Lecture 3 Todays Lecture Fermi Problems 11 Fallacies

Lecture 3 Todays Lecture Fermi Problems 11 Fallacies in Logic Structured Critical Reasoning Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 1

Fermi Problems • Enrico Fermi: – 1938 Nobel Laureate for elementary particle physics – 1942 First sustained nuclear reaction • Famous for his back of the envelope calculations. • A Fermi problem has a characteristic profile: Upon first hearing it, one doesn’t have even the remotest notion what the answer might be. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 2

Fermi Problems One feels certain that too little information exists to find a solution Yet, when the problem is broken down into sub problems, each one is answerable Without the help of experts or reference books, an estimate can be made, either mentally or on the back of an envelope, that comes remarkably close to the exact solution Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 3

Fermi Problems • • • What do you know is relevant? What assumptions can you make? How plausible are your assumptions? Is your chain of reasoning accurate? Can you do the problem another way and see if the result is the same? • In your answer, do you spell out your assumptions, reasoning, solution, and checking procedure clearly? Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 4

Fermi Problems Q: How many piano tuners in the city of Chicago? A. Population of Chicago 4, 000 B. Size of Households 4 C. Number of Households 1, 000 D. Fraction of Households that own a piano 1/5 E. Number of Pianos 200, 000 F. Number of Tunes/year per Piano 1 G. Number of Tunes Needed Per Year 200, 000 H. Tunes per day 2 I. Tunes per year per tuner 500/yr/tuner 400 Tuners Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 5

Fermi Problems Refinement Add Churches Add Schools Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 6

Critical Thinking The process we use to reflect on, assess and judge the assumptions underlying our own and others ideas and efforts. Determines how skillfully someone gathers, processes and applies information in order to identify the best way to reach a goal or navigate a complex situation. Socratic Questioning is at the Heart of Critical Thinking Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 8

Structured Critical Reasoning To Identify: • • • The conclusions The Evidence The Assumptions The Strength and Weakness of each Assumption Fallacies in logic

Structured Critical Reasoning Step 5. Identify Fallacies in Logic The following table gives eleven common fallacies in logic to look for when evaluating the assumptions used in supporting the evidence and the conclusions Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 10

Fallacies in Logic • • • Ambiguous or vague words or phrases. Citing a questionable authority Straw Person. False Dilemma, i. e. Either-Or. Red Herring. Slippery Slope. Appeal to Popularity. Perfect Solution. False, Incomplete or Misleading Facts or Statements. Causal Oversimplification. Hasty Generalization.

Eleven Fallacies in Logic to Look For 1. Ambiguous or vague words or phrases Uses words, phrases or sentences that have multiple interpretations or really don’t say anything. “The model is in close agreement with the data. ” What does the word “close” mean? What is the measure of a “close agreement? ” Within 10%? 50%? “Jill saw a man with binoculars. ” Did Jill see the man with her binoculars of did she see a man carrying binoculars. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 12

Eleven Fallacies in Logic to Look For 2. Citing a questionable authority Gives credibility to someone who has no expertise in the area. John agrees with me that consuming energy drinks is bad for you. What makes John an expert on the perils of drinking energy drinks? John could be an expert dietician studying the subject or have no basis for knowing anything about the effects of energy drinks on the body other than an uneducated opinion. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 13

Eleven Fallacies in Logic to Look For 3. Straw Person. Discredits an exaggerated version of an argument. Recent auto accidents in your neighborhood have led you to propose to city council to place speed bumps near each of the two intersections along Main Street to calm the traffic flow. Opponents complain that placing speed bumps all up and down the street is counter productive and an unnecessary burden on drivers. The straw person argument here is the expansion of your proposal from “ a speed bump near each of the two intersections” to “speed bumps all up and down the street”. The attribution of this alternative argument deflects the focus from your true proposal. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 14

3 Straw Person 1)Person A: "I don't think children should play on busy streets. " Person B: "I think it would be foolish to lock up children all day. “ 2) Santa: "We should clean out the closets. They are getting a bit messy. " Banta: "Why, we just went through those closets last year. Do we have to clean them out everyday? " Santa: "I never said anything about cleaning them out every day. You just want to keep all your junk forever, which is just ridiculous. “

5 Straw Person 4) Mike – You want to go get Hamburgers? Jake- Hmm…Could we get Pizza Instead? Mike(infuriated)- What? ? So You are saying we should only ever eat pizza ? ? That we should just burn down all Hamburger stores? !? Jake- That’s a very inaccurate and unfair representation of what I said!

