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Note on my Calculus Papers
October 6, 2006: It has just come to my attention, some four years after the fact, that I have apparently reinvented a simplified version of the Calculus of Finite Differences. That is to say, my table has been used many times before. I had assumed that such a simple table must not be unknown, I just didnít know where to look. Since I am not a professional mathematician I had never before today heard of finite differences.
From my limited reading on the subject, it appears that I may nevertheless be interpreting my numbers in novel ways. So far I have not found that current or historical treatments of finite differences make the distinction I have been careful to make about the point. I have discovered that the Calculus of Finite Differences has even been used in the past few decades in QED, but it seems that my argument about the point has been undiscovered even there, where it is most needed. As you will see, the Calculus of Finite Differences can be interpreted in any number of ways, and it has historically been interpreted much the same way as the Infinite Calculus has been. That is to say, it has suffered the influence of its much more famous sister. This means that its most useful characteristics have been missed: it has been used for heuristic reasons rather than theoretical reasons. It has not been used in QED to get around the point or to solve the problems of renormalization, it has been only been used to solve certain sorts of equations that seem more amenable to it.
In many of my papers I have made it clear how my interpretation of this Calculus of Finite Differences solves many of the most basic and fundamental problems of QED and General Relativity. It solves them not only by skirting infinities, but, more importantly, by skirting the point and the point particle. In my interpretation, proved by going all the way back to Euclid (in the long paper), the point has no place in the equations, either as a variable or a function; no place in the tables, no place in the graphs or coordinate systems, and no place on the curve.
I also show that the misapplication of the Infinite Calculus to points has caused a mis-definition of many mathematical spaces, including Hilbert Space.
Currently I am trying to sort through claims that there is a margin of error in the Calculus of Finite Differences, compared to the Infinite Calculus. I do not yet see where such error can occur. At first glance, it appears to me that the Infinite Calculus claims a precision it cannot prove. As I showed in my papers, the Infinite Calculus claims an infinite precision, by claiming to be able to find numbers at a point and an instant. If the Calculus of Finite Differences has a margin of error relative to that, then I would say the error actually belongs to the Infinite Calculus. But it may be that in analyzing some functions, the Infinite Calculus is actually to be preferred. I will leave upon that possibility until I know more.
Addendum: I now know more. I have studied the claims of the Infinite Calculus to be superior to MY Calculus of Finite Differences, and found them all to be false. I explain this in much more detail in my new paper on the derivative for the exponential function.