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Konferenzteilnahmen |
| Veranstaltung: |
CCGG2014: 3rd Croatian Conference on Geometry and Graphics |
| VeranstalterIn: |
Croatian Society for Geometry and Graphics HDGG, Supetar, Kroatien (Österreich) |
| Zeitraum: |
07.09.2014 bis 11.09.2014 |
| Beschreibung: |
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, in nitesimal 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 a ect 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. |
| URL: |
http://www.grad.hr/sgorjanc/supetar/program.pdf |
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