# Mistaking Numerology for Math

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.

## 150 thoughts on “Mistaking Numerology for Math”

1. Wayne Delbeke says:

Thank you from one who was schooled in the use of a slide rule and significant digits …

GIGO

2. John M says:

Willis,

That’s probably the number their Dollar Store calculator spit out when they did their calculation.

3. Ian L. McQueen says:

The way Science magazine has gone reminds me of an Omni that a friend used to buy regularly. For those who don’t remember, Omni aimed itself at tthose who were above-average in intelligence…..or considered themselves to be. In the Omni that I remember so well, they were discussing how a satellite could be used to deliver goods anywhere in the world. Once it had reached the destination, it would simply lower the parcel by a long cable to the ground…..

Ian

4. joshua Corning says:

I like how they used a very precise number for the square kilometers but chose 14% rather then 14.xxxxxxxxxxxx%

5. Robert of Ottawa says:

Spurious accuracy, or precision, is a new logical fallacy to be added to the classic ones. It enables us to determine the average temperature of the planet in 1855 to 3 decimal places, although the original measurements may have been accurate, at best, to +/- 1.0 degrees.

It gives the appearance of accuracy, which suggests the rightness of the argument that the number is supporting.

6. chris y says:

“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”.”

Andrew Revkin has a post over at DotEarth which explores the need for better communications on climate science. I posted this over there-

I have a 12-step program to help guide the communication of Catastrophic Anthropogenic Climate Change to the public. Here goes:

Step 1- Stop lying, lying by omission, exaggerating and emoting.

Let us know if step 1 is ever achieved.

7. ew-3 says:

Bring back slide rules… ;)

8. Skeptic Tank says:

Research shows that 73% of all people who use the term “research shows”, are just making stuff up.

9. Bruce says:

“By 2045–2059, a broad pattern of declining winter road accessibility potential on land and rising ship accessibility potential in the Arctic Ocean is observed in all ATAM simulations (Fig. 1). Most of the Arctic Ocean basin becomes newly accessible to Type A class (below Polar Class icebreakers, but capable of limited icebreaking) vessels for eight months of the year (July–February, in green). Losses in winter road potential occur from October to May (in red). Little change is projected between July and September as these months are already too warm to support winter roads today.”

Aren’t ships more energy efficient?

10. RandomThesis says:

Math: 1 + 1 = 2
New Math. 1 mod n + 1 mod n = 2 mod n when n>2
AGW Math 1 + 1 = 8 (+/- 6)

11. CRS, Dr.P.H. says:

Bingo, Willis!! However, since all of this late-season spring snow is apparently due to climate change, maybe they are a bit confused?

12. Ed Barbar says:

Somehow the case has to be made that model projections like this, the amount of arctic ice decline, temperature increase, etc., need error bands and the certainty around them.

Here’s a math challenge, then.

If the AGW scare were a corporation — say, Globwarm Inc. — which encompassed not just all the academic research but the government departments (even your local city Climate Change official is on secondment from the corporation), what would Globwarm’s revenues be, and how many employees would it have?

14. PSU-EMS-Alum says:

The idea that a hyper-accurate claim like that…
——
Not to be nit-picky, but that is a “hyper-precise” number. Only time will tell if it is “hyper-accurate”.

precision != accuracy

15. JPeden says:

Number of square kilometers of Arctic lands that already have become unaccessible by ice roads in Winter, in company with the “unprecedented” decrease in Arctic sea ice extent = 0?

16. Quoting statistical and systematic errors in so-called climate science, unlike the rest of science, seems to be optional.

Publishing in Nature and Science is, in general, difficult and often considered a high point of a scientist’s career. Again the exception is climate science which appears to get a free pass. Probably the result of replacing peer review with pal review in this specific field.

17. tango says:

to all sceptics in sydney australia a rally will be held at martin place at 12.00 mid day on the 1st of july friday to stop labour from brining a carbon tax

18. Alicia Frost says:

Typhoon: trouble is the bad stuff is spread to the whole journal. If I was a biologist worth my salt I probably would not even consider submitting any major findings to Science or Nature any longer.

19. Luther Wu says:

The claim itself is bogus, regardless of decimal point.
Still, it’s a fine example of the typical hypocrisy from those who regularly oppose Arctic access for any useful purpose.

…in 94.716% of the reported cases…

We need humorous posts now and again, thanks Willis!
(Not that almost everything the alarmists do these days isn’t laughable.)

20. sandw15 says:

“The output of a mathematical operation can’t have more significant digits than the smallest number of significant digits in any of the inputs,”
I agree with the spirit of your post…but this is a bad representation of the rules. I have taught this for over 20 years and I am well aware that there is a common error between rules for addition/subtraction and rules for multiplication/division. Mult/div relies on sig digs – least sig digs determines sig digs for the result. Add/sub relies on precision – least precise determines position of last significant digit.
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.

21. Sean Peake says:

I predict that 100.00% of all ice roads in the arctic will have vanished by the end of July 2011.

22. gcapologist says:

Mrs. Singer was my first science mentor – 8th grade.

I’d bet lessons for significant figures were taught, but I don’t remember specifically her teaching it, but at 50, I still try to follow the rule.

What I DO remember of Mrs. Singer, and will always, was how she nurtured my talents. I got to set up the experiments for class, and she gave me lots of leeway to explore my interests in science.

Thank you Mrs. Henniger and Mrs. Singer – your are in our hearts forever. (I assume Willis you have a similar fondness for Mrs. H as I do for Mrs. S.)

23. intrepid_wanders says:

Sad as always, but I find the non-peer reviewed The Economist to have far better science, information and research than ANY of the “science” mags and journals of today. Truly pathetic.

24. North of 43 and south of 44 says:

Robert of Ottawa says:
June 28, 2011 at 5:49 pm

Spurious accuracy, or precision, is a new logical fallacy to be added to the classic ones. It enables us to determine the average temperature of the planet in 1855 to 3 decimal places, although the original measurements may have been accurate, at best, to +/- 1.0 degrees.

It gives the appearance of accuracy, which suggests the rightness of the argument that the number is supporting.

_______________________________________________________________________

Even worse they add the high and low for the day and divide by 2 to get the average temperature for the day when in fact the true average temperature is somewhere between those two figures but not likely exactly half way. That makes the error bars rather large and likely well outside + or – 1 degree. For some reason 52.345 degrees F + or – 10 degrees doesn’t really mean a whole lot.

25. ew-3 says on June 28, 2011 at 5:51 pm

Bring back slide rules… ;)

That also means the use of trig tables … oh wait, those can be found on the S, T, and ST scales …

Never mind (but I DID love my TI SR-50 when it came out; still have it too!)

.

26. PSU-EMS-Alum says:
June 28, 2011 at 6:13 pm

The idea that a hyper-accurate claim like that…
——
Not to be nit-picky, but that is a “hyper-precise” number. Only time will tell if it is “hyper-accurate”.

precision != accuracy

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.

27. cirby says:

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.)

28. Ed Barbar says:

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?

29. Crispin in Waterloo says:

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.”

30. cotwome says:

In 39 years we can call their bluff!

31. But Willis, they have models and computers and climate scientists and stuff! It HAS to be right! Right?

/s

32. jae says:

“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.

33. 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]

34. jae says:

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.

35. JPeden says:

Even more “accurately”, we’re surely doomed if those ice roads are no longer needed! All we’ll have on tv is reruns.

36. jon shively says:

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.

37. Larry Fields says:

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

38. Willis Eschenbach says:

PSU-EMS-Alum says:
June 28, 2011 at 6:13 pm (Edit)

The idea that a hyper-accurate claim like that…

——
Not to be nit-picky, but that is a “hyper-precise” number. Only time will tell if it is “hyper-accurate”.

precision != accuracy

You may not be precise in saying that, but you are entirely accurate. My thanks.

w.

39. sophocles says:

I’m more than half expecting to see (on radio, no less):
“… global warming has been clinically proven …”
any time soon.

