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Gauss's Nightmare

N. B. In the early nineteenth century Gauss, one of the greatest mathematicians of all time, proposed to test whether the Moon was inhabited by intelligent beings by outlining (according to various sources: with flaming oil in a trench; by planting a forest on a plain; by planting a wheat field in a forest; or with an array of mirrors) a colossal right triangle. He expected that if they saw the shape, the people of the Moon would reciprocate it with a similar triangle.

PLANET A

From Letter to Minisalonicaro, Saboditamoni.

Dear friend:

I know not, of course, whether you are right about the appearance of our own Earth from the Moon. Certainly, plants of all sorts do appear green from our proximate position, but it is not impossible that they appear to be some other color when viewed through clouds and vast depths of air. Likewise, it is not impossible that the blues and greens of the Moon represent some other phenomena, similarly shifted away from its natural appearance.

I might be supported in this by the speculations of our late friend Tamothoditanara, whose doctrine of degrees of rarefaction allows us to speculate that great thicknesses of air might behave quite like relatively slight thicknesses of water. Consider the enormous shifts in color which an object undergoes when immersed in water, and tell me again whether it is indeed likely that the colors which we see through two atmospheres, on the moon, represent what we see at hand to have those same colors…

I must recommend that you abandon this scheme. You may have convinced your prince that it will be worthwhile, but you should remember that princes are fickle and that if the response you expect is not forthcoming, he may choose to exact punishment for the waste in labor and precious oil which you have caused him. The trenches you propose will demand at least as much as a year’s harvest of oil to fill to an adequate level with soaked fuel. Also, as I remember from my visit, the ground in your district becomes very hard and rocky just a few feet below the surface, and it will require much more manpower than you have calculated to dig the trenches.

With all that, I must confess that I do not fear at all for whether you will be able to keep the lines straight over so great a distance, after the feats of surveying which I saw you perform for the laying-out of Tabacoraca…

PLANET B

From Of the Marvellous Night of the Burning Shapes, Archives of Mong Sthro Diocese.

O supremely noble prince! O beloved brother!

I indeed saw, o Brother, o Peer, the Burning Shapes of the Moon but a Month ago, when they inspired the Fear and Admiration of all Men and Princes. O Brother! O Peer! I tremble still to think of that wonder. The Temples of my Country have not ceased to make daily Sacrifices of our most precious Animals to the Moon since it offered that terrible Warning, since it displayed the terrible Shape of the Axe over all over our heads. O Brother! O Peer! I take comfort to know that our Wisest Emperor has offered the wonderful Sacrifice of his foolish General who obscenely demolished the Lunar Temples of Brift Tankt…