Week 11 Lecture Slides - WPQ Answers (1) PDF

Cognition Lecture Outline The Machinery of the Mind One Minute Survey Questions Lecture 11: Reasoning and Problem PSY270H5F Solving Wednesdays,...

Cognition Lecture Outline The Machinery of the Mind One Minute Survey Questions Lecture 11: Reasoning and Problem PSY270H5F Solving Wednesdays, 9am - 12pm, DV 2072 Deductive and Inductive Reasoning What is a problem? Instructor: Dr. Benjamin Wolfe Problem solving strategies Office Hours: By appointment (in person) Expertise and its limits E-mail: [email protected] Constraints and self-constraints Can it be more common together? Men over 55 who have heart attacks Men who have Men over the heart attacks age of 55 Conjunctive fallacy: Failing to realize that a conjunction of events cannot be more probable than each event individually. Group A alone cannot be as big as the overlap of Group A & B ⚓ swinging around estimates Anchoring: Shifting the starting point Tversky & Kahneman (1974) to change decisional behaviour Anchoring can get you to overuse a value as a reference point, even when that reference is totally unrelated to the task! “What is the proportion of African nations in the United Nations?” So, if they show you the standard package ($14/mo) first, you’ll When the roulette showed 10, the average answer was 25% think that premium isn’t that much more money… When the roulette showed 65, the average answer was 45% This next roll of the 🎲 has to be… The Base Rate Bug Gambler’s fallacy: The misconception that prior outcomes can influence the outcome of an independent probabilistic event. You know what Base Rate is… but maybe experts are better at dealing with it? “The dice have no memory” You’re a radiologist. Let’s say the base rate for breast cancer is 1% So, 1:100 patients will have cancer Each of these sequences are equally likely to occur!  Base Rate and Errors Let’s assume a sample of 10,000 patients This is a hypothetical sample to talk about base rate neglect Let’s say the mammogram If the patient does have Mammogram result has an 85% chance of cancer, the mammogram will show it showing a nodule, if it’s there 85 / 100 times Nodule No nodule Total True diagnosis (that is, if the patient has cancer) Has cancer 85 15 100 1% Base Rate: 100 / 10,000 so, 9,900 don’t have cancer No cancer 990 8910 9900 If the patient doesn’t, And that it has a 90% chance the mammogram will to not show a nodule if a show nothing 90 / 100 times nodule is not present Let’s assume a sample of 10,000 patients Let’s assume a sample of 10,000 patients This is a hypothetical sample to talk about base rate neglect This is a hypothetical sample to talk about base rate neglect Mammogram result Mammogram result Nodule No nodule Total Nodule No nodule Total True diagnosis True diagnosis Has cancer 85 15 100 Has cancer 85 15 100 For that 1%, the image will No cancer 990 8910 9900 No cancer 990 8910 9900 only show it 85% of the time But for the remaining 99% of patients, the image will show something that looks suspicious in 10% of them And only 8.5% of the patients with a suspicious image will actually have something wrong, because the tools are imperfect  Casscells et al. (1978) Utility vs Subjective Utility Base rate neglect and (putative) experts Utility theory: assumed universal, perfectly logical, no individual Tested 60 students and faculty members P = (probability of a particular outcome) V = (value of a particular outcome) If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5 percent, what is the chance that a person found to have a positive result actually has the disease, assuming Expected Utility = P x V that you know nothing about the person’s symptoms or signs? Subjective Expected Utility: idiosyncratic, what is it to you! The correct answer is 1.8%, P = (probability of a particular outcome to you) Only 18% of them answered accurately, and almost half of the V = (value of a particular outcome to you) participants responded with 95%. The average answer was 56%. Subjective Expected Utility = P x V Even experts are bad intuitive statisticians The Sunk Cost Fallacy is the idea that putting more resources (time, money, attention) will save your investment Week 10 - WPQ1 So, [B] is the best answer - System 1 is non-deliberative, and while [D] is tempting, it’s not the best answer; [A] is wrong (you don’t tend to More effort or money or attention does not always think about running like this); as is [C], which mismaps the definition redeem your investment! Cut your losses!  