The Derivative ‘Drift’ in complex systems dynamics: the case of climate change and global warming

Mathematical Models of Complex Systems are generally formulated in terms of Traditional Differential Calculus (TDC), that is by means of linear and non-linear differential equations based on the well-known concept of derivative. Such a mathematical language, however, always introduces a “drift” between the foreseen behavior of the system and the corresponding experimental results, a drift which is generally much more marked as the order of the system increases. This “drift” is intrinsically due to the same definition of the traditional derivative. It also represents the basic reason for the insolubility, in explicit or even in a closed form, of the above-mentioned differential problems. Such a “drift” effect will be shown with reference to the case study of future Global Warming and Climate Change. Given the supposed generally increasing trends of several parameters (temperature, level of the seas, etc.), it will be shown that TDC generally tends to underestimate the real effects which, vice versa, could be much higher than the most accurate current estimations. As an example, in the worst Global Warming scenario foreseen by IPCC, the increase in temperature of about 6.4° C (in 2100) is underestimated of not less than 150%. An analogous trend can also be identified for the rising of the sea level. By comparing the results between TDC and Incipient Differential Calculus (IDC), we can conclude that current evaluations of Global Warming and Climate Change are based on the adoption of highly inadequate methods, because they foresee future trends that could, in reality, be much higher. Accordingly, the corresponding strategies, usually adopted in order to mitigate these underestimated effects, could also turn out to be significantly inadequate.