40. 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.

41. Willis Eschenbach says:

sandw15 says:
June 28, 2011 at 6:51 pm

“The output of a mathematical operation can’t have more significant digits than the smallest number of significant digits in any of the inputs,”

I agree with the spirit of your post…but this is a bad representation of the rules. I have taught this for over 20 years and I am well aware that there is a common error between rules for addition/subtraction and rules for multiplication/division. Mult/div relies on sig digs – least sig digs determines sig digs for the result. Add/sub relies on precision – least precise determines position of last significant digit.
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.

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.

42. tim maguire says:

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.

43. Joshua says:

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”.

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,

44. Willis Eschenbach says:

jon shively says:
June 28, 2011 at 8:03 pm

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 number is there, in Table 1.

w.

45. 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.

46. Philip Mulholland says:

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.

47. Anthony Watts says:

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.

best regards,

Anthony Watts

48. Jay says:

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.

49. Dave Wendt says:

99% of “climate scientists” make the rest of them look bad!

50. North of 43 and south of 44 comments:
Even worse they add the high and low for the day and divide by 2 to get the average temperature for the day when in fact the true average temperature is somewhere between those two figures but not likely exactly half way.
Preliminary calculations on the (min+max)/2 method are a little closer to the true average than I thought:-( The data I used was from a few days ago and consisted of putting a USB thermometer set to sample once/minute in an indoor non-air conditioned area away from the sun. For simplicity, I just used minima and maxima for two days which were: (72, 79) (73, 81) degrees F. Computing the average with the (min+max)/2 method yields an average temperature of 76.25 F for the two day period. When one takes all 2880 individual minute readings for the two day period and averages those, the mean is 76.15 F. Considering that one can only have 3 significant figures in this result, and application of the elementary school rounding rules I was taught, the average temperature from both methods is 76.2 F. I was surprised at the result and have to look at more of the temperature data I’ve been recording but will have to write a quick program to find daily maxima and minima so I don’t have to do this manually. The natural assumption is that more data is better but all the minute by minute temperatures may be doing is giving nicer looking graphs than just the minimum/maximum temperatures. Will dig up my winter shop temperatures to see if this simple relationship is season dependent.

The best way to get someone to have an idea about significant figures is to give them a slide rule to use for a while. On a large slide rule once can, at best, get 4 significant figures. Use of a slide rule makes one work in implicit floating point mode and often the exponent is far more important than the mantissa in medical calculations; eg 0.1 mg vs 100 mg – one significant figure but a huge difference in physiologic effect if one is computing the dose of iv fentanyl to give.

51. Wayne Delbeke says:

So speaking of accuracy and precision, I got this when I was going to UBC engineering classes in the 60’s:

An ENGINEER is one who passes as an exacting expert on the strength of being able to turn out, with prolific fortitude, strings of incomprehensible formulae calculated with micrometric precision from extremely vague assumptions which are based on debatable figures acquired from inconclusive tests and quite incomplete experiments, carried out with instruments of problematic accuracy by persons of doubtful reliability and rather dubious mentality under the influence of ….

A Climatologist is …

52. JB Williamson says:

As my engineer father says:
An expert is just a drip under pressure.

53. LdB says:

Come on its obvious

A climate scientist who doesn’t waste time on the formalities of inaccurate engineering science … whats your favourite number?

54. Neil Jones says:

I was once told by a minor political advisor that if you are going to make a number up in order to convince you audience it should end in a three or a seven. For some reason numbers which do that are the ones most easily believed. Clearly that advisor is now working for the AGW camp.

55. chip says:

I remember an old Star Trek where Kirk and Spock were stranded on a Klingon-run planet. Kirk asked Spock to estimate the chances of success for their sneak attack. His response was something like 152,432.25 to 1. Kirk said “.25?” And Spock replied, “well, its difficult to be precise.” Absurd for the same reasons cited here.

56. Berényi Péter says:

“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”.

Yeah, like “If you put this stuff on your hair (which, admittedly, costs a fortune), it could make it up to 43.12% more vibrant!”

57. Eyal Porat says:

There is the opposite too:
The over precise approximation:
“The ship can carry approximately 378 passengers on board…”.

58. Willis Eschenbach says:

_Jim says:
June 28, 2011 at 7:09 pm

ew-3 says on June 28, 2011 at 5:51 pm

Bring back slide rules… ;)

That also means the use of trig tables … oh wait, those can be found on the S, T, and ST scales …

I loved my slide rule. In addition to my K&E, I had a circular slide rule that just fit in my shirt pocket. I used that one all through high school. I ascribe the accuracy of my mental Bad Number Detector™ to the use of the slide rule. With no decimal point, you have to mentally estimate the size of the answer. As a result of making those estimations over and over, hundreds and hundreds of times, I developed a good sense of when a numerical claim was out by an order or magnitude or more.

(My Bad Number Detector™ can’t falsify anything. It just tells me where I might profitably look for something irregular.)

w.

59. John R T says:

Until the elder reached his teens, I responded to the children´s questions,¨How much longer?¨ ¨How much further?¨ ¨How heavy?¨ ¨What does it cost?¨ with precise values, including either fractions or decimals, if I was clueless. They learned to depend on my estimates: about, almost, over, more than your allowance. I trust they laugh, even now, when some authority claims prescient precision.
Thanks, Willis, for the humor. Or is it wit, more accurately?

60. reveals just how low the climate science bar is these days.”

And that is about all you can say about climate “science”. They have a bar so low that it would make a politicians wince to think what they get away with.

As far as I can tell the bar they have to get over is: “climate ‘scientists’ can say anything so long as they can’t be proven to be wrong” (this generation).

61. MannMachine says:

Just using really rough guesses here …

*if* we have entered a 25-30 year cooling micro-cycle it could reach out to 2030-ish.

*if* after that there is a corresponding 25-30 year warming micro-cycle it could reach out past 2060-ish.

That projection easily cover this mid-century talk that seems to keep popping up. Because of that rough calculation I like to simply respond to these AGW predictions by saying: “Yes, it is supposed to warm up around mid-(21st)-century. And your point is?

63. Willis Eschenbach says:

Joshua says:
June 28, 2011 at 8:42 pm

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”.

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.

Hmmm … I see that humor and indirection is, in some cases, a hindrance. So let me speak plainly.

The specificity of the number mentioned above is not the problem. It is a symptom of the problem. I’m sorry that distinction wasn’t clear to you.

The problem is the plethora of bad climate science, of which this example of innumeracy by the author and the journals is only one poor specimen among far too many.

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,

Funny you should ask that. Regarding my statements, I have discovered a truly remarkable proof which this margin of this email is too small to contain.

w.

PS – If Americans are so happy with climate science and things are going so swimmingly, why is Trenberth trying to reverse the null hypothesis? Why do mainstream AGW folks spend so much time discussing their failure to convince the American public of the urgent need for action? Heck, even RealClimate is discussing the “communication problem” and what to do about it.

Me, I don’t think that the problem is bad communications. I think that the problem is bad science. Do I have “data” to back that up? I don’t, and I don’t even know what it might look like. But the main issue that I hear brought up, over and over, is not “we don’t understand you AGW climate scientists.”

It is “we don’t believe you AGW climate scientists,” which is a very different thing.

I ascribe that to the “Fool me once, your fault. Fool me twice …” philosophy that most people have. People hate being fooled. They’d rather be wrong than be suckers. And with the foolery and the deception having been disclosed, both by Climategate and by Steve McIntyre and many others, you’ll have to go a long way before they’ll believe AGW apocalyptic predictions again.

Do I have data to back that up?

