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Additional info for Advanced Practical Physics for Students
But these conventions are not unambiguous, in fact in both possible directions: one and the same symbol does not always represent the same concept, and a certain concept is not always represented by the same symbol. The ﬁrst of these ambiguities is the fundamental one. The multiplicity of concepts in science is so much greater than the set of symbols utilized (and reasonably remembered) that one symbol must necessarily represent very many diﬀerent concepts. Which one is meant follows from the context or is decided through explicit deﬁnition.
As a consistency check one can then show afterwards that the facticity of the past and the openness of the future (in the form of the existence of documents of the past but not the future) then follows from the irreversibility of events according to the Second Law. The diﬀerence that exists between Now and past and future points in time cannot, however, be reconstructed from laws of nature that are formally valid at every point in time; it is an assumption, but not a consequence of the general laws of nature.
The remaining letters m, x, f , and the already mentioned t are also variables in this logical sense, for which, however, real numbers (for m actually only positive ones) must be substituted. , quantities that can be chosen arbitrarily once, but must then be kept ﬁxed for the form of the equation determined by this choice and the resulting nature of its solutions. There one usually calls t the independent and x the dependent variable, thus indicating that x is sought as a function of t. For every choice of the indices i, k there is a separate dependent variable xik , whereas t is assumed always to be the same quantity.