Digitation
© 29 Aug 2011 Luther Tychonievich
Licensed under Creative Commons: CC BY-NC-ND 3.0
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math

The 99¢ phenomenon (and it’s solution).

 

I am often bothered by prices. $39.95 is a silly number. You can be pretty certain no one computed the cost of all the parts and labor, added a percentage overhead, and arrived at $39.95, nor did they ball-park the value of an object at $39.95. They wanted a number that was not quite $40.00, because $39.95 feels a lot farther from $40.00 than does $40.05.

I’ve thought about a lot of ideas to try to avoid this silliness.

Most of them don’t work. Using a logarithmic instead of linear scale would reduce the number of these visually-big changes, but not remove them. Using a logarithmic scale would fix other things… but more on that later. Using base 2 would make them more common, base 16 less common, but not by much. Using a balanced Gray code would sidestep the issue, but they aren’t easy to read. Base-1 numbers also lack digit-rollover, but they take a whole lot of space to write. And so on.

Two ideas I do like, though. As a child I remember a clock that had digits on rollers. As the time moved from one minute to the next, the last digit would slowly roll upwards, so that you’d see the bottom of an 8 and the top of a 9. This makes the continuous nature of numbers visible, but it is hard to read. Another option is the analog-clock-like dials you see on older power meters: spinners that show how far along each digit is. The problem with spinners is they require a lot more space to display the same information.

So I bowl along, paying my 95¢ and 99¢ prices and grumbling to myself. An ideal solution continues to evade me, my two not-completely-bad ideas notwithstanding.

Isn’t it nice to have a world with so many hard problems to think about? As Westley Weimer is fond of saying, “‍Never a dull moment.‍”




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