Alan Turing. Oracle predicts from chaos

Alan Turing dreamed of creating an "oracle" capable of answering any question. Neither he nor anyone else built such a machine. However, the computer model that the brilliant mathematician came up with in 1936 can be considered the matrix of the computer age - from simple calculators to powerful supercomputers.

The machine built by Turing is a simple algorithmic device, even primitive compared to today's computers and programming languages. And yet it is strong enough to allow even the most complex algorithms to be executed.

Alan Turing

In the classical definition, a Turing machine is described as an abstract model of a computer used to execute algorithms, consisting of an infinitely long tape divided into fields in which data is written. The tape can be endless on one side or on both sides. Each field can be in one of N states. The machine is always located above one of the fields and is in one of the M-states. Depending on the combination of machine state and field, the machine writes a new value to the field, changes the state, and then may move one field to the right or left. This operation is called an order. A Turing machine is controlled by a list containing any number of such instructions. The numbers N and M can be anything, as long as they are finite. The list of instructions for a Turing machine can be thought of as its program.

The basic model has an input tape divided into cells (squares) and a tape head that can only observe one cell at any given time. Each cell can contain one character from a finite alphabet of characters. Conventionally, it is considered that the sequence of input symbols is placed on the tape, starting from the left, the remaining cells (to the right of the input symbols) are filled with a special symbol of the tape.

Thus, a Turing machine consists of the following elements:

• a movable read/write head that can move across the tape, moving one square at a time;
• a finite set of states;
• final character alphabet;
• an endless strip with marked squares, each of which can contain one character;
• a state transition diagram with instructions that cause changes at each stop.

Hypercomputers

The Turing Machine proves that any computer we build will have inevitable limitations. For example, related to the famous Gödel incompleteness theorem. An English mathematician proved that there are problems that a computer cannot solve, even if we use all the computational petaflops of the world for this purpose. For example, you can never tell if a program will get into an infinitely repeating logical loop, or if it will be able to terminate - without first trying a program that risks getting into a loop, etc. (called a stop problem). The effect of these impossibilities in devices built after the creation of the Turing machine is, among other things, the familiar “blue screen of death” to computer users.

Alan Turing book cover

The fusion problem, as shown by the work of Java Siegelman, published in 1993, can be solved by a computer based on a neural network, which consists of processors connected to each other in a way that mimics the structure of the brain, with a computational result from one going to "input" to to another. The concept of "hypercomputers" has emerged, which use the fundamental mechanisms of the universe to perform calculations. These would be - however exotic it may sound - machines that perform an infinite number of operations in a finite time. Mike Stannett of the British University of Sheffield proposed, for example, the use of an electron in a hydrogen atom, which in theory can exist in an infinite number of states. Even quantum computers pale in comparison to the audacity of these concepts.

In recent years, scientists have been returning to the dream of an "oracle" that Turing himself never built or even tried. Emmett Redd and Stephen Younger of the University of Missouri believe it is possible to create a "Turing supermachine". They follow the same path that the aforementioned Chava Siegelman took, building neural networks in which at the input-output, instead of zero-one values, there is a whole range of states - from the signal “fully on” to “fully off”. As Redd explains in the July 2015 issue of NewScientist, “between 0 and 1 lies infinity.”

Mrs. Siegelman joined the two Missouri researchers, and together they began to explore the possibilities of chaos. According to the popular description, chaos theory suggests that the flapping of a butterfly's wings in one hemisphere causes a hurricane in the other. The scientists who build Turing's supermachine have much the same in mind - a system in which small changes have big consequences.

By the end of 2015, thanks to the work of Siegelman, Redd, and Younger, two prototype chaos-based computers should be built. One of them is a neural network consisting of three conventional electronic components connected by eleven synaptic connections. The second is a photonic device that uses light, mirrors, and lenses to recreate eleven neurons and 3600 synapses.

Many scientists are skeptical that building a "super-Turing" is realistic. For others, such a machine would be a physical recreation of the randomness of nature. The omniscience of nature, the fact that it knows all the answers, comes from the fact that it is nature. The system that reproduces nature, the Universe, knows everything, is an oracle, because it is the same as everyone else. Perhaps this is the path to an artificial superintelligence, to something that adequately recreates the complexity and chaotic work of the human brain. Turing himself once suggested putting radioactive radium into a computer he had designed to make the results of his calculations chaotic and random.

However, even if prototypes of chaos-based supermachines work, the problem remains how to prove that they really are these supermachines. Scientists do not yet have an idea for a suitable screening test. From the point of view of a standard computer that could be used to check this, supermachines can be considered as so-called erroneous, that is, system errors. From a human point of view, everything can be completely incomprehensible and ... chaotic.