Blog Ekkehard Friebe

Ich nehme Bezug auf meinen Blog-Eintrag: Nikolai Rudakov: „Establishment”. Aus dem dort genannten Buch (1981): „Fiction stranger than truth – In the metaphysical labyrinth of relativity” von Nikolai Rudakov bringe ich nachstehend eine weitere Leseprobe:

Zitat: 

3 Mathematics
Mathematics is a product of the human mind. It belongs to the realm of pure thought and has a life of its own which is not necessarily related to, or associated with, other disciplines or intellectual activities. It is usually pursued in a way similar to the writing of literary fiction, i.e. without any relevance or correspondence to real life. Of course, parts of mathematics have achieved significance in physical science, but it appears that this happened unintentionally, more by coincidence than by design.

Mathematics deals with concepts and codes which take their beginning in the imagination of mathematicians and which frequently remain inapplicable in practice. It differs from fictional literature insofar as its „language“ uses symbolic, non-verbal means of expression, and its „grammar“ is a System of abstract operational rules characterised by a high degree of consistency. This consistency and the precision inherent in quantitativeness are the pillars on which the strength of mathematics rests. The application of the rules produces consequences which follow from initial propositions with necessity and achieve a Standard of exactitude not attainable by means of verbal language.

Mathematicians have erected an imposing theoretical edifice, but they have not been able to establish with any degree of certainty the foundations of their structure. They don’t know the real nature of numerals and Symbols, and the real meaning of their rules. Fortunately, it is the super-structure and not the foundations which has a practical significance in the study of phenomena that can be quantified, represented by Symbols and correlated with mathematical rules of Operation. This applies particularly to the study of the physical world. We find that mathematics has become a powerful tool in the hands of physicists, so powerful indeed that a separate group of theoretical physicists has developed who make it their business to expand the Status and the influence of mathematics in physics.

When mathematical methods are used in physics, the boundary between the two disciplines is sometimes hard to discern. They appear to be so closely integrated that a distinction is considered difficult and unnecessary. However, in order to understand relativity it is important to delineate exactly in what way and to what extent mathematics is used legitimately in physics.

The first task is to identify a physical Situation which contains measurable or quantifiable components. This task is usually performed by the physicist, and no mathematics is involved at this stage. The selection of suitable phenomena is a subjective process guided by the intellect of the individual researcher. Previously achieved results and conventions are taken into account, but can be disregarded if it is felt that they are not firmly established.

It is during the first phase that the limitations of mathematics become apparent. The establishment of a quantifiable component is associated with a considerable narrowing of the width and range of the available empirical and inductive material. The mathematical method is similar to a searchlight which illuminates a small and very circumscribed spot intensively, but leaves the immediate environment and the remainder of a vast domain in complete darkness. The physicist has to be selective, but the criteria for selection are by no means clear and his freedom is severely curtailed by the constraints of quantitativeness. Furthermore, the effectiveness and positive value of any mathematical operations depends on the soundness of judgment exercised in the preparation for the encoding of the physical components. It must be clearly specified what the quantities and Symbols stand for, which is not always possible. Many difficulties arise during the translation of complex physical situations into available mathematical means of expression.

The transition from the first step to the second, which is represented by the mathematical manipulation, involves bridging a gap between the real, live and non-mathematical matrix of nature and the artificial, fragmented and restrictive symbolism of mathematics, and the question whether this bridging can be accomplished successfully has been asked in the past. The opinion was expressed that mathematics cannot be applied with exactness to reality (Boutroux). Einstein himself, contradicting what he said on other occasions, expressed doubt in his Sidelights on Relativity when he declared: As far as the laws of mathematics refer to reality they are not certain. We know that mathematics, at least to some extent, is applicable to the visible world äs we perceive it, but that does not necessarily mean that physical phenomena can be, or are, described adequately by mathematical means.

The second stage is represented by the mathematical formalism. It begins with the encoded premise which is manipulated in accordance with the rules of the game in order to obtain mathematical consequences. During this stage mathematics is in complete control. Ideally, one should be able to discern the physical meaning of the mathematical operations which are being performed with the encoded information, but in actual fact we are relying on the well-established belief that the application of mathematical formalism at this stage is appropriate and adequate in terms of physical knowledge.

The third step in the process of using mathematical methods in physics is the decoding and the semantic and physical determination of the results. The consequences of the formalistic manipulation must be interpreted in physical language. Their practical meaning must be discovered if it is not immediately intelligible. They must be verified, and integrated into the existing body of knowledge. The third stage is basically non-mathematical and should be executed by physicists, not by mathematicians. If the mathematical results are physically unintelligible and do not represent anything occurring in nature, they must not be considered part of physics.

(Zitatende)

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Beste Grüße Ekkehard Friebe