Guest Article 

PLAYING SOLITAIRE

by A.F. van der Meijden

21.11.05 Copyright, 5983 words

When I played solitaire with cards being short one space would not stop me. I get annoyed at things not coming out tidy. Writers of computer card games are sticklers for the rules and most games have rules so strict as to prevent winning at all. FCPro is the exception with untold 'undo's' so you can learn about strategy and have another go when things do not come out. Most players follow whatever the layout shows and one cannot then win better than half the time. 

It follows that easy layouts can be solved by many paths and the fewer the possibilities the trickier it gets until the ultimate of having only one way to solve the game. It follows from that that learning how to win them all is near impossible under strict rules. A champion billiard player will lay out the balls in a specific way and practice until he can hole the lot. It's the same with tennis, one practices until one gets tennis elbow. You cannot get good at anything unless you do a lot of it, mistakes included. Look at babies learning to walk, it takes several years of regular practice. It takes decades to master this into mime and dance, and so for any art and skil.

This is because we are in the habit of going at it linear fashion, starting and stumbling into every wrong possibility we then have to figure out and start again until one gets the entire setup and its parts clear in the head. It's the same with bridge, Unless you keep track of every card so far played you don't know how to finesse at the end or when to hand over the game to the opposition for you to take advantage later. Since our standard memory is supposed able to manage only 7 + or - 2 items in one lump, few of us can name all the seven dwarves. But under hypnosis we can be made to recall everything by handing over control of our mind to another person. Our mind does not care who gives the orders. It does not have a self identity or ego, just keeps track of it for us. If that were not so we could not learn how to become good dance partners or be in a chorus on stage. And fish do it with far less brains than ours.

We call this playing intuitively where our trusty mind can handle any whole with untold parts, relations and interactions so we can switch tracks for whichever handicap or bumble turns up. A car mechanic has a working model of a car in his mind, as an ideal the way it should work when all goes well. Then when he listens to our wonky car he can tell what's out of harmony or kilter, though he won't allow himself to be sure he is right until he opens up that car. A cook is the same. One is either a recipe cook or an intuitive cook who can rescue any fiasco back to an edible meal. Our society does this by teaching us a method and "How to do things properly". There are untold ways to cook an egg, from putting it on the radiator to using a magnifying glass or fresnel lens. You can even put a plate in the sun, wait until it heats and then break an egg into it. Using a mirror would be better.

It is the same with windoze Fcpro. You first take a good, cool look at the layout to see what will prevent the game from being finished like the rarest of possibilities having all the aces up and the low cards below. So being a chance given opportunist to using a method won't get you through the ninnie phase. Getting to being good at it takes a while but after a while one gets a nose for it and play gets faster. One intuitively senses what will come out before it happens. And if you make a booboo short of losing you just 'undo' and try another tack. So the best way to win is to have no fixed strategy, be flexible, sass out the odds and go for it. One gets to mastery, doing it near automatic without mishaps after many, many games played. Currently I'm on near 98 percent because I'm lazy. Lazy people use their noddle more than their hands and feet. You see I wanted to find out whether its claim that one can win 100% of the time is true. Mastery or being a champion player consists of being able to anticipate a mishap before it happens. It means you have to pay attention all the time to every detail of what gives. Trouble always strikes from an unexpected quarter. You cannot 'focus' on that, one has to leave the mind open.

The shift from working at what one can do or what opportunity offers into I'm going to do it this way shows a more overall, holistic grasp of possibilities that lie open. The intuitive feeling is more: "I'm going to do it that way". Then, so to speak, in musical terms, one knows about the variations on a theme. During the Middle Ages one was made to 'turn sentences' where nowadays we are taught the right and politically correct method or approach as if there is only one way to do things. We are taught grammar as if its rules are dogma rather than offering an insight into patterns with variations built in. Although the word 'creative' is much bandied about, how it works has yet to be made clear. T.S. Eliot, the poet, coined 'paradiorthosis' in the fifties, which you are not likely to find in a dictionary today, for stealing a well put idea from a collegue. Einstein mentioned that in being creative one does not give away one's sources. 

