Knowing How One Knows

In this paper, I argue that knowledge is dimly luminous. That is: if a person knows that p, she knows how she knows that p. The argument depends on a safety-based account of propositional knowledge, which is salient in Williamson’s critique of the ‘KK’ principle. I combine that account with non-intellectualism about knowledge-how – according to which, if a person knows how to φ, then in nearly all nearby possible worlds in which she φes in the same way as in the actual world, she only φes successfully. Thus, the possession of first-order propositional knowledge implies secondorder practical knowledge, and this can be iterated. Because of the assumed nonintellectualism about know-how, dim luminosity does not imply bright luminosity about knowledge, which is expressed by the traditional KK principle. I conclude by considering some potential counterexamples to the view that knowledge is dimly luminous

Scale Dependent Dimension of Luminous Matter in the Universe

We present a geometrical model of the distribution of luminous matter in the universe, derived from a very simple reaction-diffusion model of turbulent phenomena. The apparent dimension of luminous matter, $D(l)$, depends linearly on the logarithm of the scale $l$ under which the universe is viewed: $D(l) \sim 3\log(l/l_0)/\log(\xi/l_0)$, where $\xi$ is a correlation length. Comparison with data from the SARS red-shift catalogue, and the LEDA database provides a good fit with a correlation length $\xi \sim 300$ Mpc. The geometrical interpretation is clear: At small distances, the universe is zero-dimensional and point-like. At distances of the order of 1 Mpc the dimension is unity, indicating a filamentary, string-like structure; when viewed at larger scales it gradually becomes 2-dimensional wall-like, and finally, at and beyond the correlation length, it becomes uniform.Comment: 6 pages, 2 figure

The X-ray emission of the most luminous 3CR radio sources

We investigate the X-ray properties of the most luminous radio sources in the 3CR catalogue, in order to assess if they are similar to the most luminous radio quiet quasars, for instance in the X-ray normalization with respect to the optical luminosity, or in the distribution of the absorption column density. We have selected the (optically identified) 3CR radio sources whose 178-MHz monochromatic luminosity lies in the highest factor-of-three bin. The 4 most luminous objects had already been observed in X rays. Of the remaining 16, we observed with XMM-Newton 4 randomly chosen, optical type 1s, and 4 type 2s. All targets have been detected. The optical-to-Xray spectral index, alphaox, can be computed only for the type 1s and, in agreement with previous studies, is found to be flatter than in radio quiet quasars of similar luminosity. However, the Compton thin type 2s have an absorption corrected X-ray luminosity systematically lower than the type 1s, by a factor which makes them consistent with the radio quiet alphaox. Within the limited statistics, the Compton thick objects seem to have a reflected component more luminous than the Compton thin ones. The extra X-ray component observed in type 1 radio loud quasars is beamed for intrinsic causes, and is not collimated by the absorbing torus as is the case for the (intrinsically isotropic) disk emission. The extra component can be associated with a relativistic outflow, provided that the flow opening angle and the Doppler beaming factor are 1/5 - 1/7 radians.Comment: LaTex, 6 pages, 3 figures, 3 tables; accepted for publication in A&