Friday, September 27, 2013
I Think I Forgot How To Think
I think it's time to slow down a little: let's go to college. To be precise, please attend the Universities of Rochester and Oxford. First, 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. Next, 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? Consider (in writing) how the skills the
tutorial develops help you understand and tackle the puzzles and paradoxes. If you get angry at logic, take a break and read this. Finally, an ear worm inspired by our last class. Please post by 8 am Tuesday.
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First of all I must address the amount of time that I spent looking at the title and trying to see what the two errors were. After I read the answers to the puzzles and paradoxes I learned that the word ‘the’ was repeated consecutively. This really blew my mind! It is amazing how my eye and many others just skipped over the second ‘the’ to make the title seem right or correct. This tells you how much people really do pay attention to what they are reading. While trying to decipher the puzzles and paradoxes I had to put so much concentration into them because they were very confusing. I found myself thinking contradictory thoughts and playing devils advocate with myself to understand the puzzles and paradoxes better. Reading the puzzles and paradox were not the most difficult, but did contribute to the difficulty of attempting to decide between two possible answers that I had come to. Choosing the best possible answers was the most difficult part of this exercise because it forced you to think about those conclusions in different ways and in different scenarios. The tutorials definitely helped me to be more careful in what I read so that I may be able to tell if answers/conclusions are false or even answerable. I now know how to think about the way I think better. Most of the time my thinking is more black and white, so most of my answers for the exercises were more straightforward and less complicated and broad. This exercise lets me know what I need to do to become a more advanced thinker.
ReplyDeleteFor the puzzle, On the Island of Knights and Knaves, I got it correct by using the knowledge I got from the “Arguments” section in the tutorial. I learned that the premise or premises need to be offered in favor of the conclusion and the conclusion do not have to come at the end. After I finished reading this question, I was really confused. Then I came up with the idea that I could assume one was a knight or a knave and then figure out if it fit the situation. I had the conclusion come out first and then checked the premises to see if they were logical with the conclusion.
ReplyDeleteIn the tutorial, there is a question in exercise 1.1 that helped me with the Problem of the Light Switch. The exercise says, “Peter believes that Mary is a woman and that she has three hundred children. Is what he believes consistent?” Before working through the tutorial or the answer, I would absolutely say it’s not consistent. However, after checking the answer, I realize that one has to abandon common sense or other belief in order to think completely by logic. Hence, when I was doing the puzzle, I logically write down the answer which is noon will not come because time can always be split into half and become an infinity. Even if the answer is that the light will be broken so we can not know whether it’s going to be on or not, I was so proud of myself that I am now able to think about a question solely by logic and give out an answer that is sort of crazy but on the right track in this case.
Concludingly, the tutorial absolutely helped me with these puzzles. That logic is separated from the real life is the reality that was astonishing to me before reading the tutorial, but after that, I strongly believe in that now. I think I am able to solve problems more accurately with the help of the tutorial. For the paradoxes, I am not able to answer them. There are too many answers and reasons which can explain the answers. The tutorial do help to reason though.
For the puzzles , I have to admit that I spent an ample amount of time trying to untie the knots caused in my mind to figure them out. By using the tutorials I was successful in solving some and not so successful in other areas. The puzzle that made my view on thinking and analyzing really change was "The problem of the super bullet." The puzzle stated that the bullet would penetrate anything it hits but the armor allowed nothing to penetrate it. Through the use of logics and thinking for a good half an hour I finally concluded that the bullet would not penetrate it, if the armor would not allow anything to penetrate it. Even though it was a super bullet I logically assumed that if the armor was super strong then the bullet would not be able to penetrate it.
