The Paradox of Mathematics

Rain
by Kultur

In philosophy circles, the idea of mathematics often sparks fuelled discussion. The phenomenon of number is strange in that it exists in the realm of human thought but adequately explains the natural world. Knowing whether numbers are an invention or a natural aspect of the universe is not easy because we don't see nature doing mathematics, it just happens that way and we, with our tools of language, describe it. It is this language that defines the way things work. With linguistic languages, we can make perfectly adequate lies which do not break any rules. These lies however do not alter reality. But in mathematics, if an equation is false, then it is seen to be so by nature of the language. When a statement is true, it represents the natural balance in the universe. This makes mathematics more than a language, it is a statement of perfection and balance.


But when we learn how to do mathematics at school or at home, we need time to grasp the concepts. We take each section of the subject one at a time and build from foundations of counting and arithmetic. It's not natural to us to do maths and some of us find it incredibly difficult. This presents a paradox in that for something to be naturally universal, it takes a lot of mental effort to learn. Do animals know mathematics? The answer is that some do. It has been shown that primates and other high functioning animals know how to count. Monkeys in some examples have out-performed humans. Even fishes can tell when there are fewer objects in their pool. This suggests that there is a basic non-lingual sense of number within us that begins before we learn the language of mathematics. This would bridge the paradox, in that what we describe is something within us as well as in the universe, making it truly a universal concept.


Now, it has been shown that babies also can count. Without using symbols to represent numbers, babies have been show to use number theory in the games they play. By comparing sizes, using symbols, and by comparing amounts, pre-school age children have been shown to demonstrate a variety of number skills without any formal education. This shows that the number abilities within primates are in us also, as evolved functions of our mind. It isn't just primates, various species have basic quantitative skills. But what does this mean for people? Teaching mathematics is a key part of education around the world. By understanding and appreciating how numbers are hot-wired into our minds, it is hoped that we can tap into our biological abilities to understand and use number in more inventive and managed ways.  

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