Week 10 - WPQ2 [D] is correct - since [A] is false (we totally do this) and [C] is also false (positive framing seems helpful); [B] is the conjunctive fallacy, but is correctly formed (the union can’t be more common) Week 10 - WPQ3 Week 10 - WPQ4 [B] is correct - you get some utility, and some > none This was at the end of class last week… we think losses [A] hurt [A] is wrong, you should always go for some value more than gains [B]… just a straight-up example of that study! [C] and [D] are just straight-up wrong  Since we’re almost done… This is just for fun… but if you send me pet pictures this week, I’ll add as many of them as I can to next week’s last lecture! FINAL EXAM UPDATE NEW ROOM: KN 137 19 December, 5-7pm Registrar changed this on 12 November and didn’t tell me! Hopefully you’re not asleep…  Lecture Outline Decisions vs Reasoning One Minute Survey Questions Lecture 11: Reasoning and Problem Solving Deductive and Inductive Reasoning What is a problem? Problem solving strategies Decisions Reasoning Expertise and its limits What can I do? Why should I do it? Constraints and self-constraints What are my options? How do I weigh options? Last week’s lecture This week’s lecture Reasoning: asking what’s most probable? Now let’s talk about How do we figure this out? types of reasoning Evidence How do we describe Experience and classify it? Logical Thinking  Two Types of Reasoning What animal would you expect me to use for examples? Inductive Deductive What’s likely? What must be true? Probabilistic Logical rules In the 10th week of PSY270, this should be pretty easy for you to inductively reason… This is right, and I can prove it! The Case of the Chewed Cable Deductive Reasoning: drawing conclusions about what must be true given previous evidence Deductive Reasoning: think Sherlock Holmes What are the facts? What do you know? What does Bunlock Holmes here know?  Lecture Outline Drawing Conclusions One Minute Survey Questions Syllogism: Two premises and a conclusion. If the two premises are true, then the conclusion must be Lecture 11: Reasoning and Problem true (within the bounds of the syllogism) Solving Deductive and Inductive Reasoning A→B (premise 1) B→C (premise 2) What is a problem? If the cat pushes the glass, If it moves horizontally on Problem solving strategies it will move horizontally on the table the table, it will fall off the edge of the table Expertise and its limits Test: Is this true? The glass pawbably Test: Is this also true? If it keeps Constraints and self-constraints won’t grow feet and run away from the cat moving, the cat will test gravity with it. If Premise 1 or Premise 2 Mind your ps and qs is false, it breaks! The logic of if/then statements A→B (premise 1) A crow is not a bird B→C (premise 2) All birds have a beak Antecedents (p) A→C (conclusion) If [statement] A crow does not have a beak So, you’re testing P1 and P2 Consequents (q) against what you know to be true but the syllogism’s conclusion is limited Then [statement] What if we know p is true? We didn’t observe p Modus ponens: If p is true, then q must be true Modus tollens: If p is false, then q must NOT be true If I throw a crinkle-ball, If I throw a crinkle-ball, then Howl will pick it up then Sophie will pick it in his mouth up with her thumbs! I threw a crinkle ball… I didn’t throw a crinkle ball therefore, Howl picked therefore, Sophie didn’t it up in his mouth unfold it (that’d be odd) Can the consequent alone What if the antecedent tell us anything? doesn’t happen (not-p) Affirmation of the Consequent: Forbidden. Just knowing q doesn’t tell us about p! If I throw a crinkle-ball, then Howl will carry it off If I throw a crinkle-ball, then Howl will carry it off I didn’t throw a crinkle ball Can’t say anything Howl carried off the crinkle-ball. about q We can’t know!  This broke my brain (well, me too…) Following Rules The Wason Card Selection Task Judged Second Premise Conclusion Valid? Correctly? Modus Ponens p Therefore, q Yes 97% O K 1 8 Therefore, Modus Tollens Not q Yes 60% not p Affirmation of q Therefore, p No 40% Rule: If a card has a vowel on one side, Consequent it has an even number on the other side Therefore, Not p No 40% not q Which cards should be turned over to determine We find modus ponens easily, but the rest are difficult. whether this rules is being followed? We think we can go backwards, or that negative results work logically. Why don’t people do well ? Following Rules Should you try to validate or break the rule? The Wason Card Selection Task Confirmation bias is tending to select O 8 examples that might confirm the rule O K 1 8 66% 53% 66% 26% 28% 53% Falsification asks “what would break the rule” and is better K 1 Correct answer: 2 cards! since it tells you something new! O&1 (6%) or O&8 (32%) 26% 28%  Hacking this problem One Instruction Set Permission schema: If A is satisfied, Cheng & Holyoak (1985) then B may be carried out. Cholera Typhoid Entering Transit Typhoid Hepatitis Hepatitis Group A: You are an immigration officer at Manila International Airport. Among the documents you have to check is a sheet called Form H. One side of this form indicates whether the passenger is entering the country or in transit, and the other side of the form lists names of tropical diseases. You have to make sure that if the form says “Entering” on one side, the other side includes cholera among the list of diseases. So, let’s say your an immigration officer at the airport… Which cards should you turn over? The Other Instruction Set So, which one? Cheng & Holyoak (1985) Cholera Which instruction set activated the Typhoid Entering Transit Typhoid Hepatitis permission schema? Hepatitis Group B: You are an immigration officer at Manila International Airport. Group A: 61% flipped “Entering” and “Typhoid Hepatitis” Among the documents you have to check is a sheet called Form H. One side of this form indicates whether the passenger is entering the country or Group B: 92% flipped “Entering” and “Typhoid Hepatitis” in transit, and the other side of the form lists the vaccinations the travelers received in the past 6 months. You have to make sure that if the form says “Entering” on one side, the other side includes cholera among the list of diseases.This is to ensure that entering passengers Just changing the instructions can have dramatic are protected against the disease. impacts on what decisions people make! Which cards should you turn over?  