Speaker: Gabrielle Gramelsberger
Date and Time: Thursday, January 31st 2019, 16:30-18:00
Venue: ILLC Seminar Room F1.15, Science Park 107.
Title: The challenge of non-linearity and the need for computer-based modelling and simulation in science.
Abstract. In 1946 John von Neumann stated, “the advance of analysis is […] stagnant along the entire front of non-linear problems. We believe, therefore, that it is now time to concentrate on effecting the transition to [digital] devices, and that this will increase the power of the approach in question to an unprecedented extent.” [Goldstine and von Neumann, 1946] This statement, which is still true, marked the beginning of computer-based modelling and simulation in science, although it took several years to build adequate computers and develop rules for delegating mathematics to the computer, amongst them the famous von Neumann stability analysis. However, from this point on the very nature of science changed and has increasingly turned computational. Today, computer-based modelling and simulation are expanding the methodological repertoire of scientific theory and experiment/observation, helping researchers “extend themselves”—as philosopher Paul Humphreys aptly outlined in 2004; metaphorically comparing simulations with microscopes, but mathematical ones. From a philosophical perspective these “extending capacities” of computer-based modelling and simulation are of interest. The paper will present the historical and contemporary aspects of struggling with the challenge of non-linearity. It will pose the questions as to whether the challenge of non- linearity is rooted in the cognitive boundaries of Anschauung as addressed by Immanuel Kant back in 1781, whether these cognitive boundaries reappear in the problem of Entscheidbarkeit [Hilbert, 1900], and what they mean for epistemic limitations in computer-based modelling and simulation. Finally, it will be discuss whether a logical framework could help to grasp the complexity of today’s computational sciences.
Herman H. Goldstine and John von Neumann. 1963 . On the Principles of Large Scale Computing Machines. Collected Works (vol. 5), (ed. by John von Neumann and A. H. Taub), 1–32. Oxford Pergamon.
Paul Humphreys. 2004. Extending Ourselves. Computational Sciences, Empiricism, and Scientific Method. Oxford: Oxford University Press.
Immanuel Kant. 1993 [1781, 1787]. Kritik der reinen Vernunft, (ed. by Raymund Schmidt). Hamburg: Meiner 1993.
David Hilbert. 1932 . Mathematische Probleme. Gesammelte Abhandlungen (vol. 1), (ed. by David Hilbert), 290-329. Berlin: Springer.