0000000000901481
AUTHOR
Elemer Elad Rosinger
Wealth Creation and Science Research : Science Research, the root of wealth in our Knowledge Society, is endangered
Two vastly dierent historical stages in wealth creation are the traditional one based on agriculture during past millennia, and the one based on science research in our present globalizing knowledge society. The dierences happen to be so considerable, and the emergence of the second stage relatively so recent, that the awareness of the full range of consequences regarding the proper pursuit of science research, which is the root of wealth in our knowledge society, is missing to an extent that may, even in the medium term, seriously endanger the sustainability of modern human society. Here is presented a brief account of some of such dangers, following which a parable, entitled "Is it a mere…
Four Departures inMathematics and Physics
Much of Mathematics, and therefore Physics as well, have been limited by four rather consequential restrictions. Two of them are ancient taboos, one is an ancient and no longer felt as such bondage, and the fourth is a surprising omission in Algebra. The paper brings to the attention of those interested these four restrictions, as well as the fact that each of them has by now ways, even if hardly yet known ones, to overcome them.
IN SUPPORT OF COMTE-SPONVILLE
When I was a small boy, about two years old, on occasion, I had some nightmares. One morning I mentioned that to my Mother, and she replied, in a most natural matter of course manner, as if it had been about a simple and trivial issue, that next time, when I would again have such a nightmare, I should simply remember that I was dreaming, that all it would only be in a dream, and then I should just wake up … Since my Mother’s reply came so instantly, smoothly, and without the least emotion, let alone dramatization, I simply took it as such … And next time, when a nightmare came upon me during my dream, I simply did, and yes, I managed rather naturally to do, what my Mother had told me to do …
Can there be a general nonlinear PDE theory for existence of solutions ?
Updated version of the 2004 paper arxiv:math/0407026; Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the respective PDEs. The method can also deal with associated initial and/or boundary value problems. The solutions obtained can be assimilated with usual measurable functions or even with Hausdorff continuous functions on the respective Euclidean domains. It is important to note that the use of the or…
Where and How Do They Happen ?
This is a two part paper. The first part, written somewhat earlier, presented standard processes which cannot so easily be accommodated within what are presently considered as physical type realms. The second part further elaborates on that fact. In particular, it is argued that quantum superposition and entanglement may better be understood in extensions of what we usually consider as physical type realms, realms which, as it happens, have so far never been defined precisely enough.
Heisenberg Uncertainty in Reduced Power Algebras
The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re formulated within far wider frameworks of {\it scalars}, namely, within one or the other of the infinitely many {\it reduced power algebras} which can replace the usual real numbers $\mathbb{R}$, or complex numbers $\mathbb{C}$. A major advantage of such a re-formulation is, among others, the disappearance of the well known and hard to deal with problem of the so called "infinities in Physics". The use of reduced power algebras also opens up a foundational question about the r…