ReplyDeleteAlso the tutorial enabled me to utilize a new way of thinking by the use of validity . I used the theory of validity to solve a majority of my puzzles . The way I approached them in thinking may have been a bit off, but some answers had proved to be correct. As an example of use of validity my most successful puzzle was the first one entitled "Knights and Knaves." With validity And somewhat arguments, the premises centered around the conclusion could be false and the answer true. Seeing that no conclusion could be made about the statement A made i examined the situation presented and tested different conclusions about A on B and C to assume who was a knight or knave. In the end i concluded that C is a knave and B a knight. Before doing this exercise I openly admit that I had no idea that the theory of validity and arguments was so complex and I would not have put so much thought into it.
The most difficult puzzle I encountered was "The Monkey" . I had known that theory of logics would have to be used to solve this problem , but my logic skills were quite off. Although I got the answer wrong I am quite confident that I used the correct and logical way of thinking but with wrong calculations.
The paradoxes were seemed to be a bit easier for me probably because it required a little less thinking but in all everything was challenging. The tutorials really did develop my thinking skills because before ,I would not even try to look beneath the surface of these puzzles and paradoxes and use those theories to develop an answer. The tutorials have now allowed me to see new ways available for me to think and analyze different situations.
In The first puzzle, there could be absolutely no way of knowing which persons are knights or knaves. The person in inquiring is described in the puzzle as a visitor on a strange island. Therefore, considering language as a way of knowing, they would be at a disadvantage as there is no mention or evidence of the island natives and the visitor speaking the same language. So yes in English might be no in their language and the visitor would leave with the wrong answer. Hypothetically, if everyone spoke the same language a different approach could be taken. Starting from person B. Because person B stated that Person A said he is a knave I assume that he was lying. If person A was actually a Knave he would not say he was a knave because knaves always lie. So that potentially rules out A and B and since there is only one knight I assume it was C. However this problem was very difficult for me because every time I reasoned out a logical answer and looked back I found holes in my argument. Therefore I conclude that the visitor would have no way of knowing because of language barriers and that answer seemed to make the most sense to me.
ReplyDeleteIn the Surprise test situation, the students made a lot of assumptions that were incorrect and used reasons that were not particularly true. For example they reasoned that the test could not be on Friday because they would know on Thursday evening that the test would be Friday. This part of their reasoning was true because Friday would be the last possible day they could get the test assuming they hadn't got it up until Thursday. However they used this to reason and rule out the other days of the week which was wrong to do. That was a logic of fallacy because they cant assume that because It could not be Friday it also could not be Thursday and from Thursday, Wednesday etc. These two puzzles I thought were particularly interesting.
My ways of thinking were mostly using logic and strategically planning how I could use language to effectively explain how I arrived at my conclusion. all these I learned and practiced in the tutorial. On puzzles like the Super bullet, I had to change my way of thinking from logical reasoning to simply thinking outside the box. I simply came to a conclusion that the "anything" that was used to describe the strength of each was too vague and i could not tell what would happen.
I've got to admit, this post really frustrated me for a long time until I just looked at it with a fresh perspective. I found that it is almost impossible to go into these puzzles with a close mind, thinking I was right all the time.
ReplyDeleteThe puzzle I liked the most was the Surprise Test. I found this one quite funny (especially because our entire school is basically doing this with Mountain Day as the subject). I think the students thinking it couldn't be Friday was correct, obviously because it wasn't on Thursday. I think the students went wrong when they began to go back from Thursday. This rung a bell for me, the slippery slope logical fallacy. Basically it could be Monday, Tuesday or Wednesday. I think this showed how easily we can look over key facts.
The other puzzle I liked was The Super Bullet. I found this puzzle interesting because you can look at it two ways, depending on how the sentence is set up. So if they say "nothing that hits a super strong armor plate penetrates it", I automatically trusted the last statement, which is a bad habit of mine. I would think that the bullet would not be able to pass through it. Interestingly enough, if they had put "a super bullet penetrates anything it hits" last, I would completely believe that the bullet would go through the armor. I think this is a perfect example of perception and language mixed up. The way something (a sentence) is structured, or the way an argument is argued can completely change the person's perspective.
