It is shown that, although correct mathematically, the celebrated 1932 theorem of von Neumann which is often interpreted as proving the impossibility of the existence of " hidden variables " in… (More)

The accelerated Turing machine (ATM) is the work-horse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some… (More)

In 1994 we showed that very large classes of systems of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective… (More)

For more than two millennia, ever since Euclid’s geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe… (More)

Recently the space-time foam differential algebras of generalized functions with dense singularities were introduced, motivated by the so called space-time foam structures in General Relativity with… (More)

The parts contributed by the author in recent discussions with several physicists and mathematicians are reviewed, as they have been occasioned by the 2006 book " The Trouble with Physics " , of Lee… (More)

Galilean Relativity and Einstein’s Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance, or independence… (More)

The essentials of a new method in solving very large classes of nonlinear systems of PDEs, possibly associated with initial and/or boundary value problems, are presented. The PDEs can be defined by… (More)

As a significant strengthening of properties of earlier algebras of generalized functions, here are presented classes of such algebras which can deal with dense singularities. In fact, the cardinal… (More)

It took two millennia after Euclid and until in the early 1880s, when we went beyond the ancient axiom of parallels, and inaugurated ge-ometries of curved spaces. In less than one more century,… (More)