A computational problem/task in the classical sense must find a specific solution/answer for a particular set of data. In this case, it is implicitly assumed that no other data, except for the ones as mentioned above, are used, and sooner or later, there will come a moment when a solution is obtained, or the absence of a solution is found; this means that there is a criterion for completion. A set of instructions that allow you to find a solution step by step is traditionally called an algorithm. Examples of the problem:
solve a linear system of equations with given coefficients
calculate the minimum, average and maximum value for a given set of numbers
There is, however, another type of computational activity, which, unlike a problem/task, uses data as it appears (pre-setting of data before the start of calculations is not required) and can last as long as you like. In the computer sphere, the permanent activity of this kind is usually called a service, and we will use this term in the future (previously, the term "mission" was used, but it looks less adequate). Accordingly, there is no completion criterion, but there may be a service quality criterion.
The service implementation consists of the cyclical execution of a set of instructions, which makes it, at first glance, indistinguishable from the repeated solution of the same problem with different source data. In general, however, this is not right. Besides updated “external” data (source data), there is “internal” data accumulated during previous cycles that form the system state. The system's internal state changes from cycle to cycle, and the situation potentially depends on all data processed during the entire previous system operation time. Examples of computational services:
room temperature control
investment management
operating system running
From smartphones to supercomputers, real-world computer systems are networks of asynchronously operating "elementary" computers (which include the main processors and graphics coprocessors, I/O control processors, and so on). Concurrency and asynchrony make the situation even more different from classical computational problems.
Thus, the computational problem/task and the computational service are essentially different concepts that require different ways of analysis.
AGI, of course, also belongs to the computational service category, like any control system. The cyclical nature of internal processes is combined with the accumulation of knowledge/data as an inner system state.
Computer science has become a good practice to use a Turing machine to analyze computational processes. This rule was formed at the dawn of the computer age when computers were used exclusively for solving what exactly corresponded to the definition of the computational problem/task. After the emergence of operating systems and control systems based on microcontrollers, the situation changed. Still, traditions remained largely because, unlike the "computer spring," some specialists are engaged in theoretical analysis but different ones in software development.
A Turing machine obviously fits the notion of a computational problem - and just as obviously does not fit the definition of a computational service. It is no less evident that the functioning of AGI is a computational service process with an endless flow of previously unknown and/or non-existent information and does not imply the completion of the process at a specific moment of "comprehension of the truth." That is, to put it simply, the Turing machine is inapplicable for the analysis of both AGI and any permanently working control system, regardless of its complexity.
Finally, it is essential to remember that a Turing machine is deterministic by definition: solving the same problem with the same data, a Turing machine will produce the same result. In practice, approaches based on random numbers are used, which in many cases are much more helpful than deterministic alternatives, making them a natural part of the AGI implementation.
Simultaneously with the emergence of computational services, the concept of an algorithm also began to be used in two very different senses (which is not apparent to many) - as introduced initially (description of the deterministic solution to a problem in the finite number of steps) and like any program code, including those that implement an infinite computational service process.
SUMMATION
Computational processes are divided into two essentially different categories, computational problems/tasks, and computational services.
Computing services are much more complex in nature and, accordingly, much more challenging to analyze.
The Turing machine is suitable for analyzing computational problems/tasks but not applicable for the analysis of computational services.
AGI is a kind of computational service, and therefore the Turing machine is not applicable for the analysis of AGI systems.