The Middle Ages came up with three kinds of style: Dominican "simple" for preaching, Augustinian 'claritas' and Plotinus his 'sublime' which means it could not be put any better. We have only one poets call 'dead' English. One writes "sincerely yours" at the end of a letter and who really means that rather than thoughtlessly following 'protocol'? One cannot explain this linear fashion. This entails a kind of double thinking, rather than double binding. While one is doing things one also notices what one is doing and checks this out against other possibilities. Using a word one is aware of the various meanings it can have and be given. It shows up well in the changes in Ballet which was stifled by protocol where now we have free styles self developed by dancers. In my choosing 'stifled' recall remembers A.C. Clarke in Rama II, making a comment on Bureaucrats stifling creativity. But he was somewhat lengthy so I re-wrapped the sentiment in an image of ballet thus paradiorthotically stealing from a colleague. Wrapping it up in an image of action has more impact.

One cannot teach this ready made. In Plato's "Meno" he makes Socrates have a dialogue about what he does not name but is the universal, used by Aristotle who does not explain it. Meno is focussed on "virtue" as the quality of sublime being. Socrates sums this up by saying that it has to apply always, on every occasion and ends up telling us that we can point this out but cannot teach. It has to be put at just the right, opportune moment when insight in the listener flashes into the holistic, making connections in the mind not hitherto noticed. It is what in the good old days a guru, Zen master or Lama, was able to do. This can happen only with an apprentice around. What is also obvious to the discerning reader is that the dialogue is carefully contrived to move in that direction from the start, although no such thing is mentioned 'expressly' as we are advised to do these days. Computer handbooks unexcel in this by telling us everything we don't need to know when a PC program hits a bug, hangs or crashes. Everything is assumed to work perfectly which is when you don't need the handbook whereas when one does it cannot be found. Finding a set of corrupt files the other day I tried to correct this and making mistakes the screen displayed "Bad Command". I could see that quite well myself, the command did not do as intended. Here I move into first person to share a feeling as having more impact. One cannot "express" a feeling with words but we've all been there and done that. We think of a universal as encapsulating everything in the word, but it happens in the mind and words cannot catch such an all at once and together insight. "Educare" used to mean 'to bring out' where nowadays it is made to stomp in facts.

Actually this applies to all of life. Mysticism advises us to live in the present, and I'll ignore it is often confused with mystifying. That present is a timeless present that flows on endlessly with every new moment bringing novelties which needs creativity to solve. And as one gets to "been there, done that" there's always something to pick on one had not noticed before or paid attention to. Greg Bear, a prolific writer, on his website, has an article about genes and cloning. It's brilliant as he goes through both what goes right and works versus what can and will go wrong. He finds Mother Nature a ruthless performer who weeds out all the failures at an earliest stage, though she does not always succeed. To currently produce a clone takes about a hundred eggs to get one to run full term. Between Bear's lines one catches the flavour of a hint that tells us we should learn more about how nature acts. He does not seem to know that Russian academician Gariyev has theorised that our junk DNA makes up a holographic 'projecting' tool which enables the evolving details of foetal growth. What Gariyev does not mention directly is that thereby our Quantal consciousness can intervene to a juncture of self destruction and innovation which would explain how evolution actually works. Again here it is how the foetus attends to the cooking.

The same happens with AI, Artificial computer intelligence. Amy L. Lansky, PhD, writes: "As a researcher in computer science and artificial intelligence (AI) for over twenty years, I am known for my work on a variety of automated planning systems.... For instance, I have built artificial agents that "perceive", reason about their environment and about their own "beliefs", and take actions as a result. Despite, or perhaps because of my expertise in this area, I find myself alarmed by the emerging trend in the consciousness community to equate consciousness with simple awareness, or even with more complex forms of reasoning and action based on awareness. The natural result of this equation will be to find computers capable of consciousness or, perhaps even worse, to view humans as complex machines." 

See:  http://www.renresearch.com  

Actually there are three main academic forums into this consciousness thing and they are all sociological pedagogues doing it wrong. The one I dislike most collects and classifies all the attitudes and theories around but does not move into the next level of thinking that integrates and intuits a solution. As if categorising instances does the trick. And as Karl Popper notes, progress in science move by disagreement, which does not mean argufying the case. An amusing instance is about Paradox done over in Wikipedia, listing hundreds of instances when to solve a paradox is quite simple. Paradox results in knowledge from the "well-defined" word, used as jargon by specialists, alternative meanings or interpretations, for example the Red shift and gravity, clutter up tidy theories. In effect a theory produces facts whereas 'observables' made clear by T.S. Kuhn can, "In the absence of a theory or a candidate for a theory" mean almost anything. Hannes Alfven and Halton Arp, between them, demonstrated that the red shift does not necessarily imply an expanding universe. 

