I May Have Found The Problem With the Climate Models

Via Carpe Diem:

Last quarter I taught Atmospheric Sciences 101 at the University of Washington, a large lecture class with a mix of students, and gave them a math diagnostic test as I have done in the past. The results were stunning, in a very depressing way. This was an easy test, including elementary and middle school math problems. And these are students attending a science class at the State’s flagship university–these should be the creme of the crop of our high school graduates with high GPAs. And yet most of them can’t do essential basic math–operations needed for even the most essential problem solving.

Here’s a link to a PDF version of the full test and results, and here’s a blank version to give your kids and friends.

Consider these embarrassing statistics from the exam:

The overall grade was 58%

43% did not know the formula for the area of a circle

86% could not do a simple algebra problem (problem 4b)

75% could not do a simple scientific notation problem (1e)

52% could not deal with a negative exponent (2 to the -2)

43% could not do simple long division problem with no remainder (see above)!

Actually, I am just having fun with this.  My guess is that this is a general college problem and not one limited to the atmospheric sciences, though I will say that my experience in engineering is that the “trendy sciences”  (whatever the trend might be at the moment, when I was in school it was a new energy program) tend to attract students less prepared for mathematical rigor.  Perhaps this is true of climate today?

90 Comments

  1. Evil Red Scandi:

    I’m embarrassed to say I missed one (the cosine). But then I barely graduated from high school.

  2. Metro Gnome:

    But boy, they can sure put a condom on a cucumber in a hurry.

    Assuming the Atmospheric Sciences class did not attract a disproportionate number of dummies, how could 43% of high school graduates, never mind 43% of students in a *science* class, not know the formula for the area of a circle? I wonder how many of their *teachers* in high school knew that basic fact?

    It sounds like you’ll be reduced to teaching in “grunt-and-point”.

    So sad.

  3. NancyL:

    Those who can’t, use a model to approximate it.

  4. RodG:

    I knew there was grade inflation in high school, but when did they stop teaching math altogether?? One note is that this is a 101 course and might have had some English majors that needed a science elective. However even an English major should get all of these in 5 minutes with the possible exception of one or two of the following 3: the negative exponent and the cosine (trig) and for sure the second algebra one, while not tough was the trickiest in the bunch.

  5. English Pensioner:

    Its the same here in England. I left what is presumably the equivalent of you High School, having passed my higher exams in Maths, Chemistry and Physics and went into engineering. I studied “further maths” during of my part-time engineering studies to get membership of my professional institution. I certainly wouldn’t regard myself as being a mathematician, just the essential required for electrical engineering.
    I was talking to my son-in-law who is a professor of mathematics regretting the fact that I’d never attended University, and he suggested that I should join his course as a mature student, as I would probably only need to do a little revision and he would be glad to have someone with a knowledge of the subject!
    And what about statistics and probability? I would have thought these to be essential for any form of climate studies.
    PS. Its “Maths” in the UK, not “Math”. Why we insist on the plural I just don’t know!

  6. George Barwood:

    Wow, that is quite striking, although I’m not very familiar with the US education system.

    I remember doing really quite hard maths problems for UK A level Advanced maths in the 1970s.

    Here is a comparison

    http://www.mathsnet.net/articles/article_alevel.html

    This one seems non-trivial ( from 1971 )

    If a + b + c=a^2+b^2+c^2=a^3+b^3+c^3=2, find by considering values of (a+b+c)^2 and (a+b+c)^3, or otherwise, the values of (i) ab+bc+ca, (ii) abc.
    Hence find the equation whose roots are a, b and c.

  7. Nacho:

    Yeah, 4b is actually kinda tricky. Not getting that could simply mean you forgot how to separate y-yx-x=0 into its x and y parts, or doing that simply didn’t occur to you. Not much shame in that, nor the negative exponent with the base of 2. You really don’t see that very much, and it may not occur to you to compare what you do with negative exponents base 10. So I understand those. Not knowing the area of circle or not being able to do long division though?

    Of course I’m currently training a soon to be college grad and I have to repeatedly explain to him how to make say 100ug/mL solution of X in 10 mL Y when you have a 20 ug/uL solution of X to start with. I know he had the opportunity to learn this along the way, its likely just that his teachers didn’t set high enough standards. And this guy is going to be taking the MCAT in a few months….

  8. Doug W:

    I’m with Evil Red; I got them all except for the cosine. Oddly enough, I remembered the definition for tangent; not bad, since my algebra days are about 30 years in the past. But these days, I just push the “cos” button on my calculator; I’m sure that’s what all the college students are used to doing.

    FWIW, my dad used to give me grief about not being able to use a slide rule. He was also disappointed I never memorized the log tables like he did.

  9. Doug W:

    Also, for English Pensioner: I’ve never been able to figure out why you call it “Sport” instead of “Sports”, either.

  10. Tony Hansen:

    Noticed that the average scores for each section are similar. Was this to be expected?

    Were the average scores to be expected?

    Would the scores have been much different 30 years ago?

    Is there a higher percentage of kids going to college instead of getting trades/jobs than 30 years ago?

  11. NikFromNYC:

    I do not take well to numerical mathematics. I went into synthetic chemistry to avoid it, synthesis being purely intuitive. I can visualize things in my mind but find it very hard to think intuitively in terms of equations. It’s been nearly 20 years since I’ve used math much, since I’ve been making design products instead of doing science and most of the math involvedis handled deep in the guts of CAD programs. However, I did all of these problems in my head, quite quickly, except without pen and paper I was utterly stumped by 4b. For the others I could feel how my mind was using little rules of thumb and memory tricks as an aide since this was a total pop quiz I wasn’t prepared for. Bigger/smaller rules were being verbally invoked in 1a-e, such as knowing that division by 10^-5 made the result bigger, so the question was merely how much bigger. I had forgotten what a cosine was verbally defined as, but immediately reasoned that it must be a division by the “special” hypotenuse and that sine must be the “symmetric” one (straight across from the marked dihedral angle) since cosine has always sounded like its little brother.

