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Short Quiz in Math 7 describes principal roots and tells whether they are rational or irrational

A BAD CASE OF THE STRIPES By David Shannon Parts(18): Camilla Narrator 1 Narrator 2 Narrator 3 Narrator 4 Mr. Harms Mother Father Dr. Bumble Old Woman Environmental Therapist Dr. Grop Dr. Gourd Dr. Sponge Mr. Mellon Dr. Cricket Dr. Young <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Narrator 1: A BAD CASE OF THE STRIPES By David Shannon Narrator 2: Camilla Cream loved lima beans. But she never ate them. Narrator 3: All of her friends hated lima beans, and she wanted to fit in. Camilla always worried about what other people thought of her. Narrator 4: Today she was fretting even more than usual. It was the very first day of school, and she couldn't decide what to wear. There were so many people to impress! Narrator 1: She tried on forty-two outfits, but none seemed quite right. She put on a pretty red dress and looked in the mirror. Then she screamed. Narrator 2: Her mother ran into the room, and she screamed, too. Mother: "Oh my heavens! You're completely covered with stripes!" Narrator 3: she cried. This was certainly true. Camilla was striped from head to toe. She looked like a rainbow. Narrator 4: Mrs. Cream felt Camilla's forehead. Mother: "Do you feel all right?" Narrator 1: she asked. Camilla: "I feel fine, but just look at me!" Narrator 2: Camilla answered. Mother: "You get back in bed this instant. You're not going to school today." Narrator 3: her mother ordered. Camilla was relieved. She didn't want to miss the first day of school, but she was afraid of what the other kids would say. And she had no idea what to wear with those crazy stripes. Narrator 4: That afternoon, Dr. Bumble came to examine Camilla. Dr. Bumble: "Most extraordinary! I've never seen anything like it! Are you having any coughing, sneezing, runny nose, aches, pains, chills, hot flashes, dizziness, drowsiness, shortness of breath, or uncontrollable twitching?" Narrator 1: he asked. Camilla: "No, I feel fine." Narrator 2: Camilla told him. Dr. Bumble: "Well then, I don't see any reason why she shouldn't go to school tomorrow. Here's some ointment that should help clear up those stripes in a few days. If it doesn't, you know where to reach me." Narrator 3: Dr. Bumble said, turning to Mrs. Cream. And off he went. Narrator 4: The next day was a disaster. Everyone at school laughed at Camilla. They called her "Camilla Crayon" and "Night of the Living Lollipop." Narrator 1: She tried her best to act as if everything were normal, but when the class said the Pledge of Allegiance, her stripes turned red, white, and blue, and she broke out in stars! Narrator 2: The other kids thought this was great. One yelled out, Narrator 3: "Let's see some purple polka dots!" Narrator 4: Sure enough, Camilla turned all purple polka-dotty. Someone else shouted, Narrator 1: "Checkerboard!" Narrator 4: and a pattern of squares covered her skin. Soon everyone was calling out different shapes and colors, and poor Camilla was changing faster than you can change channels on a T.V. Narrator 2: That night, Mr. Harms, the school principal, called. Mr. Harms: "I'm sorry, Mrs. Cream, I'm going to have to ask you to keep Camilla home from school. She's just too much of a distraction, and I've been getting phone calls from the other parents. They're afraid those stripes may be contagious." Narrator 3: he said. Camilla was so embarrassed. She couldn't believe that two days ago everyone liked her. Now, nobody wanted to be in the same room with her. Narrator 1: Her father tried to make her feel better. Father: "Is there anything I can get you, sweetheart?" Narrator 2: he asked. Camilla: "No, thank you," Narrator 3: sighed Camilla. What she really wanted was a nice plate of lima beans, but she had been laughed at enough for one day. Dr. Bumble: "Hmm, well, yes, I see. I think I'd better bring in the Specialists. We'll be right over.” Narrator 4: said Dr. Bumble to Mr. Cream on the phone. About an hour later, Dr. Bumble arrived with four people in long white coats. He introduced them to the Creams. Dr. Bumble: "This is Dr. Grop, Dr. Sponge, Dr. Cricket, and Dr. Young." Narrator 1: Then the Specialists went to work on Camilla. They squeezed and jabbed, tapped and tested. It was very uncomfortable. Dr. Grop: "Well, it's not the mumps." Dr. Sponge: "Or the measles." Dr. Cricket:"Definitely not chicken pox." Dr. Young: "Or sunburn." Narrator 2: replied the Specialists. Specialists:"Try these. Take one of each before bed." Narrator 4: said the specialists. They each handed her a bottle filled with different colored pills. Then they filed out the front door followed by Dr. Bumble. Narrator 1: That night, Camilla took her