19A050 How Hot is that Coffee? by Jim Davies, 12/10/2019    

Key articles of faith in the Algorian religion are that the Earth is warming, and that mankind caused it. But to maintain that faith and support it with fact and observation, it's essential first to draw a baseline; that is, to measure how hot or cold is or was the Planet before these alleged changes began - or at least now, in the present day. Temperature measurement is Job One.

So compare that large task to that of measuring the temperature of a mug of coffee. The Earth is roughly spherical while the mug is cylindrical, but that is a relatively small difference. The Earth has a solid crust but a somewhat viscous, liquid middle, and that's quite similar though the coffee isn't viscous - or if it is, it must be Espresso with the settings wrong. So the comparison is rough, but may be workable.

Our first difficulty, and it's not trivial, is to define what's meant when we ask for the "temperature of a mug of coffee." Are we interested in how warm the mug is, when touched from the outside? In how hot the liquid is, when drawn in to the mouth? Yes, and yes; but those two are quite different. The mug is made, probably, of earthenware - which is quite a decent insulator. So right off the bat, it's not even clear what the job definition means.

Next, let's suppose that we're given a very accurate thermometer, whose mass is so small that inserting it into the coffee, even though it will probably be hotter or colder than the fluid, will in no way change its temperature. That's the kind of "given" that one may read in an examination question, but it's impossible in practice; no thermometer exists with a zero mass. If precision is the aim, that problem is formidable. It's analogous to Heisenberg's uncertainty principle: how can one measure a temperature without changing it?

Undeterred by these grave obstacles, we approach the coffee with our ever-so-slender instrument. Where is it to be placed: in mid-mug, half way down? Or at the edge, where it meets the mug; and if so shall it be at the top, the bottom, or neither up nor down? These questions matter profoundly, if accuracy be our aim, for the coffee will certainly be a fraction of a degree hotter or cooler, depending on its position in the mug. And by the way, is it calm - or still swirling round after a stir? Such questions certainly affect the temperature measured.

Then there's the matter of timing, for the mug is subject, as are we all, to Newton's Law of Cooling (no, make that his Theory of Cooling, even though it's a very well-tested theory) and for every second that goes by, the temperature will assuredly fall. We are trying to measure a moving target.

All of these profound difficulties attend also the measurement of how warm or cool is the Planet Earth - but are almost infinitely greater.

The mug measures 10 cm high and 8 cm across, so as v = πr²h its volume is 502.65 c.c. - let's round that to 500, or half a liter; and its circumference at 2πr is just over 25 cm or 0.00025 kilometers. And it was very hard, as above, to tell how hot it is.

Earth has a circumference of about 40,000 kilometers and a volume of 1.1 x 10²¹ cubic meters, more or less. Since there are 1,000 liters in a cubic meter, that's 1.1 x 10²⁴ liters, or 2.2 x 10²⁴ times greater than our mug of coffee. Two trillion trillion times harder, arguably, to measure its temperature with high precision.

Despite all that, faithful Algorians insist that they know exactly how warm is our planet, to the nearest tenth of a degree Celsius - and even how warm it will get, during the next several decades. What utter hubris!

But it's not just their arrogance that is so offensive, there's also deception; seeing how hard it is to be honest, their "scientists" cook the books to make it appear they know what they are doing. At the University of East Anglia Prof. Phil Jones deliberately concealed research data that contradicted the conclusion he wished to reach; and almost the whole of the firestorm that resulted focused only on the fact that his misdeeds came to light by means of some less-than-honest hacking of emails - not on the misdeeds themselves.

The Church decided that the sun spins around the earth, so all contrary evidence be damned and all heretics, burned at the stake.

After that "church" (governments, worldwide) has imploded for want of workers, who knows, there may still be some kooks want to teach that up is down and hot is cold and that the Moon is made of green cheese. Perhaps they will found a college, in the fens of eastern England. But since all will have learned rational thinking, I doubt that they will attract many paying students; and certainly, they will not be able to dictate what the rest of us choose to do about any change in climatic conditions; for there will be no apparatus of force by which to impose their opinions.