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**Chapter II On Inspiration By Sadaputa Dasa**

In this article we will
examine how human beings acquire knowledge in science, mathematics, and art.
Our focus shall primarily be on the formation of ideas and hypotheses in
science and mathematics, since the formal nature of these subjects tends to put
the phenomena we are concerned with into particularly clear perspective. We
will show that the phenomenon known as inspiration plays an essential part in
acquiring knowledge in modern science and mathematics and the creative arts
(such as music). We will argue that the phenomenon of inspiration cannot
readily be explained by mechanistic models of nature consistent with
present-day theories of physics and chemistry. As an alternative to these
models, a theoretical framework for a nonmechanistic description of nature will
be outlined. While providing a direct explanation of inspiration, this general
framework is broad enough to include the current theories of physics as a
limiting case.

Modern scientists acquire
knowledge, at least in principle, by what is called the hypothetico-deductive
method. Using this method, they formulate hypotheses and then test them by
experimental observation. Investigators consider the hypotheses valid only
insofar as they are consistent with the data obtained by observation, and they
must in principle reject any hypothesis that disagrees with observation. Much
analysis has been directed toward the deductive side of the hypothetico-deductive
method, but the equally important process of hypothesis formation has been
largely neglected. So we ask, "Where do the hypotheses come from?"

It is clear that
scientists cannot use any direct, step-by-step process to derive hypothesis
from raw observational data. To deal with such data at all, they must already
have some working hypothesis, for otherwise the data amounts to nothing more
than a bewildering array of symbols (or sights and sounds), which is no more
meaningful than a table of random numbers. In this connection Albert Einstein
once said, "It may be heuristically useful to keep in mind what one has
observed. But on principle it is quite wrong to try grounding a theory on
observable magnitudes alone. In reality the very opposite happens. It is the
theory which determines what we can observe."__1__

Pure mathematics contains
an equivalent of the hypothetico-deductive method. In this case, instead of
hypotheses there are proposed systems of mathematical reasoning intended to
answer specific mathematical questions. And instead of the experimental testing
of a hypothesis there is the step-by-step process of verifying that a
particular proof, or line of mathematical reasoning, is correct. This
verification process is straightforward and could in principle be carried out
by a computer. However, there is no systematic, step-by-step method of
generating mathematical proofs and systems of ideas, such as group theory or
the theory of Lebesque integration.

If hypotheses in science
and systems of reasoning in mathematics are not generated by any systematic
procedure, then what is their source? We find that they almost universally
arise within the mind of the investigator by sudden inspiration. The classic
example is Archimedes' discovery of the principle of specific gravity. The
Greek mathematician was faced with the task of determining whether a king's
crown was solid gold without drilling any holes in it. After a long period of
fruitless endeavor, he received the answer to the problem by sudden inspiration
while taking a bath.

Such inspirations
generally occur suddenly and unexpectedly to persons who had previously made
some unsuccessful conscious effort to solve the problem in question. They
usually occur when one is not consciously thinking about the problem, and they
often indicate an entirely new way of looking at it-a way the investigator had
never even considered during his conscious efforts to find a solution.
Generally, an inspiration appears as a sudden awareness** **of the problem's
solution, accompanied by the conviction that the solution is correct and final.
One perceives the solution in its entirety, though it may be quite long and
complicated when written out in full.

Inspiration plays a
striking and essential role in the solution of difficult problems in science
and mathematics. Generally, investigators can successfully tackle only routine
problems by conscious endeavor alone. Significant advances in science almost
always involve sudden inspiration, as the lives of great scientists and
mathematicians amply attest. A typical example is the experience of the
nineteenth-century mathematician Karl Gauss. After trying unsuccessfully for
years to prove a certain theorem about numbers, Gauss suddenly became aware of
the solution. He described his experience as follows: "Finally, two days
ago, I succeeded.... Like a sudden flash of lightning, the riddle happened to
be solved. I myself cannot say what was the conducting thread which connected
what I previously knew with what made my success possible."__2__

We can easily cite many
similar examples of sudden inspiration. Here is another one, give by Henri
Poincare, a famous French mathematician of the late nineteenth century. After
working for some time on certain problems in the theory of functions, Poincare
had occasion to go on a geological field trip, during which he set aside his
mathematical work. While on the trip he received a sudden inspiration involving
his researches, which he described as follows: "At the moment when I put
my foot on the step the idea came to me, without anything in my former thoughts
seeming to have paved the way for it, that the transformations I had used ...
were identical with those of non-Euclidean geometry."** 3** Later on, after some
fruitless work on an apparently unrelated question, he suddenly realized,
"with just the same characteristics of brevity, suddenness, and immediate
certainty,"