    All but 4b are a measure of training (unless perhaps you are a savant who sees numbers as polytopes that combine together to make a new 3D shape that make the answer obvious). Without that training they are just digits arranged in space on paper with no formal rules of relationship attached to them so there is little chance of using high intelligence to figure them out. If you know the rules of what various types of exponents mean, there is little skill needed.

    To anyone with the proper training (maths education) only 4b is a measure of skill once you remember the rule of what the arrangement of symbols on the paper means.

    That said, when I stare at these basic mathematical relationships, I start to think intuitively and get drawn into them and things start to indeed make sense in a disturbingly uncanny way. A negative or fractional exponent *does* have perfect symmetry with their positive or multiplicative partner. It’s like color symmetry (somewhat). Trigonometry becomes fun as I visually imagine the hypotenuse swinging around like a second hand on a clock, smashing the vertical side down to zero height and then dragging it deeper and deeper below the horizon.

    I was upset that I had forgot the name of the PV=nRT equation, thinking it was named after an obscure scientist but it’s just called “The Ideal Gas Equation”. Having looked that up, I still forget what R is. Grrr! What must it *have* to be? Well, Pressure P x Volume V intuitively feels like a measure of accumulated energy, embodied in the entropic drive a gas experiences to expand. I think of a tank of gas and how violent of a rocket it would make if I used a sledge hammer to break the valve stem off. So I need an energy-like body on the right side as well or what use is an ‘=’ sign? I think n is the number of molecules or is a constant. It being non-capitalized is throwing me off, since that might indicated it being a constant. If it’s number of molecules (probably in moles…= 6*10^23 molecules?) then R would be the constant that handles the arbitrary units involved. So again, Number-of-Molecules n x Temperature T “sounds” like a measure of bad-ass-ness (energy) as well. If I heated the hell out of the tank before knocking the top off it would blow its cork more forcefully indeed. Let’s check…whew! R is called the “Gas Constant”. Now it’s “obvious” (except it wasn’t obvious before since I think I wondered if R was related to entropy).

    This type of reasoning is exactly the sort of strategies I was forced to use in order in the first place to make up for a temperamentally poor memorization and paradoxical lack of ability to hold figures in my head despite their graphical nature and my fondness for visualization in three dimensions. It’s coming back to me now. I should stop thinking now or with some beer and loud music and playing with math I’ll start to rave like the character in the wonderful movie “Pi”.

    I at one point passed senior level college calculus etc. with flying colors, including entire courses on mathematical proofs, quantum mechanics as well as statistics as a part of quantitative/analytical chemistry. In a philosophical sense this little test is not that much less difficult than advanced math. It’s just that the training required to understand this level of math at a gut level is indeed much less involved. Thank god for computers though, since trig tables were a drag. I could never figure out crystallographic symmetry groups in any intuitive way and this was profoundly disappointing. It’s not taught intuitively so it would have been up to me indeed to “crack” it. I did figure out Maxwell’s equations, intuitively. They are not so much “advanced” math as much as a very compact way to describe what magnetic lines of force are allowed or disallowed to do. That kind of blew my mind. They are utterly reliant on verbal rules about what the arrangement of symbols meant. They are a rather jury-rigged way to force geometrical ideas into the form of equations.

    Its quite disturbing though that Pi never resolves itself to a final value, meaning any real-world circle can never be a perfect one. Bucky Fuller used to rail against the very idea of straight lines and circles for this very reason, and rejected the idea that nature itself “uses” Pi at all. Pondering such drama makes it a lot easier for me to remember the equation for a circle.

    I think the real problem is that intuitive understanding is not encouraged at all and so pure memorization must be relied upon and memory is simply not up to the task of surviving long periods without practice. Maths make sense in a delightfully trippy way if you force yourself to really wrap your mind around the idea that the symbols on the piece of paper are merely the surface of things and that toy-like “entities” are being described as they move about, expand, contract and change shape. Careerism trumps the idea of a calling or the idea that maths really mean something other than mere calculation.

  12. Mesa Econoguy:

    It’s academic laziness all around.

    Government education promoted by government largesse and further academic laziness.

    Mike Mann is a moron. Fire him now.

  13. WillR:

    I want to believe that this is a joke.

    I expected something terrible when I downloaded the PDF — I expected to be embarrassed by what I forgot…

    Words fail me…

  14. RobTzu:

    I missed 4.b, but looking at the answer, I feel silly for it. I have an Associates Degree, stopped about 20 hours short of my B.S. in biology to work as a operator/chemist in a powerplant for pretty good money. Never had Calculus, if I did I would have went for a B.S. in chemistry instead of biology ^^
    It is not cool to be smart. Being smart does not get you laid. The incentive is to be too cool for school. So here we are. Privatize schools, and let them be single sex schools.

  15. Mark:

    Dang I could do all the problems in my head. The only one I was hazy on was the cos one, (was it opposite over hyp, or adjacent over hyp) but then I remembered the great Native American SOHCAHTOA.

    It is pretty sad – if you are in a science class in college you should be able to get at least 85% on that test, especially if you have paper and pencil.

  16. Waldo:

    The most pointless post yet on this blog.

  17. dearieme:

    “Yeah, 4b is actually kinda tricky.” On the contrary, it’s “do it in your head” stuff. Look on the LHS as y/1. On both sides of the equation add the numerator to the denominator. Then you have
    y/(y+1) = x/1. QED.

