Difference between revisions of "CSC103: DT's Notes 1"
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To understand '''Moore's Law''' we need to understand '''exponential growth''' first. In our context, it makes sense to consider quantities that grow over time, but exponential growth applies to a broader spectrum of things. However, if you understand exponential growth in our context, its application to other areas will make sense. | To understand '''Moore's Law''' we need to understand '''exponential growth''' first. In our context, it makes sense to consider quantities that grow over time, but exponential growth applies to a broader spectrum of things. However, if you understand exponential growth in our context, its application to other areas will make sense. | ||
| − | Something has an exponential growth if its size is doubling every fixed interval of time. A cute puzzle for which people often get the wrong answer will get started. | + | Something has an exponential growth if its size is doubling every fixed interval of time. A cute puzzle for which people often get the wrong answer will get us started. |
[[Image:LilyInPond.png|200px|right]] | [[Image:LilyInPond.png|200px|right]] | ||
::''Suppose a lily is in the middle of a lake, and every day its size is twice its size the previous day. In 30 days the lily has covered half of the lake. How long will it take it to cover the whole lake?'' | ::''Suppose a lily is in the middle of a lake, and every day its size is twice its size the previous day. In 30 days the lily has covered half of the lake. How long will it take it to cover the whole lake?'' | ||
| − | If you answered 31 days, then congratulations! Indeed, if it doubles in size every day, then after Day 30 it will be twice half the size of the lake, so it will have covered the whole lake! This simple example shows the powerful nature of exponential growth. It took 30 days to cover 50% of the lake, but it takes in only 1 day to cover the other 50%. | + | If you answered 31 days, then congratulations! Indeed, if it doubles in size every day, then after Day 30 it will be twice half the size of the lake, so it will have covered the whole lake! This simple example shows the powerful nature of exponential growth. It took the lily 30 days to cover 50% of the lake, but it takes in only 1 day to cover the other 50%. |
| − | There are many such puzzles in our cultures that attempt to demonstrate the extraordinary power of exponential growth through seemingly impossible feats. | + | There are many such puzzles in our cultures that attempt to demonstrate the extraordinary power of exponential growth through seemingly impossible feats. Another is the story of the man who did a good deed and when asked what he wanted for his reward asked for grains of wheat to be placed on a chessboard, one grain on the first square, then 2 grains on the next square, then 4 on the 3rd, 8 on the 4th, and so on. Of course it is impossible to grant such as wish, as the number of grains that would have to be put on the 64th square of the 8-by-8 chessboard is 2<sup>64</sup>, or 18,446,744,073,709,551,616, much more than the quantity of wheat produced on earth in a single year. |
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Let's stay with this second example and write down the number of the square followed by the quantity of grains: | Let's stay with this second example and write down the number of the square followed by the quantity of grains: | ||
Revision as of 16:17, 29 September 2013
--© D. Thiebaut 08:10, 30 January 2012 (EST)
