# Re: [asa] The Mathematics of Global Warming

From: Bill Powers <wjp@swcp.com>
Date: Sat Dec 12 2009 - 10:07:25 EST

John:

Not intending to comment on your application of the 1% rule to AGW, I
would like to comment on its insufficiency.

In agreeing to abide by the 1% rule in the case of seat belts and air
bags, we do so not merely because of the catastrophic consequences, but
also because we judge the cost of such precautions as commensurate with
the danger and our ability to pay.

When there are possible dangers and we are cognizant of them we take
some kind of precautions. But the measures and behavior we employ in
response is related to our available resources and the probability that
we judge the danger will occur.

We lock our house when we leave (at least some of us do), but we do not
hire an armed army, even though the probability of our house being
robbed may be far greater than needing our air bags. We employ air bags
and not uranium alloys to protect our cars and its occupants.

So it seems that "rationally" we make cost-benefit analysis in
conjunction with an assessment of the probability of an event (perhaps
the latter is contained within a cost-benefit analysis).

By saying 1% and not 0.0001% entails that we judge the probability to
not be so small that we can ignore it. Additionally, the 1% rule entails
that we judge the consequences to be "catastrophic." But neither of these
tell me what to do because they say nothing about the relationship between
the amount I invest in preventing the catastrophe and the rate at which
both the probability of the event and the severity of the consequences
decrease. Without an assessment of these, I can not distinguish the fool
from the wise.

