On the second day of class we were discussing the Fibonacci sequence and the rabbit problem. I think that gaining a full understanding of this concept will take a some extra reviewing, but it did remind me of something one of my brothers told me a few years ago. In Japan, there is an island that was once used for chemical warfare research in the 1920s and 30s. Eventually, the facilities shut down and the island was abandoned. Some years later in the late 70s some children visiting the island released a small number of rabbits onto the island. These rabbits were able to reproduce freely since they have had no predators on the island since their introduction. Without predators the rabbits are not killed (which sounds like one of the assumptions of the rabbit problem) but of course pass away for other reasons eventually. Today it's a tourist destination where thousands of rabbits roam the island free of predators such as dogs and cats since are banned from the island. In a way (but not really) it is an application of the rabbit problem. Interestingly, tests were done on rabbits in the original chemical factories, but the rabbit inhabitants today are not descended from those furry test subjects.
Now to my own thoughts: When hearing about the history and evolution of counting, my first thought was something like 'how could these ancient people not figure out counting? It's obviously so simple'. In this way I'm effectively judging people from the past for not coming up with something super complex. It's at this point where I check myself and realize that I didn't come up with this, either; we are both just working with what we have been told and discoveries take a lot of people & a lot of time. One thing this class has been doing for me so far is confirming my understanding that discovery is built from the trial and error of our human ancestors and the knowledge that they contributed. We use past insights to further develop our understanding of the world, similarly to how we prove mathematical concepts using postulates assumed to be true.
A final thought similar to the one prior came to me when we were told something like 'a fourth grader today can do more math than early mathematical thinkers'. I wondered, if placed in ancient times, I could show early humans various mathematical concepts such as how to use a base 10 number system or explain the concept of zero or of grouping numbers by tens and hundreds. I realized it would probably be pretty tough for me to do since a) I've only taught math to seventh graders and b) the prior knowledge that our math skills are built off of would be unknown to both of us. The ancient human and I are similar because we are just working with the knowledge we are presented with in our times. Maybe it's arrogant to think my skills have any more merit than his or her skills.
It is a fun thought experiment to imagine going back in time with our present knowledge. Could we change the world. Mark Twain wrote A Conneticut Yankee in King Arthur's Court with that premise. I suspect that we would find changing the world to be harder than we might imagine... People resist change. Even when positional notation was introduced in Europe, it took 600 years for it to be accepted and used widely.
ReplyDeleteLearning about how much of an intellectual leap the modern numerical system and the implimentation of the zero was gave me another idea. We mentioned that we sent out the spacecraft Voyager 1 with information about our human genome, the periodic table, etc in the hope that we could maybe find a way to communicate with any aliens who would find it.
ReplyDeleteIf mathematics is so difficult to create, would any other nearby life forms be able to do it, and does the complexity of math mean intelligent life might be even more rare than we expected? Even if those aliens were to create math, it is likely that their version of it would be far different from ours. If that is the case, would we even be able to communicate at all?
That is a good question. The committee that had to make the plaque for the Voyager 1 spent a lot of time thinking about it. They had to avoid anything that was based on human history, culture, and biology and tried to think of universal things. The ratio of the circumference of a circle to its diameter is a constant. Is that something that all societies would recognize. Maybe. But only if they thought that the idea of a circle was important enough to think about.
DeleteWhat an interesting version of the rabbit problem! I had never heard of this island before. It would be interesting to see how bringing in the rates of rabbit mortality on the island would impact the Fibonacci problem we did in class and bring a more realistic slant to the population change on the island.
ReplyDeleteI liked that you checked yourself in your thinking about ancient peoples not understanding mathematics as we do -- it can be hard to think outside of the context of what we have been taught or believe, and growing up in a different time and context with different beliefs can greatly impact ones ability to see what we might take for granted. This is an important historical skill which will no doubt be vital in this class.