Powers of Ten (so to speak)


I am not sure if you are old enough to remember the 1977 IBM movie Powers of Ten (trippy version, without narration) [also at the IMDB and wikipedia], but that’s a movie that sure put things in perspective. Thinking in terms of powers of ten helps me sort things out when I am considering a design problem. Thinking of the scale of a problem in terms of physical scale is a good way to assess its true importance for a project. Sometimes the problem is the one to solve, sometimes, it is not. It’s not because a problem is fun, enticing, or challenging, that it has to be solved optimally right away because, in the correct context, considering its true scale, it may not be as important as first thought.


Maybe comparing problems’ scales to powers of ten in the physical realm helps understanding where to put your efforts. So here are the different scales and what I think they should contain:

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Optimizing boolean expressions for speed.


Minimizing boolean expressions is of great pragmatic importance. In hardware, it is used to reduce the number of transistors in microprocessors. In software, it is used to speed up computations. If you have a complex expression you want to minimize and look up a textbook on discrete mathematics, you will usually find a list of boolean laws and identities that you are supposed to use to minimize functions.

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