I found that the lesson from Rochester University did not help me. I'm not sure if it was the way they said things or what, but it was extremely hard for me to grasp their concepts. I found myself looking back mainly on the logical fallacies website we had previously looked at. I did however like this assignment as it opened my eyes and perspective to being more open minded.
In these puzzles, my first reaction to the title, was that there was only one error. The repeated "the", was what caught my eye, however later on I realized the importance of completely taking apart a sentence and understanding each piece in relation to is phrase. The fact that the title said there were 2 errors, implies that one error is the "the", but the other would be that there are not 2 errors. If this is the case, then the title is actually right, but what I thought might be the second error, is in fact, not an actual error. This made me confused, and from this I eventually realized it is unsolvable in my opinion.
ReplyDeleteAnother hard puzzle for me, that I was not able to solve on my own, was the monkey puzzle. Maybe, it was my lack of ability to comprehend the long equation and relate it back to the puzzle. However I believe this was the most complicated puzzle on the website.
The easiest in my opinion was the light switch, which after spending time on the website, was easy to wrap my head around. Through going through these puzzles I learned a new way of breaking apart sentences to find an underlying message or idea etc. In this puzzle, I realized from practice with the others, that it would be impossible to solve since the light switch could never be turned on or off at the time specified, only leading up to that time, but never fully that time.
To me, it seems as though logic was the only possible way of knowing or attempting to answer these puzzles.
This exercise was extremely fascinating but very frustrating. I have to say that I had more than one brain malfunctions due to an overuse. I started with the tutorials, which were extremely helpful in furthering my understanding of the idea of validity, ambiguity, and argument structures. Each activity helped expand this knowledge and put it into play. Once I got to the puzzles and paradoxes I found the new knowledge I had learned extremely helpful.
ReplyDeleteThere were a variety of different puzzles, which used one if not all the new areas of knowledge I had acquired through the tutorial and activities. For example in the problem of Knight and Knave I used argument structures and ambiguity. When I first read the problem I was very confused. I came to the immediate conclusion that one could not possibly know what A, B, and C were; a knight of knave. However, I realized that there was much more to the explanation than the actual question. I went back to the argument tutorial. In this tutorial I learned how to break down an argument into 2 parts; premise and premises, and conclusion. I also used logic as a way of knowing. By using both of these ways of knowing I realized that one of A, B, and C had to be a knight and a knave and one would have to one or the other. If A is unknown, then B and C have to either be a Knight or Knave, for one is telling the truth and the other is not. I spent a while on this puzzle, thinking about the various options. I realized, after looking at the answers, that I was not incorrect. A was in fact unknown and B and C were either a knight or knave. However, the logic in the answer was much clearer than my explanation.
One other problem that was very interesting was the light switch problem. I re-read the explanation to this problem a couple times and finally understood what I thought was the logical explanation. I used my new knowledge of argument structure and ambiguity. These helped me break the problem down and find a simple solution. However, when I looked at the answer I realized I was completely off. However, I believe that I used the correct basis information and knowledge for my solution. This gave me some perspective on how I look at a problem.
After I was done curing my brain from being completely fried, I realized something very important. When I first read all of the problems and puzzles I immediately looked for the obvious simple solution. However, I realized that the best way was to close my eyes and really think: How could I potentially know this? How is this possible? A majority of the time the answers were not very logical or straightforward. You really had to think outside the box. This was a very interesting process of thinking for me. Although I was frustrated a majority of the time, once I figured out how to look at the problems, it made a little more sense. Not a lot. But a little.
The title of the page was mind blowing. The addition “the” wasn’t hard to find, only because I read it aloud. There is no second error, so the title has another error in saying that there are two errors in the title. If this is true, then the title is actually correct in saying that there are two errors in the title. This is a case where the logic actually goes in a circle, and the validity of the title is unknown…I’m confused, but at the same time, it’s actually very cool.
ReplyDeleteDoing the puzzles forces me to pay attention to the meaning of every word, instead of the overall meaning. That has changed the way that I think when working on these problems.