Only the undeniable fact that lots of people don’t believe you, and that even AGW supporters say that the constant drone of [failed] apocalyptic forecasts, each attempting to be worse than the last, is not working …

64. Hoser says:

The appearance of accuracy intended to lend credence extends to computer models. Computer-generated graphics and other output looks like it must be true, because it appears to be precise and lacking error. X-ray crystallography is one example. Protein structures look very accurate, but they are full of errors. For one thing, the crystal structure is not necessarily the solution strucuture. Also, someone has to place the amino acids into the density. That is an educated guess. The real resolution of a structure might be 3 to 10 Å, but a graphical rendering might imply 0.01 Å resolution.

Then we have the false precision based on the position of the presenter. Credibility can be enhanced by association with an institution, by official funding, a title, or a degree. The ideas might be wacky, but because of the added weight of the association, people may be less critical. Examples: Al Gore (ex VPOTUS), Michio Kaku (you won’t believe this ego trip… http://mkaku.org/home/), and AAAS Board making declarations of the seriousness of AGW. About this last one, among these highly regarded scientists making the statements about global warming, few knew much about climate or weather. At the time, then A.G. Jerry Brown had a link to the AAAS statement on his state website [1]. There are other amazing examples at AAAS [2].

65. Steve C says:

I love Mrs. Henniger already – a girl who knows (or knew) her stuff, obviously. I say that as someone whose calculations are normally done to a couple of figures in my head before I reach for the slide rule or calculator. And yes, it was learning how to use a slide rule that taught me that. Too many people born post-calculator appear to be unable to work out one plus two without their digital doodad to confirm the result – and regard the result as gospel even when they have miskeyed something in.

Jae (11th, 7:58pm) – just maybe this will help explain why that darn “greenhouse effect” just doesn’t seem to have the teeth we’ve been warned about. Seems to make sense.

JPeden says:
June 28, 2011 at 7:59 pm

Even more “accurately”, we’re surely doomed if those ice roads are no longer needed! All we’ll have on tv is reruns.

But all we have are endless reruns today…..

67. Spence_UK says:

Many unscientific statements in that quote from Science – including the word “unreachable”. So we can put a man on the moon but we can’t reach parts of the Arctic without ice roads? Obviously, we can reach those places by other means, and if the ice is gone (which I am not convinced by) then it may justify investment in other modes of transport.

Incidentally, there are operations that can increase the number of significant digits in a result over the starting data. But as a first cut rule of thumb, maintaining the lowest number of significant digits when multiplying is a good first bet, and maintaining the worst case fixed point accuracy when adding.

68. Patrick Davis says:

“Jacques Laxale says:
June 28, 2011 at 7:51 pm”

Unfortunately for Australia Labor, with increasing pressure form the Greens, will introduce a tax on carbon acting on advise from Ross “Gold Mine” Garnaut, an economist. With energy prices set to rise by about 18% on the 1st of July, petrol prices already ~AU\$0.05c/l over priced (Oil companies price gouging – What a surprise in the lucky country) and average grocery bills UP ~AU\$1300 p/a from 2 years ago, Aussie voters really have no idea what the downstream effects of this tax on carbon will be. Gillard is bribing cash poor people with “buffers” and/or “compensation” (Compo). Big businesses are also crying fowl and wanting some sort of corporate welfare compo too. Gillard is totally ignoring the trends world-wide with regards to ETS and/or carbon taxes. The Gillard Govn’t is totally broke and needs new revenue streams, namely a tax on carbon and a mining tax. Australians are begining to realise these taxes are nothing to do with the environment.

69. steveta_uk says:

Truly, you couldn’t make this stuff up

Rather obviously not true, since they did.

70. Stephen Skinner says:

Open and Close Dates for the North West Territories Ice Bridges
http://www.dot.gov.nt.ca/_live/pages/wpPages/Open_Close_Dates_Ice_Bridges.aspx

[1] Mackenzie River Crossing Fort Providence
[2] Liard River Crossing at Fort Simpson
[3] Mackenzie River Crossing at Tsiighetchic
[4] Peel River Crossing
[5] Mackenzie River Crossing at Camsell Bend

Last 10 Years Average (2000/2001 – 2009/2010)
Open [1] 28-Dec, [2] 28-Nov, [3] 21-Nov, [4] 11-Nov, [5] 19-Dec
Closed 16-Apr 21-Apr 4-May 5-May 21-Apr

Last 5 years average (2005/06 to 2009/10)
Open [1]19-Dec, [2] 29-Nov, [3]18-Nov, [4] 9-Nov, [5] 20-Dec
Closed 16-Apr 22-Apr 3-May 6-May 21-Apr

71. steveta_uk says:

Regarding the “communication problem” – this is a modern myth that has taken hold in so many areas, it may be one of the major causes of mistrust of all forms of authority.

In the UK, we have fairly regular by-elections, caused by the death of an MP, and absolutely without fail the morning after the election there will be a politician who performed especially badly claiming that “we obviously failed to get our message across”.

And the journalists simply lap it up – never does anyone raise the possibility that nobody voted for you because you did get the message across, and they don’t like the message.

If anyone read the Michael Tobis’ analogy (at Kloor’s, I believe) of how he would simply have to ignore his wife’s desire for new decking if the roof of the house was falling in, I think you’d see how these failing communicators think. They are so absolutely convinced that they are right, and that the case is so incontrovertible, that the only possible reasons for dissent are either malicious (incl. bribery from Big Oil), stupidity, or failure to get the message across.

And as most of these CAGW folk are I think basically honest at heart, and like to think the best of their fellow man, the only reasonable explanation for dissent in the general public must be a failure in communication.

72. Montag says:

“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.”

Nonsense. First, as far as I can see the ‘hyper-accurate claim’ do not occur in the original (peer-reviewed) journal article. Second, Science News magazine is not peer-reviewed. Stop making things up, will you? Of course, it is ridiculous to present the number at an accuracy of 1 km2.

73. Jean Meeus says:

< Total Volume of water on planet earth: 311,083,303 cubic miles.
< Great arithmetic, shame about the mathematics.

This reminds me of the story of a guide in a museum, who told visitors that the age of a mummy was 4003 years. To a lady who asked how that age could be known so accurately, the guide replied: "When, three years ago, I started with my job here in the museum, my boss told me that the mummy was 4000 years old."
Whence, indeed, 4000 + 3 = 4003.

74. I doubt that ice road study had even one significant digit.

What (climate) research shows is that what (climate) research shows is virtually never correct.

75. Patrick Davis says:
June 29, 2011 at 1:39 am

. Big businesses are also crying fowl and wanting some sort of corporate welfare compo too.

Why? Are they chicken? Or trying to duck the issue? What turkeys! I can imagine them goose-stepping alltogethernow, leaving foul deposits in their wake ….

;)
;PpPp

76. North of 43 and south of 44 says:
June 28, 2011 at 6:59 pm

Even worse they add the high and low for the day and divide by 2 to get the average temperature for the day when in fact the true average temperature is somewhere between those two figures but not likely exactly half way. That makes the error bars rather large and likely well outside + or – 1 degree. For some reason 52.345 degrees F + or – 10 degrees doesn’t really mean a whole lot.

Do they? I’ve spent quite a lot of time looking at temperature data – mainly from GHCN, CRUTEM3 and CET – all of these are expressed in tenths of a degree. Whilst this might well be too fine a resolution, particularly for historical temperatures, I don’t believe it’s correct to say that anyone claims thousandths of a degree accuracy.

77. Shevva says:

As each day goes by the laughter from future generations can now be heard louder and louder.

These people do realise that there vanity project will live years after they have left this mortal coil. Imagine being known for the rest of human civilisation for science such as this.

The teachers may teach in the future, ‘No that’s wrong your using climate change science, all hot air, no facts’.

78. John Marshall says:

Watching the US program ‘Ice Road Truckers’ shows that the Arctic roads are ephemeral not everlasting. They are a winter and spring use only feature because they degrade too far for safe use. Don’t these people ever watch TV.

79. Jimmy Haigh says:

Willis Eschenbach says:
June 28, 2011 at 11:40 pm

Common sense works just as well. Sadly there’s not much of that around these days.

