One has to begin some place. And any story can begin in multiple places, and still make sense. In our before, during, and after format, one has to begin with the point in the story where someone realizes that there is a problem, and realizes that there has to be separated from that story that leads elsewhere. That is why we begin with Galileo Galilei, because he delivers both the processor, and the database fully formed in his work.
Consider Galileo Galilei, working in the late Renaissance. First of all, what do we mean by the Renaissance Period? It is not a question which ordinary people really discuss, because they think they know what the Renaissance Period means, but this is an illusion. Because the Renaissance is defined by how other people use it, and the definition goes back only a century and a half. And there have been scholars that say “This is a not the late Renaissance, is a period called the Mannerist, and it is totally different from before.” they will associate the scientist Leonardo da Vinci as “Renaissance”, especially with buildings that are divided evenly, as oppose to the “Mannererist” which they associate with smaller domes with decidedly larger central domes.
Who defines it? Jacob Burckhardt, who was a historian of art and culture, and important in both of these two endeavors. And his major book is entitled the Civilization of the Renaissance in Italy. This is important, because many of people who define eras, have something in mind for what they want, and only part of this is consumed by other people, who want something else. Burckhardt had a particular idea when he invented Renaissance, but people who follow the him in English did not agree. That means when you want to use “Renaissance” you have two take into account what the owner of the work meant, and what he did not mean. When using the word reassigns in a Burkhart sense, one has two realize it is different from other people.
This means that defining Galileo as Renaissance already marked to as being in a particular vein, and you should use it knowing what it means. Most of the people want a definition which confirms the definition that they already understand, even if it is not the definition which is meant by your favorite teacher or other. This is going to get you in to trouble, just know that and go on with your work, defining the word from whichever book it is in. someone will get up at the back of the class and contradict you, because that's what people do. They will tell you that all the world defines the word the way they wanted to find not the way you wanted defined. If you know this is coming you'll be prepared to prevent it, and if you don't your in for a rough time, because some definitions do not last.
So back to Galileo Galilei, and is formula which has absorbed the attention of scholars who can't even agree on what name he was working in, begin to parts of the same question. He defined the clock, and he defined infinity. And both of them are key concepts.
Let's begin with the clock. As with most concepts in physics we do not think much about it, even though we know that his division arises from someplace. In this case, it began from Galileo wanting to measure time periods, and having no way to do so, until he discovered that swinging back and forth a pendulum had a clock that did not vary. In 1602 Galileo used the regular motion, because pendulums keep exact time no matter how much they swing. He was the first person that we know of to do this. It does not matter the length, of the so-called amplitude, and does not matter the amount of mass. The period is independent of amplitude, a property called iso-cronyism. What this means is that a simple pendulum accounts for about 15 seconds a day of error. Wikipedia reminds us that the parents of air, the mass of the string, the shape and size of the ball, and flexibility and strength of the string all take in to account there various bits of error. And still amounts to one of the smallest errors. In 1602, what Galileo grasped was that this error was small, and could be ignored for his purposes.
What this meant on the larger scale, is that some kind of pendulum could be used as a clock. We will get to all of the details, but the main thrust, a pendulum has clock, still exists even though it's form is very different. This is a principle that crops up in many places, make a small modification to a principal, and show that it is the same with a few modifications.
With this principle, that a pendulum does not need to be exact, he started a chain. Realize going back to Aristotle, people had thought that the weight matters. In other words almost 2000 years was wrong. Think about that for a moment, for 2000 years people thought that a small swing was of course different from a large swing. And Galileo disproved that. Swings don't matter in terms of how much the pendulum moves, except for small degrees, which has we have noted, you can account for. And Galileo showed this by measuring that for simple degrees, heavy and light were the same, in contradiction to Aristotle, who assumed that they would be different. There was revolution in the air.
The other thing that Galileo discovered, was that infinity was different from finite amounts of time. This is a more theoretical guide of revolution. It wasn't measured by strings, and weights, it was measured by the mind, and written down by numerous people other than Galilei, but he described them in detail, in Two New Sciences, and it began with squares, that is with numbers which can be shown to be the square of another number. At first glance, the numbers that are not square should be more numerous than numbers that are square, but for every number there is a number which is the square of that particular number.
