In every day life the World is a rational place where we can anticipate and arrange for the immediate future. But we are surprised when causeless
events takes place:
Some of them we come to understand much later in life, and some not at all. Such understanding is preceded by a change in our perspective. Several
examples from physics illustrate this:
- When a series of runners with various speeds run along a straight track, their relative order is preserved; but the same people running on a
circular track lose all semblance of order after many rounds and appear chaotic. But the chaos will disappear if we include the completed number of rounds for each runner. So the cyclic process is not cyclic but
motion on a helix.
- The maps of the spherical earth on flat sheets of paper. Some distortion and artificial cracks in the earth's surface are inevitable but they all
disappear on a globe map.
- Quantum systems described in non-quantum language also bring about anomalies and paradoxes which disappear when one sees the non-quantum
descriptions as projection of a richer quantum reality. The limits to the usefulness of such projections is the research frontier of "dechoherence theory".
- In the study of deterministic chaos we have repetitive loops of motion, and they can be unwound by including the count of the complete loops.
Chaos and indeterminacy is the price we pay for the luxury of a simpler perception and perspective. When perspective is higher, perception is altered and new connections are revealed.
Causality and Open Systems:
Both, Science and Philosophy deal with our experience of the world. Physics try to visualise the world as a set of events and processes in space and
time and connected by a chain of causality. In simple systems this chain of causality is tantamount to predictability of the later events and processes given the present state of affairs. Such a world therefore is
completely determinated by its state at any time. The future state is a reexpression of the present; and so is the past. There is time but no history. Nothing essential new ever happens.
But very often the interactions from the system include every widening groups of objects, and it is neither possible nor desirable to retain all such
objects in the system. The knowledge of the present gets degraded as time goes on and there is a gradual deterioration of the chain of causality. The direction in which this happens taken from the present to the
future establishes history, the sense of time.
This influence of external elements is often used as a device to limit the effectiveness of causality and to bring about a certain degree of
unpredictability into the system. Note that the corrupting influences of the surroundings are considered only to the future, not to the past.
But there is another mechanism of losing predictability called deterministic chaos. If a number of people is running along an open track, all starting
from the same general area, as time goes on the order of the runners would be in the order of their speeds and therefore preserved in time. But consider the same runners running on a circular track; in course of
time they would have run many loops. If we look at their order it bears no relation to their speeds and therefore the order can change in course of time. There is no problem of computing the position of each runner
after a fixed time, but their relative positions are chaotic. This case of "Deterministic Chaos" says that order is for all practical purposes replaced by chaos. This special kind is called
"Deterministic Chaos". Since, we can determine the position of each runner precisely.
When one decides to extend physics to include thermodynamics, cosmology and direct personal experience we find new perceptions of lawfulness. For
example, when we include thermodynamics the second law of thermodynamics which states that "entropy (disorder) tends to grow in time." We have a directed time. The corruption of order from lost co-relation
to the "external" world can be used to account for the second law. But deterministic chaos seems to be an intrinsic effect, independent of the surrounding which bring about the same type of phenomena. Also
if we consider the universe as a single physical system there is no physical agency outside it to provide scales of space and time, much less to provide external entropy increasing influences.
When our personal experience in the universe is considered, we certainly plan our activities according to this chain of causality and of entropy
increase. So it is very tempting to assert that we too are "merely physical". Yet we are aware of two branching trees; the phenomenal one in which causes cause effects in the future. But we also have the
conviction now and then, most often when we look back on the past that there seems to be a goal directed sequence of sets of events, where teleology applies: cause is in the result and the future branches are in the
past. It is very reminiscent of the curios Aswatha tree with branches below and roots above mentioned in the Bhagawad Gita (Urdhvamulam athasakham aswattham prahuravyam Gita X). Can the same world exhibit such
different connectivities in different perspectives?
Discerning Order in Chaos:
The change in perspective is the clue. That which appears chaotic in one perspective appears orderly in another. Consider for example that when the
runners are going around the circular track we keep the number of completed turns in addition to the position on the track. This is equivalent to unfolding the path, or equally will to see the loops as the loops on
a helix. The deterministic chaos now becomes a simple deterministic motion and can be taken in both forward and backward senses of time. There is then no loss of information, no increase of entropy. In the limited
case of this system one acquires "knowledge of the three times, past, future and present".
Similarly consider the case of correlations with "external" objects. Such connections cannot be found at any one time by measurements on the
system at one time; and if correlations happen in future, correlations must have developed in the past also. To the extent that we can study the complete enlarged system it can be closed but otherwise we can only
have a statistical description of the subsystem.
Higher Perspective Includes the Lower:
The observer with the higher quality information can not only make the prediction of the later state as seen by him; but also project from it to the
lower level perception "higher" observer can see distinctions between states of the system which are the same for the "lower" observer. Thus as the perspective becomes higher we have finer
perceptions for the world. Truly the world is conditioned by the level of our perception.
