"Which is the more likely: a charlatan of such extraordinary ingenuity,
or a mathematician of great genius?" And before long, I realized that
the probabilities clearly favored the former.
Achilles: Didn't you directly check out any of his amazing claims, however?
Crab: Why should I? The probability argument was the most convincing
thing I had ever thought of; no mathematical proof would have
equaled it. But Mr. T here insisted on rigor. I finally gave in to his
insistence, and checked all of Najunamar's results. To my great sur-
prise, each one of them was right. How he discovered them, I'll never
know, however. He must have some amazing and inscrutable Oriental
type of insight which we here in the Occident can have no inkling of.
At present, that's the only theory which makes any sense to me.
Tortoise: Mr. Crab has always been a little more susceptible to mystical or
fanciful explanations than I am. I have full confidence that whatever
Najunamar did in his way has. a complete parallel inside orthodox
mathematics. There is no way of doing mathematics which is funda-
mentally different from what we now know, in my opinion.
Achilles: That is an interesting opinion. I suppose it has something to do
with the Church-Turing Thesis and related topics.
Crab: Oh, well, let us leave these technical matters aside on such a fine
day, and enjoy the quiet of the forest, the chirping of the birds, and the
play of sunlight on the new leaves and buds. Ho!
Tortoise: I second the motion. After all, all generations of Tortoises have
reveled in such delights of nature.
Crab: As have all generations of Crabs.
Achilles: You don't happen to have brought your flute along, by any
chance, Mr. C?
Crab: Why, certainly! I take it with me everywhere. Would you like to
hear a tune or two?
Achilles: It would be delightful, in this pastoral setting. Do you play from
memory?
Crab: Sad to say, that is beyond my capability. I have to read my music
from a sheet. But that is no problem. I have several very pleasant
pieces here in this case.
(He opens up a thin case and draws out afew pieces of paper. The topmost
one has the following symbols on it:
Va:~-Sa=O
He sticks the top sheet into a little holder attached to his flute, and plays.
The tune is very short.)
Achilles: That was charming. (Peers over at the sheet on theflute, and a quizzical
expression beclouds his face.) What is that statement of number theory
doing, attached to your flute like that?
552
(The Crab looks at his flute, then his music, turns his head all around, and
appears slight(y confused.)The Magnijicrab, Indeed