Tuesday, October 18, 2011

The Problem of Counting

An Allegory: The Problem of Counting 
and Its Communication

 John W. Jacobson & James A. Mulick

A long time ago in a land far away there lived many people.  The country was wealthy in resources.  Yes, many were poor, but many more were of modest or even extravagant means.  Philosophies grew, evolved, in a slowly–changing matrix made possible by the leisure and reflection afforded by the country's agricultural riches, but hindered by a dispersed population.  People lived their simple, uncomplicated, but satisfied lives in small villages.

Over the centuries there emerged a group of elite, neither moneyed nor initially of great influence.  They wandered the land, speaking to small groups of the populace, many with apprentices who sometimes spoke in their place, and sometimes gathering in large groups to argue, gain agreement, and yet to disperse again.  Theirs was a creed strange and new to the land:  It spoke of understanding the constancies of nature, and indeed of humankind, using numbers and counts and recounts; of even having many people consider and count separately before once again gathering together.

In the beginning townsfolk throughout the land thought the wanderers to be daft.  After all, how might one understand the wonders of the world, the breeze through the trees, the variety of life, the depth of emotion, the state of one's being, through counting or comparing counts? Certainly, these wanderers were simpletons to seek such means of describing life instead of using their own eyes and ears as any sage person would, and indeed had throughout their long history.  As well, these wanderers had no appreciation of the townsfolk's knowledge of sharing thoughts without speaking, divining water wells, or detecting evil such as witches and warlocks.  To these realities, the wandering counters had no answers.

Yet, generations passed swiftly, and as was seen fitting, middle–age in one's mid–20s, death by 35, assured that their passage was truly swift.  Generations passed quickly for the counters too, who passed on their countings first by word of mouth, and later by arcane scratchings, or so these seemed to the townsfolk.  Yet the folk tolerated their presence, for their counting was amusing and harmless. Indeed, many areas lacked a suitable village idiot, and in such times and places, a counter made a good substitute.

But passing generations brought many gatherings of the wandering counters, where they argued passionately and brought together greater and greater numbers of counts, until many times the different counts themselves became difficult to number.  At one great gathering it was decided that each wanderer would count only certain kinds of things, such as things having to do with the air, the sea, the earth, animals, or maybe even the townsfolk.  The folk thought this most silly, because they knew that all life and non–life were one, and how could breaking the world down into pieces help one understand the real world?

The wanderers, though, merely because the townsfolk felt them queer, were not deterred.  They set out from their great gatherings to count many special things, and in their countings found that, if they took care to define what they counted, often their counts agreed.  Meetings on special counts began to take place where remarkable agreements were found, but there were also very big meetings on counting itself.  It came to pass that counters of different specialties would from time to time speak with one another at length about their counts, only to find that one count was related to another.

Of course, these strange wanderers found this to be truly exciting, and word spread rapidly.  Among them there came to be some who would say, "This is all very well, but what good is all this counting? We die barely out of childhood.  We are the victims of our weather.  Even counters have problems; one may hear of great counters in distant places, yet only hear rumors of their great counts for the distance to travel is so far and dangerous.  Travel to our own gatherings is even more unsafe."  Many counters saw the wisdom of these words, and many of these came to feel that they could make a better livelihood if they answered these kinds of questions than they did as a source of mirth for the townsfolk.

At the greatest counters' meeting of all time, one group hit upon a way to begin this great effort.  Instead of training all their apprentices to count, they would train some apprentices to also use the counts to improve how the townsfolk lived, and, not so incidentally, how they lived.  There were many false starts, for they had little understanding of practical things, but after many more generations, there were basic counters and applied counters, who shared the language of counting itself.  Much later, there came to be applied counters who taught apprentice applied counters, and later still, many people who were trained by them, and who helped them, but could not themselves count very well.  But that's getting ahead of the story.

Great events began after the first special meeting of applied counters.  They too found that some of their counts agreed.  They became especially interested in counts having to do with air, water, and fire.  Some had found ways to use fire and air to make objects move.  Yet others had found that villages that heated water over fire before drinking had less disease, and sometimes these villagers lived to be 40 years old.  Others found that wheels could be placed in streams, and that they would turn in ways that could be used to crush grain, and thereby free people and animals for other tasks.  In their excitement, they rushed to inform the townsfolk.

