Friday, October 17, 2014
Goat Hunting, Probably
As McKim enjoys her new, odds-defying dream car, let's review. We've considered several explanations of the best strategy when confronted with the Monty Hall Problem: the mathematical explanation (including the 100-door version); the simplified version; and the draw-every-possibility-and-count-with-Bogel version. As you think back and perhaps rewatch these, consider the ways of knowing that you employed in your responses. How did your responses change as we talked and learned? In what ways did different ways of knowing help and hinder your efforts to understand which strategy was best? Analyze and explain fully, posting your writing by 9:30 on Tuesday evening. Please arrive at class on Thursday having read all your classmates' writings. Have a great weekend.
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How did your responses change as we talked and learned? In what ways did different ways of knowing help and hinder your efforts to understand which strategy was best?
ReplyDeleteAfter watching the first video, I had a vague idea of how the math was technically correct, but I still had a significant amount of doubt about why this theory worked. Here, emotion got in the way of reason. I knew, logically, that this math equation was correct and that it DID work, but the part of my brain that was telling me no was based on the emotion of confusion.
However, the second video explained the problem in a different way, namely by focusing on the goats rather than the car. This served to solidify my understanding of why the theory worked and ended up removing the emotion-based doubt I felt after the first video. Hence, my comprehension of the problem was hindered by emotion as a way of knowing because my confusion and doubt was actually preventing me from understanding the theory.
As we talked through the problem, I began to understand more and more of the explanation. The mathematical explanation was difficult as I understood it within the confines of logic as a way of knowing and therefore could not easily visualize or understand how the Monty Hall problem actually worked. There was also a degree of emotion involved-- even with the 100 door explanation, I still felt vaguely as though the chances of the car being behind door 1 or door 37 were 50/50. This emotional doubt made it difficult for me to wrap my head around the concept of condensed probability, which logically I understood. Intuitively I knew switching would be the better idea, but the doubt was still there. There was also a degree of difficulty regarding language, given the amount of times the woman explaining used x, y, and p. I found myself confused by the variables and had difficulty understanding what they represented.
ReplyDeleteThe second, simplified explanation, explained the problem in terms of goats, rather than in terms of the car. It was easier to understand, since it removed the emotional doubt and language difficulties mentioned in my discussion of the mathematical explanation. However, the visual used in this explanation was difficult for me to understand. I rely a great deal on visual learning and sense/perception as a way of knowing, and the graphic used did not quite make sense to me.
The third explanation, "count-with-Bogel", used a drawing of nine doors. Finally, the last part of the explanation clicked with me. With a simple drawing like that and a spoken explanation paced with further arrows and check marks added to the drawing, I began to fully understand.
The visual and the discussion of it were most helpful to me; therefore, sense/perception and language, when effectively combined, helped me to understand the Monty Hall problem the best.
Starting with the mathematical discussion of the Monty Hall Problem, I used my "logical" reasoning skills. I was throughly confused even though my main way of knowing was logic, so faith is what I relied on to be able to trust the logic thrown at me.
ReplyDeleteMoving onto the 100 doors explanation, It was a visual and semi-logical based way of knowing. The "gut" feeling we felt when seeing the two doors and wanting to switch was mainly faith in our instincts (which are not correct for me, ex: bats, moose, and snakes).
The final and most clarifying example for me was the one Señor Bogel used, the three doors visual (meant to symbolize the nine different options). This example uses visual knowledge and logic actually made sense here.
As we found more and more ways of explaining this complex theory, it began to solidify in my mind. The easiest example to understand was the "three doors visual bogel" one, but this may have simply been because it was after I already had a basic understanding of the theory.
Before we watched the first video, I preferred not to change my first choice because I would be extremely regretful if I switched to the wrong door. However, if I stayed on the wrong door that I originally chose, I would just accept the truth that it was unfortunate. Also, I always trust my first choice generally. Thus, my emotion and faith employed in this response since I was afraid of regrets and tried to avoid it by believing and persisting in my first choice.
ReplyDeleteWhen we watched first video, I started to understand the mathematical explanation of this problem. However, I was a little confused since the mathematical explanation is sort of complicated for me. The explanation in the second video was simpler and made more sense. The afterward ‘draw-every-possibility-and-count-with-Bogel version’ really helped me to totally understand the best strategy by simple vision and logic. Thus, I decided to switch the door since the possibility of winning the car is bigger if I switch from my first choice to another door. At this point my logic and sense perception, especially vision employed my choice, because I made my second decision based on the actual mathematical and logical reason that I learned from logical and visual explanations. Before I understood the logic and reason in this problem, my emotion and faith have hindered my choice on the best strategy.
