All Concepts Are Simple

Believing BullshitI’ve been reading Believing Bullshit by Stephen Law. I’ll write about it more later. For now, I just want to mention something about his chapter on Pseudoprofundity. This especially has to do with postmodern academics where traditionally the field has been so weighted down with jargon that there is often nothing other than the jargon.

In my experience with science, I have found that pretty much all concepts are really simple. In order to be precise, scientists and philosophers weight down these concepts with a lot of baggage. But if students are trying to learn something and they find it difficult, they are probably missing the concept.

Here is an excellent example. Nothing is more mind blowing than Godel’s Incompleteness Theorem. This theorem says that any mathematical system (e.g. Euclidean Geometry) can never be fully formed. There will always be things that are true inside that system that cannot be proved to be true. Here is a simple proof of this from Infinity and the Mind by Rudy Rucker:

The proof of Godel’s Incompleteness Theorem is so simple, and so sneaky, that it is almost embarassing to relate. His basic procedure is as follows:

  1. Someone introduces Godel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
  2. Godel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
  3. Smiling a little, Godel writes out the following sentence: “The machine constructed on the basis of the program P(UTM) will never say that this sentence is true.” Call this sentence G for Godel. Note that G is equivalent to: “UTM will never say G is true.”
  4. Now Godel laughs his high laugh and asks UTM whether G is true or not.
  5. If UTM says G is true, then “UTM will never say G is true” is false. If “UTM will never say G is true” is false, then G is false (since G = “UTM will never say G is true”). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
  6. We have established that UTM will never say G is true. So “UTM will never say G is true” is in fact a true statement. So G is true (since G = “UTM will never say G is true”). “I know a truth that UTM can never utter,” Godel says. “I know that G is true. UTM is not truly universal.”

If I could impart any wisdom to young learners, it would be this: all concepts are simple. This of course helps in a general sense: it allows people to drill down to the bottom of what they are learning. But there is another aspect of this. It frees the student to ask what he may think of as dumb questions. If you have a professor who is droning on about something that seems very complex, just call him on it. “Excuse me professor: this seems awfully complicated. What is the concept you are trying to relate?”

Afterword

When I taught physics, students would often tell me that they understood the concepts but that the math was hanging them up. This caused me, over time, to eliminate the math and just deal with the concepts. And what did I find? They didn’t understand the concepts either. I said these concepts are simple—not trivial. One thing was for sure: the math was blinding them to the concepts. By focusing on the concepts, they found that the math was fairly simple.

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About Frank Moraes

Frank Moraes is a freelance writer and editor online and in print. He is educated as a scientist with a PhD in Atmospheric Physics. He has worked in climate science, remote sensing, throughout the computer industry, and as a college physics instructor. Find out more at About Frank Moraes.

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