bill

> William makes a compelling argument here why the climate models may be
> incorrect.
>
> Let's use Dick Cheny's "1% rule," which he used to justify the Iraq
> invasion. This rule states that if there is even a very small chance
> of a catastropic event then one is justified in taking measures
> against it. In the Iraq case, Cheney was speaking of thepossibility of
> WMDs.
>
> The obvious application to you and to me is the seatbelt rule. The
> chances of me being in a catastropic accident are very very small
> (I've driven and been driven for over 70 years and it hasn't happened
> yet). Yey I put on my seat belt and happily pay the extra \$\$ for an
> airbag in my vehicular contrivance -- because of the 1% rule. It is a
> good rule.
>
> So -- apply this to the IPCC reports. They run multiple models and all
> say we are in serious trouble. Maybe they are all wrong. Maybe the
> science is not as robust as some people think. Let's take the most
> optimistic view of all this we can. Is there even a 1% chance the IPCC
> is right and the denialists are wrong? Even a 0.1% chance?
>
> It seems to me -- in this case -- we ought to be taking all measures
> to prevent a global catastrophe. Even if it costs us something. Even
> if it costs us a lot.
>
>
>
> On 11/30/09, William Hamilton <willeugenehamilton@gmail.com> wrote:
>> Hi John
>>
>> I'm not a mathematician, but I spent 33 years developing computer models of
>> various systems. Most of the systems I modeled were pretty well-behaved, but
>> in the mid 70's I developed a radar bomb-scoring system (RBS) for the Navy.
>> The Navy uses huge quantities of ordnance in training. Not only is this
>> costly it leaves tons of unexploded ordnance around that eventually has to
>> be cleaned up. And the noise annoys civilians, making it necessary to do
>> training in remote locations. They wanted me to write a program that would
>> track an aircraft making a practice bomb run and simulate the bomb
>> ballistics to determine whare the bomb would land. In addition to being able
>> to detect the moment when the bomb was released, we had to determine or
>> estimate the bomb's initial velocity with respect to the aircraft and
>> correctly model the bomb's aerodynamics, which were highly nonlinear. There
>> was an additional complication: some bombs, known as cluster bombs,
>> consisted of a shell containing a number of smaller "bomblets". At a
>> specified altitude the shell would open and the bomblets would be released.
>> Of course the bomblets had completely different aerodynamics from the shell,
>> so the solution had to be stopped an restarted with new initial conditions.
>>
>> We tested the RBS system by having aircraft drop real practice bombs (bombs
>> without explosives but with the correct mass and aerodynamics) and comparing
>> the real impact point with the predicted. As I remember the results were
>> close enough to be usable, but had the bombing been from any higher altitude
>> or had the aircraft been taking evasive action they wouldn't have been.
>> Variations in barometric pressure and humidity affected the results too.
>>
>> But trying to predict climate years in advance is a great deal more
>> difficult than trying to predict a bomb trajectory from an aircraft flying a
>> few hundred to a few thousand feet above the deck.
>>
>> I've spent some time looking at computer models of climate. Most of them are
>> too complicated to be easily analyzed. Even a retiree has limited time :-).
>> And most of them are too big to be run on the equipment available to me: a
>> macbook pro. But the complexity of the models argues for careful assessment
>> by people not having a vested interest in the accuracy of the models. I
>> don't know whether this has been done.
>>
>> However there is one paper by Tobias and Weiss: Resonant Interactions
>> between Solar Activity and Climate that you can get at
>> http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175%2F1520-0442%282000%29013%3C3745%3ARIBSAA%3E2.0.CO%3B2
>> that uses the Lorenz equations to model the earth's climate. They find a
>> stochastic resonance phenomenon that can result in warming of the earth's
>> climate with very small variation in solar activity. Now one might rightly
>> question the simplification of using the Lorenz Differential equations to
>> model the earth's climate, but still the model points out a possible
>> connection between solar activity and earth's climate. I made a fairly
>> extensive study of the CCSM climate model, one of the models commonly used
>> by the GW community, and solar input is just a constant, so that model
>> doesn't model solar variation at all. The GISS model is somewhat more
>> difficult to analyze, and I haven't yet determined how or whether they model
>> solar variation.
>>
>> Another approach to studying climate dynamics is that used by Scafetta. His
>> web site is http://www.fel.duke.edu/~scafetta/ on which he has reprinted
>> many of his papers. In addition there is a video of a talk he gave at the
>> EPA back in February that is worth watching. Among other things Scafetta has
>> done extensive analysis of the statistics of climate data and solar output
>> and found "echoes" of the solar input in the climate data, leading him to
>> conclude that solar variation is exciting global warming. (I'm not doing
>> justice to Scafett' research, which is extensive)
>>
>> So, while I admit the possibility that the various climate models used by
>> IPCC could be correct, I am very leery of basing policy decision on them
>> until more analysis of the models and their input data and results is done
>> by an impartial party.
>>
>>
>> On Mon, Nov 30, 2009 at 6:34 AM, John Walley <john_walley@yahoo.com> wrote:
>>
>>> I found this to be very interesting. I wonder if any of the mathematicians
>>> on the list have any comment?
>>>
>>> John
>>>
>>> November 30, 2009
>>> The Mathematics of Global Warming
