**Next message:**Eliezer S. Yudkowsky: "Re: Mars in two weeks?"**Previous message:**Joe Dees: "Re: CULTURE OF GUNS: Interminable Off-Topic Persistence"**Next in thread:**Eliezer S. Yudkowsky: "Re: Mars in two weeks?"**Reply:**Eliezer S. Yudkowsky: "Re: Mars in two weeks?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

"Spike Jones" <spike66@attglobal.net> wrote:

*> > > Spike wrote: I get 847 km per second per day, c in 354 days, ignoring
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*> > > the relativistic effects of course. spike
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*> >
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*> > Eliezer wrote:You're right. I have no idea where the 611 came from.
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*>
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*> Dont lose sleep over it Eliezer. Ive posted several math errors
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*> on extropians which will survive in some electronic form to embarrass
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*> me forever. {8^D spike
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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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