TABS The first thing I noticed as I started reading is that both chapter
I have read so far have some sort of religion theme. This chapter’s main concern
however was the topic of transitivity. It is the way we can rank things and
compare them. If A is lighter than B and B is lighter than C, than A must be
lighter than C. This logic thought does not work when it comes to nontransitive
dice games. Even if you let your opponent pick their die first, you can still
have 2/3 advantage to winning. The way we think that something is “more likely
to win” is the cause for this commotion. In figure 22.1 it wouldn’t matter if
your opponent chose a die with larger numbers, as long as you get a die that
has more average numbers. 3 8’s offer a greater probability than 2 12’s. When the chapter got into the probability of
card deck color it reminded me of the games we play in class. The one game
which involved 4 cards, 2 red and 2 black, and we guessed what the next color
was going to be. And although I was terrible at this game, it made me realize
how probability impacts our daily lives. Gardner also writes about Pascal’s
Wager in life to compliment this probability discussion. He says that probability,
trusting what we put our belief in, is exactly like this Wager. Just like in
Pascal’s Wager with God, we all make wagers of life on a day to day basis. We
took the wager to come to this college, some of us take the wager to believe in
God, and others put a wager in sports.
TABS The James Cargile article had a very nice outline of what
Pascal’s Wager truly is. The Cargile article states that the reason for Pascal’s
Wager is not to say there isn’t a God, but instead to open up that question for
debate. It says that there may or may not be God, but we have to take the
chance in what we think. The part of the article I enjoyed the most was that
Cargile included that many people who follow some faith are not doing it with a
goal in mind, instead they are doing good just because it is outlined in in
their beliefs. The author did a great job and integrating this part of the
chapter, pulling from multiple sources, and not making it sound too pretentious.
TABS While reading the “Deciding for God,” I really like that
Gardner didn’t include Turner’s hypothesis explanation. I found it to be extremely
confusing, and didn’t explain Pascal’s Wager as clear as the Cargile article. Turner’s
research required more background knowledge that I can only guess was given in
the earlier pages of his paper. Turner’s paper was extremely math heavy, which
made it hard to understand
TABS The Richard Savage article entitled, “The Paradox of Nontransitive
Dice,” is the prominently used in the book chapter. Using the 3 dice game
example from this article perfectly explained the use of nontransitive dice. I
also like how Gardner let the reader decide if they wanted the answers instead
of just writing a bunch of math inside of the book. It made the chapter seem to
flow more than if he included all the math that was present in Savages’
article.
I thought this chapter was pretty intriguing with the probabilities that they explained. It was shocking to me how different the probabilities were from what I would’ve expected! I’ve always though of probability from a practical view, but the explanations in this chapter made sense as to why the probability could be different. For example, the problem when you had 4 cards, two red and two black, and you had to guess the probability of picking two of the same color. It’s an instinct to think 1/2 at first, but then after analyzing it you can realize that there are 24 possible outcomes and 8 of those are picking two of the same color, so the probability is actually 1/3. I do not quite understand the example they talked about with the five balls in which two were white. I see the formula for it, but I don’t understand why the probability is 5/12 instead of 2/5. I also thought it was a little random to throw in the thought of is God real or not. I don’t really see how that relates to this chapter, and I wasn’t expecting it in a recreational mathematics book. I don’t really think that to existence of God can be proven with math or anything similar. But other than that topic, I thought the chapter was pretty interesting!
ReplyDeleteI thought that this chapter was very interesting. I liked how, unlike some other chapters, Gardner clearly explained applications of the content of this chapter in real world situations. Like Cortney, I was reminded of the games we played in class with the discussion of card picking probabilities. However, in class we didn’t really discuss the probability of choosing the specific color of the card, we were more concerned with how to make the most money.
ReplyDeleteI think it was really random of Gardner to throw in the question of the existence of God. It’s such a hot topic for debate, now and when the book was written, but I don’t see how it ties in with the rest of the chapter’s content. I agree with molly that this is not really a question that can be solved with the simple probability Gardner described. I don’t think any type of math could answer the God question in a solid manner. This chapter reminded me of my junior year in high school, when we read many different ontological arguments from a large spectrum of philosophers.