    Do they teach anything much in school these days?

  18. hunter:

    Waldo,
    Then leave.

  19. Jeffrey Ellis:

    I spent the first ~20 years of my career working in remote sensing. I worked with countless atmospheric scientists (remote sensing requires the removal/correction for atmospheric effects). I can tell you that atmospheric science is a very rigorous and challenging discipline, not a “trendy” or fluff degree. These were some very bright people.

    Regarding global warming/climate change, what I’ve seen is that the atmospheric scientists working in academia tend to be very AGW-centric, and those who are working in industry, etc. (whose grants don’t depend on AGW) tend to be far more skeptical of AGW.

  20. English Patient:

    The key point is this:Todays students attend courses which are generally useless at preparing them for the real world.

    Education is meant to be a choice:Do you sacrifice time and effort inorder to aquire skills and knowledge such that you become more valuable or do you work with your current knowledge and contribute to maintaining your lifestyle as it is now?

    Too many students attend courses dreampt up by Institutions perpetuating the myth that education is an end in itself:it isnt .

    We have too many courses and too many institutions

    lets get people back to work and allow them to study through application of skills relevant to their field rather than wasting time on theory
    in the belief that their educated mind will pave the way to a better life.

  21. Bob Sykes:

    Many years ago, I team-taught a class in environmental science and engineering to a mixed group of graduate students in biology. The course was intended to introduce biologists to environment problems in air, water and soil, plus some public health stuff.

    One day, I put up the Streeter-Phelps equation, which describes the variation of oxygen along a river. This equation contains several terms that involve e (the base of the natural logarithms) raised to an exponent. After discussing the formula for a while, a student asked, “What is e?”

  22. Mike:

    4b almost got me too, mainly because I got sloppy and went from “y-xy=x” to “y=x-xy” instead of “y=x+xy”. But the answer just looked wrong, so I rechecked and found the problem. Even with that, the whole thing took less than 60 seconds to get done (with no errors).

    Of course, I had an advantage in that my math teacher my junior and senior years of HS was a bit of a fanatic. No calculators, of course, but by the time she was done with us, we could also calculate square and cube roots and estimate common logarithms longhand; had memorized the conversion factor to natural logs and the sine, cosine and tangent of all multiples of 15 degrees; and memorized an absolute horde of trig formulas. That all saved my grade in college when I had consecutive calculus, physics, and mechanical engineering finals, and my calculator’s battery pack failed five minutes into the first final.

    Bob – that reminds me of the time I was teaching a business calculus class, and in the middle of working out an example problem on the board, one student asked “how did you get X over X to be one?”

    Worse, though, was the HS junior I once tutored in basic math. When she got to the part in a problem where she had to multiply 6 x 6, she pulled out her calculator. The “6″ key stuck once and she actually punched in 66 x 6, getting 396, which she wrote down and kept going. I suggested she might want to recheck that, so she grudgingly punched it in again, got 36, looked at both answers, then tried it a third time on the theory that the answer that came up twice was probably the right one. After that session, I told her father that she needed WAY more remedial help than I was capable of giving.

  23. GPHanner:

    You are absolutely correct. The quality of public education sinks lower and lower. In my opinion a major factor is the insistence that the only qualified teachers are those who have jumped through the hoops set up by “teachers colleges,” excuse me, the “colleges of education and human sciences” that waste space at our universities.

  24. ruralcounsel:

    Teachers unions dislike teaching quantitiative material like mathematics and science, because problems have distinctly correct and incorrect answers. Why would this be a problem?

    Because it means that it is simple to ascertain whether the instructor is doing their job or not. It becomes too easy to distinguish the good teacher from the ineffective one, and that is anathema to teachers unions. God help them if it comes to pay for performance!

    It’s much easier for everything to be subjective, for everyone to be right, to celebrate their mediocrity, and to enhance every little ego’s self-esteem. Then everyone is happy with the teacher.

    When these kids reach college, they’re incompetent at basic math and science. Given the outrageous tuition bills they pay, universities are reluctant to flunk anyone out. So we get people with mediocre skills going into the trendy areas. Does anyone seriously doubt that climate science type classes aren’t trendy these days? Particularly given the degree of research funding heading that direction.

    Kind of goes to the peer reviewer (Ed Cook at Lamont-Doherty) who wanted to reject the “ugly paper to review because it is rather mathematical”. I wonder what Cook’s age and background is? Ahh, just looked it up…wildlife biology, geoscience, watershed management. About the same age as me. All his degrees from the same school. I’d have thought someone in watershed management would have to know math…groundwater hydrologists certainly do. But now he works in a “tree ring laboratory”…and has never held a position outside of LDEO since 1975. Hmmm. I don’t know the guy, and maybe I’m jumping to conclusions, but maybe this explains a lot.

    Yeah, Waldo, pointless for someone in psychological denial.

  25. Fred from Canuckistan:

    As bad as their math skills are, students today also have very low spelling abilities.

  26. maxwell:

    I don’t know what this class has to do with climate models. If you went and read Cliff’s whole post on this topic, you’d see that less than a quarter of the class were physical science majors. That means there were likely not even all of these students will end up majoring in atmospheric sciences. Nothing from Cliff’s post has anything to do with climate models.

  27. mahtso:

    I do not doubt that math skills are lacking, but considering that (1) there was no negative consequence to getting these questions wrong; and (2) low scores on this test would (presumably) result in easier problems on tests that do count, I question whether any relevant conclusions can be drawn from the test results.

  28. the other coyote:

    Warren, I clicked on the links but got a “forbidden” message. Any way you could email me a copy of the test? I’d like to try it. coyote_ridge_ranch@yahoo.com

  29. the other coyote:

    I could get to the test from carpe diem.

