Nuclear Waste -- the Assignment

1. Nuclear Waste -- the Assignment In a January, 1976 Scientific American article titled “The Necessity of Fission Power” H. A. Bethe wrote: For all these reasons I believe that nuclear fission is the only major nonfossil power source the U. S. can rely on for the rest of this century and probably for some time afterward. Let us now examine the objections that have been raised against this source of power. … Plutonium 239 has a half-life of nearly 25,000 years … [we are] required to cut the radioactivity by a factor of 1,000. Question: For how long must a storage facility keep the radioactive waste out of the biosphere? In view of your answer to this question, discuss the feasibility of plans to construct additional nuclear plants at this time.

2. Nuclear Waste -- Student Paper A student obtained the mathematical model P(t) = P0e-.00002776t and then produced this spreadsheet …

3. Nuclear Waste -- Student Paper and this graph …

4. Nuclear Waste -- Student Paper After ten thousand years of containment, nearly seventy-six percent of plutonium 239 will remain in the storage facility, according to the model. Even more astonishing is that it takes over fifty-seven thousand years to be reduced by a factor of five, eighty-three thousand years to reach ten percent of the initial amount, and almost two hundred and fifty thousand years to fall below the harmful zone. These time frames are so vast that it becomes difficult to even put them into a realistic context, so I remind the reader that our country itself is just two hundred and thirty years old. Modern science has done an amazing job of adapting creative solutions to many of the complex problems facing our constantly changing world, so it is very plausible that someone will discover a means to drastically reduce these decay rates. Alas, even if these times were to be cut by a tenth, it would still take twenty-five thousand years for these materials to be no longer harmful to living organisms. All the while, more waste would be constantly created to feed our technologically demanding world. Eventually, this would call for more storage sites and more dangerous risks. Our culture’s fossil fuel based energy system creates environmental problems, causes extensive international tension, and is proving to become ever more costly as its abundance diminishes. Nonetheless, the demands for energy continue to climb at an alarming rate. The time has come for a new means for power. Nuclear energy may prove to one day be such a power, yet I conclude, speculating only on the limited information given in my report, that this day has not arrived. It is my opinion that building new plants in abundance at this time would not only be dangerous, but it might be catastrophic for generations to come. Instead, I think we should try as a people to change our beliefs in a way that we could all use a little less energy. If the demand for nuclear power is necessary right now, then I hope the number of plants in use can be limited and funding to research and solve storage problems is considered a priority.

5. Nuclear Waste -- Student Paper Appendix To find the model, first assume that Po is a constant, then use the half-life of Plutonium 239 (25,000 years) to find the value of constant k: P(t)= Po ekt Po e25,000k = ½ Po 25,000k = ln ½ k= ln(1/2)/25,000 k = -2.7725 * 10^-5 P(t)= Po e -2.7725 * 10^-5(t) Find the percent radioactivity after 10,000 years: P(10,000)= Po e -2.7725 * 10^-5(10,000) P(10,000)= 75.78650072% Find the year when radioactivity will be reduced by a cut factor of 1000: P(t)= Po e^ -2.7725 * 10^-5(t) = .001* Po Po’s cancel out (-2.7725* 10-5)t = ln(.001) divide by -2.7725 * 10-5 t = ln(.001)/ (-2.7725 * 10-5) t = 249,152.5 Years

6. Nuclear Waste -- Student Reflections I would say I am pro-nuclear power, but my paper reaches a conclusion that differs from my personal beliefs. This is because the half-life portion of the paper and the visuals presented are just too great a danger to conclude that building new plants is advisable ... My conclusions were nearly direct results of my mathematical data. It’s hard to fight cold hard facts, and the facts show this waste is just as dangerous, if not more dangerous, than the CO2 emissions currently left by oil and coal burning. I actually started with the preconceived idea that we should go to nuclear energy, but through my research and what I discovered from my mathematical model, I had changed my mind. ... The mathematical model really put into perspective how long the waste would have to be stored. After you find out that it’s going to take a quarter of a million years until it is safe, you really start to second guess the whole idea all together.

7. Nuclear Waste -- Student Reflections As a person interested in science, I felt as if I did have a preconceived idea about a conclusion. Specifically, that nuclear power is a safe, effective means of power generation. Still, I approached the issue with an open mind and tried to be objective with all the data given. Although I reached the conclusion that nuclear power is safe, I was able to appreciate the concerns of those who oppose it. The extreme time durations needed to render plutonium waste “safe” really surprised me. The mathematical model, and graph, really brought out the impact of how long it really takes.

8. Contemporary Issues: the Exercises Linear Models: • Global Warming 1 - CO2 Data • Klamath Salmon Exponential Models: • Spread of AIDS • Carbon Dating - Libby • Yellowstone Wolves Breakdown of the Model: • Population of Ireland • Global Warming 2 -- Arctic Ice Cap Additional Exercises: • Olympic Running Times (the Hundred Meters) • Nuclear Waste -- Bethe • World Population -- Hardin

9. How can this material be used? • as supplementary assignments for a standard mathematics course • as the basis for a stand alone mathematics/quantitative reasoning course • as the basis for a learning community that involves mathematics • as central problems for a confluence model structure • as central problems for a freshman experience -----> discussion on next slide ----->

