There seems to be an unbridgeable gap between the large and the small. Although there usually is a scale by means of which large and small phenomena can be compared by measuring, considerable difficulties arise as soon as large things have to be reduced or small things enlarged. lt is only in this transition that it becomes apparent that different laws prevail on a large and small scale and that something that seemed self-evident on a certain interval of a scale suddenly no longer applies. Thus, rescaling is above all an epistemological problem: it is difficult to predict or estimate when qualitative changes will occur, or where theories will lose their explanatory power, or where applications will no longer be functional.

With the help of some examples, Claus Pias will derive three heuristic dichotomies (reductionism/holism, quantity /quality, unity/disunity) that might be useful for a comparative history of scaling problems in different sciences. Furthermore, he shows that an awareness of the limits of scalability was already present when the modern scaling laws were formulated in the 17th century.

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