Our excuse? People waiting for accurate data. People looking for other causes like less albedo. |

With all due respect. Not meant in the Woody-Allen context (ie, the running joke in "Broadway Danny Rose" in which he completely eviscerates someone as being the worst possible person, which he ends with "And I say that with all due respect".)

We are in the middle of an emergency situation where seconds stopped counting years ago, and you want to take absolutely not action until we can prove completely and without a shadow of a doubt that we are completely to blame? Again, I am truly and honestly disavowing that Woody-Allen Gestalt.

Think of a critically ill patient. We do not yet know what is causing the illness and hence how to ultimately cure it. But that patient is running an extremely high temperature, one which can fry brain cells. If you take no action to lower that temperature, then it will kill the patient. But you don't know what's causing that high temperature, nor even whether it's the disease's fault. What do you do? Concentrate solely on identifying the pathogen and how to treat it, in which case the patient will almost certainly die in that process? Or treat the symptoms in order to keep the patient alive?

There's yet another way to look at it. Have you studied calculus yet? Have you gotten to partial differentiation in the third semester? Understanding the basic ideas of partial differentials is key here.

George Orwell ("1984") pointed out that while we use language to express ideas, it is also true that if you lack the language to express an idea, then you cannot express it -- eg, if you succeed in restricting the meaning of "freedom" to that of a lack of something, like fleas or lice, then nobody can think of the concepts of freedom of speech or freedom of religion, etc. Within the context of "1984", the fact that Newspeak's vocabulary was rapidly diminishing means that the ability to express so many of the ideas that we value the most were disappearing.

In order to express an idea, you need the language with which to express that idea. That also means that in order to express an idea for which the language does not exist to express it, then you need to invent that language. Mathematics is a language *. As Isaac Newton was discovering the basic physics by which universe operated, there existed no language with which to describe what he was discovering, so he invented one. A mathematical language called calculus.

In the university I attended, calculus was divided into three semesters -- I would assume that most schools divide the subject up pretty much the same. The first semester covers the definition of a function, the basic properties of functions, and differentiation. The second semester covers integration, which is basically the inverse of differentiation. The third semester covers more advanced subjects, such as power series, multiple integration (which my ex-wife could do in her head even though she totally rejected algebra for purely ideological reasons), and **partial differentiation**. And at the same time, you work with analytic geometry (studying the X-Y-Z curves of geometric shapes and the equations that describe them).

Differentiation is nothing more than looking at the rates at which a function changes at various points along its curve. When I was studying first-semester calculus on my own (the only way I have ever studied it: first with a Schaum outline and then through the local university's correspondence course, since I had arrived in the area very shortly after the date for registering), the proofs for differentiation made an enormous amount of sense since you can understand them mainly through algebra.

Now for the challenge. Do you remember graphing in high school math? You're on an X-Y grid. You draw a line that represents the equation that you are graphing. OK, so on that line/curve, pick two Xes. Look at each X's Y. Draw a line form one X's Y to the other's. That line has a slope, which is (y1-y0)/(X1-X0). Now -- and this is the calculus part -- what happens when that value, (X1-X0), goes to zero? That's the mind-blowing part that calculus plays here. That is what differentiation does for us. It figures out, for any point along the curve of a function, how rapidly that function is changing.

This paragraph is for everybody who will go on to study the mathematics. First semester calculus students learn what a function is (ie, for any single X-axis value, there is one and only one Y-axis value, among other things) and what limits are (ie, division by zero is not defined, but what happens when we *approach* zero? And what is the difference between approaching zero from the left and from the right?). That is handled in first semester calculus.

In the first two semesters, each function only has one parameter. The third semester deals with situations in which there are multiple situations. For example, in an equation in which there are four variables, we find that varying this variable caused the outcome to vary by this much. If we vary a variable that has less influence, then we find that outcome will vary less. And if we vary a variable that has more influence, then we will see that the outcome will vary more.

OK, in partial differentiation, the more influential factors will have more influence and the less influential will have less influence.

Let's return to our hypothetical sick patient,AKA "our planet". If we determine that we are not at fault, do we allow our "patient" (ie, our planet) to die? Or do we try to do everything we can to keep that patient alive?