  30. Waldo:

    Glad to see so many geniuses here – you are all so self aggrandizing, it’s hilarious. Put that MIT PhD to work there, Ruralcouncel?

    However, I will concede that perhaps poor math skills may account for part of the reason that so many people are willing to be bamboozled by denier pseudoscience.

  31. hunter:

    Waldo,
    Why don’t you go ahead and just toss off that mask?
    You are not even fooling yourself anymore about not being a troll.

  32. DaveK:

    ruralcouncel:

    Be careful for what you ask for when you invoke “pay for performance!” In theory, it’s a system that should reward excellence… For PFP to work as advertised, you must have very motivated and well-trained supervisors who are devoted to performance of the organization as a whole. If the supervisors don’t really buy in to the entire program, it becomes a system that is extremely easy to game. Anybody who is even slightly clever can figure out how to set what appear to be difficult goals that are, in reality, slam-dunks, and probably do not contribute to the overall goals of the greater organization. Already, you find that when students are meet “competency requirements” in order to advance or graduate, far too many of the teachers are training students to just pass the tests, rather than to actually learn something that will help them to survive in the real world. [an aside: When was the last time that you saw someone actually "counting change" instead of looking at the register and just dipping out the amount it said they should return to you?]

    “Pay for performance” has been the downfall of a lot more organizations than it has actually saved.

    Been there, done that, got the crappy T-Shirt!

    DaveK

  33. DaveK:

    oops!

    that should be “…when students are required to meet “competency requirements”…”

  34. Waldo:

    Now, now, little hunter – get it right. I’m a troll for truth, justice, and the American way.

  35. hunter:

    Waldo,
    Trolls are never for truth, justice, and the American way. As you demonstrate so well.
    BTW in your fan dance about your educational achievements, I lost track: Are you a PhD in science, or did was that just more trollish costume?

  36. Doc_Navy:

    Why do I have the feeling that Waldo falls into the “I can’t do the basic math” section of this article?

    Do you even understand the terms “Blackbody radiation” and “Watts per square inch” and what their mathematical expressions have to do with Climate?

    Doc

  37. ouch:

    MBA of Finance and I scored under 50% –

    Back to 6th grade with me. :)

  38. Al:

    To Climate Skeptic: I hope you’ll think hard about whether you leave the comments section open on any of your posts for all and sundry, because it becomes a forum for those of least intellect, and yet clearly also the least understanding of their own limitations, to come out in force, and spray around their favorite epithets, such as “moron” and “troll”. Waldo’s comment that they are self-aggrandizing is certainly correct, but, more to the point, how do they add any value to your blog? Surely it would be better if comments were moderated to only include the insightful and germane. Otherwise the comments section is surely just a waste of time and deters the average reader from revisiting your blog.

  39. IT Guy:

    Another MBA of Finance and Information Systems. Scored 100%. Maybe the math major and physics minor undergrad helped.

  40. Matt:

    I think it is “maths” in the UK because it is short for mathematics.

    Is the subject of numbers called mathematic in the US?

    English belongs to the English. It is only on loan to everyone else.

  41. Stephen J.:

    Counting a couple of answers as half-points, because they were the correct value but simply not correctly expressed in the final answer, I got 75%. (Forgot the calculation of a cosine and how to deal with negative exponents that aren’t factors of 10.)

    Now for me it’s been, oh, cripes, nearly 22 years since I did any significant math beyond arithmetic. But that could just mean that I have an exceptionally good memory, or it could mean that the frosh coming in are *seriously* underskilled.

  42. Keith W.:

    Well, my only mistake was due to misunderstanding the problem. I thought 1F asked for the decimal equivalent of 23 and 1/7, not 231 divided by 7. I guess I over thought, but the instruction to give to the tenths position threw me off, and I was looking for something harder. Decimal listing of sevenths was always one of my favorite memorizations since it developed from the multiplication of seven, 0.142857 and back to the beginning. Technically, the correct answer, based upon the stipulation of the question, is 33.0

  43. Darren P:

    I am ashamed that I never did better but then again, I always find it easier to do math problems if there is context to it and not just a bunch of letters and numbers spewed out. Call me crazy.

  44. Waldo:

    Hunter, never said what my degrees were in. Your response to “truth and justice” cracked me up. You do take this quite seriously, don’t you?

    Doc, a black body refers to a mass or an object which absorbs radiation. And may I assume that the “watts per square inch” you are referring to has to do with California’s purposed ban on certain energy inefficient devices? Or perhaps you were referring to the use of big screen TVs in general? Is this an infringement on the American way of life?

    But, since you are apparently new to my relationship with CS, I have always claimed to be a layperson worried about the disinformation and often outright deception that blogs such as this one purvey. And I worry about the people who have some small science background but who – most likely for political reasons – prefer the deniosphere to the actual highly trained scientists and complex science that makes up the GW community.

  45. Richard Saumarez:

    This is horrifying. Can one really teach any branch of physics without elementary calculus? I have had the experience of teaching a third year class in biomedical engineering at a major UK University, having been out of academia for a while and I was struck by the difficulty the students had with some mathematical concepts, although they were well taught. When I discussed this, the reason emerged that maths has been so dumbed down in high school that the students have to have remedial mathematics in their first year.

    I suppose that this simply reflects trendy post-modern teaching in that you don’t have to learn anything but just absorb political attitudes

  46. hunter:

    Al,
    Good idea. I pledge to drop my troll feeding.

  47. Mike Blackadder:

    Climate Skeptic, you obviously don’t know anything about climate science.

