Entscheidungsproblem is unsolvable, Turing [1936] introduced his "computing machines" which are a formalization of a procedure **in Hilbert's sense.**
G¨odel [1965, p. 72] **writes:**
Turing's work gives an analysis of the concept of "mechanical procedure" (alias "algorithm" ...) ... This concept is shown to be equivalent with that of a "Turing machine". A formal system can simply be defined to be any mechanical procedure for producing formulas, called provable formulas.

Hopcroft and Ullman [1979, p. 147] **write that "the Turing machine**
is equivalent in computing power to the digital computer as we know it today". They implicitly assume that the computer is used **for executing a**
given procedure or program that was developed manually. Turing [1986] **asks**
whether a computer can be used **in another way:**
It has been said that computing machines can only carry out the processes that they are instructed to do. ... Up till the present machines have only be been used in this way. But is it necessary that they should always be used in such a manner?

Turing [1969] **discusses the development of intelligence in man and in machines:**
If the untrained infant's mind is to become an intelligent one, it must acquire both discipline and initiative. So far we have been considering only discipline. To convert a brain or machine into a universal machine is the extremest form of discipline. But discipline is certainly not enough in itself to produce intelligence.

That which is required in addition we call initiative. ... Our task is to discover the nature of this residue as it occurs in man, and to try and copy it in machines.

We investigate "the nature of this residue" called "initiative" (see Sieg, 1994, Section 5, Final remarks). Section 2 proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effective enumeration of such functions. This procedure can **be regarded as a bridge to the informal concept of computable (total) functions,**
that is, to Turing's uncomputable residue. On the basis of this procedure Section 3 defines creative machines which can, in a certain sense, "compute" function values beyond the limits of any given Turing machine. Section 4