Thursday, October 29, 2015

Chapter 48: Mathematical Zoo

Chapter 48, Mathematical Zoo, is a particularly strange chapter. This chapter talks about the authors idea of "a zoo designed to display animals with features of special interest to recreational mathematicians". They go on to say that this type of zoo would be both entertaining and instructive. They say it would be divided in to two main wings one for living animals and the other for pictures, replicas, and animated cartoons of imaginary creatures. Many of these Imaginary creatures you would not think possible to exist however Gardner explains how they are not too farfetched. One of these beings is named A Wheeler, illustrated in figure 48.5. A Wheeler is an animal that has wheels instead of feet. Gardner quotes Robert G Rogers to help explain why the idea is not so insane. He quotes that if a wheel was "mounted on a bone bearing joint, with flexible veins and arteries, and a continuous series of circumferential pads(as on a dogs paw), the wheel could be wound back one turn by its internal muscles, then placed on the ground and rotated forward two full turns". If the wheel had a diameter of one foot this process would cause the Wheel to travel 6 and a quarter feet.
                Another organism Gardner would want in his zoo is a microscopic organism called radiolaria. These are one celled organisms that are found in the sea and have astonishing geometrical symmetries. Gardner cites an German biologist Ernst Haeckel who describes thousand of radiolaria in his Monograph of the Challenger Radiolaria. In this book there are 140 plates of drawings that display the geometric details of the different intricate forms of raiodlaria.
                Another portion of this chapter mentioned how the insect room at the zoo would display bees and there use of hexagonal honeycombs.  Scientists such as Darwin have marveled at bees use of honeycombs calling the ability to utilize them "the most wonderful of known instincts," and "absolutely perfect in economizing labor and wax.". While Gardner agrees that honeycombs are a great way of economizing wax he does state that there are better ways of doing it such as with a polyhedral cell.
                In  J. Diamonds "Why Animals Run On Legs, Not On Wheels," Diamond addresses the idea of why it is animals have legs instead of wheels. This article was actually very interesting. It talked about how bikes and other wheeled forms of transportation are actually more efficient than walking. So the question is why haven't animals evolved into having wheels instead of feet or legs. One thing that would have been nice to see in Gardner's Chapter 48 would have been the fact that wheels for feet would have made transportation for many animals near impossible. Such as with an ant, while their terrain looks relatively flat to us to an ant climbing the small hills would be near impossible. This bit of information would have been nice to see in the chapter because it shows the down side of having wheels instead of legs and how it is not optimal for all animals. One thing I was glad Gardner didn't include was the part where Diamond started talking about ancient civilizations. It isn't because this part was difficult to understand it was just the fact that it is irrelevant to the idea of a Zoo.
                In Jorge Luis Borges The Book of Imaginary beings Borges talks about many imaginary creatures, as you may have guessed by its title. This book in itself is interesting however much of it is irrelevant to mathematics. I'm glad Gardner did not include all of these beings due to many of them being irrelevant though I would have liked to see him include one named "The Leveler". This one resembles an elephant and has very wide flat feet. The leveler is supposedly 10 times larger than an elephant and would be used to level ground that was going to be built on. I think this would have been an interesting animal for Gardner to include in this chapter so he could have proved or disproved its ability to exist.

                L. F Toth "What Bees Know and What They Don't Know" is another one of the sources Gardner cites in his works. One thing I wish Gardner would have included was the formula Toth mentions in his work. In my opinion this would have helped to tie the honeycomb to mathematics. One thing I'm glad he included was why some scientists believe bees build the honeycombs in the shape they do. They believe it is less a result of evolution than an accidental product of how bees use their bodies.