medicine. It was awful. Narrator 2: When she woke up the next morning, she did feel different, but when she got dressed, her clothes didn't fit right. She looked in the mirror, and there, staring back at her, was a giant, multi-colored pill with a face on it. Narrator 3: Dr. Bumble rushed over as soon as Mrs. Cream called. But this time, instead of the Specialists, he brought the Experts. Narrator 4: Dr. Gourd and Mr. Mellon were the finest scientific minds in the land. Once again, Camilla was poked and prodded, looked at and listened to. Narrator 1: The Experts wrote down lots of numbers. Then they huddled together and whispered. Dr. Gourd finally spoke. Dr. Gourd: "It might be a virus," Narrator 2: he announced with authority. Suddenly, fuzzy little virus balls appeared all over Camilla. Mr. Mellon: "Or possibly some form of bacteria," Narrator 3: said Mr. Mellon. Out popped squiggly little bacteria tails. Dr. Gourd: "Or it could be a fungus," Narrator 4: added Dr. Gourd. Instantly, Camilla was covered with different colored fungus blotches. The experts looked at Camilla, then each other. Experts: "We need to go over these numbers again back at the lab. We’ll call you when we know something," Narrator 1: said the Experts. But the Experts didn't have a clue, much less a cure. Narrator 2: By now, the T.V. news had found out about Camilla. Reporters from every channel were outside her house, telling the story of "The Bizarre Case of the Incredible Changing Kid." Narrator 3: Soon a huge crowd was camped out on the front lawn. Narrator 4: The Creams were swamped with all kinds of remedies from psychologists, allergists, herbalists, nutritionists, psychics, an old medicine man, a guru, and even a veterinarian. Narrator 1: Each so-called cure only added to poor Camilla's strange appearance until it was hard to even recognize her. She sprouted roots and berries and crystals and feathers and a long furry tail. But nothing worked. Narrator 2: One day, a woman who called herself an Environmental Therapist claimed she could cure Camilla. She said, Environmental Therapist: "Close your eyes, breathe deeply, and become one with your room." Camilla: "I wish you hadn't said that," Narrator 3: Camilla groaned. Slowly, she started to melt into the walls of her room. Her bed became her mouth, her nose was a dresser, and two paintings were her eyes. The therapist screamed and ran from the house. Mother: "What are we going to do? It just keeps getting worse and worse!" Narrator 4: cried Mrs. Cream. She began to sob. Narrator 1: At that moment, Mr. Cream heard a quiet little knock at the front door. He opened it, and there stood an old woman who was just as plump and sweet as a strawberry. Old Woman: "Excuse me, but I think I can help." Narrator 2: she said brightly. Narrator 3: She went into Camilla's room and looked around. Old Woman: "My goodness, what we have here is a bad case of the stripes. One of the worst I've ever seen!" Narrator 4: she said with a shake of her head. She pulled a container of small green beans from her bag. She said, Old Woman: "Here. These might do the trick." Mother: "Are those magic beans?" Narrator 1: asked Mrs. Cream. The old woman replied, Old Woman: "Oh my, no, there's no such thing. These are just plain old lima beans. I'll bet you'd like some, wouldn't you?" Narrator 2: she asked Camilla. Camilla wanted a big, heaping plateful of lima beans more than just about anything, but she was still afraid to admit it. She said, Camilla: "Yuck! No one likes lima beans, especially me!" Old Woman: "Oh, dear, I guess I was wrong about you." Narrator 3: said the old woman sadly. She put the beans back in her bag and started toward the door. Narrator 4: Camilla watched the old woman walk away. Those beans would taste so good. And being laughed at for eating them was nothing, compared to what she'd been going through. She finally couldn't stand it. Camilla: "Wait! The truth is...I really love lima beans." Narrator 1: she cried. The old woman smiled, popping a handful of beans into Camilla's mouth, and said, Old Woman: "I thought so." Camilla: "Mmmmmmm," Narrator 2: said Camilla. Suddenly the branches, feathers, and squiggly tails began to disappear.Then the whole room swirled around. When it stopped, there stood Camilla, and everything was back to normal. Camilla: "I'm cured!" Narrator 3: she shouted. The old woman said, Old Woman: "Yes, I knew the real you was in there somewhere." Narrator 4: She patted Camilla on the head and went outside and vanished into the crowd. Narrator 1: Afterward, Camilla wasn't quite the same. Narrator 2: Some of the kids at school said she was weird, but she didn't care a bit. Narrator 3: She ate all the lima beans she wanted, and she never had even a touch of stripes again.

