TIME REPRESENTATION IN SCIENTIFIC DIAGRAMS: GALILEO GALILEI’S SOLUTION TO THE PROBLEM OF THE MOTION OF A FALLING BODY

Abstract

Рассматриваются способы научного изображения темпоральных явлений на примере чертежей Галилео Галилея, при помощи которых он описывает и исследует равноускоренное движение. Для анализа применяется концептуальная рамка теории изобразительной и неизобразительной репрезентации Грегори Карри. Показано, что в случае научных диаграмм и графиков, представляющих время как одно из измерений пространства, основанием для геометрической изобразимости времени становится полагаемый изоморфизм между временем как континуумом мгновений и линией как континуумом точек. Парадигму такого структурного сопоставления мы находим в математическом мышлении Галилея, наиболее ярко проявляющемся в доказательстве формулы равноускоренного движения, представленном в «Беседах и математических доказательствах». The textbook narrative of the scientific revolution of the 17th century says that the early modern transformation of physics and mechanics was grounded in mathematization, that is, the application of mathematical principles and procedures to physical entities and events. However, such a transformation faces a major obstacle: compared to geometry, mechanics includes an additional dimension, namely, time. When temporality of motion is to be represented geometrically, a question arises on how a temporal succession can be expressed by a static image. The problem of representation of temporal events is not limited to science. In my paper, I apply a conceptual tool elaborated by Gregory Currie for the analysis of temporal representations in art, especially in cinema, to the analysis of scientific diagrams. In his book Image and Mind. Film, Philosophy, and Cognitive Science (1995), Currie distinguishes depictive and nondepictive representations, arguing that depictive representation requires similarity and homomorphism between an object ant its representation. Thus, it seems that any non-temporal image of temporal processes would lack the required similarity and cannot be a depictive representation. However, taking into account explanations given by Galileo Galilei for his famous diagrams of accelerated motion, I argue that the representation of time in scientific diagrams as a geometrical line is grounded in isomorphism between time as a continuous structure and continuous structure of a geometrical line. The main temporal process studied by mechanics is motion. Motion can be represented in two main ways: as a trajectory of a body over some period of time or as a functional relation of various parameters of motion (speed, path, acceleration) versus time. In the latter case, time is usually represented in a diagram as a geometrical line. We can find the origin of this type of representation in the late medieval doctrine of ‘intensio et remissio qualitatum’, intension and remission of qualities, in the context of which first diagrams representing intensity and extension of velocity of nonuniform motion as a changing quality over time were produced (Nicolas Oresme). We can find very similar graphical schemes in Galileo Galilei’s works, especially in Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638). In this work, Galileo announces with all clarity that he considers time to be the same aggregate of temporal moments as a line is an aggregate of points: every moment of time has a corresponding point on the geometrical line. This allows us to establish a homomorphic similarity between temporal duration and spatial (geometrical) extension. Thus, the essential requirement for depictive representation is met. Concluding, I have to point out that the homomorphic relation in this case is established between not real but abstract entities. The visible line itself is a representation of non-visible abstract geometrical line; in the same way, time consisting of non-divisible moments is just an abstract construction which refers to physical of psychological time-duration. However, the established relation between abstract time and abstract geometrical lines is a grounding event of the modern physical science.