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Oh, everyone go check out the second issue of the carnival of mathematics!

Serial: Chapter 3: C – Columbus

Isaac, dearest,

I was leaving through the recently published memoirs of Christopher Columbus (curiously written in the third person; surely such an odd style cannot have been introduced by the translator, whatever other factual errors he makes), last year, and I felt you might be amused with the following story; at least insofar as it contrasts with your recent proof of the finiteness of the the geometrical space in this universe.

Ah, no point faffing about; I will just quote the passage from near the end of the book you now

Columbus sat in his study, overlooking Cádiz, with a Bible on his desk. He stared across to the horizon, and thought.

“How terrible it must be,t o be a highly situated savage, to see the world about you to the horizon and think there nothing more, to feel one’s self trapped on so small a disk of earth”.

Though, then he fancied that maybe a normal man might be able to live feeling so encaged, but not an explorer such as he.

“God has set forth, he had been told, a bigger cage for us in which to live, many orders of magnitude larger than the disk to our horizon, yet finite nonetheless. More than enough to go on exploring for generations”, he reassured himself.

And yet, he felt he could not accept this: How could God imbue the greatest of his men with the spirit of exploration, if there might be some age, maybe in a few centuries, when there will be no to explore, to discover, to find, on this planet. He would have verify this himself, to see the edge of the world with his own eyes, or alternatively spend the rest of his life travelling farther and farther out, boundless.

With this monumental task in mind, he petitioned the king for enough gold to sail for five years continuously west and, after five years petitioning, he was granted this sum.

One year of eager preparations passed before he was ready to set sail to see if the Atlantic actually had an edge. Six months at sea and land ahoy! What joys he experienced, what vindication: some islands, then a whole new expanse of land – the Vatican said that there was nothing west of Europe: they were wrong, he now knew!

This meant for him one of two things: We live on a much, much larger world than the Vatican claim, or alternatively, and his personal theological views led him to regard this as being much more likely: the world is infinite in extent, that one can travel forever in any direction without reaching an edge – this would be the only possible world he could see god having created – otherwise what a cruel fate would await the noble pursuit of exploration!

Okay, so here there’s a big chapter about America, which I’m not going to quote for you in full, but essentially what happens is that I decide that I must move south along the coast, because, even if it does go on forever in both directions, the only alternative is to give up and go back and there’s no way I’m gonna do that. So we travel down around, and west for a few more months, until hitting land again. Bang. And they anchor. And, lo, what’s this? A VILLAGE. Sweet. Then:

Shortly after entering the village, he found that he himself did find the people look quite familiar, some words of their language, their customs, from his travels east of India; had these people, from the other side of Europe, travelled here first, made these vast journeys? The very notion seemed impossible; the Indians and Chinese hated sailing, he knew. And yet, as his crew went further inland, he began to find more and more similarities until there was no doubt left: they were in China.

This world repeated itself then, he realized – it was not Rome’s disk, nor was it an explorer’s world – “What a cruel trick to play”, he thought “To think, if you had a powerful enough telescope you might catch sight of yourself, looking away, that the world was, despite all of it’s illusions, really finite in extent; that one might still sail west forever, but never come across anything new, that the world was finite – there were no barriers to travel, but, nonetheless, there was only a finite amount to discover in it – how cruel a discovery for an explorer to have make!

Of course, *everyone* knows that Galileo believed the earth to be shaped like an aubergine. So this casts everything, really, in to the most terrible of doubts, don’t you think? But then again, it is a charming story, neh?

Anyway, I hope to see you in the new year.