Eleven Fallacies in Logic to Look For 4. False Dilemma, i. e. Either-Or. Assumes only the choices stated by the author are the ones that exist. At a recent cocktail party, the conversation has turned to family pets, and your friend asks you “Are you a cat or a dog person? ” Your choices here have clearly been limited to two, when in reality there are many others: you may have no interest in pets at all, you may be a bird person, or you may equally enjoy cats and dogs. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 17

4 False Dilemma Either you buy a large car and watch it guzzle away your pay check, or you buy a small car and take a greater risk of being injured or killed in the event of an accident.

Eleven Fallacies in Logic to Look For 5. Red Herring. Introduces an irrelevant topic to distract the conversation from the main topic. You call your cell phone provider to complain about how poor your cell phone battery life is after the recent software update and the representative, instead of responding to your concern, praises the providers new unlimited text messaging plans that are due to be released in the next month. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 19

5 Red Herring 1)Mother: It’s bedtime Jane Emily: Mom, how do ants talk ? Mother: Don’t know dear. Close your eyes now. Emily: But mama, do ants say hello when they meet? This conversation shows how a child tries to distract her mother so that she could stay awake a little longer 2) Ashley asked her friend Clara how she looked. Clara suddenly started talking about how good yesterday’s dinner was and started praising her cooking skills.

Eleven Fallacies in Logic to Look For 6. Slippery Slope. Assumes that if this fact is true then everything else follows. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 21

6 Slippery Slope 2)We cannot unlock our child from the closet because if we do, he will want to roam the house. If we let him roam the house, he will want to roam the neighbourhood. If he roams the neighbourhood, he will get picked up by a stranger in a van, who will kidnap him for ransom. Therefore, we should keep him locked up in the closet. 3) “Today you are late by ten minutes, tomorrow you will be late by an hour, and then someday you will simply cease to show up. ” 4)If we ban smoking, then people will start taking soft drugs and then move onto hard drugs, and the crime rate will go up and up. We should therefore prevent crime by allowing smoking. 5) Student: May, I go to toilet. Professor Replied: No, if I will allow you, other students will also come and soon the whole class will ask and nobody will be here to teach for. So no.

6 Slippery Slope 6) You shouldn’t drive and use a cell phone, Huh? Next they will say you shouldn’t drive and juggle!!!

Eleven Fallacies in Logic to Look For 7. Appeal to Popularity “You’ll be out of sinc with the rest of the group if you don’t support this issue. ” Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 24

Eleven Fallacies in Logic to Look For 8. The Perfect Solution. Assumes that if a part of the problem is not satisfied or solved (even a small part) then the entire solution should be abandoned. “Don’t waste your money on a home security system, master thieves will still be able to get into your house. ” However, many thieves may be deterred by a security system. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 25

8 Perfect Solution Seat Belts are a bad idea. People are still going to die in car crashes. Proclaiming that any medication that has side effects is worthless, or that any treatment less than 100% effective is a waste of time.

Eleven Fallacies in Logic to Look For 9. False, Incomplete or Misleading Facts or Statements. Presents data in such a way that it falsely leads someone to the wrong conclusion. “Because 90% of college students polled had no debt, education costs are not a problem. ” It’s possible that only 10 college students were polled, or that the poll was taken at a banquet for scholarship students. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 27

Eleven Fallacies in Logic to Look For 10. Causal Oversimplification. Explaining an event attributing it to a single factor, when many factors are involved or by overemphasizing the importance of a single factor. At a party you overhear a friend tell their spouse “I had high blood pressure at the doctor’s office today, I really need to reduce the stress in my job. ” This friend is obviously attributing the high blood pressure reading to job-related stress, while there may be many additional contributing or more important factors (lack of exercise, poor diet, genetic predisposition, white coat syndrome– i. e. , high blood pressure because you are in the doctors office, etc. ) Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 28

Eleven Fallacies in Logic to Look For 11. Hasty Generalization. Drawing a conclusion about a large group based on the experiences with a few members of the group. “All engineers are introverts who would rather relate to computers than people. ” Clearly there are many engineers who are outgoing. It is very dangerous to make sweeping generalizations regarding a group based on limited experience. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 29

