Multiscaling and Multifactoring of Mechanical and Biological Systems

Abstract

Multiscaling refers to the segmentation of physical systems of space-time having the same building blocks, a de facto hypothesis that is not likely to be challenged. Physical systems should be relatable to one another by space-time scale shifting. The mathematical proof will rightly so, be disrupted by the overriding force of political and economical expediency of new order of science and technology. Already in practice is that science and technology have globalized and personalized the world according to the priorities of the political and economical expediency. Personalization is definable only when distinction is made between the less from the more personalized. The “unitized function” is therefore invoked such that n number of factor types can be weighed and expressed by an “indicator”, say X0*. A similar quantity Xj* for the subject, of the mechanical or biological, can then be compared and weighed on the same basis. The subject with the least ΔX0*, the difference of Xj* and X0*, would be ahead in fitness. Physical systems are directed toward the well being of the individual. Multiplicity of scales and factor types in space-time call for partnership of “multiscaling” and “multifactoring”. The unitized function accommodates this combination and the binarism that is intrinsic to scalable data. Monolithic data are not scalable unless they are converted to be dualistic by scale shifting. Simply put, macro data should be converted to macro-micro by a process known as transitionalization. Restoration of the scalable capability in mechanics and physics is also connected with space-time non-symmetry. Non-symmetry refers to a reference (0), while (+) and (—) are directional dependence. This formalism can be degenerated to define a physical fitness ranking index for mechanical and biological systems. Monolithic data have been used in the field of fracture mechanics for decades. Only in recent times that the conversion to dualistic dependent data has restored the consistency required for shifting the space-time scale. The globalization and personalization will be discussed in terms of unitization of personal data at large. The longevity of the human subjects and physical fitness will be used for application, although the method applies to mechanical systems as well. For the human subjects, dualistic ma-mi unitized factor types are defined to avoid the violation of first principle and to show that the indicator X0* can be related to the physical fitness indices that are already in use for making health care national policies.