2 by 2 matrices

Source: Sam Altman https://twitter.com/sama/status/497877205087555584

Simplify a system down to a 2x2 matrix and it says a lot about the system. These are useful to dissect a competitive landscape, understand society and understand religion.

Peter Thiel famously used 2x2 matrices to understand the innovativeness of cultures at a societal and company level in Zero to One. It's also common for competitor analysis and it makes an otherwise completely subjective act of comparing yourself to other companies ("company A doesn't have [very niche feature] but we do.") to a relative act where you can decide if the comparisons are valid and if the axes of measurement are relevant e.g. maybe a very niche feature isn't a relevant point of comparison. The early Airbnb and LinkedIn pitch decks use a 2x2 matrix this way.
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More interestingly on a societal level 2x2 matrices uncover what is going on below the surface. These insights I attribute to Jim Keller who I am sure can attribute some of these to other people as well.

In a society there is a king, his ministers and the people. The king has power and money of course, the ministers have money, yes, but no power as they are totally at the mercy of the king. The people have neither money nor power. This looks like a stable system. However, when there is three of anything consider that there is a hidden fourth quadrant. If you break down the three into constituent parts you can find the hidden fourth.

The Hero is the hidden fourth and derives his/her power not from money or status but from the people. He/she is the one able to overthrow the king. While the king is always worried about the ministers, his real threat is the hero.