From: James Wetterau (jwjr@panix.com)
Date: Sun Jan 07 2001 - 18:14:32 MST
"Spike Jones" <spike66@attglobal.net> wrote:
> > > Spike wrote: I get 847 km per second per day, c in 354 days, ignoring
> > > the relativistic effects of course. spike
> >
> > Eliezer wrote:You're right. I have no idea where the 611 came from.
>
> Dont lose sleep over it Eliezer. Ive posted several math errors
> on extropians which will survive in some electronic form to embarrass
> me forever. {8^D spike
Arithmetic errors happen, especially when fingers slip on keyboards.
In this case Eliezer multipled by 2,600 seconds / hour instead of
3,600. How did I know?
The trick to tracing back errors when you suspect the actual operation
was carried out correctly (it gets more complicated if you think a
step in the algorithm might have been done wrong) is to figure out the
different ways of representing the constants and compare the values
that would give you the correct answer to possible values that would
give you the incorrect answer. Then you look see if any of them seem
to be off in any significant way, e.g. off by one, or approximately
one, or off by one position on a standard keyboard.
So we could start by saying that the way to get the answer is:
9.8 * 3600 * 24
or
9.8 * 60 * 60 * 24
... and in either case divide by 1,000 to get kilometers / second /
day.
Now, the approximately correct answer is 847, and the clearly wrong
one is 611. The ratio of the incorrect answer to the correct one is
approx. .7213 Then just try multiplying .7213 by all the relevant
constants:
For 9.8 you get 7.0687 - nope. For 60 you get 43.278 - nope. For 24
you get 17.3112 - nope. But for 3600 you get 2596.68 -- now hang on
that almost an off-by-one error on the most significant digit!
Now let's try doing the calculation with 2600 * 9.8 * 24 -> 611520
meters per second per day, which equals 611.52 km per second per day.
If Eliezer was using a truncating caculating program, (bc or dc on
Unix maybe?) this would yield 611.
Thus we see the wisdom of one of the few truly generally useful
lessons from elementary school -- do your arithmetic over until the
majority of times you've done it you got the same answer, aka check
your work! :-)
Regards,
James
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