Lecture Outline Inductive Reasoning: drawing conclusions about what is most probable, given previous evidence and experience One Minute Survey Questions Lecture 11: Reasoning and Problem Solving Deductive and Inductive Reasoning What is a problem? From what you expect, are wombats or geese more Problem solving strategies likely to be road hazards on campus? Expertise and its limits Alright, let’s unpack inductive reasoning Constraints and self-constraints Building on what you know Assuming universality Property induction: generalizing from properties Premise typicality: how representative is it of a larger set? or features (think way back to features!) Closely related to the representativeness heuristic Black raspberries You know raspberries are delicious Woody Nightshade Black Nightshade Leaning on what you know Dealing with Uncertainty Confirmation bias: favouring what you already know, rather than probing the situation Bayes’ Rule: posterior probability is the product of prior probability and likelihood This is Bayes the Cat You haven’t gotten to pet him, so how big is he? Prior Probabilities Range of Chonkitude Or, what do you already know? Remember, the task is to figure out how big Bayes the Cat is. Let’s assume you’ve met a bunch of cats (maybe just online), and that their sizes follow a normal distribution. That’s your distribution of prior probabilities, and you can use it to estimate how big a cat is Likelihood of Chonkitude So, how big is this boy? How many really chonky cats do you know about? How many really tiny cats? Probably large, but not huge (or too round) Lecture Outline One Minute Survey Questions Lecture 11: Reasoning and Problem Solving Deductive and Inductive Reasoning What is a problem? Problem solving strategies Expertise and its limits Constraints and self-constraints Problem? What problem? Jumping the Goal State Gap Are all solutions equally good? Problems are defined as an obstacle or discrepancy between the current state and the goal state [there must be a gap] Goal State Current State The best solution might not be what people (or cats) actually do Achieving your Goals Are my goals your goals? Maybe or maybe not; a good thing to think about when you study this topic No, this class isn’t going to sound like bad motivational instagram posts… The monitor lizard wants a snack (maybe) The shopkeeper just wants the lizard out of the shop! Talking about Problems Talking about Problems Some core definitions so we’re all on the same page Non-Insight Problems Insight Problems No, not like that. Therapy doesn’t show up Sequential steps towards a solution Solved in a flash! in PSY270 at all… now where’s the right picture? Step by Step to a Goal Non-Insight Problems: Achieving goals by going through I’ve got it! interim stages in a sequential manner Insight Problems: Solved suddenly, without awareness of interim steps Solving mathematical equations Programming, or algorithmic thinking  Studying Problems Alright, that’s a little weird Metcalf and Wiebe (1987) Solving algebra (non-insight) and insight problems How well do you think pestered every 15 seconds… you’d do if someone asked every fifteen seconds? Don’t know about the rest of you, but this would be me… Asking people to solve mind- The interesting corner of melting problems for science! problem solving Insight problems Non-insight problems have ground truth (we know if the recipe works or not) Dunker’s Candle Problem: Using the following items, fix the candle on the wall so it won’t drip candle wax on the floor  Thinking laterally Another one Insight problems often force us to think quite differently Maier’s two string problem: using only what you have, tie the two strings together (note: just standing on the chair isn’t enough - you can’t reach far enough) Using tools in ways you don’t think of The pliers can extend your reach! I’m stuck OK, the cat is cute, but there’s got to be a name for this… Functional fixedness: restricting how we use (or think we can use) an object based on the schemes we have for it  Problems are a gap between Lecture Outline where you are now and your goal One Minute Survey Questions Lecture 11: Reasoning and Problem Solving Deductive and Inductive Reasoning What is a problem? Problem solving strategies Better to find interim states Expertise and its limits So, if you try to jump too Constraints and self-constraints far, you might not land where you expect to What can you do now ? Means-End Analysis: what are the subgoals that move you closer to the ultimate goal? Their human isand