Overall, this chapter was pretty straightforward. This straightforwardness made it easy to understand and pick out all of the most interesting pieces.
The very first thing about this chapter, Nontransitive Dice and Other Paradoxes, that really got me thinking was the fact that, of the examples of the given die, Die A beats Die B, Die B beats Die C, Die C beats Die D, yet Die D beats Die A. I was confused by the fact that Die D can beat Die A, but Die A can beat all other die besides just Die D. It is also interesting to me, and also somewhat makes sense, that the person to choose first in a die contest is not necessarily always the winner of the entire game. One would hypothesize that player one would choose the winning die every time, but such a thing apparently cannot be assumed. Additionally, I found it intriguing how probability could be related to religion. While you can say “God is, or he is not”, my question is - is this statement really worth stating? We know there is really no real proof or evidence to determine the true answer to such a sentiment, especially if God is an almighty and all-powerful, benevolent and shapeless being or spirit. Perhaps that is the real point though, as was mentioned in the book as Pascal’s Wager - those who can believe without seeing or physically touching God, those who have unwavering faith in Him, cannot really be disappointed or saddened because their devotion is real enough to keep them going.
ReplyDeleteI dealt with a lot of probability problems in some of my past classes so I could understand these problems very well. These were the most basic ones and really surprise everyone. That is why I enjoy probability because you have to change the way you would approach the problem. For the most part this was a good chapter, but I do not understand Gardner's reasoning for bring God into this chapter. It is a very tough question and I do not think math would ever figure it out. Also, I think this chapter was kind of short on problems. It was honestly kind of boring compared to the other chapters. I do not know if that is because I have done probability before or what, but I thought this chapter lacked complex problems or problems that would really fool you. Overall, I did enjoy the red and black card problem since we had a similar game in class. All the problems were fun to do, but I just wish there was more history or material. It was a good chapter in how it explained probability and showed several problem types.
ReplyDeleteI thought this chapter was one of the more interesting chapters because the examples Gardner used apply to real world situations as well as mathematical applications that he uses in every chapter. probability is usually thought of in a more practical view like how Molly mentioned. But when reading this chapter, it was clear that the practical way was not the only side of probability that Gardner was discussing. The 4 card example demonstrates this side. Having the probability come out to 1/3 rather than ½ was a concept I never thought of just because I’ve always thought about it from the practical side. I agree with everyone else that it was random to throw the questionable existence of God but with further thought, I can see that the question uses more of an unpractical thought of probability. But it still could have been discussed better in the chapter. I don’t think that the question of the existence can be solved mathematically so I agree with Molly that it shouldn’t have been included in a math textbook just because it could stir up debate that did not even need to be included in the first place. I think Cortney did a good job of explaining the chapter and how the references that she included connect to it.
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ReplyDeleteI have been doing probability in my math classes for a long time now so it is kind of like second nature to me. I am able to clearly understand what they were talking about with the dice and the cards. I think when you actually do something instead of just read about it, it is easier to understand. Since we did the card one in class its easier to picture what he was talking about. I feel like people get really confused on probability just because they try and just do it in their head instead of actually performing it, because once you physically do it it's easy to understand. I am glad Gardner was able to keep it simple and make it relatable to what everyone knows and is familiar with. I feel like we do a lot of probability in recreational mathematics. This chapter was very relatable to our class room. We do a lot with cards and dice that involves probability. You can always go further and further with probability and that is what we do in class. We may start out with two cards then go to four, then six and so on so it just continues. Like everyone else has mentioned I don't see how you can relate God in with this chapter. I feel like when you talk about God there is no math that is involved, so I don't see how you can put them in the same chapter together. This chapter was easy to understand except for when he talks about God though which confused me a bit in this chapter, but other than that I understood what he was talking about.
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