In a world of logic and reason, no one likes a cheater. The inspired should stick to art and poetry. But I see no law that can stop me from cheating, so I keep on keep’n on.

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For this article, I will use two examples from Math Classes. One in Eight Grade and one in Ninth Grade. I will do my best to be as unmathematical as I can be so that the questions, “What is contemplation?” and “What is contemplative feedback?” is revealed clearly. The first example demonstrates how to contemplate while the second one demonstrates how to set up a complex contemplation and how to use it recursively as a rationality.

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Definition: Rationality is any recursive and/or iterative process of feedback. This is more of a computer science definition and quite useful for making rudimentary AIs in games. It also seems to be a good definition for intelligence as it is found in systems in reality.

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“Infinity can never be imagined”, said the math teacher…

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When I was in Eighth Grade, my math teacher gave us a very complete lecture on infinity after explaining the number line quite simply and clearly for eighth graders. Even in college, I noticed his definition of infinity was quite complete and very accessible for eighth graders. However, after he defined it so clearly he claimed that infinity could never be imagined. I was not so sure he was correct so I chose to find out if infinity could be imagined or not.

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The only way I could imagine finding this out was to hold it in my mind when my mind was most relaxed as infinity was an intimidating thing to find. I chose to do this before bed. I would settle in to go to sleep and first put everything I know, that I had learned from my teacher, about infinity in my mind and tried to hold it still until I fell asleep naturally.

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After about a week of doing this every night, the definition of infinity seemed to hold itself still in my mind. It took another week or so and then it happened. While I was staring at the definition of infinity, admiring how it just stayed put, I suddenly found myself experiencing infinity. I don’t know how to explain this but when I realized what was happening I remembered why I wanted this and “scrambled” somehow to “get back” to normal wake to write down what I found. When I was ready, light on, pen in hand with paper, experience so fresh I could slip back in a moment if I wished, I found I had nothing new to say that had not already been said.

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At the time, the point was clear, I had an answer and it was nothing I might have expected. Can infinity be imagined? Well, I can experience it but I could never describe it. On this day, I learned the difference between true perception and conception. In that moment I also realized that what everyone else was calling perception was a conception of conceptions and so completely removed from perception. This would nag at me for decades to come.

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“I want you to do every problem in the book over the weekend.”, said my grandmother…

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When I was in Algebra 2, we were learning “complex rational expressions over complex rational expressions”, a scary term for something mathematical that is far more of an intuitive art than anything logical. Well, we had practiced for the whole week and failed the Thursday test. The teacher asked us to study over the weekend and we would take the test again on monday, Yes, we all bombed the test that badly.

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I went home and told my grandmother the problem I was having with this. She instructed me to do all the problems in the book and we took a road trip to see some cousins of her’s. There were about 200 questions in the book. I first did the problems that had solutions in the back to make sure I was getting it correct. Then I did the rest with full confidence that I was getting them correct but I was still doing the problems backwards to check them.

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About half way through the problems without answers, something changed. I looked at one of the problems and “saw the answer”. I looked at the next one and also saw the answer. The third one, I only saw many steps down the road so I wrote it down and looked at it again and saw the answer. So, when I took the test, it was all answer or one random step in the middle and the answer. He graded them in the back of the room before the end of class and called me back.

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I was not sure why he wanted to see me but then he said, “I know you did not cheat because I wrote this test last night. How did you do this?” I explained what happened and he gave me a very different lesson in mathematics. He showed me the rules of square roots and showed me the quadratic equation. “Solve this without looking in the book.”, he challenged. And so I did and NOT by “completing the square”. I had actually turned the equation inside out and contemplated it to discover I should double it and it solved itself. He had me show the class for extra credit but I did not know I had done it differently until he said, “And you can see another way to solve this in the text book which I recommend you read.”

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So, …

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These experiences taught me a way I could overcome the fact that I am not very good at “logical reasoning” but I can sure work the problems backwards with basic reasoning. At the time I only sought to see what all this sort of reasoning might be used for, I was limiting it to my programming and obviously intuitive problems. Over time, I learned that this method works well for many situations as well as has the ability to pick up where any sort of reasoning comes to a dead end.

This is what I mean by cheating. I use this rationality whenever possible and what reasoning I need seems to appear before as if ready to be solved. The real point of this is that there are many forms of rationality we might find and I will post about others in time. This is the rationality I use most of the time but it is because this came very naturally for me. I do not much care for reason because it does not come nearly so naturally for me. But my sister rocks reason and I love to see her reason when it “magics”, it is beautiful!