It’s morning, stillthe asleep cat Intermediate goal: wake up the human! would like breakfast But the cat doesn’t have thumbs, and can’t open the bag  to change representations and experience insight. Increasing the salience of parity and providing hints are ways of providing external sources of search constraint. Specifically, we predict that solution times will be ordered by the ex- pected salience of parity in the four conditions. According to our salience IN SEARCH OF INSIGHT 383 Thinking differently rating study, the BLANK condition should be most difficult, followed by either the COLOR or BLACK & PINK condition, followed by the BREAD & BUTTER condition which should be easiest. Table 3 presents How might you do this? - 25 - 4 SWJCCTS CONDITIONS, (23 Naive, 5-l Subjects 2 Bxcludad Per -- Condition suspect prior knowledge) Reframing the results. the relevant initial The state: first find column,a new waythetomean showing describe the times required Reframing approaches from Kaplan and Simon (1990) - HINTS GIVCN AT REGULAR INTBRVALS by subjectsthat problem of different helps you groups to first think mention about howparity, servesitas a check to solve THE FOUR CONDITIONS: on our salience manipulation. As we originally predicted, the BREAD & e slack BUTTER board was the most salient (i.e., caused subjects to mention e P,nk. Black’sparity earliest), Problem Checkerboard followed (1946) by the BLACK & PINK board, the COLOR board, and lastly the BLANK board. Note however, that the difference between the COLOR and BLACK & PINK conditions is the smallest of all the intergroup differences. A one-way analysis of variance indicates that the overall difference between groups is highly statistically significant (F[3,19] = 12.05, p <.ooOl). The second column of Table 3 gives the mean times required by sub- jects to decide that covering is impossible. Again the times are ordered as we originally predicted with the smallest intergroup difference occurring between the COLOR and BLACK & PINK conditions. However, a one- way analysis If you remove the twoofred variance corner shows pieces,that the overall difference between groups can you is tile not31significant 1x2 dominos (F[3,19] =.83, p >.48) suggesting that time to declare to perfectly the problem cover theimpossible board? may be relatively constant. The third column confirms that time to Rough Proof is ordered accord- This ing is impossible to salience(😈)(asbut how canin the empirical salience-rating study). Here, measured BRCAD 6 BUTTER a you figure analysis one-way out that itof is?variance reveals a statistically significant overall These are all (Note: viable Boards reframing not drawn to actual approaches, sirs) but difference (F[3,19] = 4.08, p <.025). Note that the COLOR and PINK & what do youPREDICTION: think helps people solve Black’s problem faster BLACK groups differ in mean solution time by only 3 s. Most BLANK > COLOR > BLACK Difficult.........................................E~siast L PINK > BRBAD 6 BIJTTBR The fourth column, showing the number of approaches tried in each FIG. 2. Experiment 2 at a glance. Kaplan and Simon’s Results TABLE 3 Converting the Problem the salience of the critical cue, parity. Hints were provided systematically (if needed) to ensure that all subjects solved the problem within an hour. We predicted that subjects in the higher cue salience conditions would Mean Times to Points on Solution Path and Mean Number of Approaches Tried take less time and require fewer hints to solve the problem than subjects Analogical transfer: in the lower giving cue saliencethe solverWeinformation conditions. further expected in another to find evidence way, so they Time to first Time to Time to Number of Condition mention parity declare impossible rough proof approaches can extend a solution from one space to another BLANK 1980 sec. 828 sec. 2242 sec. 9.14 Duncker’s Radiation problem (1945): COLOR 1265 sec. OF INSIGHT IN SEARCH 672 sec. 383 1375 sec. 5.80 BLACK & PINK- 25 SWJCCTS (23 Naive, 905 sec. 2 Bxcludad -- suspect prior 639 sec. knowledge) 1378 sec. 5.16 Suppose you are a doctor faced with a patient who has BREAD & BUTTER- 4 CONDITIONS, 5-l 342 sec. Subjects Per Condition 483 sec. 995 sec. 4.00 a malignant tumor in his stomach. It is impossible to - HINTS GIVCN AT REGULAR INTBRVALS operate on the patient, but unless the tumor is Mean total THE FOUR CONDITIONS: 1188 sec. 670 sec. e slack 1557 sec. 6.26 destroyed, the patient will die. There is a kind of ray e P,nk. that can be used to destroy the tumor. If the rays are directed at the tumor at a sufficiently high intensity, the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities, the rays are harmless to the healthy tissue but they will not affect the tumor either… How can you use the ray to only destroy the tumor? BRCAD 6 BUTTER Hmmm… what might feel the same? (Note: Boards not drawn to actual sirs) Depending on how you frame it, 2x or more time penalty depending on task! PREDICTION: BLANK > COLOR > BLACK L PINK > BRBAD 6 BIJTTBR Most Difficult.........................................E~siast FIG. 2. Experiment 2 at a glance. the salience of the critical cue, parity. Hints