Guest Post by Willis Eschenbach
I always love seeing what Science magazine thinks is important. In their June 10th edition, in their “BY THE NUMBERS” section, they quote Nature Climate Change magazine, viz:
1,211,287 Square kilometers of ice road-accessible Arctic lands that will be unreachable by 2050, a 14% decrease, according to a report online 29 May in Nature Climate Change.
I busted out laughing. Sometimes the AGW supporters’ attempts to re-inflate the climate alarmism balloon are an absurd burlesque of the scientific method.
Truly, you couldn’t make this stuff up. I love it that they claim to know, to an accuracy of one square kilometre, both a) the current amount of Arctic lands reachable by ice roads around the globe and b) how that amount will change over the next forty years.
People continue to be perplexed that what they like to call the “scientific message of the dangers of climate change” is not reaching the US public. Over and over it is said to be a communications problem … which I suppose could be true, but only if “communications” is shorthand for “trying to get us to swallow yet another incredible claim”.
The idea that a hyper-accurate claim like that would not only get published in a peer-reviewed journal, but would be cited by another peer-reviewed journal, reveals just how low the climate science bar is these days. Mrs. Henniger, my high school science teacher, would have laughed such a claim out of the classroom. “Significant digits!” she would thunder. “What did your books say about significant digits”.
“The output of a mathematical operation can’t have more significant digits than the smallest number of significant digits in any of the inputs,” someone would say, and the class would grind on.
This waving of spurious accuracy is useful in one way, however. When someone does that, it is a valuable reminder to check your wallet—you can be pretty sure that they are trying to sell you something.
Because scientific studies have shown that when someone comes up with hyper-accurate numbers for their results, in 94.716% of the reported cases, what they are selling is as bogus as their claimed accuracy.
w.
PSU-EMS-Alum says:
June 28, 2011 at 6:13 pm
I guess I’ll give the “precision” claim, though precision is really the repeatability of a measurement, and I’m not convinced they can repeat anything except the calculation.
Accuracy is closeness to the true value.
It’s not a math problem.
It’s a qualifier problem.
I noticed a long time ago that any description that needs three or more qualifiers to describe the subject is usually worthless.
So when they’re talking about land that’s “Arctic” (1), “accessible” (2) by “ice roads,” (3), they’ve pretty much guaranteed that the following statistic is worth nothing, no matter how many significant digits are in the number they slap on it.
(This works well for advertising, too.)
Somehow the case has to be made that model projections like this, the amount of arctic ice decline, temperature increase, etc., need to be expressed with error bands of certainty. How else can the modeler’s be held accountable?
eptic Tank says:
“Research shows that 73% of all people who use the term “research shows”, are just making stuff up.”
++++++++
Dr Bill Mollison, the Tasmanian who invented the word ‘Permaculture’, used to make up statistics all the time because he know no one listening would bother to check, or cared. He was hilarious. He told me, “87% of all statistics are made up.”
In 39 years we can call their bluff!
But Willis, they have models and computers and climate scientists and stuff! It HAS to be right! Right?
/s
“This waving of spurious accuracy is useful in one way, however. When someone does that, it is a valuable reminder to check your wallet—you can be pretty sure that they are trying to sell you something.”
Yup. Desperation has definitely set in. LOL.
To all Carbon Tax opposers, Consumers and Taxpayers Association (CATA) held the first “no carbon tax “on 23rd March outside Parliament House Canberra, later that day the PM & her ministers labeled us under parliamentary privileges as extremists, ratbags, dinosaurs, klu klux klans, etc… since then CATA has held a series of rallies nationwide, the next rally is this Friday July 1 at Martin Pl 12noon, then July 2nd Newcastle, July 9th Hyde Pk, Aug 14th Tamworth.
[trimmed, Robt]
http://www.stopcarbonlies.com
Another thing that is worth somebody’s attention these days is just why the GHE Theory is not working as advertised. More “greenhouse gases” every day, but no heating? No “positive feedback.” Is the Theory wrong, or is it a very weak force? SOME inquiring minds want to know, regardless of what the “community” thinks.*
* community here includes most “skeptics,” it seems.
