are provable in the theory. The main problem in the proof of G¨odel's theorem is the construction of such a formula. Analogously to the construction of the Quicksort program (1), an undecidable formula can be constructed on the basis of elementary rules for the formation of formulas, that is, on **the basis** of elementary knowledge about the symbols the formula contains. Ammon [2] describes a proof of G¨odel's theorem and refers to further experiments with the SHUNYATA program.

## 4 Discussion

The Internet is a network of a varying number of computer programs and systems. My simple incompleteness theorem implies that no predefined formal system can completely model such a network because a program (computable function) not "captured" by the formal system can be constructed and added to the network. The proof of my theorem implies that the construction of this program can be achieved automatically.

Systems capable of communicating and interacting with humans more naturally than existing systems should be capable of reconstructing computable functions implicitly used in human forms of communication. My theorem implies that there is no predefined Turing machine or formal **system**
modeling this communication.

Computer programs must be tested and debugged before they can be used in practice. My theorem implies that there is no general predefined algorithm for the verification of programs because a program (computable function) not
"captured" by the algorithm can be constructed from the algorithm itself.

Rather, the verification of programs is achieved on the basis of experience.

The Turing machine producing a sequence of computable functions f1, f2**, ... in the proof of my incompleteness theorem can be regarded as an**
analytical space. The construction of another Turing machine producing f1, f2, ... and a computable function g **not produced by the original machine can**
be regarded as the construction of a new analytical space. Thus, **my simple** theorem implies that all analytical spaces cannot be unified into a single analytical space. Roughly speaking, the development of new knowledge in analytical spaces cannot be regarded as a completely describable "closed box". Rather, it is an open process which may transcend any frame **specified** in advance.

My work can also be regarded as an investigation with the aid of com-