In the article “The Intuition of Infinity,” Fischbein, E., D. Tirosh and P. Hess explain the problem of categorizing infinity based on the contradictory process of our thinking. They explain that this conflict is deep and that we cannot completely avoid it even with the most sophisticated mathematical tool. They made reference to Cantor’s argument that more than one kind of infinity exists. This they pointed out is definitely against our intuition of the nature of infinity.
The results of their studies show the difficulty in the process of understanding the concept of infinity based on our individual perception of infinity. Categorizing Cantor’s idea of the “Hierarchy of infinity” as abstract or as concrete is therefore based on our perception and thought process. They explain that physically performing the various examples of manifestations presented can make us categorize them as concrete- what we can see, and our mental ability of the process can lead us to categorize as abstract.
Citations:
Fischbein, E., Tirosh, D. & Hess, P. (1979). The intuition of infinity. Educational Studies In Mathematics. JSTOR.
Manfreda Kolar, V., & Hodnik Cadez, T. (2012). Analysis of factors influencing the understanding of the concept of infinity. Educational Studies In Mathematics. Academic Search Complete.
In my opinion, our perception of infinity does play a major role in how we define infinity. However, when logistics compromise how we perceive something it can definitely cause confusion. Also, if infinity is abstract how can we quantify or measure it? What if everything can be seen abstractly?
ReplyDeleteI agree with you Sara. There seems to be conflict with all these concepts of infinity. It makes it even more difficult to comprehend because they make no sense. Maybe it will if everything could be viewed from a rationalistic point of view. But then how do we measure abstract things like you said?
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