Mathematics


This statement is unprovable.

Godel is best known for the Incompleteness Theorem which reshaped our view of mathematics. This is part of the answer as to whether mathematics is a science of abstraction or an art. Godel showed that much of mathematics is beyond our understanding and that we are discovering mathematics.

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Max Tegmark hypothesizes that the universe has a mathematical origin.

This isn’t a new theory – the Greeks speculated about mathematics unexplainable relation with reality. Mathematics is isomorphic to reality and vice versa. Tegmark goes all the way and asks if the universe is mathematics.
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The pirate game produces a unique result. There are 5 pirates and 100 gold peices and they have to distribute the gold. They are ranked by strength, 5 is the strongest, 1 is the weakest. The strongest proposes a way of distributing the money and they vote on it. Any vote with 50% or more wins. If the vote is less than 50%, the proposing pirate is killed. What’s the final distribution?

Pirate 5 gets 98 gold coins, Pirate 4 gets 0, Pirate 3 gets 1, Pirate 2 gets 0, Pirate 1 gets 1. How?
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Ordering preferences are a way of prioritizing alternative choices and attaching expected utility to outcomes. We measure the magnitude of differences between alternate choices so we can determine how much choice A is preferred to choice B. I prefer choice A two times greater than choice B and choice B three times greater than choice C. This tells us the ratio of difference.

Ordered preferences tells how how agents make their choices. There are different ways to rank and measure preferences.
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Thomas Schelling demonstrated how a series of individual choices based on mild preferences can lead to racial segregation. He used nickles and dimes on a board. Every coin made a decision to move on the space based on its order of preferences. Dimes wanted at least one dime as a neighbor, and nickels wanted at least one nickle neighbor. Even if Dimes only has a slight preference for dimes over nickles, over time, dimes and nickles would segregate.

Political violence intensifies group preference. This leads to faster segregation with stronger avoidance behavior. Patriotism is a mutual defensive pact, afterall.
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Here is an explanation for the appearance of Golden Angles in Nature.

“The seeds of a sunflower, the spines of a cactus, and the bracts of a pine cone all grow in whirling spiral patterns. Remarkable for their complexity and beauty, they also show consistent mathematical patterns that scientists have been striving to understand.”

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