The theoretical background of the computer was developed at the beginning of the 20th century, but it was not until the Second World War that progress was made in developing electrical calculating machines. Now we have a new era; the era of computers. In the beginning, the computer was a machine that had a very limited capacity and calculation, and it was only used in a very few important centers. With the passage of time, computers began to be used in business centers, and eventually the production of personal computers became more widespread. Nowadays, we can see many high-tech machines, like handheld PC’s and robot dogs everywhere we look.
In the last fifty years, computer technology has developed rapidly. With respect to this, logical-thinking devices have also been greatly developed. Artificial Intelligence (AI) provides the logical thinking for these types of devices. The goal of AI is to attain the level of logic that “living systems” (i.e. humans) possess. The improvements in AI systems are encouraging to the scientists involved in the field; they now believe that not only can a humanlike machine be built, but, in fact, a machine that is more advanced than humans can be developed. The debate on this subject has separated scientists into two camps. AI advocates claim that in the future people will have the opportunity to make advanced devices that have a better ability to think and decide than humans have. On the other hand, many scientists think that the decision-making mechanism of the human brain contains something that is beyond electronics and that cannot be replicated in an electronic device.
Before going into details, we must first answer the question “what is intelligence?” A being is intelligent if it understands and evaluates some “known data”; if it makes logical inferences and avoids redundant processes and therefore arrives at a sound solution. The famous English mathematician Alan Turing claimed that “if the interrogator cannot distinguish the machine from the human” then the machine is assumed to be intelligent. The Turing Test consists of an interrogator, a machine and a human placed in three rooms. The interrogator is in contact with the human and the machine over text terminals.
The theory of computation was first propounded by Alan Turing in 1936. He described, in basic terms, “The Turing Machine” which is an abstract machine with an unlimited amount of storage space that can go on computing forever without making any mistakes. The Turing Machine only performs three basic operations; reading, writing, and moving the read-write head. According to the Turing Theorem, all computers are Turing equivalent; that is, any process that can be done by a Turing Machine, can be done by a computer and similarly any process that can be done by a computer, can be done by a Turing Machine.
Figure 1 A simple illustration of a Turing Machine
The Turing machine is an abstract model of computer execution and storage that gives a mathematically precise definition of algorithm or “mechanical procedure.”
All computers perform algorithmic processes. Algorithm means a step by step progression. In other words, you have a certain situation. You solve that situation and proceed to another situation that is better than the last one. Using this step by step solution method you are able to reach the goal situation. This is an algorithmic problem. An example will make this easier to understand:
Suppose we have any 10 numbers.
Problem: What is the sum of these numbers?
Figure 2 The algorithm that gives the sum of any given 10 numbers.
As shown above, the sum is “0” in the beginning. A loop with 10 processes is prepared and the next number is read. The number is added to the sum and the algorithm moves to the next number. The process continues until the 10 numbers have been finished. After the process is finished, the result is written.
On the other hand, there are many known problems that do not have any algorithmic solutions. A simple example is given in the following:
Problem: Find a number that is not the sum of three square numbers.
In this problem we had a bit of luck; we just tried 7 and were able to find the solution. Let’s change the problem a little bit:
Problem: Find a number that is not the sum of four square numbers.
The eighteenth-century mathematician Lagrange proved the well-know theorem that every number can be expressed as the sum of four squares. What this means for our computer is that if we were to simply go on in a mindless way trying to find such a number, the computer would simply chug away forever, never finding any answer. In order to solve this problem, therefore, Lagrange had to apply a method that was not algorithmic. Additionally, Penrose states that “there are certain classes of problems that do not have any algorithmic solutions.”
In fact, Turing described the situation where a computer fails to find a solution and therefore does not come to a stop (or a halt) as a “halting problem.” One good example of this, given by Penrose, is the completely deterministic, but non-computable “tiling problem.” We are given tiles called polyominoes and we have to place these tiles on a Euclidian plane
Figure 3. Various sets of polyominoes that will tile the infinite Euclidean plane (reflected-image tiles being allowed).Neither of the polyominoes in set (c), if taken by itself, will tile the plane, however.
In Figure 3 (a), it is obvious to see the tiling of the plane by tiling around a cross. In figure 3 (b) the same condition holds, but in part (c) the tiles cannot tile a plane by themselves, but only together. Another example is shown in the following.
Figure 4. A set of three polyominoes that will tile the plane, but in a way that never repeats.
The plane can be tiled by using three polyominoes, but not in an algorithmic way. In other words, the computer will try to tile the polyominoes by adding around each of them and, since it cannot find a pattern, it will go on forever and will not be able to arrive at a conclusion as to whether or not the polyominoes will tile the plane.
One of the most important factors that separate computers from the human mind is consciousness. Consciousness is the process of understanding. The computer can compute the data given, but it cannot understand what the data means. For example, when one of your friends calls you, you understand that he has called you and you respond. When you switch on a machine, it starts to work. It is not because the machine has understood that you have pressed the button; rather the electronic structure of the machine has been designed to work when you switch it on. The machine cannot understand; it is not conscious. Here are some more examples:
Figure 5. White to play and draw—easy for humans, but Deep Thought took the castle.
In the chess game above, by just playing the king left and right, white can bring the game to a draw. But, at first to make the game a draw, the white player has to understand the situation. Since the computer has no capability to understand, it may think that it would be more profitable to take the castle and therefore it loses the game.
Figure 6. White to play and draw—again easy enough for humans, but a normal expert chess computer will take the castle.
There is a great temptation to take the black castle with the white bishop, but the correct thing to do is to pretend that the white bishop is a pawn and use it to create another barrier of pawns. Once you have taught the computer to recognize barriers of pawns, it might be able to solve the first problem, but it would fail on the second because it needs an extra level of understanding. The situation is very easy for a human, but as we mentioned, it is quite difficult for a computer.
These examples are halting problems because both situations have endless algorithms to identify the solution, so basically they need to be understood by an intelligent mechanism. Maybe the chess problems can be solved with enough computation, but again we can make the situation more complex. That is to say, the important thing is not computation, but understanding the situation.
In conclusion, the problems we mentioned above are some of the basic problems that AI has to overcome. The present technology is very far from being similar to the human mind. The human mind is not a simple substance; in fact, quite the contrary, it is an incredibly complex structure. There are many things that play a role in the human mind; it is not easy, perhaps it is even impossible, to build a mechanism that is like the human mind.
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