Related papers: PC4 at Age 40
A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work,…
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special…
Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.
Physical processes are computations only when we use them to externalize thought. Computation is the performance of one or more fixed processes within a contingent environment. We reformulate the Church-Turing thesis so that it applies to…
The paper by Mayo claims to provide a new clarification and critique of Birnbaum's argument for showing that sufficiency and conditionality principles imply the likelihood principle. However, much of the arguments go back to arguments made…
Though Einstein and other physicists recognized the importance of an observer being at rest in an inertial reference frame for the special theory of relativity, the supporting psychological structures were not discussed much by physicists.…
The role of counter-rotating oscillators in an ensemble of coexisting co- and counter-rotating oscillators is examined by increasing the proportion of the latter. The phenomenon of aging transition was identified at a critical value of the…
The development of inventions is theorized as a process of searching and recombining existing knowledge components. Previous studies under this theory have examined myriad characteristics of recombined knowledge and their performance…
This is a write-up of introductory remarks that I made at the UIC conference in honor of Lawrence Ein's 60th birthday. It presents an informal survey of some of Ein's work, interspersed with stories and reminiscences.
In an earlier experiment, participants played a perfect information game against a computer, which was programmed to deviate often from its backward induction strategy right at the beginning of the game. Participants knew that in each game,…
We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.
An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this…
While I was dealing with a brain injury and finding it difficult to work, two friends (Derek Westen, a friend of the KITP, and Steve Shenker, with whom I was recently collaborating), suggested that a new direction might be good. Steve in…
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…
Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…
We consider weighted particle systems in which new generations are re-sampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo methods, widely used in applied…
Science is a cumulative activity, which can manifest itself through the act of citing. Citations are also central to research evaluation, thus creating incentives for researchers to cite their own work. Using a dataset containing more than…
A-theorists and B-theorists debate whether the "Now" is metaphysically distinguished from other time slices. Analogously, one may ask whether the "I" is metaphysically distinguished from other perspectives. Few philosophers would answer the…
This is an expanded version of talks given by the author at the Trieste Spring School on Supergravity and Superstrings in April of 1997 and at the accompanying workshop. The manuscript is intended to be a mini-review of Matrix Theory. The…
Poincar\'e's Polyhedron Theorem is a widely known valuable tool in constructing manifolds endowed with a prescribed geometric structure. It is one of the few criteria providing discreteness of groups of isometries. This work contains a…