Exploring the Historical Debates on Irrational Numbers Using Neutrosophic Logic as a Balance between Intuition and Rational
Description:... A short book by Dennis P. Allen, Jr, a senior mathematician, inspires this article, and henceforth it is dedicated to him. A good movie about S. Ramanujan, The Man who knew Infinity, also triggers this work. As a note, this is not a conventional math paper. Instead, its purpose is to dig deeper into how a mathematician or a scientist should deal with intuition and balance it with a logical thinking process. Literature exploration on important inventions in mathematics becomes the method of this study combined with analysis of Iain McGilchrist’s theory and Wittgenstein’s Philosophy of Language added with the Cognitive Language Theory. The findings show the absolutistic view of rationality or rational number will not suffice to give a h+olistic insight into reality. Such finding serves as a reminder concerning whom should be the Master and who should be the emissary in the path toward knowledge. Based on Neutrosophic Logic, the “intuilytics” which combines both parts of brain hemispheres might become the best contribute a holistic approach, something that hints that further exploration on the capacity of human brain or the essence of human beings is needed.
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