Most of the mathematical concepts we encounter every day - numbers, addition, subtraction - seem so basic, so hard to avoid in discussing reality on even the most basic level, that it's hard to imagine someone having to sit down and invent them. Who was the first person to look at two rocks and think, "Two more and I've got four?" The very idea almost seems absurd.
But mathematics is, in part, a language - not just a set of logical relationships and entailments that seems deeper than words, but a set of notations that allow us to discover those relationships. You can't see that twice two makes four, until you have a symbol for "two" that your brain can operate with. And those symbols - that language - did have to develop, strange as it may seem. (Prehistoric artifacts seem to indicate that the earliest humans had only four "numbers" at their disposal "none," "one," "two," and "many" - showing just how much our ability to talk about numbers depends on having the right words for them.)
We don't know which culture was the first to develop a number system more elaborate than "one, two, lots!" A 20,000-year-old bone found near the Nile River seems to show a sequence of prime numbers - which would indicate fairly sophisticated mathematical knowledge from fairly early on. Then there was the Harappan civilization of the Indus Valley in present-day North India and Pakistan. As far as we know, these folks were the first to use decimals, among many other important concepts.
Archaeology also seems to find evidence of a sophisticated number system during the Shang Dynasty in China, 1600 years before Christ. Archaeologists often turn up new discoveries bearing on the history of human consciousness - so it's hard to say who was the first to develop this or that idea with any certainty.
But many mathematical ideas - like many other things - begin with the Sumerians. This culture - considered by some historians the cradle of civilization - flourished near present-day southern Iraq between three and five thousand years ago, and besides contributing the world's first known work of literature (the still-impressive tale of Gilgamesh), they developed a numerical system based on sixes. If you've ever wondered why an hour has sixty minutes, or a minute sixty seconds - after all, it'd be much simpler if everything went by 100 (so that our basic unit of time was made of 100 smaller units, rather than sixty seconds, sixty minutes)- it's in part because of lingering Sumerian influence. As Sumer's culture declined, it was absorbed into the Babylonian Empire, which also seems to have produced mathematical thought, if the handful of Babylonian mathematical writings still remaining to us provides any indication.
Babylonians, Egyptians and ancient Indians all seem to have shared at least one important discovery - the so-called Pythagorean theorem, a rule having to do with how to figure the length of the sides of certain kinds of triangles. (Clearly, this discovery was of use to the culture that built the Pyramids.) The fact that this theorem was common to all three major ancient cultures suggests the degree of traffic they may have had with each other, despite some historians' suggestion that each culture was mainly closed-off to other places. And the fact that we know the theorem as the Pythagorean theorem - after the much-later Greek mathematician and philosopher Pythagoras - illustrates the well-known, and often-criticized, tendency of some historians to want to give the ancient Greeks credit for everything.
Not that the Greeks don't deserve plenty. Greek mathematics grew up alongside Greek philosophy and Greek science - indeed, the three disciplines weren't really separated; for the ancient Greeks, all the disciplines of knowledge were one thing. Thales, for example - whom you'll often find cited as the first Western philosopher - used geometry to calculate the height of the pyramids, among other things. In any case, Greek thinkers took the young art of math to a new level of sophistication. Euclid wrote a geometry textbook so percipient as to remain useful today, Aristotle defined laws of logic, and Archimedes remains near the top of some math historians - all-time greats list. The tight relationship between math and philosophy in ancient Greek is well-expressed by the inscription found on the door of Plato's Academy: "Let nobody ignorant of geometry enter here."
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A beautiful Cyprus apartment is a luxury that most people would like if only they were able to afford one. Well believe it or not it may be more of an affordable possibility than you think. With so much equity built up in the U.K. property market in recent years folks have at their disposal the means to owning a property abroad if they are prepared to do a little financial juggling. In the last few years more Brits have purchased property in Cyprus than in all the years that preceded them put together. That's a staggering amount of property that's been sold to English buyers who have either retired to Cyprus or bought a holiday home there.
The attraction of this beautiful Mediterranean Island paradise is perhaps it's unique Englishness which is a throw over from the days when it was part of the U.K. In fact there are still several British military bases in Cyprus and the land they stand on is in fact owned by the Queen. The British army police it and it is actually classed as sovereign territory or if you prefer a piece of England in Cyprus. The Island has always figured strategically due to it's close proximity to the middle East and the Suez canal. However with many of those Arabic countries now having good diplomatic relations with Europe the bases on the Island are only manned by a small number of personnel these days.
The Cypriot people are amongst the most friendly you could ever hope to meet and they always make visitors most welcome. Don't be surprised if they invite you over for dinner after only just meeting you it's just their way. Some Brits find this hard to get their heads around at first but the Cypriot lifestyle is very infectious so they will soon have you totally chilled out. The lifestyle is in fact very laid back and relaxed especially in the summer. Many Cypriots work very long hours but they don't stress out or rush about like the English. They pace themselves and everything is done at a leisurely pace but all in good time.
With the Island undergoing a massive property boom prices of villas and apartments are almost guaranteed to rise. It's essential therefore that anyone considering buying a property should act sooner rather than later because they could soon be priced out of the market just like the situation in Spain. The great news is that savvy investors that get in now are going to make a killing and in fact many are already doing just that! Property prices in Cyprus have at least doubled over the past ten years making buyers very rich indeed. Many areas like Paphos and Coral bay will soon be affordable for the average holiday home purchaser if they don't act soon.
The East side of Cyprus is no exception either with huge developments springing up all along the coast and in the village areas too. Obviously if you are prepared to look at property inland and away from the resort centers you will make substantial savings. There are a lot of buyers who would rather live in one of the pretty villages anyway than near a busy holiday resort. The only thing you should bear in mind when buying further inland of course is whether or not you are looking to rent the property out to holiday makers. If this is the case then the nearer the resorts the better for the best rental return on the investment.
Kevinor has sinced written about articles on various topics from Real Estate, Computers and The Internet and Travel and Leisure. Kevin Moore spends part of his year living in Cyprus and runs several Cyprus web sites as well as writing regular articles about the Island check out the site here
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