  In this paper we analyze methodological and philosophical implications of
algorithmic aspects of unconventional computation. At first, we describe how
the classical algorithmic universe developed and analyze why it became closed
in the conventional approach to computation. Then we explain how new models of
algorithms turned the classical closed algorithmic universe into the open world
of algorithmic constellations, allowing higher flexibility and expressive
power, supporting constructivism and creativity in mathematical modeling. As
Goedels undecidability theorems demonstrate, the closed algorithmic universe
restricts essential forms of mathematical cognition. In contrast, the open
algorithmic universe, and even more the open world of algorithmic
constellations, remove such restrictions and enable new, richer understanding
of computation.
