
soul and creativity. In his main brochure "La Monadologie"
the monads, related to Aristotle's "Entelechie", represent
sensitive substances, furnished with wholeness and uniqueness,
indivisible, connected to a body, and created by God (with God
as the only exception). By this construction Leibniz tried to
escape the reductionist view of contemporary science. His motive
was less the need for a unified scientific perspective than the
feeling that the mechanical view offered by Newton or by John
Locke (who died 1704) would belittle the glory of the creator,
his creation, and his creatures. The young physics was not able
to offer an explanation for the whole wealth of phenomena but
restricted itself to the measurable: the basis for its overwhelming
success later on. Nevertheless at Newton's times physics offered
an ideal of complete knowledge about the natural world which science
could approach and approximate over time, while Laplace and others
extended this ideal to an actual possibility and belief (Cassirer
1994: 143).
History of science has taught us that the law of causality has changed its content over time in essential ways. Although at any time it meant a definite connection between events, and their split into the class of "causes" and the class of "effects", nevertheless it was strongely influenced by the corresponding view of
* what is an event,
* what is meant by reality and
* what kind of determination brings the effect
to the fore.
Cassirer characterizes Leibniz' view as "metaphysical
mathematicism" (144). Nature has without libilism to obey
the same laws and rules as mathematics. It this were not so, mathematics
could not be applied to the physical world. Leibniz' causality
means the conviction that mathematics and nature are identical.
God has thought his creation, and by thinking he has produced
it. Gods thoughts are determined by mathematical terms, by size,
number, and measure. These notions do not represent mirrored reality
but are its essential prototypes or archetypes. Thinking and being
meet each other at the moment of creation. Human beings are able
to think after the thoughts of God and therefore are able to understand
nature. But nature is a realm of derived, not of basic forces:
behind the causal relations of the physical world there is one
basic cause, one simple substance, a primitive force, a "Monad".
Leibniz' world is governed by them. Monads are able to self-develop
and to self-unfold. Their utmost law is a law to change. A Monad
conserves itself within this change.
Opposed to Leibniz' thoughts David Hume did
no longer refer to simple substances. Reality is constructed by
simple perception. If we look for a justification of the law of
causality we have to look at the realm of perception. But immediately
we see that in this realm there is no hint on a general law of
causality. Whatever we observe is the simultaneity of two events,
usually we call them cause and effect, because from force of habit
we call the link between them a causal link. "Objects have
no discoverable connexion together" (Hume, D., Treatise of
human nature, Book I, Part III, Sect. VIII, zit. After Cassirer:
150). The explanation of causality cannot be found on an other
level than the psychological one, there is no a-priori, metaphysical
explanation available any longer.
A deeper insight into the problem of causality
found Immanuel Kant. Like Hume he stated: "Denn man kann
von einem Gegenstand und dessen Dasein auf das Dasein des anderen
oder seine Art zu existieren durch blo_e Begriffe dieser Dinge
gar nicht kommen, man mag denselben zergliedern wie man wolle.
Was blieb nun ¸brig? Die Mˆglichkeit der Erfahrung als
einer Erkenntnis, darin uns alle Gegenst‰nde zuletzt m¸ssen
gegeben werden kˆnnen, wenn ihre Vorstellung f¸r uns
objektive Realit‰t haben soll." (Kant, I., Kritik der
reinen Vernunft, 2. Auflage, Ausgabe Cassierer, III, 193f, zit.
Nach Cassirer: 152). Kant shifted the question of causality from
the ontological level to the level of our knowledge, to the realm
of the principles how notions are created and linked to each other.
No longer is it possible to speak of the causal law as related
to real objects or events, but of conditions for our perception
and thinking.
Modifications of the Causal Principle
Before we continue to discuss the consequences
of Kant's shift towards the transcendental we take a look to the
history of science to see how the causal principle was modified
over time.
In his "Philosophiae naturalis principia
mathematica" Newton gave the logical prototype how nature
could be explained, in his version by a reduction to mechanical
principles only, in a mathematical-like way of definitions and
axioms, and by the at that time astonishing metaphysical assumption
of forces which can act not only locally, but over large distance.
The forces are defined as the accelerations they exert to a mass
concentrated in one point. By the knowledge of a few variables
the physical system is defined, and its future and past can be
derived by mathematical methods. The principle "actio est
reactio" up to now is used in the analysis of mechanical
problems. It offers a kind of trick how to decompose the problem
into manageable and operational terms, and how to construct systems
of equations to be solved by straight forward algorithms.
