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Summary

Boethius, like his Neoplatonic predecessors, poses a challenge to contemporary readers of the Consolation seeking to understand the world he thinks we occupy. That world involves a timeless, simple, but all-knowing creator god and a time-bound, infinite creation that is patterned from the ideas in the divine mind. The purpose of this chapter is to provide a modest illumination into the world as it is conceived in the Consolation by examining two fundamental Boethian categories and their relationship: the eternal and the temporal. The chapter examines the extent to which we should see these categories providing guidance as to the nature of beings rather than expressing the epistemic perspectives those beings have. By noting the limits, we will draw conclusions about the persistence of temporal beings; the ontological status possessed by future, present, and past states of affairs; and what characterizes eternal existence.

We show that while Runge-Kutta methods cannot preserve polynomial invariants in general, they can preserve polynomials that are the energy invariant of canonical Hamiltonian systems.

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Chapter 12 - Time and Eternity in the Consolation of Philosophy

Summary

Energy-preserving Runge-Kutta methods

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2 results

Chapter 12 - Time and Eternity in the Consolation of Philosophy

Summary

Energy-preserving Runge-Kutta methods