John Fish B.Sc.Publishers of Tenby in Wales (UK)
TENBY PORTAL PAGES
How to build Stonehenge
"We tend to think of computers as either mainframes or networked desktop computers. But these are all digital computers and we tend to ignore the fact that there is another class of computer known as analog computers. Since the 1960s research and development work has concentrated on digital computers and analog computers have been practically neglected. Until now and this paper is designed to give you a start at being on the leading edge of the future of computing.
"To begin we have to start at the beginning, literally we have to go back to the future, to Stonehenge which is nowadays generally considered to have been built as an astronomical observatory, or to our new way of thinking as an analog computer. A computer which has lasted for thousands of years and built from stone with the software imbedded into its design. So there are no moving parts, no power supply and the programming has been running non-stop, continuously, without crashing.
"The essential point to grasp being that what has been incorporated, imbedded, into the design are the Laws of Nature; of physics and mathematics. Hence, the grandiose claim that you are in a position to be the future of computing since digital computers use the laws of logic; of ones and zeros. You have access to the modern understanding of mathematics and physics, you can design your analog computers to work to principles infinitely more powerful than that on which the digital computer is based.
"But wait a minute, aren't we in a bit of a chicken-and-egg situation here? With the modern understanding of physics and mathematics it is theoretically possible that you could design Stonehenge from scratch. But what if you didn't have that knowledge? Which is the situation in which the builders of Stonehenge were presumably in. So they build a computer which enables them to predict astronomical events but which in its very design incorporates the Laws of Nature which are known to you but not to them.
"So how was it built? And what we're really asking is: How was it designed? Perhaps not just Stonehenge but the school of thought to which the builders of Stonehenge belonged. What was their starting-point? Astronomical observations. Purpose of Stonehenge? Prediction of astronomical events. Method? Replication by Stonehenge of the inner workings of the Universe.
"So Stonehenge (or the school of thought that Stonehenge represents) wasn't built from scratch but grew as their knowledge grew and just as we build bigger and better computers (not just mainframes, think of all the desktops interconnected via the Internet) so did they. Did they build bigger to test out new theories? To further their research? Meaning: did they gain an understanding similar to our own of the laws of the Universe through their computer technology? Well, perhaps you ought to build Stonehenge and find out.
"Build Stonehenge you say, you must be joking. Okay, we'll try something less grandiose, simpler perhaps or is it? Your task is to build an analog computer which will automatically compute the shortest path which connects a set of points. How many points? Entirely up to you. But to set you off let's say ten. So what you're going to need is a flat piece of wood, ten nails and a length of string. Do you call that construction kit a computer? But build it first before you judge it. So hammer your nails into the board as a random pattern. Visualise it, try and visualise Binns' Analog Computer as you study this and I'll tell you why later.
"Next tie a loop in one end of the length of string and place it over a nail which has no other nail between it and the edge of the wooden board closest to it. Now run the string around all the nails and back to our start-point tightening it so that all the nails are encompassed. Then pull the string inward so that it is tensioned by each and every nail. And then you have the shortest path length it takes to connect all twenty nails. Twenty? No ten, but no matter how many nails you want to try our analog computer will still do the business. Its program will never crash. It doesn't need a power supply and its components ... well, if it got inadvertently destroyed you could easily build a new one and perhaps improve it from other materials.
"If you want to be fancy about it place a map over the wood and hammer the nails into selected place names. It will still work, but as the crow flies, of course! And now we're in a position to challenge Bill Gates of Microsoft to a duel! We'll up the stakes to a hundred cities and with our analog computer we'll challenge his fastest digital computer. Draw! Too late Bill, for although it's only taken us a matter of seconds to solve what is known in the business as the Travelling Salesman problem it's going to take Bill, believe it or not, billions of years.
"Now if you wanted to you could use this strategy to write a program for a digital computer using the strategy built into our little analog computer and the essential sequence of steps are as follows:
"Step one: Consider your set of nails to be a field of points and then place them within the positive x and y quadrant of Cartesian axes to define a frame of reference.
"Step two: Each point will have both an x and y coordinate so find the limit points of the field and there are four defined by: the smallest value of x, the smallest value of y, the largest value of x and the largest value of y.
