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[Algorithms, brains, computer. What they know and what not. II].

¹Seminar für Philosophie der Technischen Universität, Braunschweig, FRG.

Die Naturwissenschaften

|December 1, 1991

Summary

The Turing machine concept clarifies the limits of computation for both machines and humans. It reveals problems unsolvable by algorithms, showing human superiority over machines is not yet proven.

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Area of Science:

Theoretical computer science
Philosophy of computation

Background:

Understanding the fundamental limits of computation is crucial for both machines and human calculations.
The concept of an algorithm requires precise definition to discuss these limits.

Purpose of the Study:

To explicate the concept of an algorithm.
To explore the fundamental limits of machines and human calculations.
To investigate the relationship between problem-solving procedures and algorithms.

Main Methods:

Utilizing the Turing machine as a formal explication of the concept of an algorithm.
Analyzing the implications of the Turing machine model for computability.

Main Results:

Discovery of problems that are algorithmically unsolvable.
Identification of problems with existing procedures but lacking elegant algorithms.
No definitive proof of fundamental human superiority over machines has been established.

Conclusions:

The Turing machine provides a framework for understanding computational limits.
Certain problems are inherently beyond algorithmic solution.
The question of human versus machine superiority in computation remains open.

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