"Well, I found a lot more beauty than I ever knew existed.... it is called the history of human thought: art, science, mathematics... there are lots of real people who had real struggles over something they were passionate about... In the end we are all just trying to realise our idea of perfection, and to find peace with our own hearts I think...
"I discovered something amazing kathy, the beauty of being human is this.... We are able for some miraculous reason to grasp the idea of generality. We wander around in life and notice broken symmetry in the universe, innate in us is the ability to abstract that and come up with ideas like the circle... we love these creations of the mind and some of us (the artists) get so wrapped up in them that we devote our lives to drawing them out so you see, we suffer for our love of beauty ... and beauty is entirely human for it only exists in the hearts of those who percieve it :) It's all so incredible how we just came to 'exist' and be such sexy, emotional, intelligent creatures :)
"The problem with our 'perfect forms' is that we can never really get them, for if anything in life were perfect I doubt that we would even notice it... How often do you really notice the beauty of all the human creations around you which have never existed in nature? Being such, we cannot obtain our perfection but only try in vain... our passion is the labor of the soul, and we are never satisfied completely thus, the human condition... to labor forever chasing after imaginary images as incorporeal as our own thoughts and feelings. Well, we try in vain or, placing your efforts where we can never really achieve the end.
"I believe that the ability to appreciate beauty is entirely egocentric, that is, we think something is beauty for one of two reasons: 1) We wish we had something of it's nature, 2) It reminds us of something we like about ourselves.
"There was a philosopher toward the end of the Renaissance named Rene Descartes who, like Francis Bacon, thought that the ancient greeks 'Aristotle, Plato' were great, but wrong about nature. He was a Mathematician as well and being so used to perfect logical arguments, wanted everything to be demonstrated with perfect logic. He decided to pretend everything of which he was uncertain to be false, he lost grips with reality and believed that a dream was as much reality as sitting in his chair and wrighting his meditations he said 'I am so shocked by this that I am almost conivinced that I now dream' and then realized that he was sure of only one thing 'I have denied that I have body, and that the world exists. But having these thoughts, be the false or true, to think I must exist... I think therefore I am.' Of course he was too far gone by that time to recover his perceptions of reality and spent the rest of his life somewhat insane. :)
"Here was an architect in the Renaissance 'Leon Batista Alberti. ' He said that beauty is 'A complete whole from which the subtraction or addition of any part will destroy the whole.' Descartes said, 'Adding anything to the pure light of reason will serve only to obscure it,' so he thought that reasoning (rational thought) was beautiful. Yeah, the precept is 'My reality is so much intangled in my ability to percieve, and how I feel, that it is really only that.... My reality'
"I believe that 'Without perception there is no thought' for did we not think in order to arrive at that language with which we communicate? Now then did we 'think' up this language... our language is modeled after our natural way of thinking... association of unique identities to things and then abstraction of common properties to various general classes or 'ideal forms' such as 'DOG' and then logical as well as relational connectives we are capable of concieving of 'DOG' without the word.... just try and hold the concept in your mind without the word it's not very hard to do. There is little that we can communicate without a universal set of 'arrows to identites' to communicate to one another. 'These are words' so Aristotle wouldn't have been able to write his organon.
The purpose of a word is to invoice the 'word sense or concept' in the mind of someone else.. it is connected to it by a 'mapping' if you will of our external world into the collection of all finite combinations of the 26 letter alphabet, the assignments are abitrary for the most part... The structer however tends to be somewhat universal .... in fact we can prove the general concepts have set containment ideas in them such as .... animal predacted of mammal predicated of dog predicated of my dog.... with sets like these we tend to want to define a notion of proximity say that to things (A,B) are close together if there is a word concept which contains them both, like me and you are close together since we are both human this is somewhat abstract but you can see, our language structure has an inherent space concepts in it...
"The general mathematical object is called a topological space and is an abstraction of the real number system ....so two topological spaces are said to be homeomorphic when they are equivalent with respect to 'how well we can distinguish two points' all language topologies are homeomorphic so this lends a lot of insite into how the human mind puts ideas together no? And also the ability to form abstract concepts groups is just what allows us to form 'abstract ideas' such as a circle so the being able to think of the idea 'Human' is the same as being able to conceive of something which does not exist in a the sense universe so art and language come from the same place, but these are just where math come from... and science... "
These are the words of my dear friend Mike in one of our contemplative chats. ^_^ Now you can see why I love conversing with him, ya? *hugs Mike* Never have I met a guy with such a deep and profound passion for Mathematics and the Language of numbers. Mike, I think one day having a Mike Rigney #1 will exceed those that have an Paul Erdos number. LoL. *grins*