A computational theory of everything (TOE) requires a universe with discrete (as opposed to continuous) space, time, and state. Any discrete model for the universe must approximate the continuousâ€¦ (More)

The foundations of mathematics and physics no longer start with fundamental entities and their properties like spatial extension, points, lines or the billiard ball like particles of Newtonianâ€¦ (More)

Logic discovered its own limitations in GÃ¶delâ€™s Incompleteness Theorems. Before GÃ¶delâ€™s proofs, mathematicians sought a logical mechanistic process that could, with enough time and resources, decideâ€¦ (More)

Magnetic properties of thin magnetic films are strongly affected by the nature of the interface between magnetic and non-magnetic layers. In spintronic devices the extent to which spins are scatteredâ€¦ (More)

This paper expands Kleeneâ€™s notations for recursive ordinals to larger countable ordinals by defining notations for limit ordinals using total recursive functions on nonrecursively enumerable domainsâ€¦ (More)