Environmental Issues: Using Math and Critical Thinking

1. http://www.nearingzero.net (nz051.jpg)

2. Announcements Physics 8 first meeting January 20 (no lab this week). Your Environmental Issue isn’t due for 9 weeks. That means you can forget about it, right? “If you are out to describe the truth, leave elegance to the tailor.”—A. Einstein

3. Environmental Issues Issue 0: Using Math and Critical Thinking You may use this as your Issue (to be turned in before spring break). If you choose this Issue, you’ll work simple problems involving the metric system and scientific notation. You’ll read about critical thinking, and answer a number of questions regarding the role of government in society. This is a rather short Issue, so if you choose it, let me know in advance because I will ask you to do a couple of simple extra problems involving population growth and doubling time.

4. Physical Science: The Scientific Method (review and conclusion) Recall that the scientific method involves observation of natural phenomena, which leads questions and hypotheses. Hypotheses help us design experiments, and the results of experiments tell us if our ideas were on the right track. If your research is at the forefront of science, the experiments are difficult and probably produce contradictory results… but eventually you refine your techniques and your work starts to make sense. If your research is at the forefront of science, the experiments are difficult and probably produce contradictory results…

5. Finally, after many problem–hypothesis–experiment–theory cycles, you may think you have found a fundamental truth of nature, which you call a "law" or "theory." If your discovery is important, succeeding generations of scientists will thoroughly test it, and if it stands up, it may eventually get into the textbooks. In the early stages of studying a problem, confusion and contradictions abound. For example, who can tell me what "global warming" is? Who can tell me if it is "true“ or not? How would global warming affect your environment?

6. Occam’s Razor Tell me what you found. According to the Physics FAQ, Occam said "Entities should not be multiplied unnecessarily," which can be rephrased as "when you have two competing theories which make exactly the same predictions, the one that is simpler is the better." Occam’s Razor was never discussed in any of my physics classes, but it seems to be an unwritten component of a physicist’s heritage.

7. The Missouri S&T Society of Physics Students T-Shirt!

8. An example of the use of Occam’s Razor is the question of the ether. In the 1800's, Maxwell developed his theory of electro-magnetism. In this theory, electromagnetic waves such as light propagate (fancy physicist word for "travel") from their source to observers. Let’s see… ocean waves travel through water… sound waves travel through air (and other physical objects)… so electromagnetic waves must travel through… • …the ether!

9. The ether was not needed to make Maxwell's theory work. Maxwell’s theory provided no information about the ether, and it seemed that nobody could devise an experiment to detect the ether, but having it in the theory but helped scientists sleep better at night. What would Occam say about the ether? “Empirical evidence is also required and Occam himself argued for empiricism, not against it.” Occam’s Razor alone is not justification for discarding the ether. In this context “empirical” means “derived from observation or experiment” but not “depending on observation alone, without regard to theory.”

10. Anyway… physicists slept better at night for a while, until two fellows named Michelson and Morely came along and did an experiment which showed there is no ether. Occam’s razor might guide you towards discarding the idea of ether, but experimental confirmation is required. Aside: the nonexistence of the ether has some alarming consequences for physicists, because it says there is no absolute reference frame for making measurements. This is alarming because if different observers can measure the same phenomenon in different reference frames and get different results, there is no universal truth in nature and physicists are out of a job.

11. Fortunately, Einstein's theory of relativity finally showed how there could be no absolute reference frame without violating our belief that there ought to be such a thing as "physical reality." “Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT'S relativity.”—A. Einstein

12. You can carry Occam’s Razor too far. The non‑existence of the ether cannot be deduced from Occam's Razor alone. You need experimental evidence. Some people advocate the Principle of Economy, “Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses.” Taken to its logical conclusion this philosophy becomes positivism, the belief that what cannot be observed does not exist. I’m borrowing heavily from the Physics FAQ here.

13. As far as I am concerned, if something can’t be observed (such as particles traveling faster than the speed of light), I am not going to worry about it, but if you want to worry about it, that's OK with me. Interesting question: should you spend taxpayer's money doing research on things which cannot be observed? If the answer in the past had always been “no,” things like atoms and molecules would never have been discovered.

14. Occam's Razor does not say "keep things simple!" It suggests that if two theories explain something equally well, your best bet is to go with the simpler one. Is this a "Law" of nature? No. Does it reflect reality? Does it reflect reality? If you are a student, you’ll probably answer “no.” When I was a student, it always seemed like the more complicated explanations were always right.

15. “Make your theory as simple as possible, but no simpler.”—A. Einstein (Unfortunately, nobody seems to be able to find where Einstein actually said this.) “For every complex question there is a simple and wrong solution.”—A. Einstein “Occam's Razor is either profound and true, or vacuous and false.” Or maybe both at once. We seem to have lots of gray areas here. Anybody confused? Anybody bothered? Let's get a little more concrete and move on to measurements. But first…

16. Please print (legibly!) your name on the small piece of paper I hand out. Also print (incredibly legibly!) a secret code name, known only to you, that I can post your grades under. If you use your initials, I promise we will all look at the grades spreadsheet and laugh at your grades. Other guidelines: Don’t make it something I would be embarrassed to put on my web page. If I have doubts, I will censor! Don’t use your social security number! Duh! Don’t use your birth date, home town, student number, license plate number, or anything else that would make your code name personally identifiable.

