Extending Kolmogorov's axioms for a generalized probability theory on collections of contexts

Kolmogorov's axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another context. As the respective probabilities need not (but, depending on the physical/model realization, can) be of the Born rule type, this generalizes approaches to quantum probabilities by Auff\'eves and Grangier, which in turn are inspired by Gleason's theorem.Comment: 18 pages, 3 figures, greatly revise

Orthogonal vector computations

Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.Comment: 8 pages, 2 figures, some revisions and addition

Why Computation?

This paper reviews my personal inclinations and fascination with the area of unconventional computing. Computing can be perceived as an inscription in a "Rosetta Stone," one category akin to physics, and therefore as a form of comprehension of nature: at least from a purely syntactic perspective, to understand means to be able to algorithmically (re)produce. I also address the question of why there is computation, and sketch a research program based on primordial chaos, out of which order and even self-referential perception emerges by way of evolution.Comment: 4 pages, 1 figure, invited contribution to "Paths to Unconventional Computing" for a special issue on "Integral Biomathics