Critical Thinking – SCR Step 1. Step 2. Step 3. Step 4. Step 5. Identify all the conclusions. Look for the reasons and evidence the author uses to support each conclusion. List all major assumptions Evaluate all the assumptions and evidence. Identify Fallacies in Logic Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 30

Apply Structured Critical Reasoning to : Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 31

Underground Power Lines Perform an SCR on the article and determine the validity of the author’s argument. The issue of placing overhead power lines underground is raised after all major power outages. This issue when examined on a basis of the costs and benefits to customers and utilities of undergrounding power lines ends up that the costs outweigh the benefits. Studies show that underground infrastructure tends to have slightly better reliability performance than overhead power lines. However, in a major storm, the entire utility is effected, not just the overhead lines, meaning underground lines would not prevent some outages. The cost to burry aboveground power lines range from $80, 000 a mile in rural areas to $2. 1 million a mile in urban areas according to a 2009 study. This cost is simply unreasonable for the minimal added utility. Undergrounding power lines is simply not the answer to solve power outages. Darlington County Press Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 32

Underground Power Lines Solution Conclusion: 1. Power lines should not be put underground Evidence: 1. Would not prevent some outages/ only slightly better reliability 2. Too expensive for added utility Assumptions: 1. Undergrounding power lines is only worth it if it prevents all outages 2. The author correctly calculated the value of the added utility of undergrounding before calling the cost unreasonable Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 33

Critical Thinking – SCR Step 1. Identify all the conclusions. Step 2. Look for the reasons and evidence the author uses to support each conclusion. Step 3. List all major assumptions Step 4. Evaluate all the assumptions and evidence. Step 5. Identify Fallacies in Logic Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 34

Underground Power Lines Solution Conclusion: 1. Power lines should not be put underground Evidence: 1. Would not prevent some outages/ only slightly better reliability 2. Too expensive for added utility Assumptions: 1. Undergrounding power lines is only worth it if it prevents all outages 2. The author correctly calculated the value of the added utility of undergrounding before calling the cost unreasonable Strengths and Weaknesses of Assumptions: 1. Questionable assumption – increasing the reliability of the system has some value 2. Questionable assumption – the author is unknown and the facts are not cited Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 35

Underground Power Lines Solution Conclusion: 1. Power lines should not be put underground Evidence: 1. Would not prevent some outages/ only slightly better reliability 2. Too expensive for added utility Assumptions: 1. Undergrounding power lines is only worth it if it prevents all outages 2. The author correctly calculated the value of the added utility of undergrounding before calling the cost unreasonable Strengths and Weaknesses of Assumptions: 1. Questionable assumption – increasing the reliability of the system has some value 2. Questionable assumption – the author is unknown and the facts are not cited Fallacies in Logic: 1. Fallacy 8 – Perfect Solution. Just because the undergrounding of lines not prevent all outages does not mean it does not still add value to the system. 2. Fallacy 2 – Citing Questionable Authority, author is unknown. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 36

False Dilemma 1) Do you want Tea or coffee. Explanation: You are choice has been clearly limited to two either tea or coffee. In reality it might happen that you don’t like either tea or coffee or both. 2) Either you buy a large car and watch it guzzle away your pay check, or you buy a small car and take a greater risk of being injured or killed in the event of an accident. 3) Grand Father asking his grand daughter- “Do you want to become a doctor or an engineer? ” Here grandfather has closed all other choices and limited it two for her granddaughter.

Straw Person 1)Person A: "I don't think children should play on busy streets. " Person B: "I think it would be foolish to lock up children all day. “ 2) Santa and Banta are arguing about cleaning out their closets: Santa: "We should clean out the closets. They are getting a bit messy. " Banta: "Why, we just went through those closets last year. Do we have to clean them out everyday? " Santa: "I never said anything about cleaning them out every day. You just want to keep all your junk forever, which is just ridiculous. “ 3) There is no logical or moral justification for the killing of animals for food. Animals are sentient creatures that deserve the same consideration as humans. Joe: Look, if you want to eat grass like a cow, Bon Appetite! Just let me have my hamburger

Duncker Diagrams OK Not to Achieve Desired State Possible Paths to Desired State Path 1 Path 2 Path 3 Solutions to Implement Paths to Desired State Solution 1 What to do Solution 3 Possible Paths to Make OK not to Achieve Desired State Path 1 How to do it Path 2 Path 3 Solutions to Implement Paths Not to Achieve Desired State Solution 1 Solution 3 Solution 2 Desired State New Problem Statement Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 39

