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In this paper we analyze methodological and philosophical implications ofalgorithmic aspects of unconventional computation. At first, we describe howthe classical algorithmic universe developed and analyze why it became closedin the conventional approach to computation. Then we explain how new models ofalgorithms turned the classical closed algorithmic universe into the open worldof algorithmic constellations, allowing higher flexibility and expressivepower, supporting constructivism and creativity in mathematical modeling. AsGoedels undecidability theorems demonstrate, the closed algorithmic universerestricts essential forms of mathematical cognition. In contrast, the openalgorithmic universe, and even more the open world of algorithmicconstellations, remove such restrictions and enable new, richer understandingof computation.

From the Closed Classical Algorithmic Universe to an Open World of Algorithmic Constellations