Although inspirations
generally occur after a considerable period of intense but unsuccessful effort
to consciously solve a problem, this is not always the case. Here is an example
from another field of endeavor. Wolfgang Mozart once described how he created
his musical works: "When I feel well and in good humor, or when I am
taking a drive or walking,... thoughts crowd into my mind as easily as you
could wish. Whence and how do they come? *I do not know and I have nothing to
do with it.... *Once I have a theme, another melody comes, linking itself
with the first one, in accordance with the needs of the composition as a
whole.... Then my soul is on fire with inspiration, if however nothing occurs
to distract my attention. The work grows; I keep expanding it, conceiving it
more and more clearly until I have the entire composition finished in my head,
though it may be long.... It does not come to me successively, with its various
parts worked out in detail, as they will be later on, but it is in its entirety
that my imagination lets me hear it."** 5** (Italics added.)

From these instances we
discover two significant features of the phenomenon of inspiration: first, its
source lies beyond the subject's conscious perception; and second, it provides
the subject with information unobtainable by any conscious effort. These
features led Poincare and his follower Hadamard to attribute inspiration to the
action of an entity that Poincare called "the subliminal self," and
that he identified with the subconscious or unconscious self of the
psychoanalysts. Poincare came to the following interesting conclusions
involving the subliminal self: "The subliminal self is in no way inferior
to the conscious self; it is not purely automatic; it is capable of
discernment; it has tact, delicacy; it knows how to choose, to divine. What do
I say? It knows better how to divine than the conscious self, since it succeeds
where that has failed. In a word, is not the subliminal self superior to the
conscious self?"** 6** Having raised this question, Poincare then
backs away from it: "Is this affirmative answer forced upon us by the
facts I have just given? I confess that for my part, I should hate to accept
it."

Let us carefully examine
the arguments for such a mechanical explanation of inspiration. This question
is of particular importance at the present time, because the prevailing
materialistic philosophy of modern science holds that the mind is nothing more
than a machine, and that all mental phenomena, including consciousness, are
nothing more than the products of mechanical interactions. The mental machine
is specifically taken to be the brain, and its basic functional elements are
believed to be the nerve cells and possibly some systems of interacting
macromolecules within these cells. Many modern scientists believe that all
brain activity results simply from the interaction of these elements according
to the known laws of physics.

No one (as far as we are
aware) has yet formulated an adequate explanation of the difference between a
conscious and an unconscious machine, or even indicated how a machine could be
conscious at all. In fact, investigators attempting to describe the self in
mechanistic terms concentrate exclusively on the duplication of external
behavior by mechanical means; they totally disregard each individual person's
subjective experience of conscious self-awareness. This approach to the self is
characteristic of modern behavioral psychology. It was formally set forth by
the British mathematician A. M. Turing, who argued that since whatever a human
being can do a computer can imitate, a human being is merely a machine.

For the moment we will
follow this behavioristic approach and simply consider the question of how the
phenomenon of inspiration could be duplicated by a machine. Poincare proposed
that the subliminal self must put together many combinations of mathematical
symbols by chance until at last it finds a combination satisfying the desire of
the conscious mind for a certain kind of mathematical result. He proposed that
the conscious mind would remain unaware of the many useless and illogical
combinations running through the subconscious, but that it would immediately
become aware of a satisfactory combination as soon as it was formed. He
therefore proposed that the subliminal self must be able to form enormous
numbers of combinations in a short time, and that these could be evaluated
subconsciously as they were formed, in accordance with the criteria for a
satisfactory solution determined by the conscious mind.

As a first step in evaluating
this model, let us estimate the number of combinations of symbols that could be
generated within the brain within a reasonable period of time. A very generous
upper limit on this number is given by the figure 3.2 x 1046. We obtain
this figure by assuming that in each cubic Angstrom unit of the brain a
separate combination is formed and evaluated once during each billionth of a
second over a period of one hundred years. Although this figure is an enormous
overestimate of what the brain could possibly do within the bounds of our
present understanding of the laws of nature, it is still infinitesimal compared
to the total number of possible combinations of symbols one would have to form
to have any chance of hitting a proof for a particular mathematical theorem of
moderate difficulty.