A new view of causality came into existence
when in physics the interest in mechanical problems faded away
and the electromagnetic field became a focus of investigation.
At first the starting points of the new theory was expressed in
old forms: Coulomb's Law was constructed like Newton's Law of
Gravity. Newton's two masses were replaced by two electric charges,
still their distance to the power of (-2) defines the strength
of the force between them. But Maxwell's equations of the electromagnetic
field brought back the older belief that causal relations are
possible at the same location only. The electromagnetic field
and its related forces can be described locally in the static
case, and it represents a wave propagating through space at the
speed of light in the dynamic case. The reversal of view was possible
by the change in the definition of the elements of the theory:
No longer masses concentrated at certain points in space represent
the objects of the theory but extended entities, the fields. Cause
and effect is taking place at one point in space and time again.
No longer hypotheses on distant causality are needed.
One can see from this adaptation of physical
theory that the elements and the laws can change while the basic
causal principle still is in place. Nevertheless the interplay
of elements, laws, and the basic principle is modified. Later
on we will use this property to adopt causalty to the realm of
information.
Causality in Modern Physics
Although Immanuel Kant has moved the perspective
from the laws between objects to the laws of thinking he did not
follow his own ideas with sufficient consequence. In a rational
way he tried to construct the natural world by means of two sets
of assumptions, first on the axioms of classical mechanics, second
on the classical laws of logic. He identified the rational approach
with Newton's Laws and with Euclidian geometry, both - unfortunately,
as we know today - only approximations of a more general picture
which was brought up by Albert Einstein. By his Special and General
Theory of Relativity Einstein because of the empirical finding
of a constant velocity of light in vacuum irrespective of the
movement of the observer he did not only change the way how we
have to add velocities, he interpreted the notion of mass in a
new way, and he put an end to the former separation of content
and container, by showing the interplay between masses and energy,
gravity and inertia in space-time and the geometry of the universe.
Causality not only linked the events of the physical world but
there is a causal effect of a mass on the geometry and vice versa.
The geometry of the space-time exerts forces to the bodies in
the universe. Still Einstein believed in a strictly deterministic
universe: "Gott w¸rfelt nicht!".
From a completely other perspective this believe
was questioned at first by Sadi Carnot who had looked at heat
and its ability to perform work. Clausius created the notion of
entropy. Entropy shed new light at mechanical processes by dividing
them into reversible and irreversible ones, a difference not seen
before. It sharpened the awareness that the physical processes
show some preference. Boltzmann was one of the first who was able
to integrate this strange finding about nature into the body of
physics. His kinetic theory of gases allows for a new way of interpretation
of matter by statistics and probability. By these notions no longer
only a strictly deterministic possibility is available for material
entities by laws of nature, no longer a necessity for its behavior
is available, but now a more flexible way of description of the
future was developed. This change became possible by looking at
two levels of matter at once, at the particle and at the ensemble
level. While it was still possible to speak about a unique determination
of the ensemble, at the same time it became impossible to forecast
the path of a single particle.
From now on the interest in the interplay between
necessity and chance moved into the center of physics. Mechanical
determinism on the micro level could be transformed into probabilities
for certain parameters of the ensemble on the macro level.
A new stage of development was reached by the
Quantum Theory. The discrete nature of energetic states of elementary
particles was revealed, and Heisenberg's Uncertainty Relation
lead to a revision of the traditional perception of reality.
Location and impulse cannot be determined with infinite precision
at the same moment. Therefore it is no longer possible to link
causality to the particles described by space-time. Causality
and space-time description are now seen as complementary on the
level of the particle. Fortunately the probabilities for the occurrence
of the particles themselves are strictly deterministic: Causality
is preserved on the level of the absolute amount of the wave function,
y*y.
Thus one could argue that the meaning of the term "reality"
for physics has to be moved away from the particle level to the
wave function. A single particle cannot be observed with necessary
precision, thus it is not "real" within the realm of
physics.
Let us summarize the result of the above discussions
on the history of physics with other words. It showed the causal
law as a principle guiding our experience. If new experiences
can be made the content of the causal law changes in parallel.
