By Dr. T. D. Singh (Bhaktisvarüpa Dämodara Swami) and Sadäpüta däsa
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.
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