If we attempt to
elaborate a line of mathematical reasoning, we find that at each step there are
many possible combinations of symbols we can write down, and thus we can think
of a particular mathematical argument as a path through a tree possessing many
successive levels of subdividing branches. This is illustrated in the figure
below. The number of branches in such a tree grows exponentially with the
number of successive choices, and the number of choices is roughly proportional
to the length of the argument. Thus as the length of the argument increases,
the number of branches will very quickly pass such limits as 1046 and 10100 (1 followed by 100 zeros). For example,
suppose we are writing sentences in some symbolic language, and the rules of
grammar for that language allow us an average of two choices for each
successive symbol. Then there will be approximately 10100 grammatical sentences of 333 symbols in
length.

* An Illustration is
here: [Explanation of illustration:] The relationship between different
possible lines of mathematical reasoning can be represented by a tree. Each
node represents a choice among various possibilities that restricts the further
development of the argument.

Even a very brief
mathematical argument will often expand to great length when written out in
full, and many mathematical proofs require pages and pages of highly condensed
exposition, in which many essential steps are left for the reader to fill in.
Thus there is only an extremely remote chance that an appropriate argument
would appear as a random combination in Poincare's mechanical model of the
process of inspiration. Clearly, the phenomenon of inspiration requires a
process of choice capable of going more or less directly to the solution,
without even considering the vast majority of possible combinations of
arguments.

The requirements that
this process of choice must meet are strikingly illustrated by some further
examples of mathematical inspiration. It is very often found that the solution
to a difficult mathematical problem depends on the discovery of basic
principles and underlying systems of mathematical relationships. Only when
these principles and systems are understood does the problem take on a
tractable form; therefore difficult problems have often remained unsolved for
many years, until mathematicians gradually developed various sophisticated
ideas and methods of argument that made their solution possible. However, it is
interesting to note that on some occasions sudden inspiration has completely
circumvented this gradual process of development. There are several instances
in which famous mathematicians have, without proof, stated mathematical results
that later investigators proved only after elaborate systems of underlying
relationships had gradually come to light. Here are two examples.

The first example
concerns the zeta-function studied by the German mathematician Bernhard
Riemann. At the time of his death, Riemann left a note describing several
properties of this function that pertained to the theory of prime numbers. He
did not indicate the proof of these properties, and many years elapsed before
other mathematicians were able to prove all but one of them. The remaining
question is still unsettled, though an immense amount of labor has been devoted
to it over the last seventy-five years. Of the properties of the zeta-function
that *have *been verified, the mathematician Jacques Hadamard said,
"All these complements could be brought to Riemann's publication only by
the help of facts which were completely unknown in his time; and, for one of
the properties enunciated by him, it is hardly conceivable how he can have
found it without using some of these general principles, no mention of which is
made in his paper."__8__

The work of the French
mathematician Evariste Galois provides us with a case similar to Riemann's.
Galois is famous for a paper, written hurriedly in sketchy form just before his
death, that completely revolutionized the subject of algebra. However, the
example we are considering here concerns a theorem Galois stated, without proof,
in a letter to a friend. According to Hadamard this theorem could not even be
understood in terms of the mathematical knowledge of that time; it became
comprehensible only years later, after the discovery of certain basic
principles. Hadamard remarks "(1) that Galois must have conceived these
principles in some way; (2) that they must have been unconscious in his mind,
since he makes no allusion to them, though they by themselves represent a
significant discovery."__9__

It would appear, then,
that the process of choice underlying mathematical inspiration can make use of
basic principles that are very elaborate and sophisticated and that are
completely unknown to the conscious mind of the person involved. Some of the
developments leading to the proof of some of Riemann's theorems are highly
complex, requiring many pages (and even volumes) of highly abbreviated
mathematical exposition. It is certainly hard to see how a mechanical process
of trial and error, such as that described by Poincare, could exploit such principles.
On the other hand, if other, simpler solutions exist that avoid the use of such
elaborate developments, they have remained unknown up to the present time,
despite extensive research devoted to these topics.

The process of choice
underlying mathematical inspiration must also make use of selection criteria
that are exceedingly subtle and hard to define. Mathematical work of high
quality cannot be evaluated simply by the application of cut-and-dried rules of
logic. Rather, its evaluation involves emotional sensibility and the
appreciation of beauty, harmony, and other delicate aesthetic qualities. Of
these criteria Poincare said, "It is almost impossible to state them
precisely; they are felt rather than formulated."** 10** This
is also true of the criteria by which we judge artistic creations, such as
musical compositions. These criteria are very real but at the same time very
difficult to define precisely. Yet evidently they were fully incorporated in
that mysterious process which provided Mozart with sophisticated musical
compositions without any particular effort on his part and, indeed, without any
knowledge of how it was all happening.

