When I first started to read Dragon's egg, I was a little confused on what was going on, and why we were suppose to be reading it. Then by the end I realized that it was a commentary on how math may have been first discovered. To me, it seemed like the story how in order for we, as a species, to survive we must have an understanding of math. If we didn't learn how to represent our world in some abstract way, just like the cheela, we would eventually have walked towards our own doom and destruction. This story iterates for us how important math is for the continual survival and adaptation for a species.
In the second reading, it was interesting to see that even when we are first born, we start out with a basic understanding of math. To me it seemed like that author was saying that, yes we are born with an ability to do some very rudimentary math, along with our primate cousins. However, the big distinction is that we have been able to take it to the next level, to a level that other animals can't seem to get to. That is a level where we can do complex math, we can represent objects in the world using symbols. In essence, math is a human language/invention. I think that this article just furthers the argument that humans invented field of mathematics to help us understand the world around us, and that we created it out of necessity for our survival as a species, just like The Dragon's Egg.
Jared, I really like your point about how Dragon's Egg could be a story about how humans first "discovered" math. However, I would have to disagree with your conclusions about the Innate Arithmatic article. To me, the reading seems to imply that yes, while humans are the only species capable of advanced mathematical thinking, we are not the only species capable of using the simplest forms of it. Therefore, while the numerals used to represent numbers and the various symbols we use to represent mathematical ideas are indeed a human creation; mathematics itself is not. Rather, I think it is something built in to the very essence of creation, and as such, we are not the only species able to recognize its existence.
ReplyDeleteAlong with the pdf file given in class, I've also read the wikipedia article about the novel. It is about these intelligent organisms called cheela living in outer space, and it chronicles the start of their civilization, to the discovery of math, to creation of religion, and eventually the cheela becoming technologically advanced enough to figure out how to manipulate gravity.
ReplyDeleteI liked how mathematics was discovered in the cheela civilization out of necessity in order to survive their long trek to Bright's Heaven. It shows how mathematics was a useful survival skill to the cheela just like being able to run or sense danger.
I think this ties in together with the second article because the article explains how mathematical abilities are almost completely innate, and I think if something is innate, it was a survival skill that our ancestors needed in order to survive.
Jared, I share a similar outlook on the Dragon's Egg story. It's difficult to imagine the people who first struggled over understanding simple arithmetic and what that must have been like. I think the story does a good job outlining what the discovery of math could have been like. As depicted in Dragon's Egg, just because one person understands something does not mean others will comprehend their logic and I'm sure it took a while for the concept of mathematics to catch on. Dragon's Egg relates Great-Crack's discovery of arithmetic to survival, which parallels the truth of our world. Math was likely first used as a means of boosting the probability of survival, such as counting and rationing crops. I question as to why the human race has been so reliant on math and how other species are able to get by with only extremely simplistic understandings of math. Perhaps this is because, as humans, we love to make things easier (and we are much smarter). Math seems to be behind everything and we continue to use it to advance our way of life. Although, this advancement is not necessarily good for the environment and other species that inhabit the planet. This truly highlights the importance of math in history and in society today. Math could be mankind's greatest instinct in the modern world.
ReplyDeleteIn relation to the second article we see evidence of basic mathematical ability in infants. Perhaps this is why and how mankind invented math in the first place. Using our understanding of mathematics to benefit in some way and/or represent an idea is what I believe makes math a human language. I therefore agree that human's invented math to better understand the world as well as to simplify the task of survival.
I personally have to agree with Brandon on this topic. After reading both stories and reading all the comments, I agree with how the stories prove to us that Mathematics is essential for our survival. However, the topic I am struggling with is the "invention" of mathematics. Yes, humans or cheelas, made up numbers or symbols or used objects to help interpret it for us, but I still find it difficult to say that we invented math. Like the second reading says, we were born with the basics of math, whether it is differentiating the number of dots or figures on a screen, to the number of dolls that should be removed or added to the screen. Creating a type of language for everyone to be able to communicate the same idea does in a sense mean we are inventing something, but I still find it difficult to "invent" something that is already there.
ReplyDeleteI read the article from the New York Times (http://www.nytimes.com/1998/02/10/science/useful-invention-or-absolute-truth-what-is-math.html?pagewanted=all&src=pm) and it talks about Dr. Hersh's book and how he explains that math is something that was invented rather than discovered because it is a way for humans to prove or disprove science (something that is discovered). I guess that goes against exactly what I was trying to say earlier, but it still doesn't make since that we "invented" something that we were born with, that many living creatures are born with.
Jared, you bring up a solid point regarding our dependence on math for survival. Today, we take much of this elementary arithmetic for granted, but at one point, our ancestors must have struggled to “make the jump in abstract thought” that comes so naturally to us (Forward 79). If Great-Crack had not forged the connection and realized that the number of seeds she carried was an accurate representation of the number of pods she had eaten on her journey, the clan would have wandered off without sufficient supplies, and ultimately would have died on their journey. Great-Crack was not only able to develop a system of efficiently estimating the amount of food the clan would need for their journey, but she also used a systematic approach to efficiently account for the amount of food she would need. I know I for one hardly even notice all of the things I use our numerical system for in my daily life. It is difficult for me to even imagine what it would be like in the years before this number system was developed. Simple tasks such as counting pods and ensuring that one has sufficient food would be increasingly difficult. Great-Crack actually had to invent a word “great” to represent a dozen dozen pods. The excerpt clearly demonstrates the importance of the development of mathematics in relation to the idea of “survival of the fittest.” As Blue-Flow noted, “everything that slows us down hurts the chances for the survival of the whole clan” (Forward 72). Great-Crack’s development of a rudimentary number system, therefore, may have effectively increased the chances of survival of the entire clan.
