Monday, July 15, 2013

Naturally Good at Monopoly; Exponential Function of Making Money

Diverse friends make for interesting pictures.
My life can be graphed as a function - as I become older and older, my life becomes exponentially more interesting. If my life was linear, I would be at the zenith of boredom. I can imagine it, my eyes faintly gazing at the sky, with no clouds, as I write the fiftieth answer to the same algebra question, losing sanity and becoming disinterested while my peers are tossing a Frisbee outside... Boy, have I changed. High school has sculpted my personality and changed me into the social-maniac that I enjoy being. Not only have I made strong friendships that will be remembered for the rest of my life, I have also gained knowledge and wisdom much different, and helpful, than that of which I learned from a boring high-school classroom. Being able to view things from different perspectives and listen to the voices of the world, it's truly inspiring. I've met many people from different backgrounds: a Chinese student(girl) living in Guam, a French roommate living in New York, and an international student living in Shanghai, but originally from Michigan. I'm amazed at how much diversity there is.

Anyways, going back to physics class (I know, nice transition). We learned about the counter-intuitive manner that nature executes its processes. We are all used to linear relationships - $70/hr, $10 per gallon (just an example), and etc - but fortunately, nature has many tricks up its sleeves - it plays in exponents! Imagine this: a mouse is chasing a mouse, who is chasing a mouse that is chasing another mouse that chases the original mouse. It's a chain link where the position of the initial mouse ultimately affects its change in position! If it moves to a certain position, that will ultimately affect its next position. It's like snake where if you have too many blocks, you'll be forced to move differently. Knowing this, we can represent it mathematically with f(x) = df(x)/dx. The right-hand side of the equation represents a derivative (an instantaneous slope, it's useful because , in a sense, it converts a curved line into a straight line) and it is affected by the function itself. And through examinations of certain exponential relationships, we find that many natural relationships have a natural exponent - represented by e. When we graph a natural function, we will find that the derivative at any given point is equal to the function. Is this coincidental or is this just an aspect of nature? Or is it a product of the being of nature? That's diving a little bit deeper and I'm not sure where I'm heading, but that's the fun of it. We'll be examining more of this relationship through various relationships. For an example, Moore's Law says that computing power doubles every 18 months. By actually observing and making note of these relationships, the concept behind it will become much more clear and beautiful. I think this is one of the best ways to show the beauty of mathematics and physics. We dived into relativity, but going into it too deep here will use too much time. To sum it up, the speed of light is constant and when an object is moving at velocity close to the speed of light, its time is running slower relative to an object that it passes by. When an object approaches the speed of light, its time is slowed down and the object appears to become more compact (makes it seem as if the object is elastic). This is WAY oversimplified, but time is of the ether (HA).

I'm excited for this week because we'll be working in our study groups. I chose to do the gas chamber. Essentially, we'll be creating and manipulating strange quarks through the collision between positrons and electrons that are created by the collision of incoming mu-mesons (particles that are created in the upper atmosphere and fall down to sea level) with an alcohol in the chamber. Mu-mesons are particles that prove that the special relativity does exist. Mu-mesons have a life of 2.9 nanoseconds (or micro, not sure) and so it should die instantaneously when it's created in the upper atmosphere. However, since its atomic clock is different than that of ours, its time is slowed down because of the velocity it is going at. (Mathematical relationship: 1/square root of 1 - v squared/speed of light squared). Anyways, I'm expecting to learn a lot of particle physics through this study group and I can't wait to be strange! Ok... These jokes are going a bit far.

After all the shenanigans after class, I was invited to another Monopoly game. This time, I was the rich! I literally had 5 monopolies half-way through the game, it was unbelievable! I was extremely lucky in the beginning in that I earned three tiles of the same color in just three turns! This would not have been possible if I had not been lucky. The only reason I had the opportunity to get them was through the "Go to Jail" tile. Through a series of rolls, I had rolled the correct combination of numbers to land myself in jail... twice. However, this was a blessing in disguise. Because of that, I was able to backtrack to the region where I was able to take all three same-colored tiles with my probability god-like luck! I'm pretty sure I'll never be able to do this again... Anyways, I was so rich to the point where I started giving out $1000 to people because I felt bad that I owned all the money. The rich have a much easier time lazily enjoying the game than the poor have it. Monopoly is such a great concept, it really says much about society.

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