This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of letters written to various friends and colleagues

Contexts are maximal collections of co-measurable observables “bundled together ” to form a “quasi-classical mini-universe. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.-v,02.50.Cw,02.10.Ud

theorem and the effectiveness of Gleason’s

Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. 1. Gleason’s Theorem and Logical Compactness Kochen and Specker’s (1967) theorem (KS) puts a severe constraint on possible hidden-variable interpretations of quantum mechanics. Often it is considered an improvement on a similar argument derived from Gleason (1957) theorem (see, for example, Held. 2000). This is true in the sense that KS provide an explicit construction of a finite set of rays on which no two-valued homomorphism exists. However, the fact that there is such a finite set follows from Gleason’s theorem using a simple logical compactness argument (Pitowsky 1998, a similar point is made in Bell 1996). The existence of finite sets of rays with other interesting features

We defend pluralism in mathematics, and in particular Errett Bishop’s constructive approach to mathematics, on pragmatic grounds, avoiding the philosophical issues which have dissuaded many mathematicians from taking it seriously. We also explain the computational value of interval arithmetic.

This paper is dedicated to the memory of Prof. Gottfried T. Ru ttimann

June 2000, "Greece" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Carl's Preply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 07 September 2000, "Critical Letters and Reply" . . . . . . . . . . . . . . . . . . . . 133 13 November 2000, "Bush vs. Bohr" . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 01 February 2001, "An Ed/Ellen Jaynesian" . . . . . . . . . . . . . . . . . . . . . . 134 01 February 2001, "My Jaynes" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 26 February 2001, "Death of a Salesman" . . . . . . . . . . . . . . . . . . . . . . . . 135 11 Letters to Greg Comer 136 14 February 1995, "Turtle Wax" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 04 March 1995, "Saturday Slush" . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 07 March 1995, "Please, Please No More!" . . . . . . . . . . . . . . . . . . . . . . . 137 27 January 1996, "Philo" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 xi February 1996, "The Mont-Royal Sweats" . . . . . . . . . . . . . . . . . . . . . . 138 27 February 1996, "Kant Cola" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 06 March 1996, "Rub Me" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 26 March 1996, "Savagery" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 27 March 1996, "Strange Comment" . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 01 April 1996, "Puppy Scoops" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 04 May 1996, "You May Enjoy" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 19 July 1996, "Old Moods" . . . . . . . . . . . . ....

This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of letters written to various friends and colleagues