How a Theoretical Machine Model That Was Never Built Became a Precursor To Modern-Day Computers

In 1928, physicist David Hilbert posed a challenge called "Entscheidungsproblem" (German for "decision problem"), which aimed to ask if mathematics is complete, consistent, and decidable. It asked for a set of rules with the ability to decide whether a statement can be proven using the fundamental rules of logic.

During this time, mathematicians tried to find out if any given mathematical statement could be shown to be true or false using a step-by-step procedure. In modern times, this is what we refer to as an algorithm. In 1936, mathematician Alan Turing published a paper that aimed to prove that the Entscheidungsproblem is not computable and, therefore, not a general process problem.

Turing's intuitive view of computability and how it addresses all computable problems became a basic philosophical question in computer science. More than eight decades after introducing his abstract device, Turing has become one of the most recognized figures in computer science.

The Turing Machine as a Theoretical Model of Computing

To address the problem posed by the Entscheidungsproblem, Turing thought of an imaginary device with an infinitely long tape divided into cells that contain either a 1, a 0, or an empty space. These symbols are used to give instructions to the machine as it tells how the other symbols should be manipulated. As such, the tape functions like memory or data storage in a typical computer. Alan Turing used the abstract device to show that there is no general procedure in solving or calculating the Entscheidungsproblem as it is not computable for first-order logic.

This model allowed Turing to prove that certain mathematical problems cannot be solved by an algorithm and it placed limit on fundamental computation. As described by Stanford Encyclopedia of Philosophy, Turing machines are abstract computational models that were meant to explore the scope and limitations of computing.

In his seminal paper published in 1937, Alan Turing gave an account of the relationship between computable numbers and functions that could lead to developing the theory of functions of a real viable expressed in terms of computable numbers. Turing described a number as computable if its decimal can be written down by a machine calculable by finite means.

Turing Machines and the Modern Computers

Turing's machine did not only try to answer the fundamental questions of computing but also served as a precursor to modern computers. Several models were introduced outside the context of Turing's machine into the foundation of mathematics. Surprisingly, each model captured the computable functions of the Turing machine.

At a certain theoretical level, the functions of Turing machines are equivalent to that of modern electronic computers. The instructions used in Turing machines are similar to the machine-code rules for a computer. What makes Turing machines remarkable is that they are "universal," which means that given the right input, they can perform any ordinary computing task.

Although Turing's work is entirely a theoretical view, the results of his demonstration proved the possibility of developing a model of the sort he described. According to a series presented by the University of Houston's College of Engineering, the birth of the Turing machine paved the way for computer science and affected the philosophy of the human mind. Considering the human brain as a computing machine, Turing's logic supports the idea that anything that goes into our brain can be replicated using the modern computers that we have today.

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