The lucky ones went to villages where the folk did not think a lot about such things as steam or smoke, nor about fire or water or wheels.  The unlucky ones had a unique opportunity to count how long it took to die over an open fire tied to a post, or the number of stone impacts needed to produce unconsciousness.  Townsfolk could reveal their dislike for new ways with great severity.  Time passed, as it will, and the folk who tried the new ideas would see their villages prosper, while those who rejected these ideas were eventually sundered by their more advanced and healthier rivals.  Many more villages were brought together under single chiefs, and great villages, where the applied counters were especially welcome, developed. 

For many years the wandering counters continued their wanderings, holding their meetings, and training apprentices, visiting villages and great villages unpredictably.  Because they had no family or clan ties to the villages, they were not yet trusted by the townsfolk.  Advisors to the great chiefs, townsfolk themselves, asked whether the wandering counters were truly to be trusted, saying; "They go about counting and in ways and with numbers that we do not understand.  We know that they are really not like us, for they still do not understand nature or how to find evil.  They may know more than they tell us or even their apprentices; they may be hiding great things from us that could make you a greater chief.  Would it not be safer and better for them to live with us, and depend on us for their food and shelter? After all, applied counters live here, they marry our folk, we trust them."

So the great chiefs met together and agreed.  At gatherings of counters, advisers to chiefs would speak of the benefits of groups of wanderers moving to the great villages.  The great village would provide food, shelter, and protection; the wanderers would teach how to apply counting.  This, of course, was what the wanderers had sought from the time of the great meeting when applied counting had been born.  Thus they agreed, and the wandering basic counters were no more.

Still not accepted by the townsfolk, the basic counters found themselves continuing to exist in groups, even in the great villages, socially as well as in their work.  Most of the first village–dwelling counters married townsfolk, some married into the families of advisers, and even chiefs (though most who did so themselves became advisers and ceased further basic counting, becoming occupied with affairs of state).  In the large extended families in the great villages, intermarriage with basic counters remained a source of recurring embarrassment.

Nevertheless, many basic counters gained great numbers of apprentices, until they could no longer teach one apprentice at a time.  Some found that they had to teach one or two apprentices to teach many other apprentices, for there was such a clamor for solutions to problems (many folk had found that apprentices eventually lived better off than those who toiled in fields, stables, and granaries, auguring that perhaps apprenticing had its advantages).  Thus it came to be that even applied counters could find work in teaching apprentices.  Some of these new apprentices found that they could not learn all of the counting that they were being offered, or that they had to aid relatives and had no time for counting, or that there were not enough basic counters or apprentices for them to be admitted to the teaching in their villages. It was at this time that the paracounters came to be, the people who had received some training in counting, and who relied on others to interpret counting for them.  Eventually, although there could be no basic paracounters, applied paracounters came to greatly outnumber even applied counters, so great was the demand of the chiefs and their advisers for counting services of any sort.

For ages, there was an uneasy truce in the land, even ofttimes an alliance between basic counters and the advisers to the great chiefs.  The great villages came to be great indeed, and were filled with not only townsfolk, but also a great number of paracounters.  Yet, advisers remained aloof from counters and somewhat distrustful, understanding that the basics of life, and of survival and protection of the townsfolk, were beyond counting, counting being such a narrow thing.  The advisers, and their own advisers now that the villages were truly great, found that paracounters were much more docile than the basic counters; paracounters knew that one paracounter could easily do the work of another, but the numbers of true counters were limited.  In time, the paracounters' ways were embraced by the townsfolk, for they were really little more than townsfolk who used other people's counting.  Both the townsfolk and the paracounters agreed that the advisers were right:  Counting could not answer the real questions of life and living.  Some came to suspect that counting might even prevent one from asking or answering these questions.

Just as gradual changes took place in the ways townsfolk and some paracounters felt about the basic counters, there were changes taking place in the work groups of the counters themselves.  From the very beginning one of the key points of agreement among counters had been freedom of counting, the right of any counter to choose what to count and when to count it.  The obligation to define clearly what to count and under what circumstances counts were conducted developed much later.  Defining was generally agreed to be important, but not as central to basic counting as freedom of counting.  As applied counters came to be important, not only in teaching apprentice applied counters and paracounters, but also in the politics of the counting subculture, conflicts arose between applied and basic counters, with the applied counters arguing that the chiefs required them to apply counting to problems where there had been little or no counting done, and that sometimes these problems did not even seem to involve counting at all.  They suggested that there might be solutions found within counting that might make new kinds of counting necessary.