If the process underlying
inspiration is not one of extensive trial and error, as Poincare suggested, but
rather one that depends mainly on direct choice, then we can explain it in
terms of current mechanistic ideas only by positing the existence of a very
powerful algorithm (a system of computational rules) built into the neural
circuitry of the brain. However, it is not at all clear that we can
satisfactorily explain inspiration by reference to such an algorithm. Here we
will only briefly consider this hypothesis before going on to outline an
alternative theoretical basis for the understanding of inspiration.

The brain-algorithm
hypothesis gives rise to the following basic questions.

(1)* Origins. *If
mathematical, scientific, and artistic inspirations result from the workings of
a neural algorithm, then how does the pattern of nerve connections embodying
this algorithm arise? We know that the algorithm cannot be a simple one when we
consider the complexity of automatic theorem-proving algorithms that have been
produced thus far by workers in the field of artificial intelligence.** 11** These
algorithms cannot even approach the performance of advanced human minds, and
yet they are extremely elaborate. But if our hypothetical brain-algorithm is
extremely complex, how did it come into being? It can hardly be accounted for
by extensive random genetic mutation or recombination in a single generation,
for then the problem of random choice among vast numbers of possible
combinations would again arise. One would therefore have to suppose that only a
few relatively probable genetic transformations separated the genotype of
Mozart from those of his parents, who, though talented, did not possess
comparable musical ability.

However, it is not the
general experience of those who work with algorithms that a few substitutions
or recombinations of symbols can drastically improve an algorithm's performance
or give it completely new capacities that would impress us as remarkable.
Generally, if this were to happen with a particular algorithm, we would tend to
suppose that it was a defective version of another algorithm originally
designed to exhibit those capacities. This would imply that the algorithm for
Mozart's unique musical abilities existed in a hidden form in the genes of his
ancestors.

This brings us to the
general problem of explaining the origin of human traits. According to the
theory most widely accepted today, these traits were selected on the basis of
the relative reproductive advantage they conferred on their possessors or their
possessors' relatives. Most of the selection for our hypothetical hidden
algorithms must have occurred in very early times, because of both the
complexity of these algorithms and the fact that they are often carried in a
hidden form. It is now thought that human society, during most of its
existence, was on the level of hunters and gatherers, at best. It is quite hard
to see how, in such societies, persons like Mozart or Gauss would ever have had
the opportunity to fully exhibit their unusual abilities. But if they didn't,
then the winnowing process that is posited by evolution theory could not
effectively select these abilities.

We are thus faced with a
dilemma: It appears that it is as difficult to account for the origin of our
hypothetical inspiration-generating algorithms as it is to account for the
inspirations themselves.

(2)* Subjective
experience. *If the phenomenon of inspiration is caused by the working of a
neural algorithm, then why is it that an inspiration tends to occur as an
abrupt realization of a complete solution, without the subject's conscious
awareness of intermediate steps? The examples of Riemann and Galois show that
some persons have obtained results in an apparently direct way, while others
were able to verify these results only through a laborious process involving
many intermediate stages. Normally, we solve relatively easy problems by a conscious,
step-by-step process. Why, then, should inspired scientists, mathematicians,
and artists remain unaware of important intermediate steps in the process of
solving difficult problems or producing intricate works of art, and then become
aware of the final solution or creation only during a brief experience of
realization?

Thus we can see that the
phenomenon of inspiration cannot readily be explained by means of mechanistic
models of nature consistent with present-day theories of physics and chemistry.
In the remainder of this article we will suggest an alternative to these
models.

It has become fairly
commonplace for scientists to look for correspondence between modern physics
and ancient Eastern thought and to find intriguing suggestions for hypotheses
in the *Upanishads, *the *Bhagavad-gita. *and similar Vedic texts.
The *Bhagavad-gita* in particular gives a description of universal reality
in which the phenomenon of inspiration falls naturally into place. Using some
fundamental** **concepts presented in the *Bhagavad-gita, *we shall
therefore outline a theoretical framework for the description of nature that
provides a direct explanation of inspiration, but that is still broad enough to
include the current theories of physics as a limiting case. Since here we are
offering these concepts only as subject matter for thought and discussion, we
will not try to give a final or rigorous treatment.