ReplyDeleteI found it particularly interesting that the excerpt emphasized the difficulty others had with grasping the conceptual notions Great-Crack had presented. These ideas sound so elementary to us, but no matter how many ways Great-Crack tried to explain her rationale to Blue-Flow, he did not seem to be able to grasp the idea. He was cognitively stuck on the idea that “seeds are not pods” and could not make the leap any further to understand what these seeds represented (Forward 79). Mathematics is essentially a language of its own, and some people tend to grasp it better than others. A huge part of the study of mathematics, even today, is being able to present your findings in a way that others can follow. As great of a mathematician as Great-Crack was in her time, she seemed to struggle in this regard. I also found it interesting how the excerpt presented the idea that mathematics and logic in and of itself was not sufficient for survival. If the focus of leadership is centered entirely on a mathematical and logical foundation, any ethical understanding humans have developed would be forgotten. Was it ethical for the clan to leave the elders behind to die? Because our ethical understanding is such a big part of what makes us human, logic needs to be considered in conjugation with ethical values when making such decisions.
Lastly, I wonder whether the second article in some ways contradicts the ideas presented in the first article. The second article seemed to emphasize innate ability of humans to associate with numbers. The first article, however, seems to present this association as a rare and entirely learned concept.
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ReplyDeleteJared, I think you bring up some good points in your discussion of the “Dragon’s Egg” story. You mentioned “survival of species” as one of the benefits of abstract thought and mathematical application. I think the story, indeed, does point to abstract, logical thought as a characteristic which would be subject to the forces of natural selection. According to the story, abstract thought would lead to differential survival rates, and therefore, probably greater reproductive success of those who possessed the trait. And so, the frequency of the trait would be expected to increase in the population.
ReplyDeleteSeveral of you also mentioned the ethical implications of the decisions made by the leader in the story. I agree that the decisions may have been unethical, but I think the author’s purpose in setting up these situations was to make a distinction between human logic and human virtue. In the story, logic alone would tell Great-Crack to maximize survival by leaving behind those who would consume much and contribute little; virtue (ie, loyalty, altruism) would perhaps lead Great-Crack to find an alternative solution, which would avoid valuing members solely by their contributions and needs. When the dictates of virtue and logic do not overlap, humans (or in the case of the story, cheela) are left with a decision that is hopefully informed by conscience. I think the leader in the story appealed almost completely to her logical, mathematical sense, as her decision to leave the elders behind seemed somewhat cold and heartless.
For me, the story articulated well the aspects of math I’ve always found interesting and exciting, namely that the results we get using mathematics to solve problems are often surprising, or even counterintuitive. For instance, after mathematical evaluation, Great-Crack discovers what would have appeared to have been more than enough food to feed the group would actually only feed half the group. Similarly, Bad-Turn stumbles across the concept of inertia in realizing that the large mass’s(Flow-Slow) speed is easy to maintain once it is put into motion (another result which would have been surprising upon further investigation). These counter-intuitive and surprising results are, I think, what many find rewarding about mathematics.
Finally, I found the “Brain’s Innate Arithmetic” to be a worthwhile article because it provides evidence in support of the theory that we all possess some innate, basic logical ability. Jared, I agree with you that mathematics, as a discipline, is a human-created language; but, I think the language is used to express ideas or patterns that we are inherently able to recognize in the universe. In other words, I think math is a tool or a language which makes the steps in logical progression manageable and able to be expressed. I think math is much like any other language: it only gives us the tools and methods to express ideas which are already present.
Jared, I as well was confused at first as to what was going on in Dragon’s Egg. But after looking it up on the internet (namely, Wikipedia), I realized that there was more to this story than what we were required to read. While reading this, I was deeply amused with how Great-Crack was able to make abstract connections such as having a seed represent a certain number of pods, and yet when she tried to explain this concept to Blue-Flow, he couldn’t grasp the concept. At first, I thought that Blue-Flow wasn’t that bright, but then I remembered taking classes like Modern Algebra and Analysis I, where my professors would be trying to explain things to me and I wouldn’t be able to grasp the concept. With each new concept of math being developed, it would be understandable that others wouldn’t understand it as easily at first. But now in today’s society, things like counting, adding, subtracting, grouping, etc… are considered second nature to most people since we learn it at an early age and everyone around us knows the material well enough for us to teach it to us (or at least, that’s my opinion). Who knows, maybe one day in the future, Modern Algebra will be the new thing taught in middle school and would be considered “trivial” to society, and the things taught in college will still be something abstract that not that many people can comprehend immediately.
ReplyDeleteIn regards to your argument about how math is a human language/invention, I would agree with you that math is a human language, though I’m not sure about how it is an invention. Do you mean that the way we communicate math is a human invention? Or is math itself a human invention? For the former question, I would say that the way we communicate math is a human invention. After all, the number “one” could be replaced with some other word, however, regardless of how “one” is communicated, one plus one will always equal two. Like the second reading said, infants and animals are able to do very elementary math. If this is so, then how is math a human invention? Clearly, animals are also able to count.