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The Everett Box is a device in which an observer and a lethal quantum apparatus are isolated from the rest of the universe. On a regular basis, successive trials occur, in each of which an automatic measurement of a quantum superposition inside the apparatus either causes instant death or does nothing to the observer. From the observer's perspective, the chances of surviving $m$ trials monotonically decreases with increasing $m$. As a result, if the observer is still alive for sufficiently large $m$ she must reject any interpretation of quantum mechanics which is not the many-worlds interpretation (MWI), since surviving $m$ trials becomes vanishingly unlikely in a single world, whereas a version of the observer will necessarily survive in the branching MWI universe. Here we ask whether this conclusion still holds if rather than a classical understanding of limits built on classical logic we instead require our physics to satisfy a computability requirement by investigating the Everett Box in a model of a computational universe running on a variety of constructive logic, Recursive Constructive Mathematics. We show that although the standard Everett argument rejecting non-MWI interpretations is no longer valid, we can show that Everett's conclusion still holds within a computable universe. Thus we argue that Everett's argument is strengthened and any counter-argument must be strengthened, since it holds not only in classical logic (with embedded notions of continuity and infinity) but also in a computable logic., Comment: 14 pages

Does combining a finite collection of objects infinitely many times guarantee the construction of a particular object? Here we use recursive function theory to examine the popular scenario of an infinite collection of typing monkeys reproducing the works of Shakespeare. Our main result is to show that it is possible to assign typing probabilities in such a way that while it is impossible that no monkey reproduces Shakespeare's works, the probability of any finite collection of monkeys doing so is arbitrarily small. We extend our results to target-free writing, and end with a broad discussion and pointers to future work.

We study a continuum model of the lipid bilayer based on minimizing the free energy of a mixture of water and lipid molecules. This paper extends previous work by Blom & Peletier (2004) in the following ways. (a) It formulates a more physical model of the hydrophobic effect to facilitate connections with microscale simulations. (b) It clarifies the meaning of the model parameters. (c) It outlines a method for determining parameter values so that physically-realistic bilayer density profiles can be obtained, for example for use in macroscale simulations. Points (a)-(c) suggest that the model has potential to robustly connect some micro- and macroscale levels of multiscale blood flow simulations. The mathematical modelling in point (a) is based upon a consideration of the underlying physics of inter-molecular forces. The governing equations thus obtained are minimized by gradient flows via a novel numerical approach; this enables point (b). The numerical results are shown to behave physically in terms of the effect of background concentration, in contrast to the earlier model which is shown here to not display the expected behaviour. A "short-tail" approximation of the lipid molecules also gives an analytical tool which yields critical values of some parameters under certain conditions. Point (c) involves the first quantitative comparison of the numerical data with physical experimental results., 19 pages, 7 figures