were provided systematically (if needed) to ensure that all subjects solved the problem within an hour. We predicted that subjects in the higher cue salience conditions would take less time and require fewer hints to solve the problem than subjects in the lower cue salience conditions. We further expected to find evidence Speaking to the Problem What did Gick and Holyoke Gick and Holyoke (1983): control vs analogical transfer Fortress Story find with the Fortress? A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads ll? led to the fortress through the countryside. A rebel general vowed to capture the be fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a a full-scale direct attack. However, the general then learned that the dictator had g planted mines on each of the roads. The mines were set so that small bodies of rin men could pass over them safely, since the dictator needed to move his troops and workers to and from the fortress. However, any large force would detonate the s Transfer group: When the transfer group mines. Not only would this blow up the road, but it would also destroy many 30% could solve i was told to think about it th neighboring villages. It therefore seemed impossible to capture the fortress. Dunker’s problem 70% of them could solve it! s after just reading However, the general devised a simple plan. He divided his army into small groups oe Control group: the Fortress story! and dispatched each group to the head of a different road. When all was ready he 10% could solve D gave the signal and each group marched down a different road. Each group Dunker’s problem continued down its road to the fortress so that the entire army arrived together at the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator. How does this work? Looking Deeper Mapping correspondences: understanding the underlying commonalities Structural features: what are the underlying principles? What is common across situations? + Being a prep cook in a restaurant Washing glassware in a lab What’s similar, even when the superficial The surface features here are very different, but the features aren’t anything alike? structural features are very similar  Do you think you can? Set or mindset - do we think we can solve the problem? Are we ready to try to solve the problem? If your car tells you to look here are you ready to use the information? Your ability to problem solve = whether you think you can (e.g., I’m not good at X, can’t do Y)… A different purrspective What helps you be creative Smith et al. (1983) in problem solving? Task: Imagine a new life form Example Group No-Example Group Intrinsic Motivation Resources / Opportunity Told about creatures with And was more creative four legs 🐈 🐩 🦒 (a ham with an eye?) What you are told can easily limit the space of possible solutions to a problem What’s the real problem? I know what he’s trying to do The problem of identification vs description Theory of mind: trying to intuit someone else’s mental state so you can understand their actions When you say “he wants to go fast” The expert knows best, right? Human-Centred Design (HCD): The The user knows what Is she about to cross? user can’t know what they need, and they need, right? the expert can’t know, unless they observe the user in the task! PSY385 is built around this idea! What can an expert do in Lecture Outline half a second? One Minute Survey Questions Evans et al. (2018): Noticing breast cancer in 500 ms Lecture 11: Reasoning and Problem Solving Deductive and Inductive Reasoning What is a problem? Problem solving strategies Expertise and its limits Constraints and self-constraints Expert radiologists can do this. Novices have no idea how. Knowing where to look Looking Ahead Problem solving in the world is all about getting the information you need to do the task Ever played beat saber? Kelly et al. 2016 Vater et al. 2017 Intern Trainee Do you remember when you first tried to play? Near-Expert Expert Did you miss a lot of boxes? Did you learn to Structural vs Surface Features look somewhere a little differently? Expertise Not Required Solutions can come from anywhere Should we devalue expertise? No. Being an Odón Device expert means knowing you’re not omniscient Generalizing principles from one problem to a very different problem by commonality! When expertise goes bad If you’re an expert radiologist (like the ones we talked about from Evans et al.), you might not be any better than you or me at finding your keys on your desk Thinking you’re an expert Undervaluing yourself Dunning-Kreuger effect: non-experts believing they are as good as experts at a task or a domain of knowledge Mismatch between confidence and performance Imposter syndrome: high performance, low confidence  Summary Deductive and Inductive Reasoning Formal reasoning (if p, then q) Problem solving; goal state gap; best vs actual Thank you for Goals and individual actors Types of problems: insight vs non-insight filling out the Problem solving strategies Structural features vs surface features One Minute Survey Expertise; strengths and shortcomings Dunning-Kreuger and Imposter Syndrome Remember: send your pet pictures (Wk 12)