We spoke of teleology and of causality. The observed system embedded in the universe in enmeshed in a double tree of correlations. If these
correlations are only partially taken into account we have causality or teleology. These are partial views but the full picture is a web of interconnections and interconnections, with the objects and events being
the vertex points. The sub-system is an artificial cut in this elaborate structure. Once isolated we cannot directly perceive the interconnections except by the inference from the sub-system dynamics.
In the complete picture we also see the relevance of seeing the universe as a web of processes converging to and diverging from objects. In fact the
relevance of objects per se recede except in so far as it is the source or sink of processes.
Language and Distortion:
Such a realisation of the importance of processes is even more significant in the quantum world where the dynamically attributes like position and
motion are identified with processes; specifically the processes of changing the motion and changing the position respectively. When such a unification comes we cannot simultaneously be specifying both qualities at
the same time. This is sometimes called the "Heisenberg uncertainty principle".
Such an uncertainty principle is not a lack of precision in itself but only the impression that arises in expression in common language. It is like
charting a path on the globe by a line on the map on a plane sheet of paper. The map distorts, different kind of map projections distort differently. But there is no distortion on the globe itself. This simple
example is true of all attempts to give conventional descriptions of quantum processes. Sometimes people go to extraordinary sophistications of logic and propositional calculus to make up for the inappropriateness
of the language. So one can overcome some of the difficulties by using the appropriate language, often a mathematical language.
Even in everyday life we come across the need for perception to become more comprehensive. If we look at a solid sculpture from one perspective we get
one view, from another perspective another view. These are different views. Their reconciliation comes in a three dimensional union of all these views. Reality has such a nature. No one view is complete but the
conglomeration of all of them reconciled in one view at a higher level of organisation. Poetic and other artistic creation facilitates this synthetic process.
Can one think in quantum language itself? While most people would say no, it is my impression that many of us can and do. But can we express the
thoughts in sequential steps in ordinary language? Probably not. Between pasyani and vykhari it gets lost.
It is often true that when we ask for the results of measurement on a physical system we can only give a probabilistic answer. For example we ask for
the number of radioactive decays in a given time. For the number of counts on a photodetector illuminated with steady light we get a variety of answers with definite probability distribution. So does this mean that
we can talk about a stochastic process? Such a description is very practical, with the neglected correlations with the surroundings being built into the stochastic process. But it turns out that such descriptions
are not to be possible at all levels. For example in the celebrated two-slit interference experiment where suitable light is illuminating two parallel slits. The light from these two slits fall on a screen where the
interplay of the light from the two paths lead to a band of alternate light and dark patches. The pattern is called an "interference pattern". If we consier a photon (the quantum of light) it has a 50%
probability of going through each slit.
However these probabilities cannot account for the intensity pattern except for the points halfway between the bright and dark fringe. Thus a sequence
of quantum events do not always have a probabilistic description. In the rare cases that it has we talk of "decoherence". The study of decoherence is a very active research frontier at this time. In other
cases it is not meaningful to even assign a probability distribution to dynamical variables. In their place quantum mechanics allows the concept of probability amplitudes. As mentioned before, if one has to
"perceive" the quantum system in terms of amplitudes everything works well. Comprehension demands the escalation of our conceptual repertoire.
Unfolding the Golden Helix:
Let us return to the discussion of "deterministic Chaos". All these motions include instabilities in the sense that small deviations in
initial conditions would lead to large deviations in the long run. Most of these motions have almost cyclic processes. In each style the difference is small but amplified. Therefore if we take the number of cycles
as an additional role we may see the motion as more regular. The motion has to be unfolded in one additional dimension as a helix. While this is not particularly important for cases of fluid turbulence or oval
billiards, the lesson of unfolding systems in larger systems may be relevant for our comprehension of such notions as knowledge-of-three-times (trikala jnana) and seeing stillness-in-motion etc.
In an unpublished paper on "Laya" Professor Surendra Barlingay alludes to this fine perception in music: as a group of swaras are repeated a
number of times, while there is superficial periodity, tune is a subtle index counting the number of such cycles. The true cycle is when the entire sequence is unfolded on a helical time sequence. There is
progression which is hidden by the pronounced repetition.
Perhaps this also has relevance for the lessons learned in the cycle of events the cycle of births. We find ourselves often in the "same"
predicament "same" difficulty yet as we recognize the repetition we subtly advance in our wisdom. So it is said in the Gita in the dialogue between Arjuna and Lord Krishna:
Later was Thy birth,
and that of Vivasvat prior
how then should I understand
that Thou this in the beginning?
Many are these births
that have been passed by Me
and thee, O Arjuna.
I know them all,
whilst thou knowest not,
O scorcher of foes.
Know Me, O son of Pritha as the eternal seed of all beings am the intellect of the intelligent and the heroism of the heroic. [...]
As our perceptions become finer, more complete, the world reveals more features. Nature is
forever new as we renew ourselves. Truly perspective determine the spectrum of perceptions.