The three laws of Robotics

Isaac Asimov

Isaac Asimov was a prolific science fiction and popular science writer who published in the 40s a series of stories about robots, later compiled in the I, Robot collection. In these stories he invented a word that has become a part of the technological vocabulary, as the name of a discipline: Robotics. He also formulated the three famous laws of Robotics, which in his opinion should be implemented in every robot to make secure our interactions with these machines that, when Asimov formulated the laws, were simple future forecasts.

The three laws of Robotics are the following:

First Law: A robot may not harm a human being, or through inaction allow a human being to come to harm.

Second Law: A robot must obey any order given by a human being, except those that conflict with the first law.

Third Law: A robot must protect its own existence as long as such protection does not conflict with the first two laws.

These laws seem quite reasonable, but things are not as simple as they seem. In fact, almost all the robot stories written by Asimov show situations where the laws conflict with each other, or even a law conflicts with itself. This gives rise to difficult situations where the characters must act to solve the problem. However, in all Asimov stories it is assumed as a starting point that the laws are in effect in every robot appearing in those stories.

HAL9000

In the stories by other authors, however, this does not always happen. For example, in the film 2001, a Space Odyssey, written by Arthur C. Clarke, the HAL9000 computer tries to exterminate the human crew in a spaceship travelling to Jupiter. When Asimov attended the premiere of the film, he was outraged at what was happening, until a person next to him made him see that other authors had no obligation to obey his laws.

All this leads us to the following question: Is it possible to implement these laws in practice?

I think we all agree that the first law is most important. The other two refer to it. Therefore, we’ll begin by asking ourselves whether Asimov’s first law of Robotics can be implemented in a robot.

The problems that can be offered to a computer are classified into several groups:

• Simple problems, which any computer can solve with ease.
• NP-hard and NP-complete problems, which can be solved by an ordinary computer if they consist of a few data, but become intractable when the number of data is large. In fact, the computation time grows (almost) exponentially, as a function of the number of data to be processed. These are the kind of problems where quantum computing could possibly make a revolutionary breakthrough, by solving now intractable problems in reasonable times.
• Intrinsically difficult problems, which in principle can be solved, but any ordinary or quantum computer would need a time greater than the age of the universe. One of these problems is the perfect chess player, able to always find in any game a winning sequence of moves.
• Non-computable problems, which cannot be solved, either in an ordinary or in a quantum computer, whose impossibility is proved by mathematics or by reasoning.

Alan Turing

The first non-computable problem was raised by Alan Turing, who also proved that it cannot be solved. This is the Turing machine halting problem, which turned out to be equivalent to Gödel’s first incompleteness theorem.

In an article published in arXiv, I and my five co-authors have shown that Asimov’s first law is equivalent to the Turing machine halting problem, which means that it is not computable. Therefore, Asimov’s first law cannot be implemented in robots, not just now, but never. It is not, therefore, one of those problems out of the reach of current technology, that may not be feasible now, but could become so in the future. It has been proved that implementing this law is totally impossible.

The same post in Spanish
Thematic thread on Natural and Artificial Intelligence: Preceding Next

Manuel Alfonseca