Computation and algorithms are broadly classified into two categories: machine computation and natural computation. Machine computation is the generic term for computation. In machine computation, the computing subjects are humans who use computers, such as PCs and abacuses, which are separate from the computing subject.
In natural computation, computing subjects and computers are integrated; hence, the computing subjects are computers. In machine computation, as computers exist outside the computing subject, computation is completed by the computers; hence, the subjects are simply waiting for the computers to provide their result. Machine computation is essentially mathematics, and the computers that exist outside of the computing subjects have been investigated in detail.
By contrast, in natural computation, as the computing subjects themselves are also computers, the subjects must decide when to start and halt computation.
Consequently, computations through natural computation sometimes do not halt. For example, the “natural computation” of the French artist Alberto Giacometti while expressing his impression of Japanese philosopher Isaku Yanaihara did not halt easily and took several months; even if “materials for computation” such as canvas or clay could not be used (because of too much paint or sharpening sculpture), computations continued without a pause. If this scenario were to occur with machine computation, the computers would break and be physically forced to stop.