Cdmtcs Research Report Series Is the Universe Lawful?

The last 2,500 years have been dominated by the belief, expressed in di erent forms, that the Universe is lawful, that is, the Universe is a knowable system governed by rules which determine the future uniquely and completely. An extreme way to express this belief is to claim overcon dently that the study of some branches of science will soon be completed, will soon attend an end. Our aim is to challenge this apocryphal hypothesis by arguing, with complexity-theoretic arguments, that the Universe is lawless, that is, the Universe is lacking any kind of general ordered structure implied by the term \law". There are currently two opposing views of the scienti c enterprise. First of all, the overcon dent one proclaiming that science is converging towards a \ nal theory," a \theory of everything" which will describe the basic laws governing the Universe. The opposing view of the scienti c enterprise is the skeptical one that questions the power of science to ever arrive at some kind of \Truth". \Is the world just too complex for the human mind to fully comprehend?" Casti and Karlqvist's conclusion [14] is negative, that is, the physical world is not too complex for the human mind. Our thesis is that the inability of the human mind to fully understand the world of mathematics necessarily implies the impossibility for the human mind to completely understand the Universe. In what follows we will speak about the \Universe", and its presumed \lawfulness". We will start by trying to \describe" (not de ne) both terms. The fact that these descriptions are extremely vague has not escaped our attention; nevertheless, we believe them to be precise enough for the aim of this paper.