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A space-time discontinuous Galerkin spectral element method is combined with two different approaches for treating problems with discontinuous solutions: (i) adding a space-time dependent artificial viscosity, and (ii) tracking the discontinuity with space-time spectral accuracy. A Picard iteration method is employed to solve nonlinear system of equations derived from the space-time DG spectral element discretization. Spectral accuracy in both space and time is demonstrated for the Burgers’ equation with a smooth solution. For tests with discontinuities, the present space-time method enables better accuracy at capturing the shock strength in the element containing shock when higher order polynomials in both space and time are used. The spectral accuracy of the shock speed and location is demonstrated for the solution of the inviscid Burgers’ equation obtained by the tracking method.

What are the fundamental equations of motion when we consider objects that move faster, have tinier structures, higher mass densities, higher or lower temperatures than ever studied before? Here, we emphasize the importance of studying extreme conditions and situations in science so as to uncover the basic laws of nature. One of the important extremes is extreme complexity, a necessary condition for the emergence of life.

Intuition is defined for the purposes of this analysis as: the appearance in the mind of accurate information about the external world, which can be shown to have come not through the five senses, nor through a rearrangement of stored memory contents. Forms of intuition obeying this definition have been explored scientifically under such labels as telepathy, precognition, presentiment, and remote viewing. This paper summarizes those scientific findings, and presents a few theories which have been hypothesized to explain them. Those theories are largely based in theoretical physics, including quantum non-locality, holography, and complex space-time. Related biological theories are also cited, which propose to explain how information might move from the subatomic level up into waking consciousness, for example through DNA structures or neuronal microtubules.

What are the fundamental equations of motion when we consider objects that move faster, have tinier structures, higher mass densities, higher or lower temperatures than ever studied before? Here, we emphasize the importance of studying extreme conditions and situations in science so as to uncover the basic laws of nature. One of the important extremes is extreme complexity, a necessary condition for the emergence of life.