To Market, To Market The Situation: Toasty O’s was one of the hottest selling cereals when it first came on the market. However, after several months, sales dropped. The consumer survey department was able to identify that customer dissatisfaction, as expressed in terms of taste, was related to the age of the cereal. Consequently, management determined that they must streamline the production process to get the cereal on the store shelves faster, thus ensuring a fresher product. Engineering had quite a time with this problem - there wasn’t much slack time that could be removed from the process to accomplish the goal. Of the steps required to get the product on the shelves (production, packaging, storage, and shipping) production was one of the fastest. However, plans for building plants closer to the major markets were considered as was trying to add more trucks to get the cereal to market faster. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 40

To Market, To Market Sales of Toasty O’s are dropping. Consumer surveys have indicated a dissatisfaction with a stale taste. Perceived Problem: “Streamline the production process to get the cereal on the store shelves faster, thus ensuring a fresher product. ” However, production was one of the fastest steps in getting the product to market. Second Perceived Problem: Get the Cereal to Market Faster Get Cereal to Market faster Build More Plants Closer to Market Locations Improve Transportation System Charter jets for trips >1000 mi Hire former race Car drivers Ignore speed limits Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 41

To Market, To Market Sales of Toasty O’s are dropping. Consumer surveys have indicated a dissatisfaction with a stale taste. Make it OK NOT to get cereal to market faster Perceived Problem: “Streamline the production process to get the cereal on the store shelves faster, thus ensuring a fresher product. ” Stop Making Cereal However, production was one of the fastest steps in getting the product to market. Thus, the following options were considered: • Build plants closer to market • Add more trucks Make Cereal Stay Fresher Longer Add a chemical to slow down the spoiling reaction Convince Customers that Stale=Good Make boxes tighter and more impermeable to air and moisture These options require a major capital investment. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 42

To Market, To Market Original Statement How to get cereal to market faster. Make it OK NOT to get cereal to market faster The real problem was that the cereal was not staying fresh long enough, not that it wasn’t getting to market fast enough. Stop Making Cereal New Problem Statement How to make boxes tighter and to determine appropriate additive to slow down the spoiling reaction Make Cereal Stay Fresher Longer Add a chemical to slow down the spoiling reaction Department of Chemical Engineering, University of Michigan, Ann Arbor Convince Customers that Stale=Good Make boxes tighter and more impermeable to air and moisture 2/4/2022 43

You have had a very hectic morning, so you leave work a little early to relax a bit before you meet your supervisor, who is flying in to a nearby airport. You have not seen your supervisor from the home office for about a year now. He has written to you saying that he wants to meet with you personally to discuss the last project. Through no fault of yours, everything went wrong: The oil embargo delayed shipment of all the key parts; your project manager had a skiing accident; and your secretary enclosed the key files in a parcel that was sent by mistake to Japan via sea mail. Your supervisor thinks that you have been so careless on this project that you would lock yourself out of your own car.

As you are driving through the pleasant countryside on this very chilly late fall afternoon, you realize that you will be an hour early. You spot a rather secluded roadside park about 200 meters away. A quiet stream bubbles through the park, containing trees in all their autumn colors— such an ideal place to just get out and relax. You pull off into the park, absentmindedly get out and lock the car, and stroll by the stream. When you return you find that you have locked the keys and cell phone inside the car. The road to the airport is not the usual route; cars pass through about every 10 to 15 minutes. The airport is nine kilometers away; the nearest house (with a telephone) is one kilometer away. The plane is due to arrive in 20 minutes. Your car, which is not a convertible, is such that you cannot get under the hood or into the trunk from the outside. All the windows are up and secured. [Courtesy of Professor Donald Wood, Mc. Master University, Canada. ] Apply the Duncker Diagram and one other problem-solving technique to help decide what to do. (Problem courtesy of D. R. Woods, Mc. Master University. )

What to do Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 48

How to do it Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 49

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at airport Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 51

What to do Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 52

How to do it at airport Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 53

at airport Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 54

The Real Problem: Find ways to change bosses impression of you. Department of Chemical Engineering, University of Michigan, Ann Arbor 2/4/2022 55