Monday, May 14, 2012

There Are Two Errors in the the Title of This Post

Let's continue our logical immersion.  For Friday, please tackle these logic puzzles.  Work patiently and with a pencil, reasoning out the consequences of each statement and, where appropriate, its speaker.  In your post examine the ways your thinking changed or developed to accommodate this task.  What was most difficult?  How did you arrive at the answers?

For Monday, journey to reasonable old England and work through this logic tutorial on consistency and validity.  Once on the site, follow the Tutorials link, then select Tutorial One.  Continue until you finish Exercise 1.4.  Having completed this, consider (in writing) how the skills this tutorial develops help you understand the puzzles above.

23 comments:

  1. I remember getting logic puzzles like the ones mentioned in the link when I was younger. Even now, it still takes me forever to figure them out...if that. I think that this is because I am not usually a very logical person- I don't really think things through clearly or take my time paying attention to details, which is something I most definitely must change.
    In trying to solve the problems, my thinking changed because I no longer only had to look at the bigger scheme of things. I was forced to pay attention to details and try to use all of the information that was given to me in order to rule options out. In this way, I became more of a guesser than a knower, because I could not rely on every single fact given to me (like in the first logical puzzle). This was difficult for me because as I sat with my pencil and paper, I had to keep going back and forth and trying out different methods in order to get to my answer. I was able to figure some of the answers out by drawing pictures (as I am a very visual person), and then trying to add as much information into it that I felt was truthful as possible. Another thing that helped me was, as funny as it sounds, placing myself in the characters' places because then I was better able to focus on the siutation as if it were my own.
    Unfortunately, logic puzzles have always taken me a while and resulted in a headache for me.

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  2. I think the hardest part of this exercise is to read the whole description and then first, understand what is going on and, second, figure out what is it really asking. For most of the puzzles, it is simply word game and for other questions, I tried to think about the situation first, and picture if I am the speaker; to experience the puzzle by ourselves will defiantly help us think logically and sort out the possibilities and answers to the questions.One thing I realized when doing the "surprising test" puzzle, I realize that what the students were thinking is the gambler's fallacy, which they thought they would figure out on which day the teacher would give the test, and the possibilities of having a test was ignored in this case.
    The Answer for the "super bullet" is extremely confusing for me and I never understand what is it saying. Originally, I was thinking if it has to do with mineral hardness or something seriously relate to the field of science, but then i thought of the fact that these puzzles are meant to be solved by ordinary people who are not necessarily scientists or experts in the world of science, therefore I look up the answer and it still don't make any sense to me, but I was right on the fact that the answer is nothing related to the extreme point of science.

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  3. Let me begin by saying that my mind has been blown. Officially. And my patience thinned as the problems got more complicated- which was not a good combination. But let me get to the point. At first, I read each example but it felt as if I was only looking at the surface rather than actually considering the problems addressed. For the first two I found myself taking the position of interrogator. I felt as if I was analyzing each individual in depth, having several false “aha” moments. Once I understood what to pay attention to, though, the first two problems made complete sense! I understood the knights and knaves and completely trusted my own judgment In essence, I had to pay attention to the wording, it was surprisingly straightforward. I found myself paying attention to words like “mumbled” and immediately disregarding certain statements due to that word. It was quite intriguing. Once I got to the next few problems, I lost all the confidence I had mustered. To me, the most difficult ones consisted of the light switch and the monkey. It was mainly attributed to the fact that as soon as I see numbers, my brain shuts down. Ultimately, it seemed as if the answer to these were much trickier- such as the light one (the force will destroy the light switch). I tried to use mathematical approaches, making my answers illogical and therefore incorrect. It was an interesting activity, that may have killed a few of my brain cells in the process.

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  4. My thinking changed while trying to work these problems out because at one point I couldn't tell who was lying to me or not. I had trust issues after the paradoxes and the Knights and Knaves puzzle. Towards the end I just got really confused, and started over thinking things. The difficult part was the wording of the puzzles. Sometimes I wasn't sure what the questions were asking, so I didn't know how to go about it. I tried to answer the questions by writing out what I thought the question was asking me step by step. I also tried to make charts to organize my information. After all this work, i didn't get anything right.

