September 27

The most challenging things about reading about these innovative thinkers is understanding their new and complex ways of thinking. In their time period, what they were inventing was extraordinary and necessary to advance the technological world for future generations. It set the foundation for methods of communications that included shortened and sped up the process of messages. In 2013, it's completely unnecessary that we learn the methods that they used to communicate. The telegraph is long gone and we have the ease of sending someone a message straight from our fingertips within a matter of seconds. The complexity of delivering a message at a fast pace with little resources to work with is something we will never understand. Boole was said to be a "free-thinking mathematician." He saw the relationship between language and letters to signs and symbols. He changed long story problems in math to a simple equation, mixing letters and numbers. Since generations long after Boole's existence have lived with these equations since their teachings of math began, thinking about how they woud similarly inventsomething with so much meaning and existence seems impossible. He, along with some of the other names that will be mentioned later, are essentially creating a new language. In Russell's studies of finding perfections in logic and mathematics with symbols, formulas, proofs, and axioms, he sort of became obsessed with paradoxes. The more him and Whitehead, his partner, tried to perfect them, the more paradoxes came up. In his time, there were new theories he wanted to solve. A few centuries later, in the 21st to be exact, we have accepted paradoxes and can live with them. Although frustrating, the urge to find an answer one way or another isn't booming. One of the short cut paradoxes he mentions is the sentence, "This sentence is false." Due to the wording, it can not be true nor false. [Grode] was going to kill Russell's dream of a perfect loyal system. He was going to show that the paradoxes were no _________, they were fundamental. With his studies in this, he concluded that numbers were so flexible, calling it "expressive power," and that's what gave it its incompleteness.