11. Ideas • Lewis and Clark, and the American West -- Klamath Salmon, Global Warming 2 (Arctic Ice Cap), Yellowstone Wolves • Los Alamos, the Bomb, and Nuclear Power -- Global Warming 1 (CO2 Data), Nuclear Waste (Bethe) • The Tragedy of the Commons or Collapse -- Klamath Salmon, Population of Ireland, Global Warming 1, Global Warming 2, World Population • Energy -- Global Warming 1, Global Warming 2, Nuclear Waste • Wildlife and Ecology -- Klamath Salmon, Moose on Isle Royalle

12. Additional Goals, Areas of Interest • integrative learning -- the salmon assignment

13. Additional Goals, Areas of Interest • integrative learning • critical thinking -- the distinction I see is between thinking and non-thinking -- wishful thinking -- reflexive thinking -- magical thinking -- dutiful thinking -- I am interested in teaching elementary scientific thinking that: -- relies on data and evidence -- requires a willingness to question, to conjecture, and to test conjectures against the evidence -- has mathematical reasoning at its core -- The exercises are designed to: -- demystify science -- teach scientific thinking -- to demonstrate to our students that they can think like a scientist -- to illustrate the power of scientific reasoning

14. Additional Goals, Areas of Interest • integrative learning • critical thinking • writing across the curriculum -- we write to figure out what we think -- we write to to learn how to think -- mathematicians have been largely absent from this effort -- I want to provide examples of ways in which we can participate

15. Additional Goals, Areas of Interest • integrative learning • critical thinking • writing across the curriculum • quantitative literacy across the curriculum -- how do people from other disciplines even start on this? -- mathematicians must take the lead -- perhaps it should be integrated with writing across the curriculum

16. Additional Goals, Areas of Interest • integrative learning • critical thinking • writing across the curriculum • quantitative literacy across the curriculum • citizenship

17. Additional Goals, Areas of Interest • integrative learning • critical thinking • writing across the curriculum • quantitative literacy across the curriculum • citizenship • uncertainty

18. One Student’s Reflections over the Year I did not find examining the statements and how they compared to the data particularly challenging. As mentioned in the paper, I’ve found no conclusive evidence (and do not want to jump to conclusions) that manmade CO2 emissions had any effect on global temperatures. Indeed, the data made no mention of global temperature trends. Even if CO2 levels and temperatures rose during the same time period, correlation does not imply causation. There is no conclusive evidence that such emissions (which may or may not be manmade) have any significant effect on temperature. I felt as if I did have a preconceived idea about a conclusion. Specifically, that nuclear power is a safe, effective means of power generation. Still, I approached the issue with an open mind and tried to be objective with all the data given. Although I reached the conclusion that nuclear power is safe, I was able to appreciate the concerns of those who oppose it. The idea of dealing directly with the numbers and building one’s thoughts and opinions of an issue off one’s own analysis (rather than reading someone elses attempts at persuasion) is a much more logical approach that minimized bias and error. Thinking about and analyzing data this way was very productive.

19. A Faculty Member’s Reflections In the learning community, requiring students to grapple with data and modeling in their papers made them aware of their obligation to consider facts and logical thinking in addition to their "feelings." When I gave students in other classes the same assignments, but without the data, the papers seemed easier for the students to write but lacked evidence of the healthy intellectual struggle that resulted from confronting the numbers. Jean Mach Professor of English College of San Mateo

20. Concluding Thoughts -- Student Taking data from one source and having that data predict what the situation where like if 50 years were to pass are something that I have learned from this paper. Also just because a data model predicts that something is going to happen does not mean that that particular event is going to happen because there are too many unknowns that happen everyday and those unknowns might alter the situation and change the trend. However, the most important item that I have learned from this assignment was not how to make a graph with the computer,or crunching out numbers from handouts given to us. But it was making sense of the data which was handed to me and piecing together those data to make a solid thought.

21. Review of my Journey: First Steps My initial focus was relatively narrow. I saw the data-based assignments as an interesting supplement to my mathematics classes. In particular, I wanted to: • ask my students to use a spreadsheet to examine functions from numeric, geometric and analytical points of view • offer my students genuine applications of mathematics • teach through interdisciplinary problems, so that my students would see that knowledge is not constrained by disciplinary boundaries • ask my students to write about mathematics because I had the conviction that writing about mathematics would help them to clarify their mathematical thoughts

22. Review of my Journey: Shift of Focus As the year progressed, my focus shifted. I am now more interested in using the assignments as a way to provoke discussion of the following questions: • how do we decide what is really true? • can we make decisions for ourselves, or do we have to rely on experts? • what is the proper role of data and evidence in the making of decisions? • where do reliable data come from? • how do we treat and interpret the data? • what can we properly conclude after we look carefully at the data? • how can a mathematical model break down? • what are the implications when a model breaks down? • what is the interplay between data, preconceptions, opinion, and belief?

23. The next to last slide

25. Additional Resources Books about Quantitative Literacy: Mathematics and Democracy: The Case for Quantitative Literacy Lynn Arthur Steen (Editor) Achieving Quantitative Literacy: An Urgent Challenge for Higher Education Lynn Arthur Steen (Editor) More reading about my work: Carnegie Perspectives Piece: http://www.carnegiefoundation.org/perspectives/ Carnegie Scholar Final Project Snapshot: http://www.cfkeep.org/html/snapshot.php?id=61548260563564 Tools for Thought Learning Community: http://www.smccd.net/accounts/csmlcom/ToolsforThought/tools.htm