But then he put the idea, as George Gamow observed over 50 years ago, “back on to the pile”. This is not uncommon, the person who discovers an idea usually doesn't realize what is going on. But these two ideas would eventually make up the processor and the database. But of course it would be a long time.But in 1612 there was 1 that good enough, was the date that Galileo proposed a different way: the moons of Jupiter.
So the two theories, which in Galileo's day were not conjoined, would sit around and tell their was a spark from a great ideal man himself: Sir Isaac Newton.
Isaac Newton knew about Galileo's discovery that a pendulum was constant in its motion, and introduced a theory which was broader. Not only did pendulums move the same way, but all things did if one looked at them the right way. If Galileo drew a problem set, then Isaac Newton defined how the problem was to be solved. He saw the pendulum as the simplest case of what could be drawn as a more general case, The pendulum was the simplest case, but all cases were to from that, which was a surprise. Think about the fact that the pendulum is just the simplest case.
Now the good spend a great deal of time looking at just pendulum, and going a great many directions with. The pendulum is a basic machine which touches all sorts of physics, and I would like to tell you all sorts of things about. But we have a core thesis, and that is the pendulum is reproduced as a clock which you don't even see, in this processor. So we will leave you behind with two ideas, he noted the fact that the moons were in fact the same as pendulums, and that therefore there were two ways about setting a time, monitor emotions of moons, and develop precise pendulums. And so said off a race, define moons as one way of developing longitude, and the other way is to develop precise ways of measuring pensions. What it also said, is there are two places where longitude flips from positive to negative. One is at 0°, and the other is halfway round the world. This is important because every time you have a number which has a 0°, then someplace it will also have two flip back. And that is a problem, because in incident space there are numbers which only flip once, not twice. There is a hidden problem with numbers, because all that we can measure flips twice, and we can only simulate numbers which flip once. On a globe things flip twice, so there is a problem, but in flat space they only flip once. And great deal of time spent figuring out how to place the second flip a great deal for a way so it does not get noticed.
On North and South, that is latitude, there is a different problem. Eventually all numbers reach 90°, and they are is no South, or North, to turn back on. Your at 90° and can only move south in any direction. These two problems, have only a general solution, and it is by agreement, not physics.
Why does Sir Isaac Newton do this? Think about latitude and longitude, they are on a circle, and so will flip twice. Another words, no trouble, to flips in the real world, and to a two in the fictional space. So far, so good. But what about the other case? Where is there only one flip? Unfortunately the answer is there is no version of fictional space that has only one flip in the digital universe. All versions of the digital universe are mapped onto spheres. This means that you have hide one of the flips. Every fictional universe is a sphere, not a plane.
So you have two cheat, and put your plane near the 0° and hope that it will not cross the other side. This is not a problem, until it is.
Let's retrace the steps we have taken. First there was Galileo, who saw to different things: one was the pendulum, and the other was that infinite space was different from finite space. Then came along Newton who noticed that you could map two value space on to one value space, with the caveat that it would turn positive somewhere along the line. You may ask, what does this have to to do with relational databases. And the answer is that two value spaces fit in to the plan, but there is no way in digital space to do one valued logic.
Which means that a relational database has a hidden problem, dealing with space. Every space runs out and changes degree. It can be a flip as in East-West, or it can be made to run out, as in North-South. If you want and example, consider your last name. Originally it ran out after only seven letters. Newberr was my last name, because it only stored seven letters. And some very common names were that way, such as Washing, and don't get me started on names from Mumbai. Gradually fields were made large enough, but that only means that they were large enough for an ever smaller group of people. I'm sure that someone out there is cut off on some system.
So that means we have two go to George Cantor, who realizes there are at leased two infinite degrees. Not that this will help Newberr, or Washing, but it makes it clear that the problem is going to go away. In other words, it's a glitch that does not go away.