Church’s Thesis

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

We can most easily understand the operation of a computer by considering a simple example. Figure 1 illustrates a program of computer instructions for calculating the square root of a number.1 The thirteen numbered statements correspond to the list of coded instructions stored in the computer’s memory. (Here, for clarity’s sake, we have written them out in English.

Figure 1:

(1) (2) (3) (4) (5)

1. Write 0 in(2)
2. Increment (2)
3. Write 0 in (3)
4. Copy (2) in (3)
5. If (4) equals 0, go to step 12
6. Decrement (4)
7. Copy (2) into (5)
8. If (5) equals 0, go to step 12
9. Decrement (4)
10. Copy (2) into (5)
11. If (5) equals 0, go to step 5
12. Decrement (5)
13. Increment (3)
14. Go to step 8
15. If (3) is not greater than (1), go to step 2
16. Decrement (2)
17. 
    [Then follows Fig. 1, an illustration with the following explanation:Fig. 1. Computer program for computing the square root of a number. To simulate the operation of the computer, place the number in box (1) and follow the instructions, starting with step 1. When step 13 is completed, the square root of the number (rounded down to an integer) will be in box (2). (In these instructions, “increment a number” means to add 1 to it, and “decrement a number” means to subtract 1 from it).]
18. 
    The five boxes correspond to areas in the memory that store data and intermediate computational steps. To simulate the operation of the computer, place a number, such as 9, in box (1). Then simply follow the instructions. When you have completed the last instruction, the square root of your original number will be in box (2). In a computer, each of these instructions would be carried out by the CPU. They illustrate the kind of elementary operations used by present-day computers (although the operations do not correspond exactly to those of any particular computer).
19. 
    The method of finding a square root given in our example may seem cumbersome and obscure, but it is typical of how computers operate. In fact, the practical applicability of computers rests on the observation that every fixed scheme of computation ever formulated can be reduced to a list of simple operations like the one in our example. This observation, first made by several mathematicians in the 1930s and ’40s, is commonly known as Church’s thesis. It implies that, in principle, any scheme of symbol manipulation we can precisely define can be carried out by a modern digital computer.
20. 
    At this point, let us consider our hypothetical sentient computer. According to the exponents of artificial intelligence, the intricate behavior characteristic of a human being is nothing more than a highly complex scheme of symbol manipulation. Using Church’s thesis, we can break down this scheme into a program of instructions comparable to our example in Figure 1. The only difference is that this program will be exceedingly long and complex-it may run to millions of steps. Of course, up till now no one has even come close to actually producing a formal symbolic description of human behavior. But for the sake of argument let’s suppose such a description could be written and expressed as a computer program.
21. 
    Now, assuming a computer is executing such a highly complex program, let us see what we can understand about the computer’s possible states of consciousness. When executing the program, the computer’s CPU will be carrying out only one instruction at any given time, and the millions of instructions comprising the rest of the program will exist only as an inactive record in the computer’s memory. Now, intuitively it seems doubtful that a mere inactive record could have anything to do with consciousness. Where, then, does the computer’s consciousness reside? At any given moment the CPU is simply performing some elementary operation, such as ”Copy the number in box (1687002) into box (9994563).” In what way can we correlate this activity with the conscious perception of thoughts and feelings?
22. 
    The researchers of artificial intelligence have an answer to this question, which they base on the idea of levels of organization in a computer program. We shall take a few paragraphs here to briefly explain and investigate this answer. First we shall need to know what is meant by “levels of organization.” Therefore let us once again consider the simple computer program of Figure 1. Then we shall apply the concept of levels of organization to the program of our “sentient” computer and see what light this concept can shed on the relation between consciousness and the computer’s internal physical states.

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