### A Story of Stability M:July Rewound

July 30, 2006 Sunday 1:31 PM A Story of Stability M:July Rewound

July Rewound

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Well, I lived through the month of July 2006. What happened during that time?

I almost wanted to get up. I was thinking so hard about it. Not because it was complicated but because it meant something to me. 1 = .999999... -> infinity usually represented with a bar over the 9 but I can't seem to find that bar button right now. It's true. 1 is indeed equal to that. And I take it to mean that the Limit as x approaches 1 is 1. I thought of it more like a demonstration of why we can say that the limit as something gets really close to a number we call it that number. It looks like a paradox at first but I'd take it to really be true. If it wasn't.. how would limits work?A Story of Stability

I recall events on my quest to verify my stability equation.

I finally managed to validate my Energy tipping equation last night. I sort of got home and picked it up and get working the equations over and finally while I was standing in the shower during a break I realized the answer. It's hard for me to remember all the pieces of the story. It began nearly a year ago when I got the idea for the Stability equations and Tipping Energy. And I wrote it on my mirror. And it had been their ever since. I spoke of them in a movie while I waved my hand toward the mirror and that's when I picked up the idea again. In all this time I had not 'proved' the fact. I had just sort of 'known' it was true because that's the way things should work. From time to time I sort of write down equations that I just sort of 'know' to be true. The "Moving Equation" the "Hair Cut Equation" and this one.... only last night I finally managed to prove it. But I didn't start re working things over until perhaps this past Friday while I was siting out on a bench waiting for someone to get off work. I sat down to eat my sandwich and the nagging idea crept back into my skull. "I have still not proved that equation" I thought to myself. And so, with this 1 hour before my friend would leave work, I scribbled and scrawled sketches of equations and ideas. I remembered how I had lamented to Liz at her work place how I couldn't figure out how to prove this one thing that I just 'knew' was true. I recall sitting in a chair in front of her desk and madly trying to find out how to prove this wonderfully simple idea I had. The ways to prove things skipped through my head. Assume something true and show contradiction. No, that wasn't working out. Solve for one example than try to generalize? Mmmm not so good. I made many many mistakes which didn't help my attempts to prove this thing. I draw little squares on their sides and on their corners. Nothing was helping... I can't even recap the whole story. I've always wanted to, but recalling and transforming a mathematics story is tough stuff. Especially, if I want people to understand it. The prerequisite are far to great. And so I sat there with my note book in front of me, a calculator by my side and a drink I was sipping while staring off into the sunniness of the day. "It would feel so great if I could just prove this before I met with her" And alas no luck came and I had to put the note pad away and tend to academic matters with the newly off work person. The rest of the day was full of social interaction so I didn't come back to the idea. Until last night. And I struggled but I was getting closer. I solved a different little problem and I realized the same tactics applied. You demonstrate your theory.. and how you really solve for the thing and show they are the same. And then I knew what I had to do. But that's when I kept making errors of a sort. I thought I had used the wrong trig identity but knowing what I knew about sines and cosines I finally of all finally's figured out that my interval was wrong. That was what I realized while the water hit my face in the shower. Interval! I had the picked the wrong angle and I suddenly I knew I had proved it. Of course I hadn't written out the equations just then but I knew. I 'knew' it was solved and that I was correct. I had to be. It had to be. And indeed, as I wrote out a victory page I marveled at the simplicity. And scuffed at my inefficiency using al these other pages to prove the same thing that I was staring directly at now. A final result that fits on one paper and proves what I said that year ago is true. Finally, and now maybe I could erase that mirror and put some other 'intuitive' thing up to be solved a year later.

## "According to Einstein, I can't tell whether I'm in an elevator on the Earth or in a rocket ship accelerating at g through space.... but I think I'm in an elevator." The doors open and there's space outside. "D'oh."

Well, it was another full day of friendly fun. I was actually called and asked to come over. Though when I got there a bunch of people left. What a shame. But I did stay. And pizzia was good. Liz is officically in the D street house and Kristina finally moved her stuff into her room. All is well in general. Except for Lindas foot I guess.

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