Stormcaller.net: Idleness Breeds Folly...

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Tuesday, May 6, 2003 - "Idleness Breeds Folly..."
...or why not to ask me daft questions!
"How far is Hyde Park from the Hyde Park Corner tube station?"
Would you believe it, I have a huge 5057x3634, 3mb map of the whole of central London.in jpg form (how handy). So I shall tell you exactly.
The half kilometre scale on my screen is 10.35cm on my ruler.
Therefore 20.7cm on my ruler is equal to one kilometre.
I measure 2.1cm from Hyde Park Corner tube station to the nearest gate to the park (just across the road).
2.1cm is 0.10144927536231884057971014492754 of a kilometre.
Now, I think I can measure accurately on the screen with a ruler to 0.05cm, taking into account both the inaccuracy of my equipment, my vision and the parallax between the screen, the mark on the ruler and my eye. This gives a +/- 0.48% error on the first measurement, which is doubled to +/- 0.97% (carrying through further decimal places) because I doubled the half kilometre measurement to find one kilometre. The second measurement gives an error of +/- 2.38%, due to the smaller number involved, giving a total error of +/- 3.35%.
This gives a final result for the distance between Hyde Park Corner and Hyde Park itself as between 98.05 and 104.85 metres, or a mean average of 101.45m. Approximately.
That, of course, is as the crow flies. I make no allowances for roads, hedges, statues or London buses that may or may not be in the way.
Contrary to what you may think (if you bothered to read this far, of course), there is a point to this. You see, if someone asks me a question and I give them an answer like that, it dissuades them from ever asking me anything again. Which suits me just fine!
Update: Cardelia has pointed out that the error wasn't that large, and I was actually more accurate. The distance is actually somewhere between 98.98m and 103.91m. See here for the explanation.

Replies: 4 Comments

I'll restrain myself in the future :)

Posted by Rel Fexive on Tuesday, 06 May at 11:59 PM GMT.

You asked for it :-)
Right, you can measure to an uncertainty of ±0.05cm. So if you take a reading of 500m = 10.35 ± 0.05cm, that means 1km = 20.70 ± 0.10cm. A simple doubling ofthe read measurement doubles the error. But as you can well guess, that doesn't change the percentage error - we're still on a 0.48% error despite doubling themeasurement. The actual error changes, but the percentage error doesn't change. Doubling the percentage error increases the actual error four-fold to 20.1 ± 0.2cm, which isn't right.
Given (A±a)/(B±b) = (C±c), you use actual figures to calculate theerror in the final measurement, using the formula c = ((a/A)² + (b/B)²)^½, which gives you a final error of 2.465m (3dp).
This basically means you're more accurate than you thought, thedistance is actually somewhere between 98.98m and 103.91m :-)
Now, do you want to start taking into account other errors, likesurveying errors, the inaccuracy of your computer monitor... ;-)

Posted by Cardelia on Thursday, 08 May at 12:36 AM GMT.

You sad sad rabbit.
Depressing.

Posted by Vitenka on Wednesday, 07 May at 06:35 PM GMT.

far far too much time.

Posted by Richard on Thursday, 08 May at 05:21 PM GMT.