New Metric Fables: the pottery kiln

Firing the Kiln

When the world was new, Laotzu and Confucius were potters and they spent long days working the bellows at their kiln to fire the pots. When Confucius kept track of quantities he used the metric system, while Laotzu used human-scale versions of the natural units. It was Confucius' turn to blow so he was pumping the bellows while Laotzu rested.

Before they started firing, Laotzu had made a hole in the side of the kiln and fitted a plug to it. The plug was about as thick as his little finger. From time to time, when he was curious about how it was inside, Laotzu would get up and take out the plug and look in the hole.

Confucius' plan was to bring the kiln up to 1417 Kelvin and then stop blowing and let the temperature coast back down. For Laotzu that meant bringing it up to 10 grade, which was fine with him. When he removed the plug he could judge by eye how many chi of power came out the hole and that gave him an idea of the temperature inside the kiln. A chi (about 36 watts) is a unit of power used by Taoist sages and it is intimately related to temperature and to the brightness with which hot things glow.

Because he could see in the infrared and could judge the keynote frequency in the light glowing from the hole Laotzu could tell the temperature that way as well. He could judge both from brightness and from color. He figured when the target of 10 grade was reached the keynote frequency, which is an index of the color, would be 10 trillion per trice.

Confucius had a radiant heat thermometer that had been sent him by the German company of Boltzmann-Stefan GmbH, but that morning he had forgotten and left it back at the house. After a while Confucius got tired of blowing into the kiln and he said to Laotzu: "You take over and I will go back and fetch the thermometer to see if it's hot enough." But Laotzu said: "Keep on blowing. I can see that it's not hot enough yet."

Laotzu reckoned by squaring the target temperature twice (which was easy with 10 grade and gave him 10 000) and multiplying by pi²/6, which is about 1.6. That gave him 16 thousand chi which is the power a square pace area would radiate at the target temperature. Of course the area of the peephole was much smaller than a square pace, it was in fact tenthousand times smaller, but he could adjust for that. The upshot was he knew that when the kiln reached 10 grade there would be 1.6 chi of radiant power coming from the peephole. You didn't have to be a Taoist sage to judge that level of radiant power, you could feel it on the palm of his hand. Put in familiar terms, since a chi is 36 watts, it's something like 60 watts.

After a while Confucius was finished with his turn pumping the bellows and Laotzu got up and removed the plug and showed Confucius that 1.6 chi was shining from the hole. Confucius said they could leave the kiln to cool. So they closed up the shed and went back to the house for tea.

notes on arithmetic:

In the language of Freshman Physics, pi²/6 chi per square pace per quartic grade would be described as the "Stefan-Boltzmann sigma". It is the constant in the "fourth power radiation law." You might be curious about how it looks in metric units. In metric terms sigma is:

5.67051...× 10^-6 watts per square meter per quartic Kelvin.

If Confucius had been willing to struggle with the arithmetic he could have squared 1417 twice (which gets messy) and multiplied by this "sigma" number (which is even messier) and eventually found out the power from the peephole in watts. Anything Laotzu could do with human-scale natural units could also be done with metric units — it is just more bother.