In the Puzzle the surprise test, the students’ logic was not consistent. Their reasoning that the test would be Friday is under the premise that the test didn’t happen all the other days. When trying to prove/disprove that the test is on a different day, new premises need to be worked through, and the previous deduction will not be valid. Their first deduction was consistent and valid because it is true that the test would not be a surprise test if its on Friday. However, if they want to disprove that the test is on Thursday, the only valid premise would be if the test happened on Monday, Tuesday or Wednesday. And so forth.
The monkey problem is insane. It’s more like a tongue twister than a logic problem. One of the things that made the problem so confusing and difficult to solve what that it teases our common sense. All the jumbled ages of the mother and child almost suggest that the child was at some point older than the mother; it messes with our set perception of the world. This brings me back to the tutorials of validity and consistency. Logic can be completely unattached to reality, and that’s just so ironic because logic is supposed to be what is real. However, logic can be so out of this world that it makes me question what is real. Following my thoughts, I find myself thinking about the movie “Matrix”. What is real? Is what we know real or is logic real? Which is more solid? The tangible world or logic? Coming back to the monkeys. I tried to untangle the ages and the lengths and weights using mathematical reason, but eventually started seeing stars, so I looked at the answers.
The problem with the super bullet and super armor was very interesting; it has a very strong connection to the Chinese language. There was a story from when I was very young about a person who made weapons in ancient China. He claimed that he produced the strongest spear is guaranteed to penetrate anything. At the same time, he also claimed that he has the strongest armor plate, which is impenetrable. So the word for “contradiction” in Chinese is actually made out of “spear and armor”.
The ship paradox was funny and ironic in that as T replaces the parts over a time span of several years, the ones that he replaced first must be more worn than other places. He must have a very patchy boat. X would have a boat that looks newer than T’s.
The Malfunction Transporter: Although the story is totally sci-fi, I believe that both copies are “you”, because they are copies.
I thought that all of the puzzles and paradoxes were extremely interesting. For some, that I could not find an absolute answer for (which was most of them), it became a bit frustrating. The first puzzle was one that took me a while to come to a conclusion. I read it a few times and I was sure that A was unknown, but I kept arguing to myself about which B and C could be. I knew that one had to be a knight and one had to be a knave, but I could not decide which was which. Ultimately I decided that there is no way to be completely sure. And how do we know that either of them are being truthful? We don't know what is valid.
ReplyDeleteI also thought that the 2nd Knights and knave puzzle was interesting. When reading the use of language in, "Either I am a knave or else two plus two equals five", really confused me and I feel like maybe people could interpret it in different ways. This one was one of the puzzles that frustrated me the most because it looked short and easy, but I then realized that that can be deceiving and language can be a huge challenge.
I put a lot of thought into the super bullet puzzle as well. I read it over and over again and I almost gave up because I was just like these contradict each other and maybe there is no answer and maybe everyone should wear super strong armor plates so that no one in wars or fights will die. But then I thought maybe the bullet just wont hit the armor and it will miss or something so that both statements are still accurate because they won't hit each other.
Figuring out the title was also kind of fun. I couldn't believe how many times I overlooked the second the. It was so interesting how the placement of both of them can deceive you. Overall, I thought that these puzzles and paradoxes were really awesome. They forced me to think outside the box and that there is not always a concrete answer. I questioned myself and contradicted myself so many times, I thought I was going to go crazy, but I really did enjoy this exercise.
I found with these puzzles and brain teezers, that I am an extremely impatient person. Not only that, but it helped me realize what kind of knower I really am. I learned that I like a solid answer that can be proved or justified in some kind of way. Although there may be more than one answer to any given question, I like to be able to know my own answer and prove it. Some of these puzzles were impossible to prove; it was just your perception and that is all.
ReplyDeleteThat being said, I, frankly, found every one of these puzzles long, annoying, and difficult. The most difficult for me was the Knights and Knave puzzle. It was obvious that the man could not know who was telling the truth because there was no information given about these people. This frustrated me. I found that every puzzle frustrated me because there was no answer that I could prove.
