Today, a new take on ignorance. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.
Questions fascinate me. Try five familiar ones:
First: Have you stopped beating your wife?
Second: Hi, how are you?
Third: What is that supposed to mean?
Fourth: When does the next bus leave?
Have you considered the Gertz lemma in your calculation?
That last questioner is pretty sure that you've made a damaging oversight. But then, the only real question in this list is "When does the next bus leave?" "Hi, how are you?" was never meant to be answered. The other three are intended to trap, to accuse, or simply to show off.
I'm pretty sure that the only real function of a teacher is to guide students in asking and pursuing questions. Once a student develops the rare talent for seeking out his or her own ignorance, teachers become irrelevant. But it's hard to look at your own ignorance. And it's not easy to ask a true question. It feels like humiliation.
So let's liken the flow of knowledge to the flow of water. Water flows from high places to low places. It flows from a region of high pressure to one of low pressure. Knowledge likewise flows to the point of greatest ignorance.
Years ago I asked what the second law of thermodynamics was all about. My textbook put it this way: You can never build a heat engines that takes energy from a single heat source, does useful work, and has no other effect upon its surroundings. I thought I had an answer to my question -- that I understood the second law.
Then I heard someone say that the second law of thermodynamics gave an "index of the order of the disunity of the universe" (whatever that meant!) Now I had two wildly different answers to one question. My ignorance opened up before me, and knowledge was ready to flow in a way it had not flowed before.
When I owned the first answer I felt smart. But my smartness was a dam, preventing additional knowledge from flowing to me. Having two answers that didn't match, set up discomfort and dissonance. Where I'd been smart, I was now ignorant. The dam broke. I really began learning.
History offers many such cases. The checkered history of identifying the gas oxygen traces all the way from ancient alchemy to nineteenth-century atomic-based chemistry. At each troubled step, one more dam of expertise had to crumble so some bright person could again be blessed with the frustration of ignorance — with the needfulness that begets honest questioning.
The word ignorance carries so much negative freight. We use it to mean a lack of desire to know, or an inability to know. Well, put all that freight aside: To be ignorant and then crave to erase that ignorance — that is power. Whatever my business might be, I'm best served when I begin it by finding the place where I know the least. If I begin as the expert, I learn nothing. But, when I start out ignorant, then the fun really begins.
I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.
A more complete and precise statement of the heat engine statement of the second law of thermodynamics would go as follows:
It is impossible to create a heat engine which, operating in a cycle, would have no effect upon its surroundings other than cooling a single isothermal thermal reservoir and lifting a weight.