Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

Study on the Regional Distribution of Energy Efficiency from the Point of Pollutant Emissions

In this paper, the author uses super-efficiency DEA model to measure the national and regional energy efficiency in China; using spatial econometric model and from the perspective of geo-spatial spillover, the author interprets the spatial characteristies of energy efficiency and extracts the main factors that influ- ence the regional energy efficiency. The analysis results show that： （1） the national and regional energy efficiency is consistent with inverted U-shaped curve, and the nationwide energy efficiency gap is increasing; （2） energy efficiency has the obvious effect of the spatial external effect, and when the government makes energy saving strategies, inter-regional energy cooperation and the prolif- eration of advanced production technology should be given more priority; （3） energy efficiency has significant negative correlation with government intervention, industrial structure, ownership structure, the energy consumption structure, and resource endowments, and has positive correlation with the degree of opening-up and energy price.

A Note on the Expectation Value of Time

In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.

A Realistic Interpretation of Quantum Wavefunctions as Temperature Dependent Vacuum Polarization Waves

We discuss in this paper a novel interpretation of Born rule as an approximated thermodynamic law which emerges from the interaction of a quantum system with a non-stationary thermal bath associated to vacuum fluctuations induced by external environment radiation. In particular we assume that vacuum polarization is a real non relativistic phenomena caused by hidden vacuum charge oscillations which diffuses heat energy in a dispersive and dissipative dielectric medium with a temperature dependent speed of propagation. We propose a model which couples vacuum wavefunctions to vacuum charge fluctuations and we deduce a temperature dependent running fine structure constant function proportional, at first approximation, to the squared of the effective electron charge and compatible with known experimental data. We interpret the vacuum symmetry breaking energy fluctuations induced in scattering experiments of particle physics and in laser assisted nuclear reactions as thermal quasi-monochromatic beams produced by the decay of hidden non equilibrium massive photons propagating with a variable light speed. We suggest, exploiting an old analogy between plasmons and pseudo Goldstone bosons, to interpret heat diffusion of this non relativistic polarized vacuum as a real De Broglie electromagnetic scalar wave associated to the radiation emitted by the hidden massive photons with acceleration proportional to vacuum Unruh like temperature. We predict a temperature dependent deviation from Coulomb law and a generalized dispersive law of these hidden unstable photons that could be revealed as not stationary coloured noise in experiments on anomalous heat diffusions associated to the decay of unstable accelerated pairs produced in nuclear physics experiments. We discuss then how our proposal of a temperature dependent non relativistic vacuum polarization might be applied to deduce a dynamic generalization of Born rule based on a realistic interpretation of quantum wavefunctions as averaged electromagnetic waves of hidden massive photons. Finally we suggest to test our time asymmetric model looking for very fast oscillating polarization thermal waves emitted during the not instantaneous wavefunction collapse and revealed as not stationary bulk heating effects in experiments on accelerated conductors and nanoconductors.

A Methodology for Mapping and Partitioning Arbitrary N-Dimensional Nested Loops into 2-Dimensional VLSI Arrays

A new methodology is proposed for mapping and partitioning arbitrary n-dimensional nested loop algorithms into 2-dimensional fixed size systolic arrays.Since planar VLSI arrays are easy to im- plement,our approach has good feasibility and applicability.In the transformation process of an algorithm,we take into account not only data dependencies imposed by the original algorithm but also space dependencies dictated by the algorithm transformation.Thus,any VLSI algorithm generated by our methodology has optimal parallel execution time and yet remains space-time conflict free. Moreover,a theory of the least complete set of interconnection matrices is proposed to reduce the computational complexity for finding all possible space transformations for a given algorithm.