80. son of mulder says:

Here in the UK we have exactly zero ie 0.00000000 recurring Sq KM of ice-road accessible Arctic land. I’m trying to work out if that is good or bad.

81. Since this is an arctic related article, i thought I might ask a question about “polar amplification” that a “climate scientist” mentioned (that I read in a recent The Vancouver Sun article).
The average increase of the earth of 2 degrees will mean an increase of 6 degrees in the arctic.
Now I was wondering, what would the average temperature increase have to be outside of the arctic so adding the arctic regions, of 6 degrees above, to the rest of the world of some value less than 2 degrees to come up with an average of 2?
Ok, I admit that I could do the math myself, and will do so, at some unspecified time in the future. Also could you calculate the area in terms of “Manhattans” that would have to be 4 degrees below average to compensate for the 4 degrees above the 2 degrees average of the whole planet average.

Or is Polar Amplification all horse pucky?

82. Craig Loehle says:

I hear wailing about the hypothetical loss of permafrost as if permafrost was some natural treasure. Melting permafrost is only a problem to structures already built on permafrost. Once it melts, you can build much cheaper regular structures on real ground. It is much less hassle to have a town NOT built on permafrost. The same with “ice roads”.

83. JB Williamson says:

Willis Eschenbach says:
June 29, 2011 at 12:27 am

I ascribe that to the “Fool me once, your fault. Fool me twice …” philosophy that most people have. People hate being fooled. They’d rather be wrong than be suckers. And with the foolery and the deception having been disclosed, both by Climategate and by Steve McIntyre and many others, you’ll have to go a long way before they’ll believe AGW apocalyptic predictions again.

I think the problem is worse than that. The ‘foolery and the deception’ about AGW has meant that people have stopped believing in many other areas of science that we often see paraded in the newspapers etc. Perhaps that is a good thing.

84. CD says:

If this publication is so good at using math to predict the future, then maybe they can mathematically calculate for me what the winning numbers will be for the jackpot in the next Powerball or Megamillions lottery drawing. On second thought, never mind — they probably would have done it for themselves a long time ago.

85. JB Williamson says:

LdB says:
June 28, 2011 at 10:42 pm

A climate scientist who doesn’t waste time on the formalities of inaccurate engineering science … whats your favourite number?

42 of course – what other number could it be?

86. RogerinVA says:

We should take that quote seriously. I didn’t think that the glaciers of the coming ice age would have advanced so far by 2050!

87. Mike says:

I saw no support your claim that they claimed to be actuate to 1 sq km. It is obvious they are making rough estimates.

88. Joe Ryan says:

Robert of Ottawa says:
June 28, 2011 at 5:49 pm
Spurious accuracy, or precision, is a new logical fallacy to be added to the classic ones. It enables us to determine the average temperature of the planet in 1855 to 3 decimal places, although the original measurements may have been accurate, at best, to +/- 1.0 degrees.

It gives the appearance of accuracy, which suggests the rightness of the argument that the number is supporting.

————————————————————————————————–

Excellent point. But don’t give them any ideas or they will round up and claim it’s “worse than we thought!”

89. Tim Folkerts says:

While significant digits are certainly a common way to deal with uncertainly, especially by chemistry teachers it seems, they are not now, nor have they even been, best way to deal with uncertainty. For example, you can read what NIST has to say about the subject here: http://physics.nist.gov/cuu/Uncertainty/basic.html

There is not a word anywhere that I can find about “significant digits”. All the huffing and puffing above about how exactly to use significant digit is similar to worrying about how to best use epicycles to to describe the motion of planets. Sure, it can give a pretty good approximation in many cases, but it is not best way to approach the problem and can lead to errors even when done correctly.

That said, the result “1,211,287 Square kilometers” does not carry any specific estimate of uncertainty, so in that sense it is poor science. They could have said “1,211,287 Square kilometers +/- 20%” for example. Furthermore, they should have said more specifically what calculations or models were used to reach this estimate. But that does not mean they should use the “high school” version of uncertainty analysis (significant digitis) promoted by so many people here.

And has been pointed out, this is a summary of a report. And we only have as much as Willis quoted. Since I don’t have access to either the full article in Science or the original article in Nature Climate Change , I can’t comment on what they may or may not have said about uncertainty in the original articles. Maybe they did say “1,211,287 Square kilometers +/- 20%” or something to that effect!

90. Sean Ogilvie says:

Mr. Ackerman at Farmingdale Highschool (NY) used to yell “Digits!” at us all the time in my physics class in 1974. Great teacher.

91. Mike says:
June 29, 2011 at 4:48 am

I saw no support your claim that they claimed to be actuate to 1 sq km. It is obvious they are making rough estimates.

Hmm, and googling the phrase Willis quoted returns only three results, two of them here on WUWT, and one here: http://pindanpost.com/2011/06/29/nature-climate-change-numbered/ which is a repost of WIllis’ post.

Willis, can you post a link to the item on Science magazine’s website? Or is it only available in the dead tree version?

92. starzmom says:

I assume the number of miles of ice roads is exactly the same from year to year? Count me among those who finds the precision of that prediction likely inaccurate.

93. Gordon says:

Climate Science does not have a monopoly on this issue.

This from a Canadian Federal Government regulatory document relating ammonia toxicity to pH :

y = 306132466.34 x (2.7183^(-2.0437 x pH))

Odd that they didn’t provide the time of day on June 28, 2050 that the predicted reduction would be achieved

94. When you are trying to convince people that a 0.6C warming over a century is something they need to start worrying about, it doesn’t help your case if you have to admit that the accuracy of the thermometers used is only about +/- 1.0C. What you do is that you claim that by averaging all of these thermometers, you have increased the accuracy, which allows you to claim that you know what the temperature is out to .001C. Then, by magic, the 0.6C warming starts to look scary.

95. That’s nothing. Look at the computer models — they have thousands or maybe millions of input parameters which were simply made up (possibly with great care). Then when the model says the average temperature will increase by a few tenths of a degree per year people believe them. For example, what is the heat content profile of the oceans in detail per cubic unit? There is no data, so just make it up.

96. steveta_uk says:

Back in the mid 70’s I worked briefly on building sites, where they had a mixture of scaffolding boards – the older ones had “Support every 5 feet” stamped into the metal band at the end, whereas the newer ones had “Support every 1.524 metres”.

I didn’t see anyone using a millimetre scale measure to determine the spacings, tho.

97. No time to write more, heading out to the Naval Air Museum today before heading for DC.

Slide rules are great – I have Pickett N4-ES (Eye Saver) still, and know how to use it. (Shoulda gotten just the N3-ES though, never did need the haversine scales.) I could rearrange calculations and jump from C/D scales to CF/DF scales to minimize slide movement. People looking over my shoulder had no idea what I was doing.

I’ve run into store owners who still use circular slide rules to apply their standard markup to products they sell. They understand significant digits just fine!

They also run 80% off clearance sales, never “price 4X lower” (or is is 5X lower?), a major pet peeve of mine on supposedly scientific colloquial speech.

See you in DC.

98. Chris R. says:

For those asserting that Willis’ number “is not in the article”, suggest you read his reply to jon shively at 8:43 PM. He states the number is from table 1 in the Nature Climate Change article.

