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2. Mathematics and its Relationship with Physical Nature
Mathematics had its own course of development, often not depending on what we observe in nature. It is a wonderful world in itself.Philosophers like Plato have gone to the extent of proposing the existence of a separate mathematical world [3-4]. Thus the mathematical descriptions of nature are attempts to map sets of mathematical entities onto sets of objects in the physical world.
Figure 1: Counterpart of subset of mathematical world known to us in the physical world
However, only a small subset of the mathematical world known to us may have counterpart in the physical nature, as shown in Figure l.The same holds true when we try to map natural phenomena onto the realm of mathematics known to us, i.e., only a small sub-set of our observations can be described using mathematical laws known to us.