Most academic concepts have fairly narrow usage. You can draw analogies between fields, but these connections usually rest on you understanding both sides of the metaphor sufficiently well.
Consider the Fresnel equation in physics. With some effort you might be able to draw an analogy between this equation and another domain. But I’d doubt you could say that understanding the equation led to overflowing insights in history or art.
However, hidden within all the ideas with tenuous crossover implications, there are rare ideas which seem to illuminate far beyond what they were originally designed to explain.
The problem, of course, is that academic subjects are generally pursued in isolation. Each profession learns the paradigms and tools of their trade and only borrows from other schools of thought when those ideas are directly relevant to research. Specialization, not general purpose thinking, is the norm.
With that, I’d like to pose the following question: what are the intellectual ideas you’ve mastered, which have broad scope in understanding the world?
My Picks for Powerhouse Ideas
I’ll kick off the discussion with my picks for ideas which everybody should know.
1. Evolution and Natural Selection
This is an idea everyone has an opinion about, but few people really understand. Once understood, however, the analogy is powerful for explaining how complex systems develop and change over time. Languages, businesses, technology, social customs and diets are just a few of the areas which borrow similarities to biological evolution.
Some resources I recommend which show the breadth of the idea:
- The Selfish Gene 
- The Red Queen 
- The Language Instinct 
- Why Do Beautiful People Have More Daughters? 
2. Bayes’ Rule
Bayes’ Rule has been described as the secret of the universe. It is a simple mathematical formula which helps you calculate the probability of an event. On the surface, just a formula you would memorize and apply on an exam and immediately forget. But going deeper, you can see how it may even be the basis of all rational thought.
The best introduction to the rule is Eliezer’s guide: An Intuitive Explanation of Bayes’ Theorem , although the implications of this snippet of mathematics may take you years to unravel.
3. Economic Efficiency
In 1776 Adam Smith wrote On the Wealth of Nations, which would later become the foundation for modern economic theory. He laid out the basics of how automatic forces guide and improve our material existence.
The idea of efficient markets is a controversial one, if only because there are many instances when the forces Smith recognized can break down. But that doesn’t make the idea any less powerful as an explanatory concept. Just because we rarely see ideal spheres on frictionless planes, doesn’t mean classical mechanics isn’t useful for explaining motion.
4. Signalling and Game Theory
Along with evolutionary psychology, signalling  is perhaps the best single theory for explaining human behavior. The basic idea is that we take actions not only for their direct consequences, but to communicate and deceive others who have imperfect information.
Game theory is a useful intro topic since understanding the basics of static and dynamic games, and getting the mathematical intuition behind them, makes it easier to fully see signalling play out in everyday life.
5. Biases and Heuristics
The field of biases and heuristics in psychology is a popular one nowadays, with websites like LessWrong  dedicated to the art of human rationality. Even if it is a popular field, that doesn’t downplay its importance. By understanding the errors humans make in reasoning, we can at least understand our frailties, even if we cannot fix them.
As an aside, I considered myself well-versed on this topic before reading Daniel Kahneman’s book, Thinking, Fast and Slow , however even I found dozens of new insights, so I strongly recommend reading the book even if you’ve been exposed to this concept previously.
6. Gödel’s Incompleteness Theorem
I picked this one as a last concept, not because it is universally useful, but because of how profound the result is. Basically, Gödel proved logically that there exist true things which can never be proven, or alternatively, that there are truths which can never be known.
If you’re feeling like going down the rabbit’s hole, I suggest this book: Gödel’s Proof .
Now It’s Your Turn
I’ve given my shortlist, now I want yours. What’s an intellectual idea that you feel everybody should know? Bonus points for any ideas that are largely removed from pop psych or self-help. Please give your idea, along with why it is so broadly useful, in the comments .