Dear Torsten Asselmeyer-Maluga:
I've read, very carefully, your interesting paper and I am very glad that I myself attained conclusions similar to yours, though following very different paths. I plenty coincide with you concerning the non-deterministic behavior of evolutionary models. Nevertheless I would like to point out some aspects that, may be, are due to my lack of understanding your motives.
You say well that scientific discoveries cannot be planned; however that is not equivalent to having a stochastic process, since the first qualifying factor is a negative one while the second is a positive assertion. I suppose that scientific discoveries are usually either boosted or repressed by epochs, cultures or even natural causes. Isn't it too much simple your mathematical model of evolution? I agree it has to be a Master equation, but I rather would think of a Malthus-Verhulst model, namely, a nonlinear birth and death process, occurring when the individuals in a society are allowed to interact (e.g. competition processes), assuming that the transition probability is identical to that of a random walk or the diffusion equation, except that there is an additional contribution to the death rate, proportional to the density of other individuals. Such a model allows the possibility of phase transitions, symmetry breaking, bifurcations, and so on. In this sense, perhaps, we might include not only Darwinian properties of evolutionary systems (mutation selection), but Lamarckian aspects as well (environmental incidence on functions of the systems, transformism or transmutation of species).
Another point has to do with the nature of time: aren't you assuming the arrow of time rather than discovering it? That is a difficult question as we generally invert the sense between causes and effects each time we try to talk about sense, way, tendency, fitness,... Indeed, your paper makes me think about the fact that we could hardly accept that every single scientific discovery will contribute to technological advances; it is usually the contrary what happens, since most of our "needs" are artificially invented and even imposed by business interests.
Finally, I would like to mention a quite relevant subject, namely, artificial intelligence. You appropriately underline the fact that "the central instance of a computer (the microprocessor) should be exchanged by a dynamical network of communicating devices (like our brain), a non-von-Neumann architecture" (underlining is mine); however, is that enough for the accountability of creativity, improvisation, imagination, etc. so that we can ensure that computers will displace intellectual human activity?
I truly thank you for your patience in reading this and I hope that a fruitful academic discussion will emerge from this. Thanks again.
Alexandre de Pomposo