Even more “accurately”, we’re surely doomed if those ice roads are no longer needed! All we’ll have on tv is reruns.
Willis: I down loaded the Nature Climate Change article you referenced. I could not find the numerology citation you gave but Science magazine must have made up the number. The problem with the letter to Nature Climate Change by Scott R. Stephenson, et.al., is they use IPCC predictions of the temperature change by the end of the century for the regions 40 north in the artic., 2-9 C change. In addition they only make land projections with the aid of a computer program called ATAM which is described only briefly. They use the following criteria for road suitability, 2000 kg, 4400 lbs. Winter road suitability was defined for elevations below 500m and /or a slope less than 5%, surface temperatures at or below )c, ice thickness at least 22.4 cm and for rivers where 75% of the equivalent ice thickness is 22.4 cm. The loss of road area is dependant on the time the temperature lies below 0 C so that the road become soft and will not support a 2000kg vehicle. Therefore, this projection is based on a calculation of the projected areas that melt and the time that they stay melted. There are only two references to past road losses with no identification of where or when the losses occurred. That evidence is essentially anecdotal. I find it hard to believe that this represents scientific research at UCLA.
Willis wrote:
“The output of a mathematical operation can’t have more significant digits than the smallest number of significant digits in any of the inputs,”
Yes, extraneous digit noise from scientific calculators can be a problem for the post-slide-rule generation. However the solution is not trivial. I wrote my M.S. thesis on the theory of significant figures. (Then I extended the theory to include two novel data compression techniques.)
One of my conclusions was that the simple rule that’s often taught for significant figures in calculations involving only multiplication (but not squares or cubes) and division gives absurd results approximately 25% of the time.
I make the simplifying assumption of the existence of a single least precise factor (LPF), which contributes essentially all of the measurement uncertainty. Without that, we’d have to worry about which definition of measurement uncertainty to use, and that would affect propagation-of-uncertainty side-calculations.
Anyway, the basic idea is that you choose the number of sig figs for the product (or quotient), such that the implied relative uncertainty of the product is within half an order of magnitude of the implied relative uncertainty of the LPF.
And that should be independent of whatever rounding convention you use. In other words, the rounding convention is essentially a dummy constant.
You can read more about it in your university’s library. I was the principal author of a paper on the subject.
“Minimizing Significant Figure Fuzziness”, Journal of College Science Teaching, September-October 1986, pp. 30-34
PSU-EMS-Alum says:
June 28, 2011 at 6:13 pm (Edit)
You may not be precise in saying that, but you are entirely accurate. My thanks.
w.
I’m more than half expecting to see (on radio, no less):
“… global warming has been clinically proven …”
any time soon.
Sandw15:
Example: 9.8 (2 sig digs) and 0.9 (1 sig dig), both are precise to nearest 1/10.
9.8 + 0.9 = 10.7 (3 sig digs).
Both numbers are precise to 1/10 and the answer is also precise to 1/10 but the number of significant digits has increased to 3.
Wrong. The answer is 11 and the number of significant digits is 2, still.
Think about it. There is a confusion here between pure math, and the mathematics of
observation. It’s an error identical in many ways to taking all the digits from the
10 digit calculator output, when you have only put in two say, 3 sig. figures..and writing them down.
sandw15 says:
June 28, 2011 at 6:51 pm
Indeed you are correct, and I did not mean to imply that I had explored all of the ramifications of the idea of significant digits. And at the end of the day the idea of “significant digits” itself is just a series of rules of thumb for preventing over-reaching in the reporting of one’s results. And of course, as you point out, the rules are different for addition/subtraction than they are for multiplication/division. I thought about including that (the different process for add/sub) but in the end I decided not to.
The problem is that most people have a mild allergy to math, so I tend to keep it as simple as possible given the concepts involved. In addition, I wanted to keep the post short, and interesting. Discussing the subtleties of significant digits could take a few days … and lose every reader but you and a few others.
In this case, the important idea is that the claiming of false precision is a sign the promoters of the numbers don’t understand uncertainty.
