The Shāntī Pāth & Cantor’s Infinities

The interesting dichotomy of the dual usage of this word stresses the fact that there are further two levels of completeness that exceed our mental capacity; there is an inherent limitation. In the words of Swami Chinmayananda [6] –“This peace invocation reads as though a pleasant contradiction in terms. On a very superficial reading one is apt to consider only its word-meaning and then each sentence should certainly confuse and confound any modern student who dives into it especially through its literal translations available for him in English or in any vernacular. This is a philosophical truth-declaration, and as such unless we know something of Vedantic conclusions over the theme of the transcendental Infinite and its ‘relationship’ with the finite, this stanza should necessarily confuse any reader.”

On the mathematical side in 1870, Georg Cantor (1845 – 1918) gave us the ‘set theory’ – a brilliant thesis on the study of collections of numbers, points, objects, anything really in general. This revolutionized ‘number theory’ and gave rise to his– ‘Theory of Infinities’ or what is more precisely called ‘Cantor’s theory of Trans-infinite cardinals’. The word trans-infinite here maybe understood as a condensed form of transcendental Infinite – that which is beyond the infinite. How is this possible ? Let us, at this point, push our limited reasoning on the lines of Cantor and attempt to explain this brilliant equivalence between – mantra and math – separated by almost four millennia of human endeavor !