Zero-Point Semantics

Blog Post

June 1^st, 2011

From Causation to Correspondence

At great risk of oversimplification, the history of modern and contemporary mathematics, dating back at least as far as George Boole and the mid-19^th century, tells the story of all mathematicians and most natural scientist devoting a vast amount of human resources to a better understanding of the nature of counting and, as a corollary, to computing.

There are certain constants, (p, j, e, g, c) that are alleged to be independent of the human race and entirely necessary for the world, and perhaps the universe, to be exactly the way it is. During our last class with seniors I confessed to my primary motive for studying mathematics and the natural sciences, that motive being my desire to know (or not know) god.

Alistair McGrath, a scientist and theologian at Oxford, has argued that the necessary and universal constants mentioned above coalesce in such a manner as to necessitate the existence of a superior intelligence and, thus, his argument is based in mathematics. But how does his argument fit, if at all, in a Precalculus course?

To answer this question our first task will be to differentiate the radical function and to consider the nature of our result over the entire domain of the function.

Are there any values for which the derivative is meaningless?

As you are working to apply Newton's difference quotient method to the parent square root function, consider why we are examining this function and what relevance it might have to McGrath's (general) thesis. After applying the difference quotient to equation (1) below, check your result using the generalized power rule we learned earlier in the year.

(1) f(x) = x^1/2

Are there any other functions exhibiting similar behavior where by “similar” we mean, a product of squaring functions? Provide at least one example; find the derivative of your example and explain how it relates to your results for equation (1).

Can you generalize your results from the previous exercise? Note that we have only been considering integer-valued powers until our work with the radical above. Once you have several conjectures developed, test these conjectures by, applying Newton's method; by analyzing graphical behavior; by applying the power rule; and by considering the meaning of the domain and range restrictions.

There is a mathematician named, Graham Priest, who has put forth the idea that all motion is a result of contradiction. Before we relate the above work to this idea, pause to reflect on the motivations of, Calculus, as a system of inquiry. Whether Newton or Leibniz or the force of history, what factors contributed most significantly to the elucidation of Standard Calculus?

It occurred to me this morning that locomotion by steps and gaits must be in prefect correspondence with cosmological events such as the birth and death of stars. The degree to which these correspondences are significant would help us refine our various interpretations of the weak and strong anthropic principles, potentially giving them a proper quantitative framework. Of stricter relevance to today's session is the fact that walking may be understood as a repetitive contradiction. For each downward stride we are in agreement that gravity is at work and necessary for the world, while for each other stride, we stage a revolution against forces older and more permanent than ourselves. Of course I am taking liberties with our understanding of “contradiction”, and hope to develop better definitions as this work unfolds.