Paradox cannot exist in reality, which led Cantor invent his Infinite Set Theory to stop what is called an infinite regression and which brings paradox face to face with an event frame. There are some three major kinds of paradox, viz>: (1) between existence and non-existence, which si really about what  we consider so, not whether is IS so, (2) As between space and time which is held isolated by yardstick science, although not in cosmology, (3) As between appearance and reality in knowledge. All which are covered by the ultimate conundrum that action at a distance is simultaneous with local observation, as performed by a "Detached Observer" who only peers at what is in front of his nose, locally. That amkes all our localised zero sum results come out false because, beyond it all, the consciousness of the participant of the action is connected with the unity of the universe. Words isolate what is held together in reality.  Take Bertrand Russell's Theory of classes. In a town lives a barber who does not shave himself". NO self respecting barber would not shave hismelf, unelss it was a trsuted friend. So what Russell does is devise a strictly well defined barber, who exists only in the world of words and takes it that is the case for real. You may now go to wikipedia's article on paradoxes and etst whether in all cases there is an exclusionary condition in every case. I know this to be so "in principle", my argument being a 'universal'. It's a mereological problem and Anatole Rapoport, the Logician, pointed out years ago that paradox hunting makes a good source for creative thinking. Spenser Brown in his "Laws of Form" took this to an extreme of definition, making all logical terms 'expressly defined' proven by being applicable to curcuit boards and humanly a good way to go paradox huntings an extension of Infinite Set Theory. The Universe is infinite, meaning unmeasurable, whereas we go about this in an infinite way and for which antiquity relied on the universal which forces us to consider and evalute a batch of like individual instances. You cannot define or put in words what makes a given action "like", it needs intuition to see beyond the appearance of events.

After this side issue to revert to the main line of thought. That is the kind of thing Popper means by "disagreement", shaking a theory loose of its assumptions. A disagreement is not about the details but the fit of a theory to whatever we mean by *reality*. A theory is an interpretation not a statement of facts, as it is cobbled together from observables expanded by theoretical "facts" that follow if and only if the theory is correct and leads to full scale prediction by which time it is no longer a theory but the mechanics of use. Plastics makes a nice example as we can now produce almost any kind of plastic to order. It ceases to be *science* which is enquiry into unknowns, not about elaboration of knowns. It follows that only folks having their heads stuffed overfull of alternative possibilities, or who are good at finding them, can come up with an alternative explanetion. Einstein made it quite clear that he was a theorist, not a physicist. He got stuck at "God does not play dice". But god always makes all dice throws win, as shown by Carroll in "Alice" in the Madhatter's race where everybody wins. If we refuse to get upset because things won't happen the way we like them to, we might learn something.

Basically that is what our UNI-verse is comprised of, things that work, not perfectly or fully reliably, because room is left for further change always. There's the case of the four minute mile and the three minute mile and whatever else we  were told is impossible. Einstein stopped at placing a limit on the speed of light. Alan Aspect showed that particles "at a distance" are in telepathic contact, which is faster than light. This has to be the case if the universe, the size and age it is, maintains its continued stability. If the information exchange, of whatever kind it might be, was not immediate we would not have a UNI-verse and prediction be impossible. Since prediction sometimes works our knowldge is but partial. We don't have any proof of that and won't until some wit imagines forth a way to show it happens. Similarly for Quantum Physics which is stuck as a single theory for everything.  But if we take Plato's advice in "Meno" and study individual instances then the entire panoply of statistics, which allows that anything could happen, we just don't know enough to be sure, falls away. Given that for any individual organism putting forth a wish, or as put in the Rg Veda, "In the beginning is Desire" then such a desire can have but three outcomes, namely: (1)What is desired comes about, (2) it does not come about as desired but something else happens, or nothing happens at all. This, given 'action at a distance', (3) can result from everything or anything else happening elsewhere. We've now moved beyond the Rg Veda to show it is consciousness, aka soul, spirit or the numinous can be blamed. Science logically has proven its limits, which is also new.