Nevertheless the law can be seen as a selective category, maybe
a definition of the range of the realm of physics. If causality
cannot longer be found, the realm of physics is no longer applicable.
Still one has to question the notion of causality,
in particular with respect to the notions of necessity and chance.
Can one speak of cause if there is a radioactive decay of one
atom? Or should we reserve the causal law for uniquely determined
processes? It seems possible to preserve the causal law for the
process of radioactive decay for the ensemble, the decay of a
particular element is only one moment in the realization of the
causal law of the ensemble. In this way one could deal with chance
without breaking the link to causality (Hˆrz 1971).
From another point of view laws of nature can
be seen as statements about the possibilities of qualitative
change, in particular the Laws of Conservation (of energy, impulse,
mass etc.), in quantitative terms. E.g. the Law of the Conservation
of Energy states the possibility of transformation of one kind
of energy into another (radiation into solid matter and vice versa,
or potential energy to kinetic energy and vice versa).
Ambiguities in Physical Causality
If we want continuously to expand scientific
thought to other phenomena of the world we have to extend the
causal principle once more. There exist several natural ways in
physics itself. One runs along the ambiguity of solutions of mathematical
equations incorporating causal relationships. The breaking of
a stick described by classical mechanics is possible via different
mechanical oscillations, in basic mode (the wavelength of the
oscillation is the twofold of the length of the stick) and of
its overtones (the doubled length of the stick is equal to an
integer greater 1 times the wavelength of the oscillation). They
are characterized by eigenvalues of the basic equation. It depends
on chance which of the solutions will come into existence.
Another possibility consists in the well known
effects deterministic chaos. Small changes in the initial conditions
result in large changes of the trajectory. Although we can derive
a unique solution on the same computer with a fixed precision
for numerical operations, the effects does not remain constant
if we switch to another computer or if we change the initial conditions
by a small amount. This is the reason for the limitation of our
ability to forecast the weather, or to predict what will happen
in such a well defined mechanical system of more than three bodies.
In fact we know now that in case of three bodies the resulting
motion cannot be derived mathematically in a unique way except
in some special cases.
A third source which can be seen in physics
is the radioactive decay or the behavior of single particles in
quantum mechanics. Once again the predictive power of the Schroedinger
Equation is not applicable at the level of individual particles
but only on the behavior of the ensemble.
Physical and Informational Processes Compared
Now, to gain some insight in the specific features
of causality in information process, let us compare information
processes with mechanical ones. We see differences at three levels:
Symbolic representation, ambiguity, unpredictability, and the
lack of any Law of Conservation.
From semiotics we have learned to differentiate
between the syntactic, semantic, and pragmatic aspects of information.
In this article we refer to the pragmatic aspect only (although
I am aware of the fact that one cannot talk about pragmatics
without any meaning of it). Let us give a typical example of human
informational interaction. Someone is greeted by her neighbor
and - because she is a polite lady - answers the greeting with
a friendly word. What is the difference to an event described
by physics? In our everyday understanding of causality we can
say that there is a cause and an effect as in a physical experiment.
We can identify the utterance of a greeting word as the cause
and the answer as the effect.
Symbolic Representation
But there comes up the first essential difference
to physics: Although the spoken word could be measured by physical
units (decibel) it is not the important feature in this interaction.
In this respect it does not make any difference if the word was
spoken forte or piano, with a high pitch or a low one. The important
feature is the symbol of a greeting, transferred to another person.
It mus be interpreted at the receiver, ist meaniing should be
understood by the sender. In physics the physical unit cannot
be exchanched, it is fixed once for all. Information can be represented
in different ways. There is no unique link between an object of
the world and its representation by any word or gesture etc.
Lack of Laws of Conservation
In physics reactions will happen under a certain,
well defined framework of side conditions. One very important
is the particular Law of Conservation (of energy, of impulse,
or of solid matter). The Laws of physics offer a set of possibilities
for the objects or processes to behave. Stated by differential
equations the future behavior in space is dependent on the set
of initial conditions. If a particular set is fixed the future
behavior is well defined. So one could state that the cause of
the movement of a body are its initial conditions, e.g. a certain
acceleration in a gravitation field. Because of the conservation
of energy the body will move along this or that trajectory. Energy
is a general measure for qualitatively different states of the
body. There exists a tertium comparationis, a common rod to measure
states of different quality, like e.g. potential and kinetic energy,
the first is measured proportional to the location of the body
relatively to the source of the gravitation field, the second
is measured proportional to the square of velocity of the body.
