The main formal structures of generalized quantum theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.

Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relations, since regularities in very large databases are enough: “with (...) enough data, the numbers speak for themselves”. The “end of science” is proclaimed. Using classical results from ergodic theory, Ramsey theory and algorithmic information theory, we show that this “philosophy” is wrong. For example, we prove that very large databases have to contain arbitrary correlations. These correlations appear only due to the size, not the nature, of data. They can be found in “randomly” generated, large enough databases, which—as we will prove—implies that most correlations are spurious. Too much information tends to behave like very little information. The scientific method can be enriched by computer mining in immense databases, but not replaced by it. (shrink)

This paper reports on a correlation study between human intention and the output of a binary random number generator. The study comprises a total of 288 million bits from 40 equal sessions, each on a different human participant. Each participant spent 2 hours of time attempting to “influence” the outcome of the random number generator according to a pre-selected intention. During this time the participant was provided feedback on his/her performance by an analog mechanical display, with the needle of a (...) galvanometric instrument moving to the left- or right-hand side of its current position, according to the instantaneous output of the random number generator. The data analysis procedure was defined before looking at the data. Out of four pre-defined analyses, one was found to be significant with a probability p = 0.0366 that this result occurred by chance under a null hypothesis. The combined analysis of the four individual analyses is found to be not significant, with p = 0.2655 to have occurred by chance under a null hypothesis. (shrink)

We report a theory-relevant post hoc analysis of 2 Dutch retro-priming experiments that were part of a large replication project of the retro-priming experiment by Bem and colleagues. This replication project sought to investigate the role of the experimenter in psi studies. The results of the retro-priming experiments performed by student research groups at the University of Amsterdam (N=61) and of the University Groningen (N=222) however did not replicate Bem’s earlier findings of an anomalous interference of a future stimulus on (...) response times. We report the results of these two studies here, but the over-all results will be reported elsewhere. Both Dutch studies used the exact same software as Bem and colleagues. However, both studies used different questionnaires. The questionnaires asked for information that in previous research had been associated with success in psi tasks and could help us to deal with individual differences but, above all, could be used as selection criteria for participants in future studies. In the Amsterdam study, there were 14 questions, while in the Groningen there were 55. A correlation analysis revealed several significant correlations between the psi-effect in the Bem task and questionnaire items. In this paper we focus on the post-hoc research question: Is this global composition of the correlation matrix anomalous, as suggested by Generalized Quantum Theory? Rather than using the subjective number of ‘significant’ correlations as a dependent variable, we introduced 2 objective measures directly representing the correlation values in the cells to characterize the ‘Connectivity’ in the matrix. Our analysis revealed ‘Connectivity’ to be marginally significant larger (p<0.075) in Groningen and significantly larger in the Amsterdam study (p<0.025). These results are discussed in the framework of the ‘Consciousness Induced Restoration of Time-symmetry’ (CIRTS) and ‘Generalized Quantum Theory’ (GQT) that predict that as soon as there are reasons to expect replicability (or control) the extra chance psi scores will disappear or reverse. The conclusion is that these results can be seen as support, though statistically not strong, for the GQT. (shrink)