General Background
It’s had many editions over 2,000 years, almost as many as the Bible. Euclid was from Alexandria and spent most of his life in Egypt. Evidence that he studied in Platonic schools in Athens, influenced by Aristotle. He was the first to pull ideas together in a sequential way. Systematic.
Connection: from our last study, what you needed to have a successful society: a philosopher-king.
Connection: Lincoln decided to pause his law studies to work out Euclid’s theorems first. He knew that if he was to be persuasive, he would have to logically build his case.
This systematic way of studying has been applied to other schools of thought. Descarte used this as a way to explain philosophy: I think, therefore, I am. First principles. Deductive Bible Studies.
Postulates (Latin: to assume) / Axioms (Greek)
Something that stands alone, worthy or fit. #5 (Parallel postulate) was more controversial. Finally used in Proposition #29 where it was needed to move forward. There is another mathematics that does not rely on it, non-Euclidean geometry. Example is the globe: parallel longitudinal lines that meet at the poles.
Propositions / Theorems
(class did some samples here)
Pythagorean Theorem: first to lay all the building blocks that it took to build it.
Analysis
What is the value of this recorded systematic thinking?
- Used by other disciplines as a way of recording systematic thinking?
- Gives stability: principles that are proven are things you can rely on for building other things
In our culture we have elevated the process of proving things, making empirical science into a god. Applying it in areas that don’t apply, such as mathematically proving the existence of God. This is what takes us into the post-modern era, elevating our reason above all else.
Structure is at the root of all creation: all of creation is made by a God of order. Where is the math in art, music, literature, philosophy.
Music is listening to math principles ordered in a particular way.
If you don’t see the application then you don’t have a use for it. Plato was so excited about logic that it informed the way he ordered his Academy.
Model for how we learn things:
Cindy talked for quite and asked me to write: blah, blah, blah. :-) Is there a connection between rebellion against God and discarding order. Embracing the order helps us build in a direction to a great extent.
Learning is done in answer to a question, to solve a problem. Consider studying history backwards, starting with the question of the current concern, finding antecedents as you go back.