Page 49 - META

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ISSN 2309-0103 www.archidoct.net
Vol. 7 (2) / February 2020
otherwise”(Cruz Roche, 2012). And based on this possibility of a huge disparity in re- sults, all obeying rigorous laws, anew conception of the relationship between calculus and geometry was proclaimed between the 18th and 19th centuries.
This was based on the idea of a mathematical function as an analytical expression consisting of certainties but also of possibilities, with the development of systems of equations and series theory, leading towards theThree-Body Problem, etc. Through this maze of chance, a series of possible regularities replace exact laws.
It was soon accepted that determinism only had a partial role to play in the modelling of reality, since different scenarios can emerge based on processes that are not entire- ly predictable.
The reductionism became too limiting to describe phenomena, and so work began on recognizing nonlinear patterns that focused on the exploration of interactions that led to the emergence of unwonted characteristics. Emergentists admit the existence of a single physical substance,but this is organized through processes at successive levels that emerge from one other, characterized by properties that cannot be reduced.
In the 19th century, geometry was considered the science of space, and arithmetic the science of pure time. Furthermore, the first non-Euclidean geometry was devel- oped,building on the work initiated by Saccherius: this asserted the plurality of par- allel lines that passed through a point outside a straight line, and then, subsequently, proclaimed the non-existence of these parallels (Saccherius, 1733). Thus, Euclidean geometry was reduced to the status of a special case within a more general repertoire, with a consequent weakening of the intuitionist view of mathematics.
The new geometries, which at first seemed outlandish to the real world, were those that best described the true architecture of the cosmos, and generated the idea that there is an irreducible uncertainty linked to probabilistics, quantum mechanics or Heisenberg’s UncertaintyPrinciple (1927), etc. It was definitively concluded that deter- minism constitutedan incomplete picture, as would be demonstratedby Minkowskior Einstein.
And new science, which means that some complex phenomenon that was invisible to the science comes into its view now, and consequently, people’s view of the world become to change,will lead to new architecture (Li, 2015).
The Path Followed by the Meta-systemic vision
Nevertheless, in 1917Thompson,in his work “On Growth and Form”, addressingthe study of nature based on physical and mathematical tools for the first time, pointed once again towards the ideals of Euclidean geometry as being predominant in natural forms created by physical forces, because their laws favour simplicity as an optimal representation of those forces, he explained(Thompson, 1917).
Therefore: first, Euclidean geometry was considered by Kant as a form of pure a pri- oriintuition (Kant, 1781); and then by Russell as also a product of experience (Rus-
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Systemic Considerations. Regarding the Importance of the Pre- in the Post- on the Path Towards the Meta-system
Adolfo Jordán