This made me question what kind of knower I really am. Although I believe emotion is the best way of knowing, I'm not sure if I am more of a logical knower. Often emotion can't be explained or described, it is just felt and known. Logic gives a solid answer that can be proved; this is the kind of thing that I like. Working through these puzzles made me question whether I believe that emotion is the best way of knowing, or if I wish I believe that emotion is the best way of knowing.
I am extremely glad that I looked at the Rochester logical tutorial before I looked at the logic puzzles, because although they fried my brain, I'm sure that if I had looked at them before, my brain would have resembled burned scrambled eggs. I found the logical tutorial to be incredibly helpful when referring to ambiguity. This is a concept that I have always struggled with, because I find these sentences difficult to articulate to another person. When I had a guide and terms to refer to, it made understanding the different meanings presented easier.
ReplyDeleteThe task that helped me the most in the logic puzzles was the validity and arguments section. It helped me draw a clear difference between the meaning of valid, and the meaning of true. The inconsistency in arguments, and how it matches up with the validity of an argument was a concept that I had never made my brain think about before. I'm not quite sure if ignorance is bliss in this situation.
This task challenged my ability to think outside the norm. I drew charts, and considered math, but when I looked at the answers I found them to be unthinkably clear. The light switch problem was one of these. I thought about how the number could have kept being divided because numbers are infinite, however I discovered the answer to be "the switch is broken. Of course the switch is broken, it's a piece of plastic. I was so caught up in over analyzing things to make sense out of it, I ignored the answer. These puzzlers challenged me to think outside of the box by thinking inside of the box. We are so consumed with finding this challenging answer that we don't see it. It's exactly like the title of the article. Our brains are so focused on finding the error in grammatical or spelling mistakes, that we simply skip the second the. It's almost an instinct to just read that sentence, so these puzzlers challenged me to challenge my instinct, and inspect it more carefully.
The activities on logic and puzzles were incredibly confusing. I found that my mind would circle around and around each question. I did look at the logical tutorial before hand, however whether it was lack of logic, or constant second-guessing, I was frankly--mind boggled. I believe that when things are explained repetitively, but in different ways, it causes (myself personally) to over think. Despite this, I did manage to satisfyingly come across some answers. In the student surprise test for example, their logic was inconsistent. The logic only applied to Friday because it was the last possible day of the school week. Other riddles such as the true and false statements threw me off more easily. Questions such as that tend to bring ones mind into that constant state of over-thinking and contradicting.
ReplyDeleteTrying to work through the puzzles was challenging, however it was also interesting to put my mentality into prospective. Logical skills seem to be built in at a basic level, however it is also a practiced tool. I feel that with more practice with puzzles and riddles such as these, my logic skills would become more refined, and beneficial to my way of thinking and arguing.
This entire experience definitely changed the ways I'd been thinking. Realizing that there is a logical procession to every belief, idea, or even sentence that can be categorized in many different ways actually makes a lot of sense to me. It was funny that logic wasn't as linear as I originally thought. Theres a lot of lateral thinking involved that was interesting to experience, even if it did make my brain hurt a little bit. Reading the tutorial and the puzzles actually changed my view on truth and validity of arguments. I realize now that previously I never actually had a solid basis for why I thought an argument wasn't valid. A vague thought about inconsistency was probably as far as I'd ever gotten to uncovering the depths behind Logic. I think It's all incredibly interesting and I really do enjoy the word problems.
ReplyDeleteWhat was really difficult was to initially throw away any previous concepts I had about the terms and ideas being used. It was kind of hard to think that I really had no idea what validity or inconsistency was, as well as truth or falsehood. I arrived at the answers to the puzzles generally by writing them out in steps. I actually ended up with the correct answer to the monkey problem (after a half hour and lots of frustrated swear words) because I could use math to solve it. I had to work extremely slowly and it was hard to not understand what I was thinking but it definitely helped to write it all out on paper.
