on/off is enough!
'm pretty sure that many people assume that the computer must be the brainchild of Steve Jobs or that it was at least invented by some Americans 50 years ago, or... Well, wrong. The story of the most versatile tool imaginable spans centuries, has a lot to do with the old world and "standing on the shoulders of giants" as it is engraved in some british two pound coins. So let's step back in time: The year is 1614. About 70 years ago the Prussian Nicolaus Copernicus started the scientific revolution. The whole world has less than 600 million inhabitants and one of them is the scottish mathematician and physicist John Napier. He was the first who realized that the multiplication and division of numbers could be performed by addition and subtraction* And subtraction is an addition with negative numbers. Which is pretty neat because...
When you come right down to it, addition is just about the only thing that computers do. If we can build something that adds, we’re well on our way to building something that uses addition to also subtract, multiply, divide, calculate mortgage payments, guide rockets to Mars, play chess, and foul up our phone bills. Charles Petzold "Code: The Hidden Language of Computer Hardware and Software" (Amazon)
and...
Computers perform dazzlingly complex tasks, but the microprocessor chips inside them are only capable of performing very basic mathematical operations, such as adding and comparing binary numbers. Peter Dunn, MIT School of Engineering
1705 german polymath and philosopher Gottfried Wilhelm Leibniz published his "Explication de l’Arithmétique Binaire". Since then he is considered the inventor of the binary system by most historians and mathematicians. But to cite the engraving on the 2-Pound-Coin who cites Sir Isaac Newton who cited the 12th century philosopher Bernard of Chartres: All scientists are "standing on the shoulders of giants". Even this quote does it! But sometimes it's only an euphemism for good old plagiarism. At least englishman Thomas Harriot and the spaniard Juan Caramuel de Lobkowitz researched the base-2 numeral system decades before Leibniz. And 1605 - one hundred years earlier! - Francis Bacon devised a method for hiding secret messages called the baconian cipher - which looks darn binary too...
Nevertheless, Leibniz imagined calculating machines without wheels or cylinders - just using balls, holes, sticks or... switches. It seems that you can calculate with everything! And you know what? They do. Some use Dominoes, some use marbles.** These binary adders are a bit like Rube Goldberg Machines (Video), but with a mathematical function. They don't even need electricity, gravitation will do. I'm pretty sure Mr. Newton would have liked that.
Still, the binary system is unusual for decimal beings like us, since we have ten fingers and no on/off switches. But actually it is quite easy to get used to it: Instead of ten digits you have only two, so the so-called "base" is 2 and not 10. But the numbers are still evaluated according to their place; the further to the left they are, the higher their value. It's called "positional notation". You see, mathematically a decimal number (based on the number 10) like, say, "23" is not simply a two and a three, but
2 times 10 to the power of 1, plus
3 times 10 to the power of 0
or 10 +10 + 1 + 1 + 1 = 23
Nevertheless, Leibniz imagined calculating machines without wheels or cylinders - just using balls, holes, sticks or... switches. It seems that you can calculate with everything! And you know what? They do. Some use Dominoes, some use marbles.** These binary adders are a bit like Rube Goldberg Machines (Video), but with a mathematical function. They don't even need electricity, gravitation will do. I'm pretty sure Mr. Newton would have liked that.
Still, the binary system is unusual for decimal beings like us, since we have ten fingers and no on/off switches. But actually it is quite easy to get used to it: Instead of ten digits you have only two, so the so-called "base" is 2 and not 10. But the numbers are still evaluated according to their place; the further to the left they are, the higher their value. It's called "positional notation". You see, mathematically a decimal number (based on the number 10) like, say, "23" is not simply a two and a three, but
2 times 10 to the power of 1, plus
3 times 10 to the power of 0
or 10 +10 + 1 + 1 + 1 = 23