“There’s No Such Thing as Sound Science” by By Christie Aschwanden was a lead science writer for FiveThirtyEight. FiveThirtyEight, Science, Dec. 6, 2017 Science is being turned against itself. For decades, its twin ideals of transparency and rigor have been weaponized by those who disagree with results produced by the scientific method. Under the Trump administration, that fight has ramped up again. In a move ostensibly meant to reduce conflicts of interest, Environmental Protection Agency Administrator Scott Pruitt has removed a number of scientists from advisory panels and replaced some of them with representatives from industries that the agency regulates. Like many in the Trump administration, Pruitt has also cast doubt on the reliability of climate science. For instance, in an interview with CNBC, Pruitt said that “measuring with precision human activity on the climate is something very challenging to do.” Similarly, Trump’s pick to head NASA, an agency that oversees a large portion the nation’s climate research, has insisted that research into human influence on climate lacks certainty, and he falsely claimed that “global temperatures stopped rising 10 years ago.” Kathleen Hartnett White, Trump’s nominee to head the White House Council on Environmental Quality, said in a Senate hearing last month that she thinks we “need to have more precise explanations of the human role and the natural role” in climate change. The same entreaties crop up again and again: We need to root out conflicts. We need more precise evidence. What makes these arguments so powerful is that they sound quite similar to the points raised by proponents of a very different call for change that’s coming from within science. This other movement strives to produce more robust, reproducible findings. Despite having dissimilar goals, the two forces espouse principles that look surprisingly alike: Science needs to be transparent. Results and methods should be openly shared so that outside researchers can independently reproduce and validate them. The methods used to collect and analyze data should be rigorous and clear, and conclusions must be supported by evidence. These are the arguments underlying an “open science” reform movement that was created, in part, as a response to a “reproducibility crisis” that has struck some fields of science.1 But they’re also used as talking points by politicians who are working to make it more difficult for the EPA and other federal agencies to use science in their regulatory decision-making, under the guise of basing policy on “sound science.” Science’s virtues are being wielded against it. What distinguishes the two calls for transparency is intent: Whereas the “open science” movement aims to make science more reliable, reproducible and robust, proponents of “sound science” have historically worked to amplify uncertainty, create doubt and undermine scientific discoveries that threaten their interests. “Our criticisms are founded in a confidence in science,” said Steven Goodman, co-director of the Meta-Research Innovation Center at Stanford and a proponent of open science. “That’s a fundamental difference — we’re critiquing science to make it better. Others are critiquing it to devalue the approach itself.” Calls to base public policy on “sound science” seem unassailable if you don’t know the term’s history. The phrase was adopted by the tobacco industry in the 1990s to counteract mounting evidence linking secondhand smoke to cancer. A 1992 Environmental Protection Agency report identified secondhand smoke as a human carcinogen, and Philip Morris responded by launching an initiative to promote what it called “sound science.” In an internal memo, Philip Morris vice president of corporate affairs Ellen Merlo wrote that the program was designed to “discredit the EPA report,” “prevent states and cities, as well as businesses from passing smoking bans” and “proactively” pass legislation to help their cause. The sound science tactic exploits a fundamental feature of the scientific process: Science does not produce absolute certainty. Contrary to how it’s sometimes represented to the public, science is not a magic wand that turns everything it touches to truth. Instead, it’s a process of uncertainty reduction, much like a game of 20 Questions. Any given study can rarely answer more than one question at a time, and each study usually raises a bunch of new questions in the process of answering old ones. “Science is a process rather than an answer,” said psychologist Alison Ledgerwood of the University of California, Davis. Every answer is provisional and subject to change in the face of new evidence. It’s not entirely correct to say that “this study proves this fact,” Ledgerwood said. “We should be talking instead about how science increases or decreases our confidence in something.” The tobacco industry’s brilliant