99. RobR says:

Willis Eschenbach,
I’ve been reading a translation of the Russian RHYTHMODYNAMICS by Yuri N. Ivanov http://www.mirit.ru/rd_2007en.htm a theory that may be cracked, but so far a fun read. He makes the following observations:

“Natural phenomena do not require recognition: they simply are, like it or not. But their interpretation is prone to subjectivity, the interpreter’s talent as well as the condition of society which is the main customer of scientific interpretations. A society of feudal level of development requires appropriate interpretations, like existence of a philosopher’s stone with the help of which one can obtain lots of gold from lead.” …
“Modern views on objectivity of scientific knowledge are rather varying….The modern wise men are interested in such scientific mysticism: one can make a good profit answering allegedly vital questions posing mankind. Lots of these wise men are well aware that they are actually ordinary conmen. But such confession would mean their expulsion from ‘science’, the only source of these ‘wise men’s subsistence. So you can imagine what might happen should someone come to expose their ‘tricks’. In short, the old saying that “the road to knowledge is measured by inquisition fires” still holds true.”…
“Competition between scientific schools is really mind as well as science disturbing process, particularly if one speaks about formation of its fundamental elements. The modern world of science is affected not so much by the competition of ideas as by the fight for financing, a reflection of a general social scramble for better life. The winners are always those with stronger administrative power and media backing. Under such conditions any competition in the sphere of ideas is nipped in the bud. Sometime they simply steal those ideas. The fundamental science of the 3rd millennia is driven by the law of the jungle where might is right! Obviously for this very reason, to preserve the status quo, a commission to fight pseudo science was created in 1998 under the auspices of the Russian Academy of Science.”…

“One should understand that people of Newton, Maxwell, Lorentz, Puancare, Einstein, De Broile standing are not born every year; they are too few, while their followers are numerous. And these followers, especially those with bureaucratic background, are eager to reap the fruits of the glory which belongs not them, but the founding fathers. Trying to conceal their mental inaptitude they are doing their best to block the progress of new ideas by organizing struggle with the so-called pseudo-science or by falsifying the results of scientific research which they’d brought in and backed.

100. Are they trying to say; because of man made co2 caused by mans activity including logistics, man made global warming is happening? and because of this theoretical climate change, it poses a threat to logistics (the management of the flow of goods and services between the point of origin and the point of consumption in order to meet the requirements of customers).

If they are, that figure of 1,211,287 Square kilometers of ice road-accessible Arctic lands that will be unreachable by 2050, means that there will be less logistical activity therefore less co2 from mans activity reducing man made global warming… well, you get the idea!

It’s like man made co2 causes man made global warming which causes more precipitation that removes man made co2 from the atmosphere and that causes man made global cooling.

This quoted estimate of 1,211,287 Square kilometers is irrelevant in predicting the amount of “Ice road-accessible Arctic lands” that will change over the next forty years because the whole basis for the argument relies on the ice roads melting due to the effects of man made co2.

It says on this website I’ve linked below that Man Made Carbon Dioxide 3.225% and Natural Carbon Dioxide is 96.775%. And Carbon dioxide is 0.039% of the entire Atmosphere according to the “Composition of dry atmosphere, by volume” stated on wikipedia.

(Inconvenient estimations all round me thinks!!) /jk

101. North of 43 and south of 44 says:

Hoser says:
June 29, 2011 at 12:37 am

The appearance of accuracy intended to lend credence extends to computer models. [large snip]

———————————————————————————————————————

When one starts playing with massive numbers of calculations using a computer you need to take into account the internal representations used to represent the number by the programing language being used.

It is possible after repeated mathematical operations that the answer being produced is completely out of the ballpark.

102. Vince Causey says:

Mike,

“I saw no support your claim that they claimed to be actuate to 1 sq km. It is obvious they are making rough estimates.”

The value is in the link you just provided – table 1. You just didn’t see it because you have to click on it to get the full size. It gives the total value as 1,211,287 sq km, just as Willis said. Now explain why this does not represent a precision to 1 sq km.

103. Joshua says:

But the main issue that I hear brought up, over and over, is not “we don’t understand you AGW climate scientists.”

It is “we don’t believe you AGW climate scientists,” which is a very different thing.

Sure – you’ll hear that, but the question is from who, and where, and how can you understand the prevalence of who’s saying it where? And how to you understand changes in the prevalence? If you go to a Tea Party convention you’ll hear it a lot. If you hang out at this site you’ll hear it a lot. The fact is that there are a lot of people in the U.S. – polls show close to 50% – who believe that anthropogenic climate change isn’t happening.

However, then you read that some 76% of Americans trust or strongly trust scientists as the source of information about climate change.

OK – so perhaps that limits your widespread conclusions to some 24% of the American public. So let’s dig down deeper. Some % of that 24% no doubt includes Young Earth Creationists (a majority of Republicans believe that humans were created in their present form by god less than 10,000 years ago) who inherently distrust anyone who might say that humans could affect changes in the climate no matter where the weight of the scientific evidence might lead to. Some other % of that 24% would include political extremists of one sort of another who are entirely convinced about conspiracies of libz and commies to control the world – and as a result would disbelieve the science promoted by “elitists” no matter the scale of the claims or the strength of the supporting evidence.

What that leaves you with, Willis, is a relatively very small % of the public who are disbelieving the work of climate scientists because they think that their claims are inflated.

That leads us to the determination that your assertions, Willis, are based on your tribal orientation rather than the facts that we can establish. Your gathering of evidence is selective and it diminishes the outcomes of your analysis.

Tsk, tsk, Willis. Didn’t your mother teach you that two wrongs don’t make a right?

104. reason says:

“Math: 1 + 1 = 2
New Math. 1 mod n + 1 mod n = 2 mod n when n>2
AGW Math 1 + 1 = 8 (+/- 6)”

A thing of beauty.

105. “I assume the number of miles of ice roads is exactly the same from year to year? Count me among those who finds the precision of that prediction likely inaccurate”

The big mines in the far north have to do all of their heavy hauling in the winter. Without ice, you can’t have ice roads. Much of the terrains up there are a swampy mess when they’re not frozen. And if the surface didn’t freeze every year, vast regions would become completely inaccessible, except by air.  They are assuming that they can predict which routes will no longer freeze enough to support heavy traffic.
Heaven forbid that the big mega mines up north might have to invest in honest to goodness infrastructure like real paved roads.

106. Bruce Cobb says:

Tim Folkerts says:
June 29, 2011 at 5:21 am
They could have said “1,211,287 Square kilometers +/- 20%” for example.
Or, If they wanted to be more honest, they would say “1.2 million Square Kilometers +/- 20%.
There’s a very basic lack of integrity inherent in the article, but who cares about such things? It’s all about “communicating” climate change to an ever-increasingly skeptical public, so the ends justify the means.

107. I hope nobody minds if I ask a slightly off-topic question.

Some of the side-discussion in this thread has renewed my interest in something I tried unsuccessfully to research a while ago, namely the relative accuracy of thermometers throughout history. Reading on Wikipedia, for example, leads me to believe that we measure temperature nowadays to a hundredth of a degree, but that most certainly hasn’t always been the case. The question is in several parts:

– What is the usual accuracy for a thermometer used in weather stations?
– What was the accuracy historically? e.g. if it’s +/- 0.1C nowadays, when was it +/-1.0C? When +/-2.0C?
– What was the accuracy when thermometers were first used to measure in meteorology, and how quickly did that accuracy improve?

108. woodNfish says:

“trying to get us to swallow yet another incredible claim”

This would be accurate if it said “ridiculous” instead of “incredible”.

109. mike restin says:

What Willis Eschenbach says in his June 29, 2011 at 12:27 am post I kind of agree with but,
Since I am not a climate scientist but rather a high school drop out with a ged and an AS degree I cannot dispute the math nor the ability to stick a thermometer in the earths several butts and tell the world to party like it’s 1910 or the earth will burn up. So, I read the “harry_read_me” file and the climategate emails and have set my own standards as follows:
When harry comes forward and explains his “read_me” file and how and why he MADE UP the numbers;
when the “team” comes forward and explains their emails to my satisfaction;
when algore admits to lying throughout his false movie
then I could be convinced about cagw.
I haven’t heard a word from harry, the emails were whitewashed but never investigated and algore is still a liar.
I have watched the “science” unfold with the constant changing of the rules by supporters of algore and cagw.
There is just too much money to be made to allow so much trust to politicians like ipcc, greenpeace, wwf and algore.

110. mike restin says:

Mike says:
June 29, 2011 at 4:48 am
I saw no support your claim that they claimed to be actuate to 1 sq km. It is obvious they are making rough estimates.
———————————————————–
“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.”

