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Glaeser, Georg o. Univ.-Prof. Mag.rer.nat. Dr.techn.

CCGG2014: 3rd Croatian Conference on Geometry and Graphics
Computer animation, Applied geometry, Geometry
Vortrag: Georg Glaeser: Nature and numbers: But where are the numbers? abstract: Mathematicians tend to model natural shapes which can be put into a certain unam- biguous category. The crystal structure of a diamond, for instance, is perfectly tetra- hedral. However, this is only hard to prove photographically. On the other hand, there exist plenty of less perfect crystals, and insofar as their crystalline structure is visible to the naked eye, it is hardly perfect. Nature is a pragmatic mechanism and accepts many supposedly imperfect so- lutions (see the attached gures), which emerge by means of selection or random chance, insofar as they improve an organism's reproductive success. If they are advantageous or more optimal, new forms are always ready to be accepted. This holds equally true for the development of life as for the emergence of shapes and patterns. The digital age has provided mathematicians with unprecedented possibil- ities, allowing them to visualize ideas which used to be unreachable. It is especially practical for the simulation of natural processes. Here, computer-aided mathematics allows for a free experimentation with parameters { a legitimate and indispensable method in order to achieve results more eciently. Solving a problem in this way might entail a comprehension of how the various mechanisms of nature proceed on their own and intertwine among each other. It is remarkable to recognize that many such processes are very simple, but only if considered locally. The complexity of the mechanism as a whole often escapes immediate explanation. This principle may lie at the heart of using mathematics to understand nature successfully. After all, innitesimal calculus uses a similar approach, focusing on increasingly tiny localities in which certain properties hold true. Integration is then used to ascertain the big picture. In the modeling of dynamic processes, the smallest change can aect the whole result, and yet, nobody will deny that weather forecasts today are many times more accurate than a few decades ago. Still, there are so many parameters at play that certain degrees of inaccuracy are unavoidable.
Croatian Society for Geometry and Graphics HDGG
Georg Glaeser
date, time and location
2014-09-07 – 2014-09-11
Supetar, Kroatien (Österreich)