I minored in mathematics in college, so I did not have to come to grips with ∞ in a serious way. Nevertheless, while I can subscribe to most of the protocols that mathematicians have attributed to ∞, the concept that one ∞ can be bigger than another is preposterous to me. Thanks for an interesting article.
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Well the story around the continuum hypothesis has certainly not come to an end! Its provability was included by the great mathematician David Hilbert in his list of the 23 great open questions of mathematics in 1900. So far, the great Kurt Gödel and Paul Cohen have wrapped their heads around it along with many others, and the proofs that are currently on the table is that the continuum hypothesis is actually independent of Zermelo–Fraenkel set theory, which is the collections of axioms underlying modern theory about collections of numbers. Cohen was awarded the Fields Medal for it, which is regarded a bigger achievement than an Nobel Price by many. Independence of ZFC implies that both proving as well as disproving the continuum hypothesis is impossible within the current axiomatic system. An astonishing conclusion to me!
This is wild conjecture on my part; just intuition, but "both proving as well as disproving the continuum hypothesis is impossible within the current axiomatic system" suggests a portal to an unknown dimension. Mathematicians have developed a powerful sytem that mirrors our reality on an abstract yet practical level; counting, calculus, probability theory etc. However, when something is shown to be neither proveable nor disproveable it reminds me of Schrödinger's cat and the paradoxes of the quantum world. When our mathematical axioms fail a portal to a new reality opens before us.