    The students should have ‘peer-reviewed’ the other students’ test results and built a scientific consensus. Then you would obtain proper answers to your questions. For example: What is the equation of a circle? Pi radius squared is the skeptic view and as far as I know has not appear in the climate science literature. The consensus view is that circles are causing catastrophic and irreversible changes to our climate, and it is recommended that government take action by immediately imposing heavy taxation on eyeballs, nipples, and double taxation on testicles.

    Besides, what’s with all this focus on ‘answering questions’. The science is settled. It would have been far more useful if you assessed their ability to properly wipe a hard-drive.

  48. Clive G Smale:

    Thanks for the info. My daughter (13) is in 2nd Year of High School, Special Science Class, here in the Philippines, which concentrates on math and science subjects. The trig she has not done at this time until next year but she is OK with the rest.
    Interesting results from your sample – sad, really, and confirms the generally reported feeling of the dumbing down of the US education system.
    Anyway,she achieved 70% in a 10 minute workout on the paper, leaving out the coursework not yet done. I think she would have achieved her passmark of 85% doing the complete paper.
    Thanks for the test.
    Clive G. Smale – Philippines

  49. Richard Saumarez:

    @Mike Bladder
    You have missed the point here. The sceptic view is that pi is an irrational number defined by an infinite series.
    The consensus view is that pi=3.

  50. hunter:

    The problem is not really that the models are not very accurte, or that the cliamte scientists make mistakes.
    The problem is they cover it up.
    As crugate shows, and the IPCC glacier scam confirms:
    http://bishophill.squarespace.com/blog/2010/1/17/ipcc-glaciers-some-explanation.html

  51. BobC:

    Waldo: “And I worry about the people who have some small science background but who – most likely for political reasons – prefer the deniosphere to the actual highly trained scientists and complex science that makes up the GW community.”

    So, that makes you, a person of small science background (compared to Doc_Navy, for sure: I’ve seen his stuff elsewhere) someone who – most likely for political reasons — prefers the government-funded, fraudsters to independent scientists?

    Scientific truth may be, for you, simply a matter of picking the (self-proclaimed) ‘expert’ to believe, but to many highly trained scientists not on the government AGW gravy train it is a matter of verification and replication of claimed results. The gov’t fraudsters do their best to prevent this kind of review, leaving those of us with unimpaired reasoning ability to wonder what they are hiding, and eventually to uncover it.

    Believe these people (the CRU gang, etc) if you wish — after all, as P. T. Barnum said, “There’s one born every minute”.

    (BTY, none of this would have surprised Eisenhower — he predicted the political capture of science in his farewell address.)

  52. Mike:

    It’s just as bad here in Canada. What are we going to do about it? This is a much more serious problem than CO2-induced climate change ever was or will be.

  53. Ric Werme:

    I had a very nice high school education, and (even better) remember it, so I got 100%. Two quibbles:

    3b) On your silly triangle, the side opposite angle alpha is “a”, not “b”. I had a college prof who liked to swap x & y once in a while to verify we could still think, and I had to check myself twice that cos() in this case was not b/c. Grr!

    4a) PV = nRT, I forget with, moderate shame, that I don’t remember what n & R are.
    fortunately, that’s completely immaterial to the question, as long as they are non-zero, of course.

    My father spent part of his retirement teaching a couple courses at the local state college. He was always amazed at some of the basic things we always knew that his students didn’t, like the number of feet in a mile.

  54. Waldo:

    Well BobC, probably you don’t know the history of myself and the CS crowd; we have been debating this very thing for some time now.

    For the record, and I’ve posted this before on other threads, I am willing to believe that there is some viable anti-AGW science out there. But it is not posted on places like this.

    As for your “independent scientists,” usually these are people who are rather dependent on, say, the coal industry, the Heartland Institute, or the petroleum industry. Look them up – or, actually, skip over to “Defending the Tribe” or “Analyzing the Global Warmist” thread. They are rather long but saves us going down the same path again.

    I’m wondering, Bob, do you see yourself as an objective, unbiased, reasonable critic in this debate? Did you come to your stated, rather generalized conclusions above before or after you looked into AGW?

  55. hunter:

    BobC,
    You are wrestling with a pig.

  56. David:

    Well Waldo you seem to have done a good job of playing the man and not the ball here, which may be why you have got so much abuse. If you want to know about scientists who take money from the oil industry, have a look at Mr Pachauri’s or the UEA’s list of supporters, so at worst it is a level playing field. From what I have seen, there are a lot of posts on these websites from people who are engineers, mathematicians, statisticians or software engineers who have been shocked at the shoddy work of the CRU and the IPCC, the political rather than scientific mindset of people like Michael Mann and James Hansen, and the outright lies peddled by Al Gore. There are also people like myself who have seen how much damage has been caused in the financial sector by over-reliance on enormously complex models built on very limited and often inaccurate input data (black boxes), and were astonished to find the same thing going on here.
    I don’t know if there is AGW. I think global temperatures are increasing, but the records have been so corrupted that it will be a major effort to establish by how much, let alone whether CO2 emissions are a major driver. I think the probability that the GCM is a valid predictive tool for global temperatures over 20-50 years is vanishingly small. The onus must surely be on those who wish global economic and political policy to be driven by such models to prove them beyond reasonable doubt, not on those of us who question them to generate alternative models.

  57. Ted Rado:

    I graduated from engineering school in 1949. I have regularly been told that I am getting more and more obsolete because of new technology. As it happens, I kept up with my field, learning Fortran programming, computer process simulation, and many other things over the years. In the meantime, engineering education went from 161 hours for a B.Ch.E. to 125, even though there is now more to learn.

    My experience is that today’s graduates are undertrained and overgraded, and are much less competent than engineers of my age who have kept up with their field.

    We will shortly reach the point wher you will get an A in college level math if you can answer that 2 plus 2 is “duh”.

