Reality and Mathematics. Reality and Mathematics. 0210527.pdf. Reality and Mathematics. Physical Reality: Less Is More. Physical reality is composed of properties like distance, duration, velocity, area, volume, mass, energy, and temperature. To quantify these properties you need to measure them. And the act of measuring boils down to comparing against an agreed yardstick, a unit of measurement such as a foot, a gram, etc. Do you need a dedicated yardstick for each quantifiable property? Would the answer to this question be 'yes', then physics as we know it, would not be possible. We would not be able to relate the various properties to each other, physics laws would not exist.
Fortunately, the answer to the question is a clear 'no'. Consider measuring velocity. The widely accepted answer is 'three'. But there is another number of three that pops up in fundamental physics, and that number is related to the number of yardsticks. In the following it will become evident that the number of dimensionful physical constants must equal the number of independent yardsticks. No, it is a manmade conversion factor. Relational order theories. A number of independent lines of research depict the universe, including the social organization of living creatures which is of particular interest to humans, as systems, or networks, of relationships. In physics and philosophy, a relational theory is a framework to understand reality or a physical system in such a way that the positions and other properties of objects are only meaningful relative to other objects.
In a relational spacetime theory, space does not exist unless there are objects in it; nor does time exist without events. Space can be defined through the relations among the objects that it contains considering their variations through time. The relational point of view was advocated in cosmological physics by Gottfried Wilhelm Leibniz, Ernst Mach (in his Mach's principle). Although Albert Einstein was impressed by Mach's principle, he did not fully incorporate it into his general theory of relativity. Correlational processes have been observed at several levels. Wandering set. Wandering points[edit] A common, discrete-time definition of wandering sets starts with a map of a topological space X. A point , the iterated map is non-intersecting: A handier definition requires only that the intersection have measure zero.
To be precise, the definition requires that X be a measure space, i.e. part of a triple of Borel sets and a measure such that Similarly, a continuous-time system will have a map being a one-parameter continuous abelian group action on X: In such a case, a wandering point , the time-evolved map is of measure zero: , the set An element is called a wandering point if there exists a neighborhood U of x and a neighborhood V of the identity in for all Non-wandering points[edit] The definition for a non-wandering point is in a sense the converse.
Is non-wandering if, for every open set U containing x, one has that for some and any arbitrarily large. Wandering sets and dissipative systems[edit] A wandering set is a collection of wandering points. The intersection. Life gravity and the second law of thermodynamics, LineweaverEgan2008v2.pdf. PF thread problems concerning reductionism. Reductionism.