Once upon a time, there were two species of numbers, evens and odds, and each endeavored to live according to their ways, as odds and evens displayed quite different properties. Odds are odd and evens are even, as everyone knows and can clearly see.
Odds (O) were considered special in several ways. Any ensemble of O's (even when carefully sampled in the most random manner) always correlated to a greater number of primes than did Evens (E), and as the process of replication amongst the numbers boiled down to their going forth to multiply, the fact that primes were indivisible was an indication of their purity. Quite a lot of effort was spent with understanding this correlation, and many mathematical devices were used to help distinguish the most pure forms of these numbers. The poor E's could only claim one prime amongst them.
Finding the greatest prime occupied many. It was felt that the most highly prized secrets of the universe were to be found in the greatest primes. As the offspring of two married numbers was their product, the single child of two greatest primes became much sought after (even though it could never be prime).
But there was sorrow too in marriage. An O's marriage to another O always resulted in an offspring that, while never prime, was at least another O. E's of course always begat E's, but the banal fact was that a mixed marriage of and O and and E also always begat an E. And so upward movement by children in number society was impossible, while the downward movement was inevitable for many. Furthermore the rules around marriage were fraught with contradiction. A marriage between any two O's summed to an E, and hence their pairing was fleeting -- only so much to get the job done. The combination of an O and an E however, always summed to an O, and this intermixing, while producing a E offspring, made a quite happy pair and the marriages were often long lived.
One day there appeared a scientist named "Foo" who aimed at uncovering all this behavior obviating the strict separation of the numbers. He invented a way of factoring the numbers, so that one could tell if an E was indeed a most pure E. To be so meant that it was a product of two purely E parents. If one or more of the childs factors turned out to be odd, well, then one would know... an intermixing occured. This became known as the "Foo effect", after the scientist who invented it. Thus the study of factors became popular amongst those who worked with numbers. Filtering methods, such as the "Sieve of Eratosthenes" help to segregate the E's and those that were not pure E's were allowed to attend a buffer school appropriately called "Colander".
Foo also found other ways to distinguish the O's and the E's. By graphing the progression (A Cartesian graph, of course) of rank ordered O's and E's, he found the E's to lag the O's by one, thereby demonstrating the developmental superiority of O's. This finding was greeted by much controversy -- both lines went to infinity. The scientist retorted cogently that the odds simply got there first. His bottom line: "To explain this finding solely in terms of rank bias and numerical differences would mean that these rank-numeric influences perfectly simulate developmental differences in test scores within each number group." has left several puzzling over his intricate logic.
In the meantime, the odds and even numbers have been trying to convince the scientist named Foo of just one thing -- that both belong to the larger societies of the rational and complex, and it is this fact that really counts.
Bill Barowy, Associate Professor
Lesley College, 29 Everett Street, Cambridge, MA 02138-2790
Phone: 617-349-8168 / Fax: 617-349-8169
http://www.lesley.edu/faculty/wbarowy/Barowy.html
_______________________
"One of life's quiet excitements is to stand somewhat apart from yourself
and watch yourself softly become the author of something beautiful."
[Norman Maclean in "A river runs through it."]
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