The picture of universal
reality presented in the *Bhagavad-gita* differs from that of current
scientific thinking in two fundamental respects.

(1) Consciousness is
understood to be a fundamental feature of reality rather than a by-product of
the combination of nonconscious entities.

(2) The ultimate
causative principle underlying reality is understood to be unlimitedly complex,
and to be the reservoir of unlimited organized forms and activities.
Specifically, the *Bhagavad-gita* posits that the underlying, absolute
cause of all causes is a universal conscious being and that the manifestations
of material energy are exhibitions of that being's conscious will. The
individual subjective selves of living beings (such as ourselves) are
understood to be minute parts of the absolute being that possess the same
self-conscious nature. These minute conscious selves interact directly with the
absolute being through consciousness, and they interact indirectly with matter
through the agency of the absolute being's control of matter.

In modern science the
idea of an ultimate cause underlying the phenomenal manifestation is expressed
through the concept of the laws of nature. Thus in modern physics all causes
and effects are thought to be reducible to the interaction of fundamental
physical entities, in accordance with basic force laws. At the present moment
the fundamental entities are thought by some physicists to comprise particles
such as electrons, muons, neutrinos, and quarks, and the force laws are listed
as strong, electromagnetic, weak, and gravitational. However, the history of
science has shown that it would be unwise to consider these lists final. In the
words of the physicist David Bohm, "The possibility is always open that
there may exist an unlimited variety of additional properties, qualities,
entities, systems, levels, etc., to which apply correspondingly new kinds of
laws of nature."__12__

The picture of reality
presented in the *Bhagavad-gita* could be reconciled with the world view
of modern physics if we were to consider mathematical descriptions of reality
to be approximations, at best. According to this idea, as we try to formulate
mathematical approximations closer and closer to reality, our formalism will
necessarily diverge without limit in the direction of ever-increasing
complexity. Many equations will exist that describe limited aspects of reality
to varying degrees of accuracy, but there will be no single equation that sums
up all principles of causation.

We may think of these
equations as approximate laws of nature, representing standard principles
adopted by the absolute being for the manifestation of the physical universe.
The *Bhagavad-gita* describes the absolute being in apparently paradoxical
terms, as simultaneously a single entity and yet all-pervading in space and
time. This conception, however, also applies to the laws of physics as
scientists presently understand them, for each of these laws requires that a
single principle (such as the principle of gravitational attraction with the
universal constant G) apply uniformly throughout space and time.

The difference between
the conceptions of modern physics and those presented in the *Bhagavad-gita*
lies in the manner in which the ultimate causal principle exhibits unity. The
goal of many scientists has been to find some single, extremely simple equation
that expresses all causal principles in a unified form. According to the *Bhagavad-gita*,
however, the unity of the absolute being transcends mathematical description.
The absolute being is a single self-conscious entity possessing unlimited
knowledge and potency. Therefore a mathematical account of this being would
have to be limitlessly complex.

According to the *Bhagavad-gita*,
the phenomenon of inspiration results from the interaction between the
all-pervading absolute being and the localized conscious selves. Since the
absolute being's unlimited potency is available everywhere, it is possible for
all varieties of artistic and mathematical creations to directly manifest
within the mind of any individual. These creations become manifest by the will
of the absolute being in accordance with both the desire of the individual
living being and certain psychological laws.

We have observed that the
attempt to give a mechanical explanation of inspiration based on the known
principles of physics meets with two fundamental difficulties. First, the
process of inspiration can be explained mechanically only if we posit the existence
of an elaborate algorithm embodied in the neural circuitry of the brain.
However, it is as hard to account for the origin of such an algorithm as it is
to account for the inspirations themselves. Second, even if we accept the
existence of such an algorithm, the mechanical picture provides us with no
understanding of the subjective experience of inspiration, in which a person
obtains the solution to a problem by sudden revelation, without any awareness
of intermediate steps.

If it is indeed
impossible to account for inspiration in terms of known causal principles, then
it will be necessary to acquire some understanding of deeper causal principles
operating in nature. Otherwise, no explanation of inspiration will be possible.
It is here that the world view presented in the *Bhagavad-gita* might be
useful to investigators. The *Bhagavad-gita* provides a detailed account
of the laws by which the individual selves and the absolute being interact, and
this account can serve as the basis for a deeper investigation of the
phenomenology of inspiration.