assignment 7 36

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1. Please read the following narrative, and perform the embedded coin sorting and stacking exercise.

2. Answer the questions.

a. In Chaos Theory, why will neatly sorted stacks of coins always collapse into disorder?

b. What does it mean when we say that Laws 1 and 2 of Thermodynamics can be summarized as “You can’t Win, and you can’t break even?”

This week we will look at the first two laws of Thermodynamics: 1) E= MC2; and 2) Entropy.

The first is one of Einstein’s most brilliant insights, that, in the entire universe, energy can neither be created nor destroyed. In other words, the amount of energy present at the origin of the universe, will be the exact same at its end. This is dependent on, and illustrated by, his corollary, that energy and matter are interchangeable, essentially the same thing, except that in the matter form, it must be multiplied by the speed of light squared. Just to keep us squared away, don’t forget that the speed of light is 186,000 miles/second.

The second law is also called entropy. Entropy means that all systems in the universe, and the universe as a system itself, must eventually run down. So, in entropy: In all closed systems, if we measure the energy present at one point, and no energy enters or leaves the system, and then we make a second, separate measurement, there will be less energy present at the later measurement than at first.

Astrophysicists are a jolly lot, and I knew a number of them when I taught at MIT. They summarize the combined affect of E=MC2 and entropy, that is: a) balanced energy in the universe through time, and; b) in closed systems, a constant decline in energy present, in the words of a familiar song: You can’t win; You can’t break even; You can’t get out of the game. They are poker players too, and it works out fine. You can’t win, because the amount of energy/matter is balanced and will never change. You can’t break even, because Entropy states that the systems will constantly run out of energy. And you can’t get out of the game; we’re here to stay folks, subject to the laws of the universe, for good or ill.

It has been said that “Nature abhors a vacuum.” This is, of course, true, but only under terrestrial gravitational and atmospheric conditions. We are in a very special situation here on earth, where it is very difficult, and very expensive, to maintain a vacuum. The Scanning Electron Microscope (SEM), for example, requires a vacuum in which to carry out its observations which can magnify to 200,000 x. It takes a huge supporting fund, close to $1 million/year, with an assigned technician, to maintain that vacuum on earth.

In deep interstellar space, however Nature is all vacuum, with intermittent star clusters, and chance encounters with stray trace elements from the periodic table. What “Nature Abhors” really, both out there in interstellar space, and even in the earth’s environment too, is higher order organization of molecules, and in fact, higher order organization in general.

Some examples of things “running down,” illustrating entropy, are a watch spring, and an internal combustion engine. The old-fashioned clocks and watches had a “main spring,” a spring inside that, if wound tight, would provide energy to run the clock, or watch, for, usually, about 8 days. At that point, you can renew them to FULL potential energy, and they would start running again, for about another week. Energy into an exhausted closed system, now revived. Even more simple as an example is your car. The internal combustion engine will take you wherever you want to go, but that tank of gas, as it runs down: Entropy. If not replenished with its petrochemical energy source, the car will simply “run out of gas” and stop. Entropy.

Now, Chaos Theory builds on Entropy. NO, NOT Jeff Goldblum in Jurassic Park with Amazon Butterflies! Entropy is, itself, a measure of disorder, the idea that things are not supposed to be arranged into self-fueling, higher orders of organization. Let’s look at one example: Stacking coins.

SCIENCE EXERCISE EXAMPLE

Get yourself a mix of all the coins you can find around the house, perhaps 20 or 30. Now, divide them by denominations, and begin stacking them in their own denominations: pennies with pennies, dimes with dimes, etc. What you are doing is imposing a higher order organization on an otherwise random pile of coins.

!KEEP STACKING!

What is happening is, that you are inputting a huge amount of energy into the equation. Your brain neurons, commanding your eyes, feverishly looking to pull out the dimes, and burning hand/eye coordination energy. Then, with your hands forcibly controlled, you place penny on penny, dime on dime, without letting them collapse.

THEY WANT TO COLLAPSE, because of gravity, sure, but gravity is only another mechanism for destroying higher order organization. Your body, a supreme energy-burning mechanism to maintain higher order organization, IS ITSELF a barely-willing higher order arrangement of molecules, waiting to return, randomly, to earth.

Chaos Theory is, ultimately, a statistical argument. Once you have put all your time and energy into your coin-sorting experiment, and have some nice, and precarious, stacks, how long will they last? How will they ultimately fall? Whether it is your room mate, your baby sister, the family dog, or even you, yourself, someone will jiggle the table, and they will fall. Most importantly, the stack will not just lie over on its side, or invert to a still-nice stack, but upside down. They will scatter RANDOMLY across space, in the relaxed way that they, and all molecules in the universe, are meant to be. Chaos Theory simply says that there is only one way to make a stack of coins, defying gravity and defying random arrangement, but when they fall, there is an infinity of chaotic arrangements available for them. Only one way to be a higher-ordered arrangement; an infinity of ways to be spread, chaotically, throughout the universe.

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