Although the small number of people who had been trained in both basic and applied counting sided with the basic counters in arguing that the nature of counting itself, and especially ways of defining counts, should not be altered, they were greatly outnumbered by the applied counters who stressed freedom of counting as their credo.  Some basic counters who had spent many years counting about the nature of counting itself also supported the plea for a revised definition of counting.  Through the time of their first migration to the cities, the basic counters had intermarried greatly, partially from necessity given the townsfolk's reactions to them.  They had few roots or ties to the townsfolk, those ties which had existed had withered with time.  The applied counters, though, had strong roots in the villages, many were second generation paracounters.  Because their work was with paracounters (mostly) and with townsfolk, they shared many views of local villagers.  It was no surprise that they argued counting should be changed to include the true values of life and the detection of good and evil.  So it was that, within the counting subculture, many applied counters changed the way they defined legitimate things to count.  Some even proposed to practice counting by intensive observation combined with a general type of estimation.

The chiefs, and the advisers who manipulated the chiefs' ideas, and the paracounters who carried out the advisers' orders were immensely pleased at this turn of events.  It was now becoming obvious how inadequate the conventional counting of the basic counters had been.  Confident now that the future was bright because the applied counters would address real–life problems, they awaited developments with growing anticipation.  They didn't have to wait long.  It turned out that intensive observation and general estimation took much less time to answer questions than counting by many people and comparison of counts.  It also produced many answers, unlike basic counting, that made good sense to the townsfolk and the paracounters.  As these answers emerged from intensive observation and estimation, specialized advisers informed the townsfolk and the new solutions were rapidly applied.  These new solutions addressed day–to–day problems in agriculture, social life, support and training of helpless villagers, in fact, almost all aspects of village life, including the determination of good and evil.  Indeed, as we have already noted, the new methods and solutions made good common sense to the townsfolk if not to the applied counters.

Time passed some more, although somewhat more rapidly than in past eras, and within a few decades it became apparent that some of the widely–applied solutions were either short–term in their effects, had been superseded so quickly by new solutions as to be unworkable and incomplete, or had done severe damage.  Advisers skillfully deflected the responsibility from the chiefs to the counters.  Townsfolk became much more suspicious of the basic counters:  "Why did they not tell us how important the ways of counting could be?"  They came to feel that there had been a conspiracy of evil among the basic and applied counters, with the applied counters fronting for the basic counters, and began to reject even paracounters as contaminated by the conspiracy.  Townsfolk availed themselves less and less of paracounters' services, particularly those who had any continuing contact with applied counters.  Fewer paracounters, and no townsfolk, applied to be apprentices.  Basic and applied counters were barred from village meetings and councils.  In smaller villages, basic counters were expelled, in larger and great villages both basic and applied counters wisely chose to depart.

Over the next century village life changed.  The exodus of basic counters resulted in a period of renewed wandering, although now, as anathema to townsfolk throughout the land, they eventually took up hermitage or other protective coloration, most typically that of the itinerant tinker, with tinker's apprentices.  Applied counters found more stable means, usually in manual labor.  Paracounters, the last to be forced into exile from their townsfolk kin, often found sustenance as clerics in a new realm of faith.  The consequences of the inadequacies of widely–applied solutions, and the loss of the counters who might have helped to solve some of the problems, were to confront the townsfolk.  Unable to support the complexities and resource demands of large gatherings of villagers, the great villages, and the great chiefs, along with their advisers, ceased to exist.  Their thronging multitudes slowly but constantly migrated to small villages, where, in turn, they had to cope with the challenges of arid or desiccated fields, declining health and fewer means to treat illness, and dwindling food stores.  Their numbers decreased, but few were counting.

A long time ago in a land far away there lived many people.  The country was not as wealthy as it once had been.  Many were poor, but only a very few were of modest means.  Philosophies did not grow or evolve because there were no riches to make possible leisure and reflection.  People lived their simple, uncomplicated, not–so–satisfied lives in small villages or roving bands of hunter–gatherers.

There were no elite wanderers.  Thus was the solution to the problem of counting and its Communication Facilitated.

The End

An RIP Publication 

“Serving the world through mankind”
Raritan Institute for Practical Studies

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