  58. Waldo:

    Hello David, that was a very thoughtful commentary.

    I, like you, do not know if there is AGW. But I do have a mind open to both sides of the debate. What I am not convinced of is that places like Climate Science are legitimately debating it or simply venting a political POV – which always leads to hubris.

    And yes, I see a number of people here who obviously have a scientific background (although there a good many who fake experience and expertise and are eventually outed). As a rule I do not doubt that these people have some understanding of science, admittedly far more than I do, but what I do doubt is their objectivity and emotional response to a now very politicized issue. This comes up over and over again. So yes, I liked the metaphor – I am playing “the man” because I believe the men and women here are untrustworthy. I also “play the man,” I suppose, because – while these are engineers, mathematicians, etc. – I find them playing zone defense with the hardcore climate experts from the safety of the blogosphere. As smart as they are, I believe these smart people would be out of their league anywhere else. Look around at the sources of information on CS – very, very questionable to say the least.

    I must disagree with you on one point, however: I “take abuse” because I am not convinced by the reasoning here. I, unlike you, do not see positive proof of collusion of conspiracy, and the more I look at the claims of the deniosphere, the less likely it seems to me. So, very slowly, I am becoming alarmed about the state of the climate.

    Cheers.

  59. PHilemon:

    Well, there is the New new math, which many parents have protested, because apparently it involves students forming teams to reinforce their mutual ignorance of problem solving heuristics.

    Of course, I still remember the Old new math, which was elementary set theory; very helpful. I still think of math in set theoretic terms, when I’m not thinking in geometric terms, that is.

    http://www.youtube.com/watch?v=SXx2VVSWDMo&feature=related

    On the other hand, I have encountered students in logic who were petrified by any symbolic notation, other than arithmetic. When confronted with novel symbols, they were too scared to think. Something went wrong when they being taught math. And it was a shame, because they were industrious; they kept coming for tutoring, they really tried to follow the reasoning, and many times they could follow, but they just couldn’t replicate it on their own. It was as though they had a circuit blown in their minds.

    It was almost as though somebody sabotaged their ability to learn the simplest novel formal systems. And it was sad.

  60. PHilemon:

    Edit: “Something went wrong when they being taught math.” Should be: “Something went wrong when they were being taught math.”

  61. mandolinjon:

    I share your frustration about the mathematics knowledge retained by today’s graduates of high school. I taught mathematics and science in junior high 50 years ago and taught physics and physical science in a California State University over the last 30 years. So I am part of the problem. Your title is correct. One of the main reasons that the mainstream media and politicians have been able to hoodwink the world in believing there is man-made catastrophe at hand due to global warming is that many people including college graduates are innumerate. For example, one point that struck me very early in my introduction to global warming is that a gas, CO2 in the quantity of 300 ppm could be a major cause of climate change. Now 300 ppm is a very small fraction of the gas in the atmosphere and it would have to have a strong mechanism for absorbing energy from the sun to produce a 1 degree C temperature rise in 100 years. If you do not know that 300 ppm is small fraction of the atmosphere, then you might think 300 is really a large quantity. In analogy a football field is 100 yards long and 0.0003 is 0.03 yards or 0.36 inches, a very small fraction of the total length. When the proponents of global warming told me that 300 ppm was enough CO2 to raise the earth’s temperature one degree and I became skeptical and nothing has been revealed since then has removed my skepticism. The observation that I have made is that most people do not have an appreciation for importance of mathematics and they do not have a feel for what a number and the units mean. Three hundred seems pretty large, doesn’t it? 400 is larger.
    One of the biggest culprits in mathematics education is the hand held calculator or its baby, the lap-top computer. If I push a bunch of buttons out pops an answer. But how do you know this number is correct or has any meaning for the question? Why is this ability missing today? Mental calculations and estimating are not taught any more because we can use a calculator and it performs the operations perfectly. Right? Only if you push the buttons correctly and in the correct order and know the units will the answer be meaningful. When I was in college, we used a device called the slide rule. It didn’t have any numerical output to 10 decimal places. You had to mentally estimate the size of the answer in order to place a decimal point or an exponent in your answer. Now if an answer came from a computer, it has to be correct. Just like the models for global warming use very big computers and therefore they must really be correct. As a result being innumerate, people rely on science experts or talking heads on television to keep them informed about what is correct. They do not have the mathematical ability to delve into the science nor can they read and understand the science or the mathematics presented. So it is easy convince these people that a carefully drawn graph that looks like a hockey stick shows that the world is doomed if the CO2 continues to increase in the next 4 years.
    Bring back mental arithmetic.

  62. Caine:

    Waldo,

    I also do not see proof of collusion or conspiracy, nor do I think there are any evil agendas at play on either side of your deniosphere. It is a moot point, however. It doesn’t matter how unqualified or questionable the members of either side of the argument are because there is no room in the scientific method for proof by contra-positive. The scientific method places the burden of proof squarely on the empirical evidence from tested hypothesis, and, therefore, directly on the scientific observer by proxy. The least scientific among us is equally qualified to question the validity of any theory or model regarding AGW.

    I have questioned AGW from the beginning simply because none of the evidence I have ever seen has given me a compelling sense that it is the whole truth. Counter-AGW evidence has left me similarly underwhelmed, but it’s not their responsibility to suggest a valid counterargument. I throw my lot in with the skeptics by default in this case in defense of the institution of science, regardless of how irritating or illogical I find many of the unqualified, pseudo-scientific arguments to be. I side with them because I find AGW to be a basically unprovable theory either way, and therefore unworthy of a very costly change in global lifestyle.

    And if I find a bit of occasional amusement in making them squirm like a worm on a fish hook, well, that’s because I am both a scientist and a troll.