The theoretical facts are used in order to provide opportunities for further testing by *hypothesis" which only means a "guess". No theory is ever "proven as by the time some 70% of a theory has some sort of proof the anomalies found are ground for a fresh theory most theorisers are reluctant to engage on and usually arrive from an unexpected quarter. Or As Fred Hoyle, Nobel Prize winner, not pop with the Establishment, tells us to consider all the angles and tangles around. One only needs to go through the bibliographies of so called textbooks to look for names that are missing from the list, to find out who belongs to which school of thought. After putting that lot of gossip groups together one may have a fair clue about what is not mentioned everywhere.

There's a tricky bit here because to succeed, at anything, one has to have an Ideal to aim for. But there's a difference between having a pattern or theme in one's mind with all the tiddlypoms, negative and positive variations, versus a goal to aim for with hardly any details known, as happens to all beginners. Feedback is an example, Going fom Point A towards point B unless and only when we also have feedback from point B, our target, can we streer a straight line, allowing for wind, weather and who knows quite what. That makes an illustration of action at a distance by radionics which is a weird kind of telepathy. We should realise it took Lansky some twenty years to express his misgiving insight that AI won't reach its goal unless we learn some radical details. The scientific method, which originates in ancient oracles, consists of having, like a car mechanic, (1) an ideal model, everything working perfectly as it should - which it never does - all other things taken as equal, (2) something that scrambles things up, called the random, which is unpredictable and a-causal, and (3) comparing 1 with 2 by their difference that shows up what went wrong. If a flight of geese is not in a perfect V formation something is wrong and the thing is to figure out exactly what is going wrong, which is only the start of getting to fix it. Einstein mentions: "The significant problems we face cannot be solved at the same level of thinking we were at when we created them." So discovering that consciousness affects the action needs a transcending insight to solve it. 

The modern version of the scientific method additionally isolates the possibilities down to our crucial one which is then tested by one parameter. But we have no certainty that it is THE crucial one. The problem there is that if you do not also watch all other things ongoing you cannot be sure of what mucks things up. The sillier thing is that when an experiment fails the same routine is used again and again. If it failed first time why should it work next time? If it fails with one tester and succeeds with another, what contribution is made by the man? A rat trapped in a box will seek out all possible escape routes, after which it sits down and thinks, rat fashion. Rats don't go in for repeat actions, once is apparently enough. That's funny if rats are not supposed able to think. NLP tells us humans go in for repeat actions, especially when things fail. What happend with Pavlov? If you read his papers then training results fall into the (1) as expected or predicted by hypothesis (2) paradoxical, (3) ultra-paradoxical. Now if we give dog credit for being able to think, without the benefit of words, then for (1) we get as desired, (2) dog shows uncertainty because things don't happen as fixed, it is led to expect food on hearing the bell, shown by salivating. (3) On negative testing, that is to ring the bell and not produce food, Dog either sulks or bites the hand that feeds it, which forces dog to be destroyed because dog is no longer treating man as a reliable friend. Break a dog's trust and it goes paranoid. Try that on a crocodile and you won't get anywhere. The problem with a dog is that one has to keep it simple and consistent. Dogs does not go in for ambiguity. Don't try that on a human being, they go devious. I was once told to be good or careful at which my spontaneous reply was: "Nope, just fast enough to get out from under". At which a friend suggested my pet animal should be an octopus.

Recent design using computers makes up a test model and runs it through in every conceivable setup, context or environment. Chaos Theory was discovered when a computer was left running a simple program only to find that it started to change the results here and there, which does not tend to happen with short runs. Our favorite pet hate, Winmpdoze, does it routinely. We discovered that we have 23 chromosomes instead of 24 when a nurse made a mistake. The preparation was supposed to be rinsed in pure alcohol, which made things clump together. Microsope slides are routinely pickled in alcohol. Nurse used water and found all the chromosomes separate. Luckily she told her supervisor, who, luckily, understood and the routine was changed. So serendipity works both to make things come out right and even when we make mistakes as well to help us learn from our mistakes when watching what goes on. To melt gold or silver to make castings one has to watch how fast across the heated surface of a crucible the oxidised metal flows. Get it right and your castings won't be filled with bubbles because the melt cooled too fast for the distance it has to flow. Using an optical or mechanical thermometer is just not good enough. There's no substitute for an alert mind watching for the right clues. That can be 'caught' only in situ at just the right moment, while you're doing it. Currently we have four thermometers, Reaumur, Fahrenheit, Celsius and Kelvin, which shows there's always several ways to solve a problem.

