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Science Forum Index » Geology - Earthquakes Forum » Precision in Magnitude
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| Charles |
 Posted: Tue Jan 15, 2008 11:56 pm |
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On Tue, 15 Jan 2008 22:42:42 -0500, JimLillie <jimlillie@comcast.net>
wrote:
Quote: Jo Schaper wrote:
Charles wrote:
Poking around on Google Earth I find the point of an earthquake
Date: 1973/8/20 Magnitude: 3.89999999999999991118
that's pretty precise, it seems to me.
Look at the date. That's probably a computer glitch, or someone enamored
of their new pocket calculator.
Pocket calculators, in case you didn't know, can generate up to 14
places east of the decimal point, but because of the binary to decimal
conversion error, nothing beyond 5 or 6 means anything but a numerical
artifact. I bet in 1973, seismic computers were such a new tool, people
were still trusting the box. Precision does not equal accuracy.
The other day, my husband did a calculation from a digital people
counter which 'proved' that 20/4 = 4.9999999998. This small error,
incremented over tens of thousands of people, was resulting in an errant
count. He even did the math for the people with the people counter, and
they wanted to believe the box over their own knowledge of 4th grade
division.
About 25 years ago digital displays matured and suddenly had a major
price drop. We engineers were being offered instruments with impressive
numbers of digits. An EE journal got 6+ voltmeters of the same
make/model. Hooked up a common bus voltage and ground, then
photographed the displays.
All the same, right? Haa! 3 digits the same, #4 close, 5, 6, 7, & 8
garbage. Precision is NOT accuracy.
Jim Lillie
when I worked I used to try to persuade people of that. Not sure I
ever did. Lots of digits looks impressive.
Thinking about this since I first posted, I wonder if there is any
precision in magnitude. It seems that there should be. |
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| Timberwoof |
| Posted: Wed Jan 16, 2008 3:14 am |
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In article <8uvqo3tmr886dv42bft49946uk4mhmqqsq@4ax.com>,
Charles <ckraft@SPAMTRAP.west.net> wrote:
Quote: On Tue, 15 Jan 2008 22:42:42 -0500, JimLillie <jimlillie@comcast.net
wrote:
Jo Schaper wrote:
Charles wrote:
Poking around on Google Earth I find the point of an earthquake
Date: 1973/8/20 Magnitude: 3.89999999999999991118
that's pretty precise, it seems to me.
Look at the date. That's probably a computer glitch, or someone enamored
of their new pocket calculator.
Pocket calculators, in case you didn't know, can generate up to 14
places east of the decimal point, but because of the binary to decimal
conversion error, nothing beyond 5 or 6 means anything but a numerical
artifact. I bet in 1973, seismic computers were such a new tool, people
were still trusting the box. Precision does not equal accuracy.
The other day, my husband did a calculation from a digital people
counter which 'proved' that 20/4 = 4.9999999998. This small error,
incremented over tens of thousands of people, was resulting in an errant
count. He even did the math for the people with the people counter, and
they wanted to believe the box over their own knowledge of 4th grade
division.
About 25 years ago digital displays matured and suddenly had a major
price drop. We engineers were being offered instruments with impressive
numbers of digits. An EE journal got 6+ voltmeters of the same
make/model. Hooked up a common bus voltage and ground, then
photographed the displays.
All the same, right? Haa! 3 digits the same, #4 close, 5, 6, 7, & 8
garbage. Precision is NOT accuracy.
Jim Lillie
when I worked I used to try to persuade people of that. Not sure I
ever did. Lots of digits looks impressive.
This is why I'm glad that I learned to use a slide rule in high school
chemistry. Nothing illustrates the concept of accuracy as well as a
slide rule. We used the enormous six-foot slide rule to get one more
digit of accuracy out of the calculations than we could get from our own
one-foot slide rules.
Quote: Thinking about this since I first posted, I wonder if there is any
precision in magnitude. It seems that there should be.
Ordinary precisions are expressed in ± some number; with magnitudes,
they have to be understood to mean * some number. The calculation is
straightforward: A magnitude is simply an exponent for multiplying by
some standard amount. Earthquake magnitude is approximately base 32.
Thus the precision implied in a two-digit magnitude number is not very
high. Estimates of earthquake magnitudes often change from first
reports. IIRC, Loma Prieta was originally reported to be 7.0 but the
final magnitude was 6.9.
32^7.0 / 32^6.9 = 1.4
So the initial estimate, off by a tenth of a magnitude, was off by about
a factor of 1.41. The answer coincidentally turns out to be the square
root of two because
32^7 = 2^5^7 = 2^35 and 32^6.9 = 2^5^6.9 = 2^34.5
Therefore
32^7.0 / 32^6.9 = 2^35 / 2^34.5 = 2^(35 - 34.5) = 2^(.5) = sqrt(2)
This generalizes to a difference of .1 being a factor of ~1.41. A
difference of .2 means a factor of 2.
--
Timberwoof <me at timberwoof dot com> http://www.timberwoof.com
"When you post sewage, don't blame others for
emptying chamber pots in your direction." ‹Chris L. |
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