## [Computational Complexity] What would the best base be?

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• (A partial continuation of the last post). We use Base 10 because we have 10 fingers on our hands. But if we could pick a base based on what is better
Message 1 of 1 , Apr 28, 2008
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(A partial continuation of the last post).

We use Base 10 because we have 10 fingers on our hands. But if we could pick a base based on what is better mathematically or computationally or some objective criteria, what would it be?
1. When I was young I thought that if we had always used base 8 then computer science would be easier and computers would be faster. While partially true, not MUCH easier or MUCH faster.
2. In 1934 there was an article with title An Excursion in Numbers, by F. Emerson Andrews, in The Atlantic Monthly urged abanding Base 10 for Base 12. (Yes- the The Atlantic Monthly not The American Mathematically Monthly. I'm surprised too.) There are some advantages- 12 is divisible by 2,3,4,6 and since 12 is used for eggs there may have been some reason for it. The Duodecimal Society advocates changing to base 12. They have (or perhaps had - I could not find it on the web) a newsletter The Duodecimal Bulletin, which is translated into one other languauge and has the title Ekskurso en Nombroj. I'll let you figure out what language that is. (ACK- this info comes from Mathematical Cranks by Underwood Dudley.)
3. Picture that you want to represent every number between 1 and n. Lets say its in base 10. In an adding machine (whats that?) you would have log10 n columns and each one of them has 10 keys. So the total number of keys you need is 10log10n. More generally, if its base b then you need blogb keys. What value of b minimizes this? The answer is e. Since we can't use e for normal counting, this does indicate that 2 or 3 would be best. Since 2 is also good for computer science, my vote goes to using base 2.
4. To end where we began this- I wonder how Obama, Hillary, and McCain would vote?

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Posted By GASARCH to Computational Complexity at 4/28/2008 11:58:00 AM
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