Are they sure the number is 1,211,287 or maybe it’s 1,211,000?
Why wouldn’t they say ” approx. 1.2M km squared”………………………… who knows?

111. Ged says:

@ Mike

1,211,287 is accurate to 1 sq kilometer (7). That’s the number they presented, instead of something actually mathematically correct like 1,210,000 (three sig figs). Hyper-precise like that where you can go all the way down to the last sq kilometer digit, is mathematically a no-no unless all their values had this number of sig figs and this high of precision.

It just shows bad form and untrustworthy math, and is something that shouldn’t have (and wouldn’t have in my field) made it through peer-review.

112. Steve from Rockwood says:

Skeptic Tank says:
June 28, 2011 at 6:00 pm
Research shows that 73% of all people who use the term “research shows”, are just making stuff up.
==================================================
That research has since been discredited.
And why the extra “k”?

113. sandw15 says:

Willis: “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”. I realize that and agree with your point completely. I apologize for sidetracking the discussion. My teacherly instincts got the better of me.

114. ferd berple says:

When a “scientists” tells you that 9 thousand tons of ice per second are melting in Greenland, they are not being scientists. A scientists tells you both sides of the story.

When a scientists tells you that 9 thousand tons of ice per second are melting in Greenland, and it will take 10 thousand years for it to all melt, then they are being scientists.

There used to be a time when you had to be good in math to become a scientist. Then they invented climate science and suddenly you didn’t need math. Just give your paper to another climate scientists with poor math skills for peer review and you will get a pass. Opposing papers with the correct math were no problem, simply don’t allow them through peer review.

That is why Steve McIntrye is so feared and hated by climate science. He took on Mann, the number 1 bad boy in climate science that the mainstream fears to cross, and defeated him. He showed that Mann’s math was wrong, and the hockey stick disappeared from the IPCC.

Climate Science is not science. It is environmental activism dressed up to look like science, using strong arm bully tactics to keep the faithful in line. Step out of line and ask questions, like Judith Curry and you are branded a heretic. Forget the scientific method. It matters not if the science is true, so long as enough people believe it is true.

115. Willis Eschenbach says:

Mike says:
June 29, 2011 at 4:48 am

I saw no support your claim that they claimed to be actuate [accurate?] to 1 sq km. It is obvious they are making rough estimates.

Mike, a rough estimate would be a number like “1.2 million square kilometres”. It is only reported to the nearest million, or something like that, because it is the “rough estimate” you mention above.

They have said that the loss is 1,211,287 square kilometres. Since they report the number to the nearest square kilometre, this is the precision they are claiming—one square kilometre.

w.

116. Willis Eschenbach says:

Derek Sorensen says:
June 29, 2011 at 5:31 am

… Hmm, and googling the phrase Willis quoted returns only three results, two of them here on WUWT, and one here: http://pindanpost.com/2011/06/29/nature-climate-change-numbered/ which is a repost of WIllis’ post.

Willis, can you post a link to the item on Science magazine’s website? Or is it only available in the dead tree version?

I dunno if it’s online. I quoted the entire thing from page 1248 of the 10 June 2011 dead tree version except the last line, which says (explanation mine)

Iceland alone will lose 82% [of the area served by ice roads].

w.

117. Willis Eschenbach says:

sandw15 says:
June 29, 2011 at 10:40 am

Willis: “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”. I realize that and agree with your point completely. I apologize for sidetracking the discussion. My teacherly instincts got the better of me.

Your exposition was not a sidetrack, it just didn’t need to go in the head post. As a comment it was great.

w.

118. ferd berple says:

“1,211,287 Square kilometers of ice road-accessible Arctic lands that will be unreachable by 2050”

They probably meant to say 1,211,286.66666666666666666666666666666… but the editor made them round it up.

119. 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.

Unless the climate science paper doesn’t toe the consensus line, then a combative reviewer will “go to town” on it.

120. sandw15 says:

Max Hugoson wrote
“Wrong. The answer is 11 and the number of significant digits is 2, still.”

“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. “

Wow! I think we just went from adding 2 numbers which were precise to the tenths place to getting an answer which could range somewhere between 9 and 12.

Maybe people ought to get together and agree on a way to handle this so that measurements are interpreted more or less the same by everybody. Oh yeah, somebody already thought of that.

There is an explanation at this website:
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html

Or a little more detail at this website:
http://www.usca.edu/chemistry/genchem/sigfig2.htm

Pay special attention to the sections on addition and subraction.

121. sandw15 says:

I was mistaken.

If the answer is 10, the 1 is the estimated digit.

Correction
“Wow! I think we just went from adding 2 numbers which were precise to the tenths place to getting an answer which could range somewhere between 0 and 20.”,

122. Septic Matthew says:

This gaffe is worth a small chuckle, like reading a mispelt word.

Yes, I know its “misspelt”.

Yes, I no it’s “it’s”.

You get the iddea.

123. ShrNfr says:

The beauty of the slide rule was that it was hard to kid yourself.

124. Mark Besse says:

“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.”

9.8 could be anywhere from 9.75 to 9.84.
.09 could be anywhere from 0.85 to 0.94.
The sum could range anywhere from 10.60 to 10.78 or 10.6 to 10.8.
Therefore in 10.7, the 7 is not significant and the answer is 11.

125. 1DandyTroll says:

Mistaking numerology for math, that’s a clever title considering there’s a waning bunch still mistaking climatology for math.

126. Wayne Richards says:

94.716% of all computer model predictions of future climate temperatures are inaccurate.

Mind you, that’s just a ball-park figure.

127. Steve in SC says:

The long and short of it all is
43% of all statistics are made up.

128. bobdroege says:

One main road I have heard of, may be many short ones around the coast.

Maybe a good portion of Alaska has never been accessible by ice roads.

I think all you have found is some magazine filler.

129. sandw15 says:

Mark Besse says:
“9.8 could be anywhere from 9.75 to 9.84.
.09 could be anywhere from 0.85 to 0.94.”

I’m OK with that interpretation to this point.

“The sum could range anywhere from 10.60 to 10.78 or 10.6 to 10.8.
Therefore in 10.7, the 7 is not significant and the answer is 11.”

In the number 10.7, the 7 is not necessarily exact. It’s called the estimated digit and is counted as a significant digit with the understanding that the last digit isn’t perfect but that 10.7 is closer to the actual value than 11. Addition and subtraction retain the position of the least precise estimated digit.

Googling “estimated digit” gives lots of hits that explain this.

“The number of significant figures is the number of digits believed to be correct by the person doing the measuring. It includes one estimated digit.”
from http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html

130. Tim Folkerts says:

Again, all the worrying about the precise meaning of significant digits is exactly why they are NOT a great way to deal with uncertainty.

Look at the example of “10.8 + 0.9” above
* does 10.8 mean “between 10.75 and 10.84″ as claimed at least once above?
* or perhaps it is 10.75 and 10.849999999”
* or perhaps it is 10.75 and 10.85
* or perhaps it is 10.7 to 10.9

If it truly means 10.8 +/- 0.05 and 0.9 means 0.9 +/- 0.05, then one standard way of estimating the combined error is ( 0.05^2 + 0.05^2) ^ 0.5 = 0.07. If you add four such numbers the uncertainty doubles from +/- 0.05 to +/- 0.1

Interestingly, the uncertainty in the average of the four numbers DROPS by half from 0.05 to 0.025. This is one way that the average of a large number of instruments can be more precise than the individual instruments.

For example, consider a room with 1000 digital thermometers that read to the nearest degree C. Even if the thermometers are mis-calibrated and read different numbers, if the room warms by precisely 1.0000 C, then pretty much every thermometer will show 1 C higher than before. More interestingly, for every 0.001 C increase, there will on average be 1 thermometer that raises its reading. This means that the set of thermometers will be able to detect pretty close to 0.001 C temperature swings. Certainly it is not perfect, but a change of 0.01 would be easy to spot.