Running habits, for a method is a trained habit, as are social customs and tradition, tends to dumb down one's mind. Not that there is anything 'wrong' with them, just that they make good servants and and bad masters. The current revival of interest in things spiritual and being allowed to be human results from an earlier loss of craftsmen's skills. This happened in Greece which invented philosophy by wealthy folk who owned villas and had slaves, called villeins, who did all the work. Words isolate things from one another so we need Logic to stitch Humpty Dumpty back together again. Our mind does not need logic, it is far better than a logical machine, as it tracks everything that goes on and only alerts us when something needs dealing with, like being hungry or sensing a storm coming. A logical machine hangs when things go wrong, humans need not hang. Minds revel in ambiguity, programs excel in exactitude, if they are any good. There's no such thing as a bug free program or a bug free human being either.

The division between our conscious and unconscious mind rests on this. Consciously we are reputed to use a one track mind, needed to pay attention to whatever we choose. The unconscious both tracks that without us paying attention to it and watches everything else just in case it needs attention. This is laid on and automatic, organised by billions of years of evolution. The thing to learn to do is to allow that unconscious to be our helpmate. Our misgivings are clues.  Some of the evolutionary mishaps have been weeded out but there's always another lot to come next as we learn more. Our brain has about five parts of which the forebrain gets most of the praise and attention while without the other parts it could not work at all. More important is our hindbrain, said to govern rhythm and if you think about it everything has its own proper rhythm. It is well known that in cooking it depends on the cook as to how the flavour comes out, be he English, Indian or whoever. The herbs and ingredients are pretty well the same the world over; except in China. It's the rhythms of the action that decide and the order in which you add the ingredients. Cookbook recipes don't tell us about that. To make brass, an alloy of copper and zinc, mainly, to first melt the copper which melts at about a thousand degrees Centigrade and toss in the zinc, which melts at half that, will get you brittle, bubbly, poor quality bronze. You have to first melt the zinc then add the copper in small bits letting that mix in so that the temperature slowly rises to somewhere above zinc and below copper. It depends on the amounts mixed. Then you get a fine, even brass as a result. Done the right way the atoms do the work for you.

So sometimes we have to go contrary to what seems common sense, unless you acquire your own which takes a lot of experience and practice. Our social common sense consists of customs and traditions of what was done in the past. By that we will always be in a handicap with the future which is never quite like the past. The current popularity of Catastrophism and our now ability to peer into the sky in many ways at once informs us that the solar system has about 20,000 bodies in it instead of the traditional seven, ten or twelve planets, which are obvious because they are so big. It only takes a small pebble to break a window. A fly squashed on a windscreen can result in an accident, so can mud and snow, because you cannot see any more. One well placed meteor can kill a world. No wonder ancient man was an avid skywatcher.

The idea that we cannot access our unconscious functions is a big fib because as we change tasks or what we do, which can change by the second, different functions combine and foreground. Children are ritualists who can do but one thing at a time. Alchemy tells us to marry conscious and unconscious so they can cooperate. By the time we get to be adults we can interrupt any of our doings if something else needs attention "right-now", before it is too late. That done we can revert to what we were doing in a stack of up to a dozen or so different things. When we cross the road we consult five or so different memories, like watching the cars, bearing in mind where we are going and why, whether there are any cops about and so on. When a housewife prepares a meal she sniffs around the cupboards for what she can use. At the same time she memorises what to shop for next, the order of planning, storing foodstuffs, preparing them, what to start cooking first so it's all ready together. None of that needs logic. It's laid on in our mind.  We won't go into what else she may have on her mind or thinks. Women don't come from Venus, they multitask and, I fancy, mainly because many don't get eddikated.

Professor Ritchie Calder in "Science in our Lives" (1962) states: “A great discovery depends on three things: The Method-The Man-The Moment.”. I have focussed on the man. The idea was actually put forward by Arnold, the literary critic, in the 19th Century. J. B. Conant. now ex-president of Harvard, called it the alleged scientific method. The best appraisal of the Scientific method I found is at: http://www.scientificmethod.com/   compiled by Norman W. Edmund of Edmund's Scientific Company. Edmund has an SM-14  "general" phases recipe for which the way varies per stage. It's actually more complex than that as its origin is found in ancient oracular methods which were not limited to testing only one possibility at a time or using only yardsticks. It consists of:

1: Constructing an Ideal model of whatever turns you on or off; as complete as you can make it, including variations on that theme.