tactic was to turn this baked-in uncertainty against the scientific enterprise itself. While insisting that they merely wanted to ensure that public policy was based on sound science, tobacco companies defined the term in a way that ensured that no science could ever be sound enough. The only sound science was certain science, which is an impossible standard to achieve. “Doubt is our product,” wrote one employee of the Brown & Williamson tobacco company in a 1969 internal memo. The note went on to say that doubt “is the best means of competing with the ‘body of fact’” and “establishing a controversy.” These strategies for undermining inconvenient science were so effective that they’ve served as a sort of playbook for industry interests ever since, said Stanford University science historian Robert Proctor. The sound science push is no longer just Philip Morris sowing doubt about the links between cigarettes and cancer. It’s also a 1998 action plan by the American Petroleum Institute, Chevron and Exxon Mobil to “install uncertainty” about the link between greenhouse gas emissions and climate change. It’s industry-funded groups’ late-1990s effort to question the science the EPA was using to set fine-particle-pollution air-quality standards that the industry didn’t want. And then there was the more recent effort by Dow Chemical to insist on more scientific certainty before banning a pesticide that the EPA’s scientists had deemed risky to children. Now comes a move by the Trump administration’s EPA to repeal a 2015 rule on wetlands protection by disregarding particular studies. (To name just a few examples.) Doubt merchants aren’t pushing for knowledge, they’re practicing what Proctor has dubbed “agnogenesis” — the intentional manufacture of ignorance. This ignorance isn’t simply the absence of knowing something; it’s a lack of comprehension deliberately created by agents who don’t want you to know, Proctor said.2 In the hands of doubt-makers, transparency becomes a rhetorical move. “It’s really difficult as a scientist or policy maker to make a stand against transparency and openness, because well, who would be against it?” said Karen Levy, researcher on information science at Cornell University. But at the same time, “you can couch everything in the language of transparency and it becomes a powerful weapon.” For instance, when the EPA was preparing to set new limits on particulate pollution in the 1990s, industry groups pushed back against the research and demanded access to primary data (including records that researchers had promised participants would remain confidential) and a reanalysis of the evidence. Their calls succeeded and a new analysis was performed. The reanalysis essentially confirmed the original conclusions, but the process of conducting it delayed the implementation of regulations and cost researchers time and money. Delay is a time-tested strategy. “Gridlock is the greatest friend a global warming skeptic has,” said Marc Morano, a prominent critic of global warming research and the executive director of ClimateDepot.com, in the documentary “Merchants of Doubt” (based on the book by the same name). Morano’s site is a project of the Committee for a Constructive Tomorrow, which has received funding from the oil and gas industry. “We’re the negative force. We’re just trying to stop stuff.” Some of these ploys are getting a fresh boost from Congress. The Data Quality Act (also known as the Information Quality Act) was reportedly written by an industry lobbyist and quietly passed as part of an appropriations bill in 2000. The rule mandates that federal agencies ensure the “quality, objectivity, utility, and integrity of information” that they disseminate, though it does little to define what these terms mean. The law also provides a mechanism for citizens and groups to challenge information that they deem inaccurate, including science that they disagree with. “It was passed in this very quiet way with no explicit debate about it — that should tell you a lot about the real goals,” Levy said. But what’s most telling about the Data Quality Act is how it’s been used, Levy said. A 2004 Washington Post analysis found that in the 20 months following its implementation, the act was repeatedly used by industry groups to push back against proposed regulations and bog down the decision-making process. Instead of deploying transparency as a fundamental principle that applies to all science, these interests have used transparency as a weapon to attack very particular findings that they would like to eradicate. Now Congress is considering another way to legislate how science is used. The Honest Act, a bill sponsored by Rep. Lamar Smith of Texas,3 is another example of what Levy calls a “Trojan horse” law that uses the language of transparency as a cover to achieve other political goals. Smith’s legislation