It's D&N quiz time again! Let's get straight into it!

Starter for one: Who said this? ...

“…we should recognise that we are dealing with a coupled nonlinear chaotic system, and therefore that the long-term prediction of future climate states is not possible.”

No? A rabid climate change denying fossil fuel company CEO? Me? Well yes, obviously in my case. But in the case of the fossil fuel company CEO - and all CEO's for that matter - they'd rather chew their own dicks off than utter a cancel culture provocation like that! Watch their depots get blockaded by Stinking Rebellion and Isolate Britain? Get voted off the board by the shareholders? Not bloody likely.

Astonishing though it may seem, *that was the UN's IPCC! *Yes, the doyen of anthropogenic climate change and "carbon causes warming" linear orthodoxy made that statement in their climate pronouncement named "IPCC AR4 WG1".

A series of articles on the WattsUpWithThat site by someone called Kip Hansen brought the claim to my attention, and the implications of it are explained in layman's terms beautifully in those articles, the first of which is linked here and the subject of this post ...

https://wattsupwiththat.com/2015/03/15/chaos-climate-part-1-linearity/

I'll overlay my commentary onto those articles one-by-one, per my post title.

So linear systems right, you remember them from school? You take a range of input values and you mark them up on the x axis. Then you process them one-by-one through a calculation to produce the output, with the caveat that you do not feed the output back into the input of the calculation in any way. You plot the output on the y axis.

In their strictest, simplest form, linear systems have their output directly proportionate to their input. For example: y = 2x. Take the input on the x-axis and double it, then plot that on the y-axis ...

*Linear system: A system in which alterations of an initial state will result in proportional alterations in any subsequent state.*

*In mathematics there are lots of linear systems. The multiplication tables are a good example: x times 2 = y. 2 times 2 = 4. If we double the “x”, we get 4 times 2 = 8. 8 is the double of 4, an exactly proportional result.*

To help us along, let's use a maths run-book rather than stale graph images shopped by someone else. Take a hike over to the Desmos site, in particular, click this run-book example ...

https://www.desmos.com/calculator/smufmlkkam

Let's explain what's going on here.

In the body of the chart you can see the x axis going from -10 to 10, and the y axis running from -15 to 15.

Also in the body two linear equations are plotted, one red, one blue, and their crossing point a green dot.

In the run-book steps panel you can see three steps. Steps 1 and 2 are the formulae of those two equations plotted in the chart. Don't worry about them yet, we're going to delete them in a sec and do our own anyway. And the third step is the cross over point: -1 on the x axis and 3 on the y axis: (-1,3).

The run-book works its way down the steps plotting the results of the formulae and points that you've "coded" into the steps.

So, click on the "X" on the right of each step and delete the three of them. Your chart should be blank and the run-book steps empty and waiting for you to input your equation(s).

Click in the step 1 formula field and type: y = 2x .

You'll notice a purple line drawn across the chart from bottom left to top right. Congratulations! You've just coded your first linear system equation in the Desmos run-book tool! Much quicker than plotting the dots on graph paper like we old farts and fartettas used to do at school!

To check it's working, pick a value on the x axis, like 2 for example. Trace it up to the purple line and then across to the y axis, you get 4. So y = 2x, putting x = 2 into the formula yields y = 2 times 2 = 4. So y = 4. Check - the purple line is correct.

Now you can play with the formula - knock yourself out!

Push the line up by adding 3 to the formula ...

y = 2x + 3

The line gradient stays the same but instead of running through the origin (0, 0) it runs through the point (0, 3) higher up the y axis. That's as complicated as it gets for linear systems: still proportionate but also offset by an amount.

Flatten the line by changing the 2x to 0.5x ...

y = 0.5x + 3

Now the line is flatter with a gradient of only 0.5 but still passes through the offset point (0, 3) instead of the origin (0, 0).

To change the gradient to a downward slope from left to right make the 0.5 negative, so -0.5x. To pass through a point lower on the y axis change the +3 to -3 ...

y = -0.5x - 3

Congratulations again! You've just mastered linear mathematics! You've gone bottom left to top right, top left to bottom right, changed the gradient, and raised and lowered the offset of the line. There isn't much more that you can do with a straight line on a two dimensional surface! That's a linear system for you.

Back to Kip's narrative ...

He makes a fantastic observation. It's one of a plethora of state education brain prepping techniques to turn pupils into linear minded simpleton authoritarian type people ...

*Aside: It is this feature of linearity that is taught in the modern schools. School children are made to repeat this process of making a graph of a linear formula many times, over and over, and using it to find other values. This is a feature of linear systems, but becomes a bug in our thinking when we attempt to apply it to real world situations, primarily by encouraging this false idea: that linear trend lines predict future values. When we see a straight line, a “trend” line, drawn on a graph, our minds, remembering our school-days drilling with linear graphs, want to extend those lines beyond the data points and believe that they will tell us future, uncalculated, values. This idea is not true in general application, as you shall learn.*

To be continued ...

SoD

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