One, the Number

ONE

       One may be the loneliest number, but it is also the most interesting number between zero and infinity.  The number “one” represents unity.  Zero means null or void. We are told in early math or algebra, that (1) we can multiply any number by 1, and the result will be that number.  Likewise, (2) if you multiply any number by zero, the result will be zero.

       These two statements seem so obvious that we do not perceive their having any significance or usefulness.  But, ahhh… we are mistaken.

       The science of calculus is based upon three numbers: zero, one and infinity.  Actually, only one of these is a number, the one in the middle.  But all three can be treated as numbers.  We are familiar with these terms, but may not know of their uniqueness. 

         If you divide a line in half, then divide one of the remaining halves in half, and continue this process over and over— although the length may become too small to measure, or even to conceive— it can never be equal to zero. This concrete idea becomes abstract when the length becomes un-measurable. It becomes more abstract when you think of the number of times the line can divided in half as infinite. (Keep in mind that we are dealing with concepts.)

        It is by treating these infinitely small and infinitely large quantities as numbers, that formulas can be defined which can solve problems not solvable using ordinary mathematics or geometry.  The formulas will include the phrases such as as x approaches zero, as x approaches 1, or “as x approaches infinity.”

       Before a mathematics student is exposed to the concepts of calculus, he will have learned that the geometric terms “point” and “moment”, do not have dimension. Points and moments are pure concepts, ideas, but do not have quantity or magnitude. A point divides a line into its length up to the point and the length of the line that follows the point. The point separates these two portions of line, but has no (zero) length, itself.  A point in space occupies zero volume. It is a point where three lines intersect in three dimensions (height, length and width).  A moment is a dividing line between the past and the future.  A moment is what we call “the present”, but it has no duration of time.          

       There is, of course, an ambiguous use of the word “moment “ in language, which describes a short, undefined period of time.  But for mathematics, science and some spiritual philosophies and religions, a moment, or “the present”, is a period of time equal to zero.

       These concepts, unity, null and infinity, while simple concepts on the surface, are the basis of mathematical systems which make today’s technology possible: x times one equals x; x times zero equals zero; zero divided by x equals infinity.