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  5. I started to read the prompt on the site and I knew exactly what was coming. Somehow every time I worked it out, I came to the same conclusion- That B was telling the truth and then C was lying. It that was so, then A would have to have been telling the truth disproving B. Therefore, they only way it would make a little but of sense to me is if B were lying and C were telling the truth.

    I took out paper to answer these questions and stared sketching and writing down numbers but I found myself crossing things out and trying to erase with my non-existent eraser. I started second guessing myself and I started playing my own mind game- I got in my own head and couldn't even sort out thoughts not in regards to the prompts. I could hardly even read them aloud after a bit. It was really difficult to get passed all the word in all of the questions. After I wrote down individual parts, it was easier to come to the correct or in my mind correct conclusion. I agree with Sara-Sara that I was coming closer to guessing than to knowing- especially with the light-switch prompt. In my mind, I actually said, "I guess that is what would happen."

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  6. When doing these puzzles, I had some fun, but I know these puzzles are not my type of hobby. My thinking became more and more jumbled as I tried to solve the puzzles. I became more and more impatient with the puzzle, and just chose to sit back and enjoy the beauty of the puzzle. It was difficult for me to make a final decision, especially for the first puzzle. So, I literally ended that problem by answering that B and C are knights, or knaves. It is a true statement, just not precise. I accepted that I didn't know the answers, even after I tried a few times. I chose to go as far as I could, and just praise the awesomeness of the puzzles. The only two puzzles I felt like I came to an "answer" in was the Pop Quiz. I decide that the student's thinking went wrong when they thought that the quiz wasn't on Wednesday, it must be on Thursday. I thought it could be on Thursday or Friday at that point, thus the class was wrong. But then I read the answer, and it said nothing about that. So, that was that. My thinking pattern was the same as always, I try to make sense of it, and if not I accept that I do not know.

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  7. Just like TO, the most difficult thing for me was reading the little blurb at the beginning that told me what was going on; I had to read it about 3 times to know what was going on. I also think that was part of the task, to try to make you pay close attention to wording, just like the title. However, even though I finally got what was going on, it was still difficult for me to come up with a definite answer.
    I arrived at most of my answers by going with my instincts, even though I knew my instincts were incorrect. Pretty much, my answers came from my own logic, which probably does not make sense to anyone else. Like with the surprise quiz, I was with the students saying that it couldn't be on a Friday because that would be predictable and not a surprise, but then the students' logic didn't make sense to me. I think that there may be answers that were shown on the separate website, but even then it didn't make sense because I may have interpreted the question/problem differently.

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  8. I loved this! I found primarily that a lot of it was math. The lightswitch problem, for instance, was something Ms. L-T has said to us many times. Then when I took a closer look at the knave problem, it reminded me of probability problems we have been studying in math class. In order really to figure out the puzzle, one needed to examine two different outcomes (in this instance, either any given inhabitant was telling the truth or was lying). From there, one can figure the likelihood of each. It was immensely satisfying to be able to solve some of the puzzles.
    (I don't know if we are to share answers we figured out just yet, or at all, so I shall refrain.)
    I don't know if I considered the problem about Theseus and Xanthippe a puzzle or simply a matter of opinion - the others had a clear, if not immediately obvious, answer.
    I also found the last problem, about the duplicate person, was a question about identity and complicated things like that, and was beyond my simple mathematical skills.
    I enjoyed stretching my brain out a little, as always, and had to remind myself several times to look deeper than "Oh pshhh, that's a good one."

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  9. I have done the majority of the logic puzzles a long time ago. So this task also played a memory game on me. I found that a lot of the times the answers were right in front of me, yet it somehow took another shape. My brain had to go back and forth through different ideas and still keep other given information. It took me less time to figure out the first three questions (especially the ones about the Knights and Knaves) than it did the last couple ones. I had to read the questions carefully and make sure that there was not missing a piece or that I misinterpreting information. I lost all faith in the questions to be clear cut after the first problem. I was over thinking it and going in circles and still end with no answer.
    I guess the most difficult one for me was the title question. I recognize the first mistake but could not get the last one only to find out that there is no mistake, which makes it a mistake...

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  10. When trying to do and solve the problems on a piece of paper it was as if I could see myself think. I probably re-read them too many times, and I think that is why I always tried to tacle it from a different point and analyze it differently. This did not help so much, because I later saw that I was over thinking the question.

