Difference between revisions of "CSC103: DT's Notes 1"
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While the technology used in creating today's computer is the result of an evolution and choices driven by economic factors and scientific discoveries, among others, one thing we can be sure of is that whatever computing machine we devise and use to perform calculations, that machine will have to use rules of mathematics. It does not matter what technology we use to compute 2 + 2. The computer must follow strict rules and implement basic mathematical rules in the way it treats information. | While the technology used in creating today's computer is the result of an evolution and choices driven by economic factors and scientific discoveries, among others, one thing we can be sure of is that whatever computing machine we devise and use to perform calculations, that machine will have to use rules of mathematics. It does not matter what technology we use to compute 2 + 2. The computer must follow strict rules and implement basic mathematical rules in the way it treats information. | ||
| − | You may think that Math may be necessary for programs that, say, display a mathematical curve on the screen, or maintain a spreadsheet of numbers representing somebody's income tax return, but Math might probably not be required or involved in a video game where we control an avatar who moves in a virtual world. Or that the computer inside a modern data phone is probably not using laws of Mathematics for the great majority of what we du with it during the day. This couldn't be further from the truth. Figuring out where a tree should appear on the screen as our avatar is moving in its virtual space requires applying basic geometry in three dimensions. Our phone's ability to pin point its location as we're sitting in a café sipping on a coffee, requires geometry again, figuring out how far we are from various signal towers for which the phone knows the exact location, and using triangulation techniques to find our place in relationship to them. | + | You may think that Math may be necessary for programs that, say, display a mathematical curve on the screen, or maintain a spreadsheet of numbers representing somebody's income tax return, but Math might probably not be required or involved in a video game where we control an avatar who moves in a virtual world. Or that the computer inside a modern data phone is probably not using laws of Mathematics for the great majority of what we du with it during the day. This couldn't be further from the truth. Figuring out where a tree should appear on the screen as our avatar is moving in its virtual space requires applying basic geometry in three dimensions. Our phone's ability to pin point its location as we're sitting in a café sipping on a coffee, requires geometry again, a ''program'' deep in the phone figuring out how far we are from various signal towers for which the phone knows the exact location, and using triangulation techniques to find our place in relationship to them. |
| − | So computers, because we need them to perform mathematical operations, must know the rules of mathematics. Whatever they do, they must do it in a way that maintains mathematical integrity. They must also be consistent and predictable. 2 + 2 computed today should yield the same result tomorrow, independent of which computer | + | So computers, because we need them to perform mathematical operations, must know the rules of mathematics. Whatever they do, they must do it in a way that maintains mathematical integrity. They must also be consistent and predictable. 2 + 2 computed today should yield the same result tomorrow, independent of which computer we use. This is one reason we send mathematical equations onboard space probes that are sent to explore the universe outside our solar system. If there is intelligent life out there, and if it finds our probe, and if it looks inside, it will find math. And the math for this intelligent life will behave the same as math for us. Mathematics, its formulas, its rules, are ''universal''. |
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| + | But technological processes are not. So computers can be designed using very different technologies, but whatever form they take, they will follow the rules of math when performing computations. | ||
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| + | In our present case, the major influence on the way our computers are build is the fact that we are using electricity as the source of power, and that we're using fast moving electrons to represent, or ''code'' information. Electrons are cheap. They are also very fast, moving at approximately 3/4 the speed of light in wires<ref name="speedElectrons">Main, P., "When electrons go with the flow: Remove the obstacles that create electrical resistance, and you get ballistic electrons and a quantum surprise". New Scientist 1887: 30., 1993. </ref>. We know how to generate them cheaply (power source), how to control them easily (with switches), and how to transfer them (over electrical wires). This ability | ||
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-The choice of the source of power will dictate how the information is transfered, and this will dictate how many states information can take. This will define a system with a given base. | -The choice of the source of power will dictate how the information is transfered, and this will dictate how many states information can take. This will define a system with a given base. | ||
-For electricity it's 2: ON, and OFF. | -For electricity it's 2: ON, and OFF. | ||
Revision as of 08:48, 30 January 2012
