Levels of Organization

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

Although the square-root program of Figure 1 may appear to be a formless list of instructions, it actually possesses a definite structure, which is outlined in Figure 2. This structure consists of four levels of organization. On the highest level, the function of the program is described in a single sentence that uses the symbol square root. On the next level, the meaning of this symbol is defined by a description of the method the program uses to find square roots.

This description makes use of the symbol squared, which is similarly defined on the next lower level in terms of another symbol, sum. Finally, the symbol sum is defined on the lowest level in terms of the combination of elementary operations actually used to compute sums in the program. Although for the sake of clarity we have used English sentences in Figure 2, the description on each level would normally use only symbols for elementary operations, or higher-order symbols defined on the next level down

Figure 2:

1. Find the square root of X.
2. The square root of X is one less than the first number Y with Y squared greater than X.
3. Y squared is the sum of Y copies of Y.
4. The sum of Y and another number is the result of incrementing that number Y times.
   Fig. 2. Levels of organization of the program in Figure 1. The program in Figure 1 can be analyzed in terms of a hierarchy of abstract levels. The level of elementary operations is at the bottom, and each higher level makes use of symbols (such as squared) that are defined on the level beneath it.
5. 
   These graded symbolic descriptions actually define the program, in the sense that if we begin with level 1 and expand each higher-order symbol in terms of its definition on a lower level, we will wind up writing the list of elementary operations in Figure 1. The descriptions are useful in that they provide an intelligible account of what happens in the program. Thus on one level we can say that numbers are being squared, on another level that they are being added, and on yet another that they are being incremented and decremented. But the levels of organization of the program are only abstract properties of the list of operations given in Figure 1. When a computer executes this program, these levels do not exist in any real sense, for the computer actually performs only the elementary operations in the list.
6. 
   In fact, we can go further and point out that even this last statement is not strictly true, because what we call “the elementary operations” are themselves symbols, such as Increment (3), that refer to abstract properties of the computer’s underlying machinery. When a computer operates, all that really happens is that matter and energy undergo certain transformations according to a pattern determined by the computer’s physical structure.
7. 
   In general, any computer program that performs some complex task can be resolved into a hierarchy of levels of description similar to the one given above. Researchers in artificial intelligence generally visualize their projected “intelligent” or “sentient” programs in terms of a hierarchy such as the following: On the bottom level they propose to describe the program in terms of elementary operations. Then come several successive levels involving mathematical procedures of greater and greater intricacy and sophistication. After this comes a level in which they hope to define symbols that refer to basic constituents of thoughts, feelings, and sensory perceptions. Next comes a series of levels involving more and more sophisticated mental features, culminating in the level of the ego, or self.
8. 
   Here, then, is how artificial-intelligence researchers understand the relation between computer operations and consciousness: Consciousness is associated with a “sentient” program’s higher levels of operation-levels on which symbolic transformations take place that directly correspond to higher sensory processes and the transformations of thoughts. On the other hand, the lower levels are not associated with consciousness. Their structure can be changed without affecting the consciousness of the computer, as long as the higher-level symbols are still given equivalent definitions. Referring again to our square-root program, we see that this idea is confirmed by the fact that the process of finding a square root given on level 2 in Figure 2 will remain essentially the same even if we define the operation of squaring on level 3 in some different but equivalent way.
9. 
   If we were to adopt a strictly behavioristic use of the word consciousness, then this understanding of computerized consciousness might be satisfactory-granting, of course, that someone could indeed create a program with the required higher-order organization. Using such a criterion, we would designate certain patterns of behavior as “conscious” and others as not.
11. Generally, a sequence of behavioral events would have to be quite long to qualify as “conscious.” For example, a long speech may exhibit certain complex features that identify it as “conscious,” but none of the words or short phrases that make it up would be long enough to display such features. Using such a criterion, one might want to designate a certain sequence of computer operations as “conscious” because it possesses certain abstract higher-order properties. Then one might analyze the overall behavior of the computer as “conscious” in terms of these properties, whereas any single elementary operation would be too short to qualify.

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