Thinking is a mental process which allows humans to model the world, philosophy is the attempt to understand the world using logic and reason. The world being both the external and the internal, and both the knowable and unknowable.
For an overview of philosophy see our branches of philosophy page, for an introduction to philosophy check out Reason at Work (Amazon). Philosophy includes everything from economic and political philosophies, to the philosophies of emotions and mind, to cosmological and other other metaphysical questions, to the nature of god and religion, to the very nature of what we can know. Given that every subject has a science and philosophy (with the two often merging, such is the case in theoretical physics or mathematics) we have to be careful not to undervalue the practical aspects of this non-science.
Past results of random independent events, like a coin flip, don’t affect future results. The mistaken belief that past results affect future results is known as “the Gambler’s Fallacy” (AKA the Fallacy of the Maturity of Chances, or the Monte Carlo Fallacy).
Most people have about 6 degrees of separation (small world theory), but not everyone has 6 degrees of separation from Kevin Bacon or any other given person.
Multiple discovery is the hypothesis that many discoveries and inventions are made independently, and more or less simultaneously, by multiple people.
A Factoid is a brief piece of information that appears to be true, but isn’t necessarily factual or verified, yet is repeated as fact anyway.