[ExI] Anders on io9

[Mike Dougherty]

On Fri, Feb 7, 2014 at 12:01 PM, spike <spike66 at att.net> wrote:

> *>...* *On Behalf Of *Anders Sandberg
> >...Currently I am making a math paper (besides the things I *should* work
> on, of course) about the statistics of mistyping numbers. Here is a hint:
> if you randomly change a digit in a number, does it become larger, smaller
> or stay roughly the same?
>
>
>
> Anders it depends on how you interpret the question.  I wrote a sim based
> on the way you worded the hint, rather than the way your original question
> implies.  My sim takes random numbers between 0 and 999 inclusive, replaces
> exactly one of the digits with a random number.  I ran the sim 6 299 370
> times with the following results:
>
>
>
"roughly" the same can be taken to mean many different things.

I like Bill Hibbard's rationale:  many numbers that have recently rolled
over to the "1" of the next larger power of ten would be more likely to
miskey upwardly.  However, the environment of the miskey is critical to
modeling this test.  Spike imagined the miskey on the keys above the
letters.  A different pattern exists in those intensely using keypads.
Another kind of "random change" is introduced with a sensor (either analog
or digital data stream).  So what domain are we guessing in?

Is "roughly" within 5% of the original number?  As in Q: "How far is it to
the convenience store?" A: "roughly 5 miles"  (makes little difference if
the actual distance is over/under by a small margin) ... or is it some
amount of significant digits, or within an order of magnitude?  Again the
question should be asked "what domain (and scale) of measurements do these
numbers represent?"

Or was this question entirely within the realm of pure Math?  In that case
the answer will be determined entirely by how you define the set of numbers
and the nature of your "random" error/mutation.  (but that's the beauty of
pure Math, isn't it?)
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