The energy units may be applied to both different types of energy.
While in physical processes there exists some
Law of Conservation this is not necessarily so for the information
process itself. Usually in aphysical event the energy balance
before and after the exertion of the cause remains the same. In
an information process this need not be the case. E.g. in electronics
one can control the grid of an electronic valve or the basis of
a field effect transistor by applying a small voltage. The effect
of such an amplifier will be large compared with the small cause.
Of course the Law of Conservation is not violated, because there
has to exist an external source of energy, a battery or a plug
to an electric power network, but this is not the point of view
interesting us. Here, the "cause" in the information
process is the small signal at the grid or the basis, the "effect"
is the change in voltage at the anode or the collector. In fact,
such amplifying processes are characterized by the gain, the multiple
of the size of the output compared with the input signal.
In the realm of information not necessarily
there is a common denominator between cause and effect. Not even
measuring units need to exist on both sides of the causal relation.
The connection between input and output is not a physical one
but a symbolic one. It depends on the interpretation of the input
and the output by the partners of the communication process to
see the link between the two. This link may be defined (or created)
on a subjective basis only.
Creative Power
The most important information processes are such which result in completely different output compared with the input. The reaction of the other person is not determined in a unique way. A lot of usual and predictable answers are possible (hi, hello, good morning etc.), but as well it is possible that the person reacts with a completely unpredictable and thus unpredicted answer. The person could react by a gesture, or by a sentence you have never expected etc. It could be possible as well that the greeting person cannot see any connection between its greeting and the reaction (although there may be one, but only understood by the answering person).
Two different cases are possible:
* Case 1 (Ambiguity): The output is an element of a well defined set of alternatives. The surprise consist in this case just in the selection of the respective element. This first case is very similar in the physical and the informational world.
* Case 2 (Novelty): This case is the more interesting.
In this case any forecast is impossible because we do not even
know the resulting set of possible outputs. This is the case if
a new theory is created, or if a completely new technical device
is developed, or a completely unexpected behavior of an animal
or a person can be observed. "New" could be new to the
person in interaction, or it could be new to humankind in general.
A scientific innovation like Einstein's theory of general relativity
was at the time of creation of the latter type, the answer in
a foreign language unknown to the other person would be an example
of the first. Of course the adjective "new" to an event
has to be exchanged by "known" after its first appearance.
This astonishing fact of creativity became
the cause for Leibniz to think of inborn ideas which were put
into the individual by God, or for Augustine to believe in the
existence of a realm of Platonic ideas we have just to remember.
This position can be found in modern discussions again (Penrose,
Nørretranders 1994). In my opinion they do not take into
account the potential of the human brain to produce genuine new
ideas, therefore they have to shift the solution to external powers.
Still they had to answer the question for the origin of these
Platonic realm.
Causal links ex post
As we have seen above chance and ambiguity
may be shared by physical and infomation processes. But there
exists an essential difference in information compared to physics:
the possibility to determine the reason ex post. The notion of
chance in physics is an other expression for: "No reason
on the level of physics can be found". Random processes of
Brown's motion of particles or radioactive decay are as undetermined
as a human reaction to the salute. But in case of a human reaction
the person could utter some inner motive for its specific answer,
although we know from experiments with split-brain patients and
from psychoanalysis that these explanations could be ex post rationalizations,
as well.
References
Cassirer, E., Determinismus und Indeterminismus
in der modernen Physik - Historische und systematische Studien
zum Kausalproblem, in: Zur modernen Physik, Wissenschaftliche
Buchgesellschaft Darmstadt, Darmstadt 1994: 127-376
Hörz, H., Materiestruktur, VEB Deutscher
Verlag der Wissenchaften, Berlin 1971
W.Leibniz, G.W., Monadologie, Reclam, Stuttgart
1994
Leibniz, G.W., Neue Abhandlungen ¸ber
den menschlichen Verstand, Vorrede und Buch I, Reclam, Stuttgart
1993
Vogel, H. Gerthsen Physik, Springer, Berlin
etc. 1995, 18. Auflage
Nørretranders, T., Spüre die Welt,
Rowohlt, Reinbek bei Hamburg 1994
Penrose, R., Computerdenken, Spektrum der Wissenschaft,
Heidelberg 1991