27 September 2011 - Pure Muck

Post date: Sep 27, 2011 8:32:07 PM

When I was in college I took a course called "Great Ideas". The purpose of the class was to give students an introduction to the great philosophies of civilization: Religions, Sciences, Politics, etc.

I met a life-long best friend in this course. He is a smart fellow. He intrigued me throughout the Great Ideas course for his stoic silence. He would sit through every class with his arms crossed. Sometimes he would frown and sometimes he would look bored, but mostly he looked like was listening to the heated debates.

One day after class - before we became friends - I asked him what he thought of the discussion that day. In so many words, he said it was mostly garbage. I was floored. By definition the Great Ideas course should be full of great ideas, not garbage. I do not remember exactly how he explained his position, all those years ago, nor do I recall why that debate was a step on our path to friendship. What is important is that we are friends and my friend is right!

I will defend his position with my modern finite knowledge.

In my view, all of the "Great Ideas" are important because of their utility. Great Ideas help a person or a civilization to get along in this universe more efficiently and effectively.

Sciences predict an egg will plummet to Earth at 9.8 m/s² and break when dropped over a concrete floor from shoulder height.

Religions predict the eternal consequences for mortal actions.

Politics predict the life, liberty, and pursuit of happiness enjoyed by a populace that adheres to certain principles and codes of conduct.

To wit, the Great Ideas boil down to “Given this situation and this course of action then generally there will be this result.” That is science!

XKCD explains neatly that science, in its purist form, is applied mathematics.

Neat. However it is also a trap because mathematics is mostly muck. See Kurt Gödel’s incompleteness theorems…

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, a corollary of the first, shows that such a system cannot demonstrate its own consistency.

In short, if a system is advanced enough to explain something that is interesting in real life then that system can not prove itself to be true. All of the Great Ideas get murky when reduced to their purest essences. The clearer the Great Idea, the more murky its provability.

My friend is right. Great Ideas are garbage.

That does not mean the Great Ideas not useful, though!