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Abstract In 1809 Carl Friedrich Gauss' masterpiece “Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium” on the motion of celestial bodies was published. This book contains also a first version of the famous error propagation formula, which is still the basis of modern metrology and of any relevant national and international standard. Gauss' ideas are reflected in the GUM, the “Guide to the Expression of Uncertainty in Measurement”, published in 1993 by ISO, which is a key document for national measurement institutes and industrial calibration laboratories for evaluating uncertainty in the output of a measurement system. Uncertainty constitutes the main problem of any measurement theory. Because uncertainty is investigated in stochastics, any serious measurement theory should necessarily take into account the state of the art in stochastics. Stochastics was initiated by Jakob Bernoulli in his masterpiece “Ars conjectandi”, which appeared posthumously in 1713, i. e., about 100 years before Gauss established the basis of metrology. The difference between Jakob Bernoulli and Carl Friedrich Gauss is the following: Bernoulli aimed at quantifying and measuring uncertainty, while Gauss aimed at quantifying and measuring a measurement error. In this paper a modern measurement theory based on stochastics is briefly outlined. Subsequently, the antiquated concepts and methods as recommended in the GUM, which go back to the early 19th century, are discussed and their weaknesses are listed.
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