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Redazione RHC : 30 November 2025 09:15
Nearly everything artificial intelligence does today is based on a simple but fundamental idea: any problem can be reduced to finding a path from a starting point to a goal.
The computer considers several states, evaluates which are closest to the result, and proceeds in sequence until it finds a solution.
The most obvious comparison is navigation. When a person plots a route on the London Underground, say from Bond Street to King’s Cross, they mentally consider the options: the Central Line to Oxford Circus, a transfer to the Victoria Line, Warren Street, Euston, and finally the final destination.
A computer does the same thing, only faster and without guesswork. It systematically searches for a path, choosing the most efficient steps.
One of the earliest and still best-known algorithms for such search is A* (pronounced ” ay-star” ). It was devised in 1968 , when engineers were trying to teach a robot to move autonomously around a room .
This robot, called Shakey , was created at the Stanford Research Institute in Menlo Park. It looked clumsy, but it was a real breakthrough for its time: a camera, a microphone, a rangefinder, collision sensors, motorized wheels, and a personal computer.
If told to ” go to the library and get an item,” it would plot a route using an internal map, calculate its steps, and begin moving, comparing its path with sensor readings. Shakey was the first robot to make decisions autonomously , rather than simply following commands.
In 2004, he was inducted into the Carnegie Mellon University Robotics Hall of Fame , alongside HAL 9000, R2-D2 , and other icons of the era.
The A* algorithm proved so accurate that it quickly became a classic. If there is a path between two points, it finds it. If there are multiple paths, it chooses the shortest. It doesn’t waste resources on unnecessary detours: it works as economically as possible.
This is exactly the principle used in today’s GPS devices: while a phone instantly plots a route, taking traffic jams and roadblocks into account, an improved version of A* works behind the scenes. The irony is that an algorithm designed to control robots now helps people navigate the real world every day.
But the idea of search doesn’t just work in space. It can also be applied to logical problems, which don’t have roads or maps, but rather possible states and transitions between them . A clear example is the “figure eight” puzzle: a 3×3 grid, eight numbered tiles, and an empty cell. The task is to rearrange the tiles so they are in order. Each move creates a new state, and the solution boils down to finding a sequence of steps that leads from the initial combination to the ideal one.
In the 1950s, two American researchers, Allen Newell and Herbert Simon , decided that the same principle could be applied to human thought. At a conference at Dartmouth in 1956 , they presented the Logic Theorist program, a system that sought proofs of mathematical theorems. Newell was then working at the RAND Corporation and later moved to Carnegie Mellon , where he continued to collaborate with Simon. Simon, a professor of management sciences, later won the Nobel Prize in Economics for his research on how humans make decisions with limited knowledge and time. Their shared goal was simple: to understand whether it was possible to train a machine to reason according to the same principles as humans.
Logic Theorist was the first artificial ” mathematician .” The program viewed proofs as chains of logical steps leading from axioms to conclusions . It proved 38 of the 52 theorems in Bertrand Russell and Alfred Whitehead’s famous work , Principia Mathematica , some even more concisely and elegantly than the original. In essence, Logic Theorist did the same thing as A*: it found a path, only not from a map, but in a space of formulas.
The Principia Mathematica itself, written in the early 20th century, attempted to create a logic on which all mathematics could be built. One example is the law of modus tollens : if the truth of P implies Q, then the falsity of Q implies that P is also false. In a modern example, if winning the lottery makes someone happy, then the unhappy person certainly hasn’t won. Logic Theorist was able to find such connections on her own, starting from the premises and applying logical rules until she reached the desired conclusion.
This achievement was a milestone. For the first time, a machine not only computed, but reasoned, proving , step by step, statements once considered the preserve of human reason. Historians of artificial intelligence later called the Theoretician of Logic the moment when computation became reasoning. Newell and Simon’s program demonstrated that the thought process could be represented as the search for a solution within a vast space of possible steps.
Thus, the idea of seeking—movement from one point to another—has become the heart of artificial intelligence. From the robot Shakey, which chooses a path through a laboratory, to a program capable of proving mathematical truths, all are manifestations of a single principle: to think and make decisions, one must be able to find a path to a goal, even if the map exists only in the machine’s imagination.
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