Thanks for the clarity of your explanation,
w.
It works the other way too. Even on this site I sometimes see average global temperatures cited to within a 10th of a degree as far back as 1850. Never mind that in 1850 roughly 99% of the surface of the planet was not within 100 miles of a thermometer.
A constructed “Central Netherlands Temperature”, precision in 5 digits:
http://www.knmi.nl/klimatologie/onderzoeksgegevens/CNT/tg_CNT.txt
About the construction (how the do it):
http://www.knmi.nl/publicaties/fulltexts/CNT.pdf
Good point, Willis. Clearly, the reason why “the dangers of climate change is not reaching the U.S. public” is the specificity of the numbers published in journals like Science Magazine.
I’m sure that you have the data to back that up, because unlike Science Magazine, you’d never make unsupported statements. Any minute now, you’ll document the fact that articles such as that are the reason that recent polls show that some 76% of the American public trust or strongly trust scientists as a source of information about global warming,
jon shively says:
June 28, 2011 at 8:03 pm
The number is there, in Table 1.
w.
Whoops, I should make this clear. The problem here is that 0.9 really would have to be
9.0 X 10^-1 in scientific notation. Or 2 significant figures.
If it is truely one significant figure, I believe that when you add 9 X 10^-1 plus
9.8 X 10^0 you get 1 X 10^1, or an answer with only ONE significant figure. (As the lowest significant figure of the two numbers added. This does dramatically illustrate the amount of significant error which can be introduced into calculations by ignoring the “most limiting significant figure” number rules.
Willis,
My favourite example of the use of spurious accuracy came from a Hydrology lecturer at college. The class was being shown how to estimate the total volume of water that occurs on planet earth. His process of reasoning went like this:-
Volume of water in the oceans: 300,000,000 cubic miles
Volume of water in the polar caps: 10,000,000 cubic miles
Volume of water in the sedimentary rocks: 1,000,000 cubic miles
Volume of water in the lakes: 60,000 cubic miles
Volume of water in the peats & soils: 20,000 cubic miles
Volume of water in the atmosphere: 3,000 cubic miles
Volume of water in the rivers: 300 cubic miles
Volume of rain falling from the clouds: 3 cubic miles
Total Volume of water on planet earth: 311,083,303 cubic miles.
Great arithmetic, shame about the mathematics.
Note to “moderate republican”
The 24 hour timeout I gave you yesterday to get cooled down a bit (see the reply here: http://wattsupwiththat.com/2011/06/27/center-for-american-progress-and-romm-to-mock-heartland-conference-with-a-phone-call/#comment-690286 ) would have expired tonight at 8:30PM PST, but at 5:57PM tonight you posted a comment on this thread, not only under a false name, but under a false gravatar using my full name in it. The IP address confirms this is you and matches your previous comments.
Thus, due to this behavior (which violates site policy) your timeout has been extended, now for 48 hours.
It is up to you whether you want to be a member of this community or not. We have many people here who don’t agree with what we do at WUWT, and they maintain a solid presence. They learned to do that by not being insulting, rude, and petty, qualities which you have demonstrated regularly, but especially tonight.
I’ll give you another chance to begin commenting in 48 hours, but if you pull another stunt like the comment you posted where you put my name in it, then my tolerance will for your behavior be quite limited. Your choice sir.
For your review here is the site policy http://wattsupwiththat.com/about-wuwt/policy/
best regards,
Anthony Watts
Tim maguire says:
June 28, 2011 at 8:39 pm
“It works the other way too. Even on this site I sometimes see average global temperatures cited to within a 10th of a degree as far back as 1850. Never mind that in 1850 roughly 99% of the surface of the planet was not within 100 miles of a thermometer.”
I have my training in chemistry including Dr Ophardt’s analytical class, and many materials science measurements. And the correct treatment of data (real measurements of reality) is to carry the number of minimum significant figures plus one more in the case of data averages. So in the example cited, of temperature averages have more physical value in computation than individual temperatures. So if temperatures were to a degree, an average temperature would be with an added decimal, tenths of a degree.
99% of “climate scientists” make the rest of them look bad!