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Getting it straight ...
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Classic buildings, from the pyramids in the Egyptian dessert to the arctic igloo's, are built on the rather obvious observation that a pile is a pretty stable construction. Even without any knowlegge about center of gravity and equilibrium and what not, you will find it very hard to imagine that a pyramid can tip over. You'll even have an intuitive comprehension that this has to do with the fact that the base is wide and the top is narrow. Same thing with igloo's. Igloo's have the additional advantage that they are a bit faster to build than pyramids. But in any case, those ancient Egyptians and ancient or less ancient Inuit knew what they were doing. Modern construction, on the contrary, builds of scientific notions that are clearly wrong.
Contrary to those classic exemples, the pyramid and the igloo, modern buildings are designed to be straight. The have walls that are either parallel, or meet in corners at a 90 degree angle. Walls and floors are expected to be flat and level. As floors are horizontal and walls are vertical, the angle between a floor and a wall is, again, assumed to be 90 degrees. A 'right' angle.
On the other hand, any do-it-yourself handyman knows for a fact that there's some fishy about this. Like, you install straight cabinets between the (straight) walls of your kitchen, but you can't get it exactly right. Decorating walls is another fine exemple. No matter how precise you start, sowhere along the line your wall paper just does not look that straight anymore. And the volume and surfaces you've calculated to decide how much paint to buy, always leave you buying haf a tin too little, or liters (kilo's, gallons, buckets ...) too much.
The unexperienced handyman might think he lacks knowledge or skill. But he is not to blame. Scientifically, builders can't get it straight, so you can't get it right.
Imagine a rectangular building : just 4 walls, opposite walls paralell to each other, a flat roof. The common assumption here is that these walls are vertical. That might still be the case. Buit that's where it goes wrong. The earth is not flat, it's round. Scientifically, vertical is defined as : in the direction of the center of the earth, i.e. following the force of gravity. So a vertical line (wall, ...) would look like this :
Consequently, 2 vertical lines will look like this :
and it is already clear that both (red) lines are vertical, yet not parallel to each other. Try to build a rectangular house like that, with 4 vertical ribs (the corners), and you'll and up with something like this :
A perfect upside-down pyramid. quite the opposite of the intuitively stable ancient constructions in Egypt. Not to mention : Try fitting your perfectly straight bookshelf in a contraption like that and you'll grasp the frustration of many a house renovator or do-it-yourself interior decorator. Yet, that's how modern day building is done. So no house can be considered 'straight' or 'right'. At most, there may be some notion of 'correctly wrong' : If we all make the same mistake in the same way, it won't be noticed.
Euclides, a greek carpenter turned philosopher, spend some time investigating this problem and came op with a solution : Euclidian Geometry. He defined vertical as perpendicular (so at 90 degrees) to a horizontal plane. Consider 2 (or more) lines, each at 90 degrees to a horizontal plane, and you'll have 2 (or 3 or 4 ...) vertical lines, parallel to each other. This was quite a good start.
However, where do you find a horizontal plane. Or how do you establish for a fact that a plane is horizontal. Horizontal is derived from the word 'Horizon', and assumably means 'parallel to the hozizon'. However, in those days, the earth was thought to be flat, so the horizon would be the edge of the world. We know know that the earth is a sphere, and the horizon is an imaginary line that may look straight at first, but if you look well in a wide angle, you'll see that it is curved.
According to Euclides himself, the notion of 'parallel to a curved line' is meaningless. It does not help us any further in building either : When we apply the Euclidian notion af horizontal and vertical to a bulding on a spherical earth, we do end up with walls that are indeed parallel to each other, but something seems still wrong.
The error is obviously in the attempt to build on a non-existing horizontal plane. Construction usually starts with levelling, and a so-called water-level is used to establish that a surface is flat. And that while the waters of the earth follow the curve of the earth's sphere, so they can hardly be flat, or horizontal or anything but spherical, round, curved. Nonetheless, this approach was experimented with by building companies in 12th century Italy. The results were somewhat peculiar, and Italian building companies have had somewhat of a reputation ever since.
Things get really complicated if we not only consider that the earth is round, water-level is a convex surface, and vertical lines are not parrallel to each other, but also add the fact that space itself is curved, as demonstrated by A. Einstein. No wonder you can't get those kitchen cabinets to fit in their designated space, no matter how precise you've measured. Your measuring rule may be straight, all the rest isn't.
All this notwithstanding, we have our architects and engineers study mathematics and geometry, and we continue to train our bricklayers, carpenters and other construction workers in the use of squares, water-levels and the likes, so that they can go on trying to fit a square peg into a round hole. True craftsmen also use these tools, but they add an undefined quality to theis use. The bricklayer's eye, or the carpenter's eye, it is sometimes called : you calculate, measure, apply all your tools and skills to get something straight, right, level, precise, and correct, and then, with the naked eye, you have another look at it and adjust it until it you're satisfied with how it looks. It's a Zen thing : you know it's right when it's right.
This quality separates the skilled from the experts, the trained workers from the true masters : the ability to leave rationality, science and technology behind and intuitively know how it should be.
Even the ancient Greek, the first known rationalists in human history, knew better then to rely on tools and techniques for their buildings. The Parthenon, build on Akropolis near Athens in 447 B.C., is regarded as one of the most exquisite examples of classical Greek culture. Close investigation reveiled that in the whole building, not one angle is right, no two lines are parrallel. It is build to look geometrically correct, so it can't be.
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