From: | shadowrn@*********.com (Hahns Shin) |
---|---|

Subject: | Extrapolation (was Re: [OT] Earthdawn Questions) |

Date: | Sat Feb 2 14:40:01 2002 |

average. You can

> > >only extrapolate... :-)

> >

> > Sorry to disappoint you, but you can. Let's get a dice with d

sides. To get

> > the average of the results with this dice, open-ended style, you

just have

> > to mulitply its usual average (d+1)/2 by d/(d-1). This last factor

is the

> > sum of the (converging) numercial serie 1+1/d+1/d²+1/d^3....

>

> Isn't that extrapolating?

No, actually, it isn't. Because it is a converging sequence, when

taken to a limit of infinity it will sum to a finite number. Thus, you

CAN get an exact average (of course, sometimes this is like

calculating pi to the nth digit). It's sort of like the converging

sequence you get from Zeno's Tortoise and Achilles paradox (the

debunking of this paradox is a popular way to introduce middle school

students to the fact that infinite converging sequences can sum to a

finite number). Extrapolation, by definition, estimates a value that

is outside a given known range by using the values within the given

known range. An example would be predicting the world population 2

years from now (easy) or predicting the Dow-Jones industrial average

tomorrow (hard). But this is nitpicking... I think the word you want

is estimation, rather than extrapolation. However, there are many

infinite sequences that sum to a rational number or even integers,

thus not being an estimation at all. Of course, a sufficiently

powerful estimation can functionally act as the final result (e.g. pi

is 3.14159 for the purposes of most high school science classes), and

such is the way with calculating the averages for Open Ended Earthdawn

tests (phew!).

Link to proving and debunking Zeno's paradox:

http://www.mathpages.com/rr/s3-07/3-07.htm

Hahns Shin, MS II

Budding cybersurgeon

"Fairy tales do not tell children the dragons exist. Children already

know that dragons exist. Fairy tales tell children the dragons can be

killed."

-G. K. Chesterton