17. Environmental Issues Issue 1: Human Population Growth (how long would it take to fill up the world?) Also, let me mention another environmental Issue. If you choose this Issue, you’ll use some simple* math to project future human population. You’ll consider the impact of human population on our planet. You’ll also study the potential effect of AIDS on populations. Finally, you’ll examine population densities. You don’t have to do “for further study” part. If you consider logarithms and exponentials “simple.”

18. Homework Assignment #2 (due Wednesday, January 18). Use the Internet to learn about the Tacoma Narrows Bridge. This is indirectly related to environmental issues… …and helps me verify that you can search for and find relevant information. Print one page out to hand in. It is sufficient to hand in just one page. I don’t want all the pages of a 15 page web site plus a cd with a video on it! Also tell in one brief sentence how you think this relates to the environment and physics.

19. Physical Science: Measurements We will begin with a short activity, followed by a discussion of the activity. I will give each of you an inch-long Precision Measuring Device. Please work by yourself and measure the length of the room. At the end of the activity, I will have you report your "best" measurement for the length of the room. Then we will discuss the meaning of measurements and how we "know" anything about the world. I’ll give you 10 minutes to finish. What are you waiting for?

20. The process of science begins with observation, but if we intend to make exact predictions, we must also measure. If something isn't measurable, then it probably isn't of scientific interest to physicists (I can think of a few exceptions). Scientists have a very good feeling for length. If you say something is a femtometer (10-15 m) long, we'll say "oh, that's about the size of a nucleus…" or if you say something is 10 light years away, we'll say "oh, that's a really close star." We also expect you to have the same feeling for lengths, which means you may have to stop us and rephrase things in non-technical terms.

21. Write down your answers to the following questions on a piece of paper, and turn it in at the end of class. You don’t need to put your name on the paper. 1. Answer yes or no: if a country is importing 10 million barrels of oil a day, does that country have an oil production problem or not? 2. Answer yes or no: suppose you learn that you have one part per billion dioxin in your tissues. Should you be worried? 3. Answer with a fraction between 0 and 1. You just bought a “tank” of gas. What fraction of this year’s US oil imports did you just buy? If you don't have a feeling for what a "barrel of oil" means, or how much dioxin is dangerous, you won't know. You need to have a feeling for "units" before you can understand the issue.

22. When we measure properties of an object, we are interested in where it is in space and time, and what is happening to the object’s matter. Matter can be characterized by its mass and charge. I will finish this lecture by describing how we measure length, time, and mass. I will discuss mass (in more detail) and charge in later lectures.

23. To measure with accuracy, we must have precisely-defined standards of measurement. Scientists usually use SI units: meters, kilograms, seconds. Here’s how I heard the story of our standard for length: in the old days, the king set the standard for measurement. A foot was the length of his foot. Don’t laugh! With the ability to set standards comes power and wealth. Unfortunately, I have to report that our present-day foot was not the length of anybody’s foot…

24. King Henry I (1068-1135) “decreed that 1/3 of his arm’s length would be the standard measurement for the foot.” With the French revolution came the idea that the standard of length belonged to the people. A meter was defined as one ten millionth of the length of the arc from the north pole to the equator, through Paris, France.

25. With the definition of the meter in hand, surveying teams set out to determine the meter. This being during the French Revolution, it proved hazardous work… …and members of the survey team died bringing you the meter… …which they didn’t get right anyway! http://www.metaphor.dk/guillotine/Pages/Guillot.html

26. Subsequent definitions of the meter improved the accuracy with which it could be measured, while minimizing changes to the actual (incorrect) length. A meter is now defined to be the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 second. Interesting reading: http://www.mel.nist.gov/div821/museum/timeline.htm http://physics.nist.gov/cuu/Units/meter.html http://www.sfu.ca/phys/100/lectures/lecture2/lecture2.html http://www.sizes.com/units/meter.htm

27. A second was once defined as 1/86,400 of a mean solar day, except a “mean solar day” varies constantly. http://www.skyscopes.com/scope/motions.html In 1956 the second was redefined as 1/31,556,925.9749 of the length of the year beginning in January 1900. Right. So you have to be an astrophysicist to measure time.

28. A second is now defined in terms of the frequency of radiation emitted by a particular state of a cesium atom. You can see the definition here, if you wish. This is all you need to have a clock accurate to better than 1 second over 20,000,000 years. Get your up-to-the second time here.

29. A kilogram is defined as the mass of a platinum-iridium cylinder stored in Paris. Except that this kilogram seems to be “shrinking!” Maybe some day we will devise a more “scientific” definition of the kilogram! NASA can tell you why it is important to keep your units straight! I suggest you not repeat their mistake.

30. Using Units in Problems Showing all units in every step can be tedious. Do, however, show the units for your answers. If all your input parameters use SI units (mks), then your answer will be in SI units. Example of unit conversion. How many seconds are there in a 365-day year?

31. Environmental Issues Issue 3: Coastal Population Growth Bangladesh If you choose this Issue, you’ll investigate the relationship between human population and coastal environment. You’ll consider the effect of possible climate changes on coastal human population. This Issue is so short that if you want to do it, you must also do Issue 4 (population growth and migration).

32. Reminder... Homework Assignment #2 (due Wednesday, January 18). Use the Internet to learn about the Tacoma Narrows Bridge.