The Last Number

by Stuart_Armstrong 1 min read10th Apr 201058 comments



He paused for a moment, and licked his recently reconstructed lips. He was nearly there. After seventeen thousand subjective years of effort, he was, finally, just seconds away from the end. He slowed down as the finish line drew into sight, savouring and lengthening the moment where he stood there, just on the edge of enlightenment.


Those years had been long; longer, perhaps, in the effects they had upon him, than they could ever be in any objective or subjective reality. He had been human; he had been frozen, uploaded, simulated, gifted with robotic bodies inside three different levels of realities, been a conscript god, been split into seven pieces (six of which were subsequently reunited). He had been briefly a battle droid for the army of Orion, and had chanted his numbers even as he sent C-beams to glitter in the dark to scorch Formic worlds.

He had started his quest at the foot of a true Enlightened One, who had guided him and countless other disciples on the first step of the path. Quasi-enlightened ones had guided him further, as the other disciples fell to the wayside all around him, unable to keep their purpose focused. And now, he was on the edge of total Enlightenment. Apparently, there were some who went this far, and deliberately chose not to take the last step. But these were always friends of a friend of an acquaintance of a rumour. He hadn't believed they existed. And now that he had come this far, he knew these folk didn't exist. No-one could come this far, this long, and not finish it.


There, he had done it. He had fully pronounced, defined and made his own, the last and greatest of all integers. The Last Number was far too large for standard decimal notation, of course; the first thousand years of effort, while there were still many other disciples around, filling the air with their cries and their joys, had been dedicated entirely to learning the mathematical notions and notations that were needed to correctly define it. But it seemed that for the last ten trillion digits of the Last Number, there was no shorter way of stating them than by listing them all. Entire books had been written about this fact, all untrue or uninteresting (but never both).

He willed a pair of lungs into existence, took a deep shuddering breath, and went on:

"... + 1 ..."

Had he been foolish enough to just list the Last Number, then he would have had to spend another seventeen thousand years calculating that sum - or most likely, given up, and contented himself with being semi-enlightened, one who has seen the Last Number, but not the Final Sum. However, he had been building up the mathematics of this addition as he went along, setting up way-stations with caches of buried theorems and lemmas, and carrying the propositions on his back. It would take but a moment to do the Final Sum.

"... = 4.2"

It was finished. Gödel had been more correct than that old Austrian mathematician could ever have imagined. Two integers, summed according to all the laws of arithmetic, and their sum was not an integer. Arithmetic was inconsistent.

And so, content, he went out into the world as an Enlightened One, an object of admiration and pity, a source of wisdom and terror. One whose mind has fully seen the inconsistency of arithmetic, and hence the failure of all logic and of all human endeavours.