What exactly is "Infinity"...?

The following is the unedited version of an interpretation currently featured in the 20^th revised edition of Malleus Maleficus'  The Moonshine Memorandum.

    “What needs to be remembered here,” he said, and I realised the repercussions were far-reaching, “is that those truths we deem to be self-evident are not self-evident at all. The Quantum theory is neither comprehensive nor complete. Quantum mechanics was but a rudimentary innovation in 1926, the atom still visualized as if it were a mechanical device.  In fact, we all recognize the necessity for a basis of observed reality, but no material theorem is ever absolute. Believe me, Malleus, a theory aims not at the truth, but at viability. And the contemporary formulation of the logic of science is peculiar to the cast of its Zeitgeist. Which may be one reason why freedom of speech and the liberation of the mind are equally sanctified as self-evident and inalienable. A triumph for the sans-culottes,” he

said, his  imperious haughty figure silhouetted against the starlit viewport, “but of no evident value to anyone else. What democracy achieved by a bold stroke of dogmatism, the world now acknowledges as an inherent good, which evidently it is not. It is nothing but the identification of the ‘will of the people’ with the supremely self-serving expedient – designed to impede progress, rather than encourage it. You are deluding yourself, Malleus,  if you remove the temptation to scepticism, but mutability is the one inalienable certainty of life.” 

          Undoubtedly, O’Brien believed we shape the world far more than it shapes us. He also believed that one could prove almost anything from an astute deployment of scientific principles. And it was clear that he meant it. Like a Vedic sage entrusted with some of the most cherished principles of human understanding, he then went on to challenge the most confounding conundrum of all.

          “What exactly is infinity?”

          Traditionally, I knew, infinity was anathema to science; calculations began to go awry and yield nonsensical answers. Nor was this to deny that cosmologists, today, were  exploring the fundamental properties of time and space beyond the periphery of human perception. But I knew that there was a problem with that. For one thing, it was clear even to me, that the so-called ‘boundary conditions’ had to do with information, and for another that the presumption of  a finite radius believed to be some fifteen billion light years, fundamentally determined the criteria which limit the potential complexity of the ‘final frontier’ - the fundamental limit of space-time – to a  point where space-time stops behaving like the smooth continuum. Reason dictates that everything in the universe, including time and gravity, can be described in terms of information. 

But because spatial and temporal infinity has no boundary, and therefore no identity, there can be no up or down in an infinite void,  no measurable dimensions or quantifiable limits. Some considerable plausibility, therefore,  would have to be given to the fact that beyond such an imaginary radius physics was faced with uncertainty, with something inherently indeterminate. And if indeterminacy was an essential, unavoidable property of the 'edge of the world' - the classical notion of a single, unique identity for a system as the sum of its parts - then there was only one conclusion one could draw: the universe was neither finite nor infinite, but an ongoing and ever expanding self-comprehension...

          “Knowledge is relative.” I said carefully and thoughtfully, quoting Einstein. “Imagination encircles the world.”

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