"Step three: Now what our limit points tell us are the coordinates of four points which define the corners of a rectangle which will encompass our field of points. Defined by: smallest x and smallest y, smallest x and largest y, largest x and smallest y, largest x and largest y.
"Step four: You now automatically have the coordinates of the centre of the rectangle: midway between smallest and largest x, and smallest and largest y.
"Step five: Find which one of your field of points is closest to the centre of the rectangle. This we shall define as our start-point.
"Step six: Change the coordinates of each point from Cartesian to Polar so that each point is now defined by its distance from the origin of the Cartesian axes and by the angle that a vector of the distance, the line joining the origin to the point, makes with the x axis.
"Step seven: Decide on a clockwise or anti-clockwise pathfinding direction.
"Step eight: Beginning at the start-point select the next point, in terms of the value of its angle.
"Step nine: Continue until all points are charted remembering that all angle values have been defined in terms of a single quadrant of a Cartesian frame of reference and two or more points could have the same value so you'll have to put your thinking cap on!
"Step ten: Join the last point charted, the end-point, to the start-point.
"But what is the strategy we're using? And this is where our analog computer is starting to score over its silicon cousin. It's using trigonometry: built into it are the laws of trigonometry. Analog computing technology can incorporate any mathematical system, any of the Laws of Nature. The whole World's like an analog computer and even manmade things like an economy. The essential law of economics is a free market: if things are in short supply they're expensive, if they're in abundance then cheap.
"So how do we build an analog computer that incorporates other systems than trigonometry? That's for you to find out and so surf on the leading edge of computing's future. But our little analog computer operates in two dimensions, can you make one for three dimensions and if you could make one for four dimensions would you have a time machine?
"Was Stonehenge built to be a time machine? A computer whose program never crashes certainly has a timeless quality but perhaps you'll be the one to figure all that out, the job of this paper being to point you on your way.
"Now it's interesting but when we used our analog computer we started with a nail, a point, on the periphery of our wooden board. Yet when we transferred the methodology to a digital computer we began at the centre. Why?
"Perhaps there's an analogy here between the way in which Stonehenge is constructed, circular shapes of standing stones, and networking desktop digitals. What would happen if you put a length of string around your model of Stonehenge and operated it as you did previously with our little analog computer? If networking desktop digitals then, even if it's only an illusion, it's like you are at the Centre of the Universe. And what if Stonehenge is really like an ultra- small-scale model of the Cosmos?
"Are we with digital computers on the inside looking out and with an analog computer on the outside looking in? Because what's in-built is the philosophy which we are imbedding in the design of our computer.
"Enough of speculation, by all means you carry on and surf the leading edge, but what are we going to do with our analog computer? We've already hit on one application: as a means, a methodology, for programming a digital computer. But if we remember our history then digital computers are used for games so can we use our analog computer likewise?
"I've thought of a game using our analog computing techniques and it's called European Union Air Navigator. To play it you'll need a map of the European Union, a ruler, a protractor, two dice and a pack of playing cards. And a set of rules which go like this - but, remember, you can make up your own game with your own set of rules if you so wish.
"Choose thirteen major European cities with airports. Why thirteen? Well there are thirteen playing cards belonging to each of the four suits in a pack of playing cards. So the game is for up to four players and you can assign one of the thirteen cards to each city. Take it in turns to throw the dice: the one with the highest (or lowest if you like) score starts and you go around clockwise (or anti-clockwise if you like).
"So it's your turn and you throw the dice. There are two dice, with two different colours. One dice decides how far you are able to travel, so you'll need to determine a scale for your map with six as the maximum distance between any two airports and one as the minimum. The other dice determines direction, say: one - north, two - south, three - east, four - west, five - any direction, six - fogbound so miss a turn.
"Now with the navigational information from the two dice we use the protractor and ruler to determine which airports are in range and select one to land on. Everytime you land on a city you pick up a card which is unique to that city and the one who gets a complete set first wins. You'll have to sort out what to do about your start-point airport, perhaps if you land on an airport someone is already at then they miss a go ... what the heck, just make it up as you go along!"
Extract from Preseli Bluestones by Sion Pysgod
Published at Tenby in the Pembrokeshire Coastal National Park (Wales, UK)
As a Star of Pembrokeshire Series Paperback