SCIENCE AND SANITY - online book

An Introduction To Non-aristotelian Systems And General Semantics.

Home | About | Philosphy | Contact | Search




CHAPTER XIX
MATHEMATICS AS A LANGUAGE OF A STRUCTURE SIMILAR TO THE STRUCTURE OF THE HUMAN NERVOUS SYSTEM
In recent times the view becomes more and more prevalent that many branches of mathematics are nothing but the theory of invariants of special groups.                                                                                             s. lib
A natural law, - if, strictly speaking, there be such a thing outside the conception thereof, - is fundamentally nothing more nor less than a constant connection among inconstant phenomena: it is, in other words, an invariant relation among variant terms. (264)                   cassius J. keyser
Whatsoever things are invariant under all and only the transformations of some group constitute the peculiar subject-matter of some (actual or potential) branch of knowledge. (264)                               cassius j. keyser
The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant), (iss)            A. einstein
i
The things hereafter called tensors are further characterized by the fact that the equations of transformation for their components are linear and homogeneous. Accordingly, all the components in the new system vanish, if they all vanish in the original system. If, therefore, a law of nature is expressed by equating all the components of a tensor to zero, it is generally covariant. By examining the laws of the formation of tensors, we acquire the means of formulating generally covariant laws. (155)            a. einstein
The thalamus is a centre of affective reactivity to sensory stimuli, while the cortex is an apparatus for discrimination. (411)                 Henri pieron
Section A. Introductory.
It becomes increasingly evident that we have come to a linguistic impasse, reflected in our historical, cultural, economic, social, doctrinal., impasses, all these issues being interconnected. The structural linguistic aspect is the most fundamental of them all, as it underlies the others and involves the s.r, or psycho-logical responses to words and other events in connection with meanings.
One of the benefits of building a system on undeniable negative premises is that many older and controversial problems become relatively simple and often uncontroversial, disclosing an important psycho-logical mechanism. Such formulations have often the appearance of the 'discovery of the obvious'; but it is known, in some quarters, that the discovery of the obvious is sometimes useful, not always easy, and often much delayed; as, for instance, the discovery of the equality of gravitational and inertial mass, which has lately revolutionized physics.
268