After creating the identity of the null set and the difference between the null set and 0, the chapter continues with how the null set creates the numbers that come after it. The chapter tells of how John Von Neumann defined 0 as the null set, 1 as the set whose sole member is the null set, 2 as the set whose members are the null set and 1 , and so on. This is how they believed that numbers worked. The combination of sets to create the next number. This brought forth two crucial rules:
1. Every number corresponds to two sets of previously created numbers, such that no member of the left set is greater than or equal to any member of the right set.
2. One number is less than or equal to another number if and only if no member of the first number's left set is greater than or equal to the second number, and no member of the second number's right set is less than or equal to the first number.
These rules were set in place to satisfy counting and why it works.
The chapter then moves away from the number side of nothing and into a more theoretical side of looking at nothing. The example of holes is given for us to ponder. The author provides us with an old riddle; how much dirt is in a rectangular hole of certain dimensions? Although the hole has all the properties of a rectangular hole, the answer is that there is no dirt in the hole. This example transitions the chapter into why nothing can be important. Gardner provides other examples of nothing we don't even think about in our every day lives. The various holes in our body that are essential to our health, spokes share a wheel's hub and it is the center hole that makes it useful and lastly, how the holes in windows and doors make them useful. These examples are all occurrences in our everyday lives where "nothing" is actually important. Gardner also uses examples of how the world was created and art to prove the importance of nothing. He asks the question, "When the god or gods of an Eastern religion created the world from a great Void, did they shape nothing or something that was almost nothing? Questions like this one make us think of how the world was created and did it really come from nothing. Gardner continues to provide different examples to make us as the reader think about how nothing is actually evident in our lives and not just in math.
The main purpose of this passage in my opinion is to show how something as simple as nothing can be so complicated and have meaning. The last example Gardner gives us in this chapter explains the fear of death is not of dying, but of becoming nothing. This is a deep question with a lot of meaning and thought. This chapter shows how nothing can play a part in our lives and our thoughts.
This chapter was a bit difficult to understand in the beginning when talking about the mathematical side of nothing. I found the concepts of the null set to be a bit confusing along with the two rules explaining the numbers and sets. However, as the chapter transitioned to the theoretical side of nothing, I rather enjoyed the examples provided in the chapter. The examples gave me food for thought and a better understand of the concept of nothing and how it affects us. I liked how the questions asked in this part of the chapter had deep meaning, like the one that ponders if the world was actually created from nothing. The chapter of nothing was one that got better as it went a long and overall, gave me something to think about when I was done reading.
While reading this chapter, I, like Ryan, was confused at first. I understand the idea that the null set has zero things in it, but it took me a while to wrap my head around the fact that the null symbol did not have the same meaning as zero. My biggest source of confusion was the two rules that the combination of sets caused to come into play. I had to re-read each rule three times before I could make any sense out of it. I do think that it was interesting how Gardner addresses “everyday nothings”. Personally I never thought of holes as nothing, but after reading this chapter, I guess I don’t know any better way to describe them. It is cool how something having nothing in it, or being nothing, can, on some occasions, have just as much importance that the presence of something. The last point about the fear of death actually being the fear of being nothing reminded me a lot of things that we are talking about in my philosophy class. We are reading about a Greek philosopher named Epicurus who’s main goal is to rid people of this fear of dying by setting up a safe haven of sorts in the countryside. He believed that his would get rid of the fear of dying because people would be more fulfilled with a simple life doing nothing
ReplyDeleteI first read this chapter and was very lost. After reading it again and focusing on the ideas, I was able to understand it a little better. I have read about null sets in my statistics class, but never had to deal with them so i never understood them. After reading the book and these two posts, I was able to understand it and interpret well. I think the book did a good job in using examples to help the reader understand the different perspective. I also think the author did a very good job in explaining nothing. Nothing, as ironic as it sounds, is a lot to understand. You must think of it in a whole different way. The examples are the best way of understand this. In the hole example, you think of it as a hole but it is actually nothing. There is one thing i still can not understand, and that is the two rules of sets and combination of sets. It is very difficult for me to interpret this at all, so I kind of gave up on it. After the sets though, I really enjoyed the chapter, it gave me a bunch of easy ideas and examples to understand nothing more. The example about death, makes a lot of sense in the way that everyone wants to make an impact on someone or something in life. They do not want to die thinking that they were unimportant in life because that means they were "nothing".
ReplyDeleteThe most confusing concept I have come across so far in the Colossal Book of Mathematics has to be on Chapter 45 which discusses “Nothing”. It took me a little while to understand the part that takes about the basket of apples and if you have 3 apples in that basket you can take any where from 1,2 or all three apples. You can also take no apples, but if the basket has no apples you can takes exactly zero apples. Where my confusion with this chapter came was the part discussing the two critical rules for the combination of sets to create the next number.
ReplyDeleteRule 1: Every number corresponds to two sets of previously created numbers, such that no member of the left set is greater than or equal to any member of the right set, I can see how that makes sense because you need two numbers added together to get to the next number. But Rule 2: One number is less than or equal to another if and only if no member of the first number’s left set is greater than or equal to the second number, and no member of the second number’s right set is less than or equal to the first number. At this point I was no longer able to follow the rules for the sets and how to achieve each number. When the chapter transitions into the theoretical side of nothing, that’s when I was able to understand how nothing works. The holes in windows and doors how you need those empty spaces filled with “nothing” when the door is open to allow you to walk through, the same with a window you need that empty space to allow air to pass through. All in all the theoretical aspect of nothing makes a lot more sense to me than the numbers end of nothing.
The beginning of this chapter was very confusing to me when it was dealing with the basket and the apples. It starts saying how you can have different number of apples in the basket but how can demonstrate nothing when there are still things there. When I think of nothing pertaining to this example is if there were neither apples nor a basket left. The more theoretical part of this chapter though made me think a lot more about the subject of nothing. For instance, how are you able to create anything from nothing, there is just nothing there for you to start something. Just thinking about this simple subject is a lot more complicated as I previously thought. Before I read this I didn't really know how nothing was part of our everyday lives. Like we usually say nothing when we are bored or texting but that still means we are doing something not nothing, but after reading this I can see how it is in our lives everyday. Another thing he talks about is what happens after you die. Eventually you will like everybody else, but what really happens. So when your heart takes that final last beat then what is next do you just turn into nothing, like what really happens to you when you die. Although the theoretical part made you think a little more I think it made more since and was less confusing as the beginning of the chapter.
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