  63. Waldo:

    Interesting Caine. I guess one must throw his or her lot into one stable or the other. For my own part, I tend to give the benefit of the doubt to the scientists with their degrees, labs, equipment, time and expertise. But that’s just me.

    I’m not sure I buy this statement: “The least scientific among us is equally qualified to question the validity of any theory or model regarding AGW.” Ummm…don’t mean to be rude, but…that doesn’t even meet the criteria for common sense. And I wasn’t sure what a “contra-positive” is – maybe that’s jargon for something. You being a scientist and all…

    I posted this somewhere else on this blog, but what I don’t understand is what sort of “empirical evidence from tested hypothesis” the doubters are looking for. In my admittedly layperson’s understanding, the “evidence” for GW comes from observable data – in fact, I already posted this on another thread and got no real response, so I’ll re-post it here.

    I go to Real Climate or any of the government scientific sites I find links to code, publications, and data. It’s all out there for the world to see. I am also confused because, again whenever I visit one of these sites I mentioned above, the claims for climate change comes from observable data (weather stations, satellites, boreholes, tree rings, etc.) so I’m wondering what “reproducible results” people are looking for? Can’t we make scientific deductions from the properties of physics and observations as we do for, say, a supernova which, obviously, is a little hard to reproduce? Do we also doubt geologists because they cannot reproduce a subduction zone in a lab or volcanologists because they cannot create a magma chamber? These may be dumb questions for a scientist like yourself, but as a layperson I have to wonder.

    Likewise, isn’t it well established that CO2 is a greenhouse gas? With results reproducible in a laboratory? I sometimes feel that the people on this site reason the same way anti-evolutionists do when they claim as evidence for creationism that fact that evolutionary biologists cannot present a half-man / half-monkey missing link or when creationists cite the Piltdown Man (nearly a century old by now) as evidence for vast fraud or quote creationist science on dinosaurs living at the same time as humans as proof that the world is 5,000 years old. But maybe that’s an unfair analogy…

  64. hunter:

    I wonder why our AGW troll pretends the code is ‘all out there to see’ at the AGW promo sites,w hen it is proven that is not the case?

  65. hunter:

    And- sorry, hit submit too quickly-
    To be on this site and to fall back on the empty strawman of pretending that since CO2 is a ghg, then all of AGW theory is correct, is an an exercise of willful ignorance about this site and most skeptics, only matched by the sad attempt to link creationism to AGW skepticism.

  66. Caine:

    Proof by contrapositive is a logical proof where one state is proven to be true because all other possibilities are proven false. Applied here it means your point will never be proven regardless of how many skeptical opinions or arguments you shoot down or how many scientists’ credentials you attempt to discredit.

    I’ve been on Real Climate. I’ve been on many government sites. I’ve followed links to original journal articles in peer-reviewed journals. I’ve done a fair amount of research because there are so many conflicting reports from scientists with impeccable credentials on both sides of the AGW hypothesis. I searched because I was sure that a direct review of the reported empirical findings would point me towards an overreaching consensus from the majority of the world’s scientists.

    The only thing I have found with any certainty is that there is no major consensus in the scientific community. For every climate scientist who says AGW is a real threat, there is another equally qualified climatologist who quotes the exact same graphs, charts, and journal articles and comes up with the exact opposite conclusions. There is no smoking gun; there is no absolute proof, so there will always be people on both sides of this argument.

    Proof is very hard to come by, and rightly so, since disproof only requires one counterexample and AGW provides a nearly endless supply of them.

  67. hunter:

    Caine,
    You have stated the case very clearly.
    The historical record does not indicate that we are experiencing anything particularly unusual or foreboding, much less dangerous. AGW theory postulates that we are experiencing something unprecedented and dangerous, but based on what?

  68. Waldo:

    Again interesting, Caine.

    I like the definition of “contrapositive” although I failed to see exactly how my “point will never be proven regardless” – just didn’t follow the line of reasoning. But it does not matter. There is, if the polls are to be believed, a consensus among scientists about the issue and I am not aware than anyone has “proven” AGW to be false. So a contrapositive position has not yet be proven, if I understand correctly. Anti-AGW I like

    Pielke
    Bryson (although he only made a few off the cuff remarks during an interview)
    Spenser
    Richard S Courtney
    Timm Ball

    Who do you follow? What journal articles have you read?

    For my own part, I have not found an infinite number of impeccable scientists on both sides of the issue – and that is one of the main problems with us laypeople trying to decipher the AGW science. As a whole I would trust the pro-AGW scientists by a mile…but I have posted so much on this point it has become tiresome and shall not do more. Suffice that I have and continue to be underwhelmed by a great many arguments, many posted here on CS.

  69. Ron H.:

    Has everyone forgotten trig? I’m ashamed to say I forgot SOH-CAH-TOA.

  70. Ron H.:

    Steve, it would seem that all this time you have been using the wrong methods in your lengthy and frustrating attempts to pry data and code from climate scientists. According to Waldo, all you ever needed to do was read RC.

  71. Waldo:

    Very intelligent riposte, Ron. Surely “prying” information is very difficult when scientists publish their stuff on the web and in scientific journals and such. Darn scientists!

  72. hunter:

    Waldo,
    Since the scientists in question did not, in fact, publish their code on the web or in journals, yes it was hard to pry the information out.
    It is surprising, even for a troll, to not find some new dodge when the old one is so well falsified.