There are lots of more detailed questions to answer about drift and changing conditions and such. But there is NO intrinsic problem spotting small changes using large numbers of imprecise instruments.

131. Tim Folkerts says:

Willis,

While i agree that the degree of precision reported is a bit silly, your reply

“They have said that the loss is 1,211,287 square kilometres. Since they report the number to the nearest square kilometre, this is the precision they are claiming—one square kilometre.”

is also slightly off the mark.

For example, the currently accepted best value of Planck’s constant is
h = 6.626 069 57 x 10^-34 J s
This does NOT mean that the last digit is between
0.000 000 065 x 10^-34 J s and
0.000 000 075 x 10^-34 J.

The uncertainty must also be quoted. The standard uncertainty is
0.000 000 29 x 10^-34 J s, which can also be summarized as
h = 6.626 069 57(29) x 10^-34 J s

With no estimate of the uncertainty given, it is merely an ASSUMPTION on your part that they mean +/- 0.5 square kilometers (and we all know assumptions are also bad science). As someone else pointed out, it is poor COMMUNICATION to present so many digits, since so many people DO cherish the significant digit rules. And any magazine should strive for good communication, which Science failed to do here.

“Doctors say that Nordberg has a 50/50 chance of living, though there’s only a 10 percent chance of that.”
— Naked Gun – From the Files of Police Squad (1988)

133. JPeden says:

Joshua says:

a majority of Republicans believe that humans were created in their present form by god less than 10,000 years ago

The vast majority of “Climate Scientists” – what, 77/80? – and those who parrot their views believe that the “climate” itself started only about 1000 years ago and that there was and can be no “climate change” other than that which would be and is allegedly caused Anthropogenically, as per their very own definition of the term, “climate change”, = “CO2=CAGW”.

Such “Climate Scientists” are therefore Anthropomorphizing the climate, think its control must be Anthropogenic, and are therefore pre-enlightenment evolutionary dead end Anthrowbacks who see humans, especially themselves, as “god”!

And they likewise, therefore, have no use for engaging in real scientific method and principle science – as proven. Nor do you, Joshua.

134. Willis Eschenbach says:

Montag says:
June 29, 2011 at 2:09 am

“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.”

Nonsense. First, as far as I can see the ‘hyper-accurate claim’ do not occur in the original (peer-reviewed) journal article.

Before you get all dismissive and contemptuous and all, you might look at Table 1 in the original article, because as was noted in the comments, that is where the claim is … feel foolish now? You should.

Second, Science News magazine is not peer-reviewed. Stop making things up, will you? Of course, it is ridiculous to present the number at an accuracy of 1 km2.

Before you start accusing me of making things up, you should note that you are the only person here saying anything about Science News. Before you showed up, we were all discussing an article in Science magazine, which is peer reviewed … feel foolish now? You should.

In short, Montag, you should learn that taking a contemptuous tone while making unsupported and untrue statements here is not a good career choice. It just leads to people pointing and laughing. You are welcome to post here … but posting bogus accusations in a condescending manner is not the best plan for getting any traction.

w.

135. Willis Eschenbach says:

Gary Mount says:
June 29, 2011 at 4:19 am

Since this is an arctic related article, i thought I might ask a question about “polar amplification” that a “climate scientist” mentioned (that I read in a recent The Vancouver Sun article).
The average increase of the earth of 2 degrees will mean an increase of 6 degrees in the arctic.
Now I was wondering, what would the average temperature increase have to be outside of the arctic so adding the arctic regions, of 6 degrees above, to the rest of the world of some value less than 2 degrees to come up with an average of 2?
Ok, I admit that I could do the math myself, and will do so, at some unspecified time in the future. Also could you calculate the area in terms of “Manhattans” that would have to be 4 degrees below average to compensate for the 4 degrees above the 2 degrees average of the whole planet average.

Or is Polar Amplification all horse pucky?

Near as I can tell, the poles swing more than the tropics when the earth’s temperature swings.

The poles together (above the Arctic and Antarctic circles), however, are only 8% of the total planetary surface. So to answer your question,

6°C * 8% plus X°C * 92% = 2°C

I get 1.7 degrees, but you should check my math.

w.

136. Willis Eschenbach says:

Joshua says:
June 29, 2011 at 7:47 am

… That leads us to the determination that your assertions, Willis, are based on your tribal orientation rather than the facts that we can establish. Your gathering of evidence is selective and it diminishes the outcomes of your analysis.

Tsk, tsk, Willis. Didn’t your mother teach you that two wrongs don’t make a right?

“Tsk tsk”??? What, in your fantasies you’re the Miss Manners of climate science or something?

You keep coming on as though I’m making up all the stuff about communication, as though everyone from here to Judith Curry to RealClimate and folks in between weren’t discussing it. But I’m not going to argue with you, Joshua. If you think that the problem really is bad communication rather than bad science, you should run with that.

However, if you think it is a communications problem, then you quickly run up against the fact that the AGW hypothesis has ruled and totally dominated the mainstream media, the educational institutions, the politicians, and the scientific press for the last two decades … so if you actually believe your message hasn’t gotten across, after it being taught in the schools and the colleges and blasted by the media 24/7 and parroted by the politicians and NGOs for twenty years, then you have a whole lot of ‘splaining to do as to why not one of the methods you’ve tried have worked to convince the public of the imminent need for climate action NOW.

Me, I look dispassionately at the fact that you guys have tried every kind of media, from print to documentaries, and every educational method, from songs to indoctrinating children to leading college students by the nose around the inconvenient parts of the AGW hypothesis so they won’t notice. I consider all of that and I say “Well, maybe the undeniable fact that trying every method of communication for twenty years hasn’t worked to spread the AGW Gospel, just possibly might mean that this isn’t a communications problem after all.”

I mean, if I try fifty ways to try to fix a problem with a hammer and I’m unsuccessful every time, at some point shouldn’t I pause and think “Maybe I’ve defined the problem wrong, maybe it’s something a hammer can’t fix.”

But like I said, if you want to believe it is a communications problem, you are free to do so. I have no problem with that at all, as it guarantees that you won’t succeed in fixing what’s wrong.

My (admittedly unsolicited) advice would be not to say “tsk, tsk” while you are doing that, though. It makes you sound like an old maid, and I doubt greatly that it wins you any converts to your beliefs.

w.

PS – As to the humor of the situation, let me note that while I say the problem is bad science, you say it is bad communication. You’ve busted me for not providing citations establishing that the problem is bad science … however, you haven’t provided a single citation yourself to show that the problem is bad communication. Where are the people claiming that the problem is that they don’t understand what the scientists are saying, or that they haven’t heard (dozens of times) that we’re about to burn up in the fabled Thermageddon and we need to act now? You have not identified those people or shown that they even exist.

And as an aquaintance of mine once remarked, that leads us to the determination that your assertions, Joshua, are based on your tribal orientation rather than the facts that we can establish. Your gathering of evidence is selective and it diminishes the outcomes of your analysis.

Tsk, tsk, Joshua. Didn’t your mother teach you that two wrongs don’t make a right?

137. Willis Eschenbach says:

Joshua says:
June 29, 2011 at 7:47 am

… a majority of Republicans believe that humans were created in their present form by god less than 10,000 years ago)

Yes, and according to the same Gallup Poll, 40% of the Democrats and 38% of the Independents hold the exact same belief. In addition, over 80% of both Independents and Democrats say that god either “guided” our evolution or created us less than 10k years ago, while less than 20% say it was just plain evolution, no god necessary … so other than the fact that humans have got a long ways to go yet, I’m not sure what your point is.