2: Allowing or making it get scrambled up by the environment as it is here and now; called random, and which happens anyhow if one just hangs around.

3: Comparing the two for what's different between them, which begets you a whole washlist of possible wrongs.

4: Deciding how to tackle the result, which is where the complications get moved in as:

5: What is to be taken as evidence varies relatively by the context  and situation in which it applies.

By and large modern science relying on the "Detached Observer" has removed the man out of the picture whence things internal to the man, which cannot be measured nor can be judged or observed by this external to the event detached observer fiction as he is very much involved in the action; totally absorbed by it so it sticks around in the mind. Nor, as Edmund points out, does he go about things in a haphazard way. It consists of taking careful note of every aspect and possibility that may or could affect everything working as it should and if possible elimitating them one by one together with testing that, in what is called creative problem solving. Victorian German Chemistry succeeded because it did just that. This may be assisted by intuitive hunches, either from past experience or sheer overall understanding  which may shortcut problem solving. Again it is obvious that dissecting a cow or tackling a car engine won't work the same. You cannot peel an orange with a hammer. Nor can you take a good look and think about it when snagged under water.

By and large this also gave rise to Logic and the Bureaucratic Method which stifles all alternative creative ways of getting things done in favour of making us do what we should do, as decided by a desk pilot and enforcing it by punishment or fines. Me and a Lecturer were once stuck on a very windy road around lake Whakarimoana, New Zealand, not knowing what to do. Along came one Maori, uneducated, of course, who laughed, wrenched a signpost out of the ground, used it as a lever and the bumpers came apart. We were both driving slowly, just as well. Keeping it simple does not work. Making it simple will. Getting it there is anything but simple. 

How antiquity solved the riddle of keeping space, time, volume and weight all consistent with each other as the four corners of our universe is quite simple, in hindsight. It imagined, geometrically, a circle around the earth. The sun moving reasonably regularly around earth, to an observer that will trace in an equal amount of time an unequal distance on earth which has a weird shape usually called a geoid. It flattens at the poles and humps at the equator. Then by taking pre-dawn heliacal sightings of sun, planets and stars it drew a 144 acre, 'sacred' plot on the ground through which lines were drawn to devise a centre that became a sacred place or navel of the universe of which there were many. "In Xanadu did Kublah Khan...", wrote Samuel Taylor Coleridge, giving us the recipe. This created a locally adjusted system of measures that were used to check what distance was traversed by the sun moving through a second, minute and degree of a perfect 360 degree circle. Next to that it dug angled tunnels into the ground to check the passage of a given star or planet, which if the tunnel is long enough and at the right angle you can do that in the daytime. At Selene in Egypt is a straight down hole in the ground where during an equinox the sun casts no shadow. The hole was dug to match the edge of the sun so you can even decide on the size of the sun as it moves by, using a timed yardstick. Some Chinese bronzes with squiggly tracks are, when used to burn incense, fixed measures of time. Temples had the statue of a God in line with the door so at a given moment the face would light up. When it lighted up again a year would have passed.

A still older method was to use the edge of one's cave and poke sticks in the ground where the sun casts a shadowed edge. That produces a half circle of sorts. But at the poles where half the year is dark and the other half light it does no such thing. Apparently the earth was modellad as a hexagon by where it changed the relation between a fixed time and given distance. One can also do this with an omphalos, menhir or stone pillar to watch when the height of the pillar matches the shadow made by the sun, which makes an equilaterial triangle and for halfway round you can use a 3,4,5 unit triangle. This takes keeping records but as archaic man had a flypaper memory as well as full visualisation, that was no problem. Out of all that came an understanding which led to the system of latitudes and longitudes we still use, all designed around the rhythms of the solar system and stars. Lacking the benefit of our advice archaic man was also psychic, which helps some in detecting what is otherwise not observable. Basically it all works with relations which cannot be observed, only imagined. 

Beyond this antiquity used (1): precise, divine measures for Temples and Palaces around which settlements grew, (2) averaged by provinces and plots made up by longitude and latitude, (3) near enough is good enough for carpenters and commoners. In England at one stage the foot was measured by placing 14 people's feet in a row. Apparently 14 makes a mininum number to get an average. I have not tested this but you can. Fifteen would be better as then you don't end up with a half foot in the middle folding up a string or would you?

Editors note: The author sent me this article in response to my web site article, The Limits of Science (http://ldolphin.org/scilim.shtml).