After spending much time on solving these brain challenging puzzles, I realized that logic is every essential in life. However, I had to be very upset after spending much time and realizing that none of my solutions were correct except the first one. This made me kind of angry, but the exercise was an interesting thing to do.
ReplyDeleteThe first puzzle about the topic was very easy for me to solve because I immediately realized the mistake about the repetition of "the". This was because I applied well my knowledge of language use.
The second puzzle about the students, who thought they were clever enough to guess the day of the surprise quiz, was so funny. After reading this, I immediately realized that except Friday, it was likely for the teacher to give the test on the other days. The teacher would not use the last day for surprise because everybody would tell after class on Thursday that the only remaining is Friday which wouldn’t be a surprise. I used my logic to come up with this conclusion.
The hardest paragraph for me was the one for the monkeys on a pulley. I couldn’t even understand the question itself because the question was written in a complicated way. As I started thinking about the problem, I couldn’t keep straining my head because I thought that I did the best I could to solve the problem and that my reason couldn’t go further.
The puzzle about the super penetrating bullet and super strong armor plate that wouldn’t allow anything to penetrate through was the most interesting problem. Thinking of what would happen when the two super weapons crashed against each other; I reached a point where I stopped thinking of what could happen. This is because both super weapons have the same power of resisting each other. I came to a conclusion that the super bullet couldn’t penetrate the super armor and so, they would collide and immediately part. I just can’t think more…I reasoned a lot but still, my conclusion also doesn’t make sense to me.
Reasoning can be annoying as Mr. Bogel said because frankly speaking, my brain is now boiling. I spent much time on the puzzles which also showed me that reasoning can drive you crazy. You just think and think, but don’t come up with a solution sometimes which is pretty annoying.
Firstly, I read the tutorial, which amazed me a lot. They break down a simple sentence by their element and use characteristic to mark them. Then, they rearrange the order and make the formula like the mathematic expression. For the exercise part, I always think about extreme situation. For instance, the question is "Peter believes that David has exactly four children, that his (David's) sister is Mary and that her only brother has only three children. Is what Peter believes consistent?". So I consider that David and his sister were or are in relationship, and they have three children together. However, David was or is divorced now, and has a child with another wife. Also, for the question "Is the following set of sentences consistent? {Marmaduke is a man, Marmaduke is a cat}". I thought that "man" means male, the gender, but not the human being which was totally wrong. Also, the puzzle and paradoxes make me frustrated. I need to think about it over and over, and it likes solving the mathematic problems for me. I need to read the sentence carefully and find the burst seam.
ReplyDeleteAll of the puzzles were confusing and took some time for me to do, but after thoroughly reading and understanding the lessons on the consistency and validity of sentences and ideas, I found more holes and clues to understanding the problems than I would have if I had not learned about consistency and validity. For example, in the first puzzle , “A mumbled an answer that the stranger could not understand. The stranger then asked B, ‘What did he say?’ B replied, ‘A said that there is exactly one knight among us.’ Then C burst out, ‘Don't believe B, he is lying!’” After thinking a little bit, I used what I learned in the exercises we were to do. A lot depended on what B meant that “there is only one knight among us.” If ‘us’ referred to all of the inhabitants of the island, then it was clear that he was a knave, because that a lie. On the other hand, if ‘us’ referred to AB and C, then he may have been telling the truth, or he still may have been lying. A lot of the other puzzles were open to interpretation and I found lots of other ambiguous sentences in the puzzles. All in all, even though the puzzles that we did were a struggle and made my brain hurt, I liked that I had to force myself to be creative in my thinking, and think about my thinking. The exercises were really beneficial because they helped me not only realize the mistakes that I often make in my writing, but it also helped me think about thinking. It also taught me to value language more and think about what I am thinking or saying’ because in many cases, the ideas that I try to get across are not consistent or valid.
ReplyDelete