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Posts Tagged ‘Alan Turing’

## Toy Problems

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In mathematics and information science, a toy problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique.

Why is games fun? In part, because they challenge our ability to think. Even simple games like Tic-Tac-Toe, Nim and Kalah, or puzzles like the Eights Puzzle, are challenging to children. More complex games like checkers, chess, bridge, and Go are difficult enough that it takes years for gifted adults to master them. Nearly all games require seeing patterns, making plans, searching combinations, judging alternative moves, and learning from experience, all being skills which are also involved in many daily tasks.

It’s no surprise that Alan Turing proposed chess playing as a good project for studying computers’ ability to reason. In many ways, games have provided simple proving grounds for many of AI’s powerful ideas.

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## The Turing Test

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The phrase “The Turing Test” is most properly used to refer to a proposal made by Turing (1950) as a way of dealing with the question whether machines can think. According to Turing, the question whether machines can think is itself “too meaningless” to deserve discussion.

However, if we consider the more precise and somehow related question whether a digital computer can do well in a certain kind of game that Turing describes (“The Imitation Game”), then at least in Turing’s eyes we do have a question that admits of precise discussion. Moreover, as we shall see, Turing himself thought that it would not be too long before we did have digital computers that could “do well” in the Imitation Game.

Turing’s Imitation Game

Turing (1950) describes the following kind of game. Suppose that we have a person, a machine, and an interrogator. The interrogator is in a room separated from the other person and the machine. The object of the game is for the interrogator to determine which of the other two the person is, and which the machine is. The interrogator knows the other person and the machine, by the labels ‘X’ and ‘Y’. He does not know which of the other person and the machine is ‘X’ and at the end of the game says either ‘X’ is the person and Y is the machine’ or ‘X’ is the machine and ‘Y’ is the person’. The interrogator is allowed to put questions to the person and the machine of the following kind: “Will X please tell me whether X plays chess?” Whichever of the machine and the other person is X must answer questions that are addressed to X. The object of the machine is to try to cause the interrogator to mistakenly conclude that the machine is the other person; the object of the other person is to try to help the interrogator to correctly identify the machine. About this game, Turing (1950) says:

I believe that in about fifty years’ time it will be possible to program computers, with a storage capacity of about 109, to make them play the imitation game so well that an average interrogator will not have more than 70 percent chance of making the right identification after five minutes of questioning. … I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.

There are two kinds of questions, which can be raised about Turing’s Imitation Game.

• First, there are empirical questions, e.g., Is it true that we now or will soon have made computers that can play the imitation game so well that an average interrogator has no more than a 70 percent chance of making the right identification after five minutes of questioning?
• Second, there are conceptual questions, e.g., Is it true that, if an average interrogator had no more than a 70 percent chance of making the right identification after five minutes of questioning, we should conclude that the machine exhibits some level of thought, or intelligence, or mentality?