My responses changed as we talked from a lot of confusion, to a little confusion. As we talked, I realized that a lot of people in the class were very logical and mathematical. The first explanation seemed to satisfy them, while I was unsatisfied with the explanation. Although numbers do make sense, and can easily explain things, when someone just explains something to me in numbers, it does not help much. The reason being is that it is too overwhelming to attempt to calculate the numbers in my head, or understand why the calculations are doing what they are doing, as well as understand the concept at the same time. I did realize however, that same people who I thought were satisfied with the first explanation actually understood the second explanation better. The second explanation made more sense for me, but I still was unable to fully understand it immediately. I am more capable of understanding things that are abstract due to my immense faith, emotion, and memory. I like to put my faith in a lot of things, and use emotions of past experiences as well as my intuition to understand how things work. This held me back in understanding the concept when we were taught the mathematical way via the first video. My use of faith helped me understand the second video more, because I had faith that the explanation would make more sense, therefore I was more open to the mans explanation, and understood the concept a little better. At the end of the day, the easier explanation for me to understand was the explanation in the second video; but if I were ever put in that situation again, I may use the math concept or follow my intuition once more.
ReplyDeleteHow did your responses change as we talked and learned? In what ways did different ways of knowing help and hinder your efforts to understand which strategy was best?
ReplyDeleteMy responses were quite varied as we talked and learned. I thought that I had a solid understanding of the mathematical explanation. I realized later on in our discussion that this wasn't a good understanding at all. This is mainly because of faith and reason. I put my faith into the numbers because they seemed logical and the girl who was explaining the problem seemed to know what she was talking about. Therefore, I thought I understood too. This same type of misunderstanding occurred in the second simplified version as well. I knew that it would be a 2/3 chance of picking the door with the car after both explanations. This knowledge made me think I knew why. As you can see here, my intuition kind of led me into the wrong direction in terms of complete understanding. The draw-every-possibility-and-count-with-Bogel version seemed to complete my comprehension of what strategy was best to picking the right door. It seemed as though this is the only explanation I really needed to have a full understanding. This is an example of how language as a way of knowing helped and hindered my efforts to understand. The first two explanations were not as helpful and had completely different forms of communicating the right strategy for the Monty Hall problem than the third, more visual explanation.
How did your responses change as we talked and learned? In what ways did different ways of knowing help and hinder your efforts to understand which strategy was best?
ReplyDeleteMy response about switching doors stayed the same throughout the discussion, but for different reasons as the discussion continued. At first, I chose to switch because using my memory, I had remembered a movie that said that in that situation, a person has the best chance of winning the prize if they switch. At that point in the discussion, faith and logic were fighting inside of me. Logically, I could not figure out an explanation for why switching was better because I thought that it would be 50-50, but I also had faith in the movie for providing me accurate information. In the end, my faith in the movie won out and I said that I would switch if I was in that situation. Then, we watched the video of the lady explaining why switching was better mathematically. I kind of understood what she was saying, especially with the hundred doors scenario, but her explanation with the equation was confusing. In that way, I was hindered by logic and language because I was confused. I instead put my faith in the lady and her equation. However, the next video made everything clear. The person explaining used different language and a different approach than the first lady, which made him easier to understand. He focused on the goats rather than the car. This is when logic began to aid me in understanding why switching was better. Even though this explanation really worked for me, I liked the final one with Mr. Bogel the best because I could see myself explaining it to another person more easily using that method. It seemed to be the most simple one to grasp. Overall, faith and memory proved to be really reliable for me as ways of knowing. Language and logic hindered me at first, but slowly became valuable tools in this situation. They enforced what I had learned from my memory and faith.
I think that the more we talked about the problem and the more we tried different explanations the better I understood it. After the first video I was inclined to agree just because she sounded like she knew she was talking about. The concept of concentrated probability was hard to wrap my head around. However, by the time we got to the demonstration of every possibility I fully understood how the problem worked.
ReplyDeleteLanguage helped because without it the problem could not have been communicated effectively, but in the original video it hindered me because I could not understand the words she was using. Her use of language made it harder for me to understand the solution. Without vision and sense perception I would not be able to see the diagrams such as the ones Mr. Bogel drew on the board and the 100-door example. They reinforced the idea of concentrated probability. Reason was another hindrance because I had this set idea of how to solve the problem and the concept of concentrated probability did not fit in there. For me to understand the solution I had to push past the assumptions I had made based on other knowledge I had collected via reason or logic.
How did your responses change as we talked and learned? In what ways did different ways of knowing help and hinder your efforts to understand which strategy was best?
ReplyDeleteMy immediate response to this question was just to choose a random door and stick with my decision. I did not know this could have a rule by solving with Mathematic concept, so I just believed my six sense. After I watched the video explanation, I was more confused by the lady's logic. Then we watched the second explaining video. I tried to follow the cartoon and the logical explanation, but still did not understand how can the winning possibility be higher when we choose to switch. However, when we actually drew every possibility on the board, I understood the logic more.
When I heard this question, I had no ideas how to choose the correct door, so I just used my instinct to help me to choose. When I decided wether to change or not, I applied emotion as my first way of knowing. Because I did not want to regret if I changed to the wrong door, so I decided just follow my instinct. This belongs to emotion. After we watched the explanation video and experienced the possibilities on the board, I tried to use logic to help me to know and learn this possibility concept, which was the possibility is higher to pick the car when we decide to switch. By learning and understanding this concept, I had to look at the cartoon and drawing visually, which applied sensory as another way of knowing.