Not only that, but credible reports say that an overwhelming majority of AGW climate scientists believe that the same god in question got a virgin pregnant (without having intercourse) long ago and then killed their only child in a horrible way specifically so that someone can burn down an orphanage and kill all the kids and then say he’s really sorry, honest he is, and he can still be forgiven for the 56 murdered children and can go on to experience the endless delights of a mystical never-seen place called “Heaven” … but unfortunately, only after he is dead. I am reliably informed that the people holding these strange anti-scientific beliefs, beliefs which are unsupported by any observations or data or facts and which contradict our everyday experience of how the world works, go by the name of “Xtians” or something like that. I’m also told that they hang statues and pictures on their walls of a man being tortured, but I’m not sure if I’m ready to swallow that story, I mean, who’d want to look at a scene of brutal torture all day long?

You want to discuss strange creeds? You want to talk about people who believe incredible things that make no scientific sense? You want to pretend that someone who believes way bizarre stuff isn’t qualified to hold a scientific opinion?

Don’t get me started …

w.

138. David Falkner says:

Willis:

You really think that a person holding a religious belief is unqualified to study science? I mean, you went through a description of Christianity, my religion, as though the religion itself were a reason to discredit any scientist that followed it. Do you really feel that only an atheist is ‘qualified’ to study science?

139. David Falkner says:

Also, Willis, reading your exchanges with Joshua, I would say that he rhetorically pwned you by consigning your thoughts to that 24%. I mean, 76% of Americans trust climate scientists, but we really don’t believe them when it comes to AGW, do we? What say you Joshua? Why the large discrepancy? Communication problems? Psssh. That’s as lame an excuse as religion. How about the fact that the world isn’t getting perceptibly warmer to people like me, who remember the late half of the 80s, and the 90s and aughties? I mean, you’ve had plent of time to let reality show the theory. Where’s the beef?

140. David Falkner says:
June 30, 2011 at 12:34 am

You really think that a person holding a religious belief is unqualified to study science?

David, read Willis’ last paragarph again:

You want to discuss strange creeds? You want to talk about people who believe incredible things that make no scientific sense? You want to pretend that someone who believes way bizarre stuff isn’t qualified to hold a scientific opinion?

It seems to me he is saying the exact opposite. It doesn’t sound as though he shares your faith, but he is certainly NOT saying that subscription to that faith disqualifies anyone from studying science.

141. When I was in school back in the 1950’s and 60’s they taught reading and comprehension skills, critical thinking was included in college prep courses in High School, discussion was encouraged, debate was for put down artists, and we played chess at lunch time with a slide rule in our back pocket.
From age 8 on I went Indian artifact hunting with my dad on weekends, or to the local glacial till gravel pit [the filled in remains of a pre-glacial creek bed that ran East / West] By the time I left for the service when I got drafted, I knew the changes in the glacial till deposit as I picked of rocks, minerals, fossils, agates, petrified woods, and corals every summer as they dug up screened and put on rural road beds the 1 1/2″ and smaller gravels and sands.
The output of the screens condensed the agates, fossils, and geodes of good size to make for easy hunting for collection and study of the progression of accumulation of the sorted interesting strata of the debris of the past.
I knew the geological history, and the story of the lives of the indigenous peoples from the assortment of artifacts found at different soil horizons, and types of terrain, open breezy summer camps from sheltered winter camp grounds, and the changes in the basic foods and animal debris left at different times of year. Understanding the whole picture of how prehistoric peoples lived in the changes of the weather, by responding in choices in camping locations several times a years to keep the hunting better than marginal.
With the advent of freeways and rental moving trucks, I cannot see where we cannot accommodate the shift in populations in the future as needs be due to small environmental drifting trends in the overall climate, the hunters follow the animals, who don’t follow the roads, and the fences only keep in the domesticated animals, as things change people move about.
Basic premise hasn’t changed over a couple of ice age cycles, what seems to be the problem?

142. Philip Mulholland says:

If I said that there are seven billion people alive in the world today, then I am reasonably sure that most readers would recognise that the seven billion number is at best an estimate (actually it’s just a guess on my part). If I write the words “seven billion” in digital form as 7,000,000,000 (I am doing American usage here) at least one point of potential confusion is removed.

The digital representation of any number is very convenient because the number is then capable of being read in many different languages. The problem however with using digital numbers for estimates is that they are too precise. There really is a precise number 7,000,000,000 (it is one more than 6,999,999,999) and so there is a potential for confusion between accurate and estimated numbers.

For example the statement “this mountain is 3,000 feet high” can be converted to the metric form “this mountain is 914.4 metres high” only if we are certain of the precision of the measurement. Given that 3,000 feet is an estimate to the nearest 50 feet then “this mountain is 900 metres high” is a more appropriate conversion of the information.

As the digital notation for precise numbers clearly has precedence, we need to stop using the same representational form for both types of numbers and use a different notational form for estimated numbers. The solution to the problem of false accuracy, when we want to present an estimated number, is very simple, we stop using the digit zero as a marker of uncertainty.

Suppose instead we replace the zero with a dash when we wish to show our limit of certainty. Seven billion now becomes:-
7,—,—,—
using this form it is very clear that I have no idea as to the accuracy of the count beyond the first digit seven, but the number is clearly seven billion.
If I now report that my confidence limit for my estimated number is plus or minus a fifth ( +/- 20%) then I am justified in writing my estimated number as:-
7,0–,—,—

The above representation, using a dash instead of a zero digit, is conventional presented by using scientific notation (real numbers with exponents) so 7,—,—,— should actually be written as 7*10^9 (one significant figure) and our more confident number 7,0–,—,— with two significant figures written as 7.0*10^9

From this we can see that even though we know from personal experience that our family has grown in size by the addition of one new baby, we cannot say that the population of the earth is now 7,000,000,001 all we can say is that the estimated population is still seven billion. In effect for estimated numbers 7,0–,—,— plus 1 equals 7,0–,—,—

143. Mark Besse says:

So using Philip’s method the quote should have read:
1,2–,– Square kilometers of ice road-accessible Arctic lands that will be unreachable by 20–, a 1–% decrease, according to a report online 2– May in Nature Climate Change.
/sarc

144. Willis Eschenbach says:

David Falkner says:
June 30, 2011 at 12:34 am

Willis:

You really think that a person holding a religious belief is unqualified to study science? I mean, you went through a description of Christianity, my religion, as though the religion itself were a reason to discredit any scientist that followed it. Do you really feel that only an atheist is ‘qualified’ to study science?

Say what? Sorry for my lack of clarity. Read what I wrote again. I hold that the only thing we need to consider in science are the scientific claims themselves. Whatever else the person may believe is immaterial. I’m tired of the “X% of republicans believe Y, therefore skeptics are jerks” kind of logic that goes around. I’m not a Republican myself, and I usually vote against them, but that doesn’t mean I’m voting Democrat.

It’s the bogus pigeonholing that drives me spare, that somehow because someone did some X (voted republican, got a grant from Exxon, believes in creationism, got a grant from Greenpeace) that their science is suspect. My point was that if strange beliefs disqualify someone from science, there’d be very few scientists left, most scientists have them.

w.

145. Philip Mulholland says:

Well Mark,
-/10 for effort
The twenty ninth of May is not an estimated date.
/humour

146. Bart says:

“The output of a mathematical operation can’t have more significant digits than the smallest number of significant digits in any of the inputs…”

I agree that the number they give is spurious. But, as a general rule, this is overly conservative, sometimes dramatically so. For example, binary fixed point sensor data is quantized so that the output is a factor of 2. Following this rule would say you cannot glean information to better than 1 bit. However, if the signal is rapidly transitioning through quantization levels, the quantization can be modeled as a uniform probability density, white noise process with RMS of Q/sqrt(12), where Q is the 1 bit quantization. Averaging N samples of such a signal then reduces the error due to quantization to Q/sqrt(12N). Since the signal is changing, an average biases the information. And, so, you run into the classic trade-off between bias and variance.

147. False comparison. Quantized and integer measures must be assessed on the basis of the larger phenomenon each is used to quantify. Determining what is a “significant digit” has to do with the accuracy of measurement: i.e., the physical and procedural constraints on said precision. The point remains: if you have one element which is accurate only to 1 part in 10, then the whole ensemble is only accurate to 1 part in 10.