    The main problem I encountered is how the puzzle problems used diction, the word choice, i think, made it so much more trickier. I tried to solve it straight from my first intuition, I thought to myself since I don't really understand it and re-reading it plus over-thinking how its sentence structure is not really helping. I should just stick to the way I first and originally wanted to think about it. This worked out well for the "Pop Quiz" problem, because I knew that if the test was not on Wednesday or Thursday, so leaving it to only be two answers which is friday or no test at all.

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  11. When I first read the introduction I was intrigued by one of the last sentences which read, 'The paradoxes provide an amusing way to raise deep philosophical problems.' So I knew that what I was about to read would cause my thinking to go around in circles (paradox).
    When I started reading the knight and knave problem, I immediately jumped to the conclusion that the person who told an obvious lie would be the knave. But as I read the problem over and over I started to doubt my reasoning. The most difficult part was trusting that my conclusion would be right. B could be the obvious liar, or is C telling a lie that appears to be truth. Ultimately I had to reach an answer based on my thinking.

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  12. The skills in the exercise really helped me rethink how to read the questions.The last point, I found particularly confusing. I think i found it confusing because the question/prompts seemed to have more than one answer- like a lot of the other questions. The last part seemed very vague and left a lot of room for questioning or being confused- a state I find myself in frequently while doing TOK homework. For the last part, I found myself understand the sentences on the page leading to the question but when I had to apply the knowledge, I was unable to- something I find myself also doing in math class- When we put examples on the board, they are easy but when I have to apply the concept to my homework or to a test, I am sometimes lost. These exercises really helped me to think about breaking each part up and them putting them together and seeing how the pieces affect one and other.

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  13. The link on the introduction to logic was helpful because it broke apart questions and really allowed to to focus on the context of the situations I was being asked. It was helpful because it defined types of sentences differently, yet, I was still confused. It helped me understand the puzzles above a bit better though, because now I had new skills that allowed me to focus on certain words in the questions and be able to identify them as consistant, inconsistant, contradictory, etc., and so I could better work out the events that happened in the situations. The exercises were also helpful because after answering the questions, the answers gave explanation for each of the points. I was then able to apply this to the questions. With a little bit of guidance from the tuitorial, I could focus on the problems a bit better than when I was looking at it on my own, so I found it a little bit easier to understand this time around compared to the first time.

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  14. When I first started reading the subject matter of logic I was quite confused. Sentences like, 'A set of beliefs is consistent just if it would be possible for them all to be true together: that is, if they are either in fact all true or could all have been true.' In order to truly comprehend sentences like this, you have to read them over and over again until the light bulb switches on. But there were a few statements that really helped me relate to the logic puzzles we had done previously. I read one which was, 'A single belief which could not be false is said to express a necessary truth.' So in terms of the knight and knave problem, we cannot automatically reason that B is lying and C is not. Neither of their statements, in my opinion, can be considered a necessary truth. But if we are following the logic of this sentence then B has to be a knave. For in the problem, C said, "Don't believe B, he is lying!" This is a single belief that could possibly not be false, therefore it is a necessary truth. B would have to be the lying knave.
    These logical sentences, although difficult at first, helped me to better understand the logical puzzles.

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  15. Mary, that first part was most definitely confusing. I though I wasn't reading English for a bit. But besides that, the tutorial became very clear and concise as I kept moving along. The tutorial helps with solving the logic puzzles because it clarifies the reasoning of the puzzles. For instance, the Surprise Test puzzle match very well with the first part of the Tutorials. The first part of the tutorials talked about consistency. The puzzle asks when did the student's thinking go wrong. Well, due to their arguments' lack of consistency, they student guessed incorrectly about what day the test would be on. In the answer to the puzzle, it says, "If they [the students] are willing to consider that [the fact there there is no test at all]a possibility at the end of the argument, they should consider it one at the beginning". Basically, those students should drink more consistency juice. In addition, the Knights and Knaves problem is based off of consistency. The statements said by the three people on the island were able to reveal the truth of B being a knave and C being a knight because of the correlation between the label of each person and the things they have said. Basically, for the sake of consistency, that conclusion must be drawn.

