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Sythesis Paper to Nature's Number by Ian Stewart

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Name: Genecel Cabulay                                                     Date: June 28, 2018

Instructor: Ms. Dianna Limjap                                                  Subject: Math 4

Nature's Number

(Synthesis Paper)            

               Mathematics, in the social construction of reality is what we all need to know. It is more than just a numbers incorporated with logic.  It is not just  an academic requirement needed to be taken; mathematics is a way of life. Life? Yes,  life. You might wondering why but my answer is reserved for the last part of this paper.

                   Ian Stewart's Nature's Number served as an eye opener to all of us and make us see the world from a Mathematician's point of view. On the first chapter, he helped us welcomed the idea of mathematics being all around us. Through the presentation of obvious patterns, integral relationships of strange things,  how all this things continuously interact with each other; he showed how generalities and regularities of these things in this universe contributed a lot in  achieving universality despite of their diversity and he called these tiny symmetrical details, patterns. Patterns that can be seen everywhere, patterns that are present in every object you can and can't visibly see and patterns that are difficult not to notice. He further explained this patterns through giving examples like the stripes on hyenas and tigers, the honeycomb, the symmetry of the ending points of a snow flake, the shape of the raindrops falling form the clouds and the same number of petals for each flower. And as humans being an intellectual beings,  we created a formal system of thoughts for recognizing, classifying exploring pattern which we called mathematics.  Mathematics,  doing it's part to change the world,  has reached the peak of it's relevance by making an uproar through its practical applications. Here, Stewart differentiate pure mathematics from applied mathematics. On pure mathematics, he discussed the special role of mathematics in human culture. It is a more or less systematic way of digging out the rules and structures that lie behind some observed  pattern or regularity, then  using those rules and structures to explain what's going on and indeed, mathematics helped us understand the laws of nature. While the applied mathematics shows its practical applications and how mathematics made things better by enforcing it with some other things like knowing how gravity works, how acceleration became rate of change of rate of change, how to solve puzzles of the world through explaining the planetary movements, describing the change of quantities through calculus and discussed the evolution of the eye.  On the further chapter, Stewart mentioned about the two opposing viewpoints of the world where according to one view, the universe obeys fixed, immutable laws, and everything exists in a well-defined objective reality while the  opposing view says that there is no such thing as objective reality; that all is flux, all is change.But Newton's Mathematics first made significant step toward world view it transcends and unite both rigid and flexible flux. Soon, Newtom realized that change obeys rules not only can law and flux exist but law generates the flux. On its sixth chapter, "Broken Symmetry", Stewart defined symmetry as a mathematical concept as well as an aesthetic one, and it allows us to classify different types of regular pattern and distinguish between them. Looking back at first chapter, Stewart already seeks to define what we actually mean by “a pattern”, coming to the conclusion that we see a pattern in some�thing that has symmetry, but not too much symmetry — that is, broken symmetry. Symmetry breaking is a more dynamic idea describing changes in pattern. For example, we do not see a pattern in the still surface of a pond, as there is too much symmetry. If we then toss a pebble into the pond, the perfect symmetry is broken: we lose all but the symmetries which fix the point where the pebble strikes the surface in the resulting pattern of circles. The ripples in the pond break the symmetry of the plane in a sense that the pebble disturbed the pond.



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