Consider the ways of knowing that you employed in your responses. How did your responses change as we talked and learned? In what ways did different ways of knowing help and hinder your efforts to understand which strategy was best?
ReplyDeleteI know it is not a way of knowing, but originally I was very confused when given an explanation to the Monty Hall Problem. When we were initially given the question as to whether we should switch to a different door or not, I wrote that I would not want to switch because of my emotions. Sio talked about this in class, but I believed that I would rather be wrong because of my own original choice than choose wrongly because of ‘pressures’ or ‘persuasion’ from Monty. I also know that typically when I doubt myself on something, my initial response is the correct one and I applied that to the Monty problem as well. This encompasses my use of intuition as a way of knowing when choosing whether to switch or not. I did not consider reason at all in my initial thought process, which, I found later, was a big mistake. After we watched the mathematical explanation to the Monty Problem, logic and reason influenced my perspective to the problem but I was still very confused until the last bit of the video. The speaker talked about a 100 door Monty problem and talked about the 1/3 probability in simpler terms. I still did not completely understand but with faith, I then believed that you should switch within the Monty Hall Problem. Language also hindered my understanding of this explanation because it was explained in a way that seemed complicated for me to understand.
The simplified version confirmed my new perspective and I was able to completely understand the reason behind this ‘answer.’ This time, language helped me understand because it was explained in simpler terms with examples and a reinforcement of words that were important. I no longer needed faith as a way of knowing the answer to the Monty Problem because I actually understood through different methods. Emotion also influenced my new perspective because the speaker of the simplified version was more relatable and persuasive in his explanation. Lastly, when Mr. Bogel drew an example of the Monty Problem, my confirmations of the answer to this problem were reinforced. Sense perception helped me understand Mr. Bogel’s way of explaining the problem because it involved seeing the problem rather than listening to the problem. Overall, my emotions and a lack of reason hindered my understanding of the Monty Problem, but language and sense perception helped me understand the Monty Problem fully.
In general, I find that the problem with attempting to explain something using mathematics is that even if it is possible to make the numbers actually make sense, it is still hard to apply them to the real world, because they seem to be no more than numbers. This was the issue with the first video, that even though the numbers may have worked and made sense, the path to heir application to the problem at hand was still covered and hidden, since usually complicated number patterns cannot be translated over to the world very easily. I know that for me, the first video did nothing to help my understanding of exactly how the problem worked. I could see that a bunch of mathematics proved that it was possible that the speaker was right, but those numbers did a poor job of proving that there was no other possible answer.
ReplyDeleteThe second video applied more to the viewer's logic, and in my opinion was able successfully explain the problem without being confusing or disconnected. For me, the second video provided the needed explanation that the answer given in the both was the right answer and that it could not possibly be the other way around.
Finally, Mr. Bogel's explanation, which also appealed to logic, used pictures to explain by showing all the possible things that could happen and solidified the explanation given in the second video.
While watching the first video explaining the Monty Hall problem, I had a difficult time applying that specific area of knowledge, math, using my logic. The probability theorem with its multiple variables confused me, and I had trouble following its purpose and validity within the context of the problem. I was not until the very last minutes of the video, when the woman spoke of concentrated probability, that I began to comprehend why it was a better choice to switch doors. However, applying that same theorem to a wider body (100 doors versus 3 doors) allowed me to practically see the attraction of switching doors. Using a wider body of examples enabled me to understand the theorem more in-depth, and the logic began to unfold. However, if someone asked me to explain the Monty Hall problem to them using that particular theorem, I would not be able to explain it adequately, because I learned the practicality and reason behind the theorem, not the theorem itself.
ReplyDeleteThe second video, which explained the problem by beginning with the 2/3 probability of the zonks behind the doors instead of beginning with the probability of the car, switched my entire perspective and was much clearer in my mind. In my memory, I could recall the logic of the 2/3 concentrated probability from the previous video, but the logic made more sense when the language used to explain the problem was altered.This video was the clearest in my mind because the language came across in people-friendly terms (without any fuzzy numbers to confuse me) and I had an epiphany (an emotional Ah-ha! moment) as everything clicked into place.
Finally, Mr. Bogel's diagram helped solidify my understanding of the problem, because he stimulated my sense perception using a visual aid that showed all possible outcomes. Seeing the images connected the pathways between my logic and language.
That day in class was crazy. My first instinct had been to stay with the first choice, and although the videos were clearly saying that you should switch, I wasn't interested in believing them, because I had a hard time understanding their logic. The math was simply too complicated. Obviously, reason and logic were at work as ways of knowing here, but they weren't quite... working. For my own response and decisions, I was more employing emotion (not wanting to feel stupid if I switched from the right answer to the wrong), and faith (in my instinct to choose the right answer the first time). One way of knowing employed a lot in the harder to understand explanations was language, and in this case the language used made it very hard to understand. But in Mr. Bogel's explanation, it was a lot clearer. The ways of knowing used here still included reason and language, but the use of sense perception (with the hand drawn visual) helped to tie it all together for me.
ReplyDelete