>>> By Peter Landesman
>>> http://www.americanthinker.com/2009/11/the_mathematics_of_global_warm.html
>>>
>>> The forecasts of global warming are based on the mathematical solutions of
>>> equations in models of the weather. But all of these solutions are
>>> inaccurate. Therefore no valid scientific conclusions can be made
>>> concerning
>>> global warming. The false claim for the effectiveness of mathematics is an
>>> unreported scandal at least as important as the recent climate data fraud.
>>> Why is the math important? And why don't the climatologists use it
>>> correctly?
>>>
>>> Mathematics has a fundamental role in the development of all physical
>>> sciences. First the researchers strive to understand the laws of nature
>>> determining the behavior of what they are studying. Then they build a
>>> model
>>> and express these laws in the mathematics of differential and difference
>>> equations. Next the mathematicians analyze the solutions to these
>>> equations
>>> to improve the understanding of the scientist. Often the mathematicians
>>> can
>>> describe the evolution through time of the scientist's model.
>>>
>>> The most famous successful use of mathematics in this way was Isaac
>>> Newton's demonstration that the planets travel in elliptical paths around
>>> the sun. He formulated the law of gravity (that the rate of change of the
>>> velocity between two masses is inversely proportional to the square of the
>>> distance between them) and then developed the mathematics of differential
>>> calculus to demonstrate his result.
>>>
>>> Every college physics student studies many of the simple models and their
>>> successful solutions that have been found over the 300 years after Newton.
>>> Engineers constantly use models and mathematics to gain insight into the
>>> physics of their field.
>>>
>>> However, for many situations of interest, the mathematics may become too
>>> difficult. The mathematicians are unable to answer the scientist's
>>> important
>>> questions because a complete understanding of the differential equations
>>> is
>>> beyond human knowledge. A famous longstanding such unsolved problem is
>>> the
>>> n-body problem: if more than two planets are revolving around one
>>> another,
>>> according to the law of gravity, will the planets ram each other or will
>>> they drift out to infinity?
>>>
>>> Fortunately, in the last fifty years computers have been able to help
>>> mathematicians solve complex models over short time periods. Numerical
>>> analystshave developed techniques to graph solutions to differential
>>> equations and thus to yield new information about the model under
>>> consideration. All college calculus students use calculators to find
>>> solutions to simple differential equations called integrals. Space-travel
>>> is possible because computers can solve the n-body problem for short times
>>> and small n. The design of the stealth jet fighter could not have been
>>> accomplished without the computing speed of parallel processors. These
>>> successes have unrealistically raised the expectations for the application
>>> of mathematics to scientific problems.
>>>
>>> Unfortunately, even assuming the model of the physics is correct,
>>> computers
>>> and mathematicians cannot solve more difficult problems such as the
>>> weather
>>> equations for several reasons. First, the solution may require more
>>> computations than computers can make. Faster and faster computers push
>>> back
>>> the speed barrier every year. Second, it may be too difficult to collect
>>> enough data to accurately determine the initial conditions of the model.
>>> Third, the equations of the model may be non-linear. This means that no
>>> simplification of the equations can accurately predict the properties of
>>> the
>>> solutions of the differential equations. The solutions are often unstable.
>>> That is a small variation in initial conditions lead to large variations
>>> some time later. This property makes it impossible to compute solutions
>>> over
>>> long time periods.
>>>
>>> As an expertin the solutions of non-linear differential equations, I can
>>> attest to the fact that the more than two-dozen non-linear differential
>>> equations in the models of the weather are too difficult for humans to
>>> have
>>> any idea how to solve accurately. No approximation over long time periods
>>> has any chance of accurately predicting global warming. Yet approximation
>>> is exactly what the global warming advocates are doing. Each of the more
>>> than 30 modelsbeing used around the world to predict the weather is just a
>>> different inaccurate approximation of the weather equations. (Of course
>>> this is only an issue if the model of the weather is correct. It is
>>> probably
>>> not because the climatologists probably do not understand all of the
>>> physical processes determining the weather.)
>>>
>>> Therefore, logically one cannot conclude that any of the predictions are
>>> correct. To base economic policy on the wishful thinking of these
>>> so-called
>>> scientists is just foolhardy from a mathematical point of view. The
>>> of the mathematical community, ensconced in universities flush with global
>>> warming dollars, have not adequately explained to the public the above
>>> facts.
>>>
>>> President Obama should appoint a Mathematics Czar to consult before he
>>> goes
>>> to Copenhagen.
>>>
>>> Peter Landesman mathmaze@yahoo.comis the author of the 3D-maze
>>> bookSpacemazes for children to have fun while learning mathematics.
>>>
>>>
>>>
>>>
>>>
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>>>
>>
>>
>>
>> --
>> William E (Bill) Hamilton Jr., Ph.D.
>> Member American Scientific Affiliation
>> Austin, TX
>> 248 821 8156
>>
>
>
> --
> Burgy
>
> www.burgy.50megs.com
>
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Received on Sat Dec 12 10:07:52 2009

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