would severely limit the kind of evidence the EPA could use for decision-making. Only studies whose raw data and computer codes were publicly available would be allowed for consideration. That might sound perfectly reasonable, and in many cases it is, Goodman said. But sometimes there are good reasons why researchers can’t conform to these rules, like when the data contains confidential or sensitive medical information.4 Critics, which include more than a dozen scientific organizations, argue that, in practice, the rules would prevent many studies from being considered in EPA reviews.5 It might seem like an easy task to sort good science from bad, but in reality it’s not so simple. “There’s a misplaced idea that we can definitively distinguish the good from the not-good science, but it’s all a matter of degree,” said Brian Nosek, executive director of the Center for Open Science. “There is no perfect study.” Requiring regulators to wait until they have (nonexistent) perfect evidence is essentially “a way of saying, ‘We don’t want to use evidence for our decision-making,’” Nosek said. Most scientific controversies aren’t about science at all, and once the sides are drawn, more data is unlikely to bring opponents into agreement. Michael Carolan, who researches the sociology of technology and scientific knowledge at Colorado State University, wrote in a 2008 paper about why objective knowledge is not enough to resolve environmental controversies. “While these controversies may appear on the surface to rest on disputed questions of fact, beneath often reside differing positions of value; values that can give shape to differing understandings of what ‘the facts’ are.” What’s needed in these cases isn’t more or better science, but mechanisms to bring those hidden values to the forefront of the discussion so that they can be debated transparently. “As long as we continue down this unabashedly naive road about what science is, and what it is capable of doing, we will continue to fail to reach any sort of meaningful consensus on these matters,” Carolan writes. The dispute over tobacco was never about the science of cigarettes’ link to cancer. It was about whether companies have the right to sell dangerous products and, if so, what obligations they have to the consumers who purchased them. Similarly, the debate over climate change isn’t about whether our planet is heating, but about how much responsibility each country and person bears for stopping it. While researching her book “Merchants of Doubt,” science historian Naomi Oreskes found that some of the same people who were defending the tobacco industry as scientific experts were also receiving industry money to deny the role of human activity in global warming. What these issues had in common, she realized, was that they all involved the need for government action. “None of this is about the science. All of this is a political debate about the role of government,” she said in the documentary. These controversies are really about values, not scientific facts, and acknowledging that would allow us to have more truthful and productive debates. What would that look like in practice? Instead of cherry-picking evidence to support a particular view (and insisting that the science points to a desired action), the various sides could lay out the values they are using to assess the evidence. For instance, in Europe, many decisions are guided by the precautionary principle — a system that values caution in the face of uncertainty and says that when the risks are unclear, it should be up to industries to show that their products and processes are not harmful, rather than requiring the government to prove that they are harmful before they can be regulated. By contrast, U.S. agencies tend to wait for strong evidence of harm before issuing regulations. Both approaches have critics, but the difference between them comes down to priorities: Is it better to exercise caution at the risk of burdening companies and perhaps the economy, or is it more important to avoid potential economic downsides even if it means that sometimes a harmful product or industrial process goes unregulated? In other words, under what circumstances do we agree to act on a risk? How certain do we need to be that the risk is real, and how many people would need to be at risk, and how costly is it to reduce that risk? Those are moral questions, not scientific ones, and openly discussing and identifying these kinds of judgment calls would lead to a more honest debate. Science matters, and we need to do it as rigorously as possible. But science can’t tell us how risky is too risky to allow products like cigarettes or potentially harmful pesticides to be sold — those are value judgements that only humans can make.

Principal of induction and binomial theorem part-1

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