5 comments:

  1. Chapter 48 is definitely a strange topic to read and talk about, like Alex mentioned. The thought of animals having wheels for legs is a very out there thought and would make little to no sense in the real world we live in. If animals had wheels would they still be considered animals? I believe people would feel very different towards animals in this case because they are different and humans find different to be challenging. The amount of studies that would take place on these “animals” would be immense and thorough because us as humans also feel the need to understand the things around us. If were the case, it could also lead to more animal cruelty and extinct species due to the studies and want to understand these creatures. The way Gardner explains the way the wheel would work is also a bit confusing to me. How would the animal be able to run and top of the food chain animals be able to hunt? Would all muscles in the wheel be equal in each animal? Would each animals wheels be of equal size? These are some questions that I pondered while reading. Overall, the chapter was a very different chapter and had some outlandish ideas, but was kind of interesting to think about and imagine what could be.

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  2. The title of this chapter really intrigued me; I though it could be a really fun and interesting passage to read. However, after reading, I do find it a little strange just like Ryan and Alex. The animals they described just had bizarre characteristics that made me question if they actually could be animals. I thought it was interesting how there was different sections of this zoo described, like a insect room and a microorganism section, kind of like a real zoo. The people who came up with these animals had some serious imagination. The thought of animals with wheels for legs is strange, but i guess it could be rather interesting. I also really enjoyed how the creators of these “animals” created the creatures with mathematical qualities. The geometric symmetry and the hexagonal honeycombs mentioned really tied in the theme of math with the zoo. I really wish that Gardner had listed more of these imaginary creatures and the logic behind them, because I found it strange, but also rather fun. I also wish all the creatures mentioned had fun names like “The Wheeler” because I found it rather entertaining. Overall, I found this chapter pretty enjoyable to read!

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  3. The main reason I chose this chapter is because I miss the zoos back home in Colorado. I found this chapter to extremely exciting. I remember being young playing games with my friends to see who could find specific shapes on the giraffes. The part that stuck out most to me was the formula of F + C – E = 2. It is fantastic that simply connected polyhedral can be inflated to be a sphere. This chapter was so amazing for me because it mixed math and a topic we just learned about in biology, symmetry. The chapter was much easier to comprehend because I had the background knowledge from my science class. I also liked this chapter because it showed how animals used shapes and their certain skills to make the most out of what they had. For instance the dung beetle and the scarab of ancient Egypt both use their bodies to roll up its food into perfect spheres. These spheres will be rolled into their burrows to be consumed. Alex made a good statement when he pointed out that Garnder didn’t use much negative information for wheels in this chapter. There is no point for bugs to have wheels if they can’t even use them.

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  4. I found this chapter to be really fun and creative. It is definitely recreational math but exhibited on animals. It was really different from other chapters as it demands a lot of imagination rather than all analytical math thinking. I also get a very strong biology feel to this chapter as well which is pretty cool considering I can relate it to what were learning about now in biology. I found the concept of the wheel on animals to be the most interesting. I like how there was a depth of explanation of how the wheel could work on an animal. It’s also pretty funny imaging an animal with a working wheel. Since the wheel concept interested me greatly, I went on to read the source mentioned in your blog to see why animals don’t have wheels. I also found this very interesting to read about but I still think it would be cool if at least some animals could have wheels! Anyways, you did a good job covering the topics of the chapter and it was a very enjoyable one to read. I wish there were more of these chapters connected to science because they can relate this to my classes now. It is really fun to put a connection to the two and see how they correspond with each other.

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  5. The whole idea of a Mathematical zoo, at first glance, seems a bit confusing. I had no idea where the chapter could have possibly gone with this title. When I eventually discovered that it was looking at the geometrical shapes of organisms under a microscope it seemed to make a little bit more sense. One point in this chapter that I found to be interesting was the formula F+C-E=2. With this formula you can easily determine whether or not a two dimensional geometrical shape can cover a sphere if the vertices are connected. A formula to this kind of problem is much simpler than trying to prove every perfect polygon on a sphere. Another point chapter 48 makes is how geometry or math present themselves in more complex organisms as well. Fore example, a narwhal whale has a horn similar to that of a unicorn on its head. What’s interesting is that it always forms a perfect geometrical cone that include spirals as well. These kind of mathematical consistencies occur all of the time in the natural world. The writer did a good job of highlighting the main points of the chapter. All in all, this chapter was extremely interesting because I really enjoyed how it related to the real, natural world.

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