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.
“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.
Mistaking numerology for math, that’s a clever title considering there’s a waning bunch still mistaking climatology for math.
94.716% of all computer model predictions of future climate temperatures are inaccurate.
Mind you, that’s just a ball-park figure.
The long and short of it all is
43% of all statistics are made up.
But that is 70.51164% of Alaska that is accessible by ice-road.
One main road I have heard of, may be many short ones around the coast.
Trying to download a map, it is taking awhile.
Maybe a good portion of Alaska has never been accessible by ice roads.
I think all you have found is some magazine filler.
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
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.
Willis,
While i agree that the degree of precision reported is a bit silly, your reply
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)
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.
Montag says:
June 29, 2011 at 2:09 am
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.
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.
Gary Mount says:
June 29, 2011 at 4:19 am
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.
Joshua says:
June 29, 2011 at 7:47 am
“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?
Joshua says:
June 29, 2011 at 7:47 am
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.
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?
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?
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.
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?
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–,—,—
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
David Falkner says:
June 30, 2011 at 12:34 am
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.
Well Mark,
-/10 for effort
Grade F
The twenty ninth of May is not an estimated date.
/humour
“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.
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.
I wrote a post last year about this very topic, except concerning Google’s calculation of its own economic impact in the US: Google’s Addition Problem is Significant
It’s dismaying to see this grade-school-level issue popping up in peer-reviewed journals like Science.