  73. Waldo:

    Try here at Real Climate: http://www.realclimate.org/index.php/data-sources/#GCM_code

    For data sets, try the IPCC data distribution center: http://www.ipcc-data.org/ar4/gcm_data.html

  74. Waldo:

    For data and information, see the IPCC data distribution center: http://www.ipcc-data.org/ar4/gcm_data.html

    For code see RC: http://www.realclimate.org/index.php/data-sources/#GCM_code

  75. Waldo:

    Well, for some reason I can’t post the urls. So, hunter my man, google key words:

    “Real Climate code”

    “IPCC data distribution center”

  76. Waldo:

    Oops. Not sure how that happened…oh well, thread is dead anyway.

  77. hunter:

    Waldo,
    Do you beleive that when Jones and pals were talking aboutt how to hide the data, and to not release the data, and to destroy the data, irt requests for the same, that they were simply pretending?
    Do you think that Briffa did not in fact hide the data for nearly ten years regarding his phony tree ring study?
    Showing that code is available does not prove that the above mentioned issues were not true, nor does it show that in fact all relevant code has in fact been made transparently available.

  78. Waldo:

    Sorry man, I am not convinced of any of the above. Posted that before. Code there. Data there. You are falling back on blog propaganda.

  79. Waldo:

    Wanna know something funny? The above blog post and math test comes from Professor Cliff Mass from W Washington. Sorry folks, Cliff Mass is a proponent of AGW. Read his blog here

    http://cliffmass.blogspot.com/2009/08/global-warming-misconception-ii-and-san.html
    and here for his take on Climategate
    http://cliffmass.blogspot.com/2009/12/climategate.html

    But this was the most interesting thing he says -

    “There is an almost tribal separation going on today between the scientific community and their ‘allies’ (generally of a liberal persuasion) and the denier and critic crowd (many of them of a conservative bent). The denier folks have become angry, with conspiracy theories and accusations of far-left agendas. Whenever there is an article on climate change in newspapers, these people leaves large numbers of online comments. And few of them are well informed about the science. And there is a lot of misinformation on the “pro” global warming side as well. Scientists, unaccustomed to being on the firing line, have gotten defensive–and the emails from climategate really document this attitude.”

    Interesting, no?

  80. Angus S-F:

    Warren

    VERY interesting graph here:

    Mike Flynn’s Journal – Sufficient Causes
    http://m-francis.livejournal.com/47705.html

  81. hunter:

    Waldo,
    I would suggest that you will never be convinced.
    You are immune to evidence. You are not really as clever as you wish.
    Sort of like Baghdad Bob.

  82. BobC:

    Waldo:

    Edmund Scientific use to (about 40 years ago!) include a pamphlet in every order that explained the “scientific method” — you should try to find a copy and read it.

    The beauty of making data and analyses available for others to replicate if they can and criticize if they can’t is that it doesn’t matter who works for whom and how much money they make — the data and analyses speak for themselves.

    When “scientists” (and I use the term loosely) keep their data and analysis algorithms secret, then you have no option but to trust them or not. You would be advised to not trust people who don’t want others to check them. It doesn’t count if they are “checked” by their friends (who also keep the data, etc. secret). This kind of behavior almost always means that you are being conned.

    There is only one side in this debate that behaves this way (keeping crucial data and analyses methods secret) — the AGW side. (Read the CRU emails, for Pete’s sake, if you don’t believe me.)

    If you’re too dumb to spot when you’re being conned, that’s your business. The rest of us here have a little more sense.

  83. Waldo:

    Oh Bob, pulll-eeeease. Look at the links above (I accidentally posted them 7 times) – data there, my man. Plenty more other places too. You just don’t want to admit it. Cling to your rationals and the reality is only a Google search away. And yeah, I’ve read the CRU emails – nothing there except allegations from people like yourself.

    How do you suppose ‘your’ side of the ‘debate’ is behaving? You may not have as much sense as you assume you have.

  84. BobC:

    Waldo:
    “pulll-eeeease”! Now there’s a coherent argument. Perhaps it the best you can do.

    You ask: “…what I don’t understand is what sort of “empirical evidence from tested hypothesis” the doubters are looking for.”

    A simple answer is “demonstrated predictive skill of climate models”.

    Before this would be accepted, however, both the data and the models would have to be available and replicated. Currently, the data and models are not open source but that doesn’t matter as climate models currently have demonstrated predictive skill statistically indistinguishable from zero.

    The AGW alarmists claim to be able to predict the climate for 50-100 years in advance. On the basis of this claim, they insist that the main energy source of modern civilization be abandoned with probable dire results.

    This is a remarkable claim, as climate is aggregate weather and weather is known as a chaotic system, predictable for only a few days ahead. Surely the burden of proof lies with those who claim to be able to predict a chaotic system.

    What would constitute such proof would be demonstrated predictive skill, as mentioned above. Unfortunately for the AGW alarmists, climate models exhibit no such skill.

    What is offered as “proof” instead? Peer reviewed papers that don’t include enough data to replicate the results — you are asked to simply believe the authors on faith. Unlike you (I’m guessing) I’ve actually participated in the peer review process (on both sides). The purpose of peer review is to keep journal editors from being embarrassed by publishing something their readership considers nonsense (Hence the review by “peers” — e.g., readers of the journal). There is NEVER enough information in a submitted paper to allow replication — peer review is incapable of determining what is correct.

    Again, what would be necessary (if not completely sufficient) to “prove” climate models correct would be predictive skill, of which they currently show none.

    “And yeah, I’ve read the CRU emails – nothing there except allegations from people like yourself.” Really? Just what do you make of threats to destroy data instead of releasing it under FOIA? Do you imagine this is just “normal scientific process”? How dumb are you, really?

  85. JM:

    To be correct for 3b, you should indicate that the angle opposite c is a right angle (or say it is a right triangle), otherwise it becomes an exercise using the law of cosines. Then again, I see it’s corrected in the answered version.