Most data sets shown in this paper are publicly available and the sources were cited in the text. Apart from these, K. Lehnertz and C. Elger at the University clinic in Bonn kindly permitted us to use their epilepsy data. Thomas Schürmann at the WGZ-Bank Düsseldorf is acknowledged for providing financial time series data. A fair fraction of the ideas and opinions expressed in this paper we had the opportunity to discuss intensively over the past few years with a number of people, most notably James Theiler, Danny Kaplan, Dimitris Kugiumtzis, Steven Schiff, Floris Takens, Holger Kantz, and Peter Grassberger. We thank Michael Rosenblum for explaining to us the spectral estimation of spike trains. Bruce Gluckman pointed out the computational advantage of binned correlations over spike train spectra. Finally, we acknowledge financial support by the SFB 237 of the Deutsche Forschungsgemeinschaft.