Formal Amendment of the Constitution of Canada

Canada\u27s Constitution Act of 1982 is discussed. The act changed the way in which amendments to Canada\u27s constitution were made. Previously, the Imperial Parliament made the amendments

The homotopy type of the space of degree 0 immersed plane curves

The space of all immersed closed curves of rotation degree 0 in the plane modulo reparametrizations has the same homotopy groups as the circle times the 2-sphere.Comment: 7 page

Fault-tolerant quantum computation

Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer, thus making long computations impossible. A futher difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering the output of long computations unreliable. It was previously known that a quantum circuit with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per gate. We show, for any quantum computation with t gates, how to build a polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of inaccuracy and decoherence per gate, for some constant c. We do this by showing how to compute using quantum error correcting codes. These codes were previously known to provide resistance to errors while storing and transmitting quantum data.Comment: Latex, 11 pages, no figures, in 37th Symposium on Foundations of Computing, IEEE Computer Society Press, 1996, pp. 56-6

Basic differential forms for actions of Lie groups

A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on $\Sigma$ which are invariant with respect to the generalized Weyl group of this orbit, under some condition.Comment: 10 pages, ESI Preprint 87, AmSTe

Our Liberation and the Liberation of Our Images: Friedrich Schiller and the Politics of the Image

In this paper, I will compare the aesthetic philosophies put forward in Friedrich Schiller’s On the Aesthetic Education of Man and Plato\u27s Republic. Using Schiller\u27s more robust aesthetic philosophy and its political import, I will argue that the government of Plato\u27s Republic would not create freedom for its citizens. Then, I will carry Schiller\u27s aesthetics and politics forward to argue, using Freud and a number of thinkers who champion Freud’s work, that economic interests can also limit the freedoms of a nation\u27s citizens. Finally, I will argue that Schiller\u27s aesthetic philosophy can deliver a political freedom free from the state control depicted in Republic and the economic control of modern consumer culture

Relativistic Constraints for a Naturalistic Metaphysics of Time

The traditional metaphysical debate between static and dynamic views in the philosophy of time is examined in light of considerations concerning the nature of time in physical theory. Adapting the formalism of Rovelli (1995, 2004), I set out a precise framework in which to characterise the formal structure of time that we find in physical theory. This framework is used to provide a new perspective on the relationship between the metaphysics of time and the special theory of relativity by emphasising the dual representations of time that we find in special relativity. I extend this analysis to the general theory of relativity with a view to prescribing the constraints that must be heeded for a metaphysical theory of time to remain within the bounds of a naturalistic metaphysics