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  16. The logic tutorial is clear until the exercise 1.4, exercise 1.4 was very complicated for me when I finished exercise 1.3, because all the sudden I have to combine the two ways of thinking logic. When I looked back to the puzzles, it does makes more sense to me after the exercise but I think part of the reason might because of the fact that I've already read the answer.

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    Replies
    1. And in additional, when I look back to the puzzles, I think of the questions in the same way as I was thinking during the logic tutorial, and for sure, I was not thinking the exact same way at the first time when I was doing these puzzles.

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  17. Although I did not understand some of what was being explained in this tutorial, it did turn out to help clear up certain things in the logic puzzle. The main thing that this tutorial helped me do was to pay attention to certain things (such as a conclusion) and look at where it goes and what it is saying. By knowing what the conclusion is I can therefore pay more attention to the point that the statement is trying to make and therefore draw the appropriate information from it. In essence, this tutorial would make my mind think in the ways that it would have to think to full understand the logic puzzle. I completely agree with Sara, the tutorial broke things down to help us focus on the context rather than the nonsensical words that were being added for confusion. Although the tutorial started off a little bit tough to comprehend it was incessantly successful in its attempt to wrap my brain around logic puzzles.

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  18. I didn’t really understand the puzzles that I did on Friday. At certain points I became really confused. I do understand what this tutorial is trying to make me understand, but I haven’t gotten to the understanding stage yet. Doing things like this is particularly difficult for me because I am a very visual person. After doing the exercises it does help me think in a way that I should be thinking in order to do the puzzles.

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  19. From the tutorials and exercises, I was starting to make a connection to the logic puzzles which we previously completed. I think that they would have helped tremendously because there were exercises which I got a lot out of which would have helped me. For example, I believe Exercise 1.3 about arguments made me carefully look at the wording of each sentence, which is something I lacked in the logical puzzles. It was interesting to see in this exercise how some arguments were not properly phrased/organized. I also think that the two different types of Ambiguity would have helped as well because this helped me with sentences with one meaning or more. Exercise 1.1 would have helped the logical puzzles with the knights, for example (and other puzzles similar, when trying to decide who is telling the truth). Again, just like TO Exercise 1.4 was complicated, so I'm not sure if the skills learned in that one would have helped me with the puzzles or not.

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  20. While doing the tutorials, I felt like my IQ had decreased 3%. A lot of the information it gave me made me more confused. The logic puzzles was a matter of patience and a catching little loop holes to answer the questions. The tutorial had some very helpful concept in the beginning like the "Ambiguous" section. However on sections like the "Validity" section, I could not find the reasoning behind the concepts. I know its attempt was to help me understand the puzzles on Friday but it did not fulfill its purpose. In other words it did not help enhance my understanding of the logic puzzles. I think the tutorial section confused me more than the puzzles.

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  21. I hadn't fully understood the puzzles but when I looked at the answers they made so much more sense, although I have to say that if the same kind of puzzles and problems were given to me, I would not be able to understand and generate the correct answer, the specific type of analysis and critical thinking is what the tutorial was explaining. Although I understood the tutorial I cannot really say that my understanding and knowledge of my newly acquired skills can help me solve the problems and the puzzle. I think that just means that I have a general understanding of what is going on and how the solving and thinking should be done but I don not understanding well enough to apply those skills to other puzzles if I were asked to.

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  22. The first thing I noticed when beginning my mental journey through these tutorials was that I quickly learned to take absolutely everything into account. Being overly literal or scientifically correct was of no use whatsoever; all possibilities and definitions had to be considered. Also - if this even means anything - the exercises, especially the arguments tutorial, made me very systematically parse out each strand of thought, though the sentences were quite simple, to see which followed from which. In this way, and because the validity page mentioned calculus and probably thus planted some sort of seed in my head, I was reminded once again of mathematics. (I know that mathematics and logic are inextricably linked, I've just never experienced it so practically before.)
    I must admit the premises/conclusions/validity exercise left me somewhat in the dust, due partly to loss of willpower after getting several wrong. I don't know where my thinking went wrong. I suppose the most important thing I learned was patience with mental processes, of which I normally don't have much. And, as Emilie said, I'm not positive that I've become expert enough at such thinking to successfully apply it to other challenges, but certainly I have thought this way now and I consider that valuable.

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