Leslie Bigelow | published Apr, 1953

added Jun 9, 2024
cover Image
First Date of Publication
Apr, 1953
Original Source
Startling Stories
Original Source Type
Magazine - Pulp
Short Story
Original Language
Kasman Review
Summary: A very satisfying tale which blends some hand-waving magic realism and mathematics to create a vision of the fantastic.

Story Tag Line: “Was the professor a prophet or a demon? Under the savage sun he looked like a prophet in some dreadful valley…” […] At last Griffenhoek chuckled. “ Now ! I seem to remember that you were troubled by the square root of minus one ?” “Well, damn it all, Griff . Minus one has no square root. How in the devil can you take a square root which can’t be taken ? What is the square root of minus one, anyhow ? Oh, of courge, you mathematicians pretend to take it, just by putting the sign of the radical over minus one. But what then ?”


  • Vijay Fafat
    Published on

    Noah Griffenhoek is professor of physics, and the narrator, Patrick Lanson, is a professor of English. They are both good friends, and in that friendship, Lanson constantly ribs Noah about some of the more “nonsensical” parts about mathematics, particularly those which do not seem to have any real-world representations. In a particularly memorable example, Lanson launches into a monologue:

    “Mathematics!”, I snorted, resuming our noisy quarrel. “Systematic jabberwocky!”
    Why, take any group of objects and certainly you can weave a tissue of numbers around them. Some web of relationship. So far that’s all you prancing mathematicians have ever done with the world. But then you erroneously argue that those numbers of yours correspond with reality. Correspond with reality ! Fantods and tarradiddles!”
    But Griffenhoek merely smiled.
    “ Very well,” I said. “Consider the number 1 or the number 7. Just why they correspond with reality, only Pythagoras could say. But they do—somewhat. At least, you can have two wives or seven houris. But what about negative numbers ? Oh,” I went on with what I hoped was maddening condescension, “Oh, I suppose negative numbers are ‘real’ too. A negative 7 might be seven houris you can’t get.”
    Good ! His fingers pattered ; his neck distended. So I proceeded, “But now 1 have you. Griff . What about imaginary numbers ? What do they correspond to ? What about the square root of minus one ? What does that match in the real world ?”
    With an effort, Griffenhoek still smiled.
    “Charlatan !” I sneered. “Impostor ! Show me what a surd corresponds to in the real world and I’ll believe you. But until you do that, your mathematics is the kindergarten trifling of deluded theorists.
    “ Mathematics! Pooh! Consider, Griff : we have a mind of a certain limited kind, which perceives the universe in a certain limited way. Very well. In our mind we perceive certain relationships which we call mathematical. Then we slap those relationships on the universe and say eureka! the universe is just like our minds. What impudence!”

    Lanson is actually only half-kidding, for he does appreciate eccentricities of genius and the nature of mathematics, thinking about it more than superficially. To wit:

    “God bless eccentrics, for it is the eccentric, the sport, who, seeing things at an odd angle, sometimes really sees them. If Riemann had not devised the non-Euclidean geometry required by Einstein’s theory, could that geometry ever have been devised by some snuffling pedant ? Or as Einstein himself declared, if Gauss had not invented some of his equations, what reason is there to suppose that anybody would ever have invented them ?
    “I mused on the problem I had set him. The problem had vexed me for years ; I had consulted academic mathematicians in vain. It is easy to understand—vaguely —what a 1 or a 2 is. Vaguely, because there are riddles in Number, just as there are riddles everywhere. But there’s a vexing aspect of the imaginary numbers. Exactly what in our world of “reality” corresponds to sqrt(-1) or “i” in the same way that a single elm loosely corresponds to the number 1 ? Nothing, so far as I can see ; nothing at all. Yet by the use of sqrt(-1) bridges and dams are built, the airfoil of a plane is created, electricity is manipulated, and one day soon Mars will be reached. The surd “i” is a thing unreal, yet usable ; imaginary, yet operative. It is, in fact, a good deal like a thought, which is itself immaterial yet which penetrates the world.”

    Noah Griffenhoek, on the other hand, is a much more serious personality. Not just a theoretician but one who can build intricate devices, as we witness soon.

    “Certainly his monograph on the 24-dimensional universe of the electron is already a classic. [but] Professional skill aside, Griffenhoek is that capital fellow, the old time master craftsman, cranky and exacting: the sort of man who peers at you over steel-rimmed spectacles in a job print shop; or mends watches in a small southern town and invents his own escapements; or like Cerberus guards the precision”

    Noah is a Pythagorean. As he explains to Lanson,

    “According to Pythagoras, numbers are eternal things, the final realities of a misty world. Plato concurs: to him numbers are among those essences, those ultimates, which alone are real.”

    But he also knows that most people require demonstration of every aspect of life. as he says to Lanson, “You are like Lord Kelvin. You can’t understand a thing unless you see a model of it.”

    And that sets the stage for the fantasmical elements of the unfolding story. Noah has a small morocco case which holds a finely chiseled cube 4 inches to the side, with tiny tracks on the sides and symbols and hieroglyphics etched. There are also representations of various numbers: two, minus one, sqrt(-1), etc. And by some infernal magic, when the numbers are kept on the cube and the clockwork set to go “tick-tick-tick-tick”, the numbers seem to end up performing the exact operation on the cube. The number 2 doubles up the cube, minus one makes it shimmer on the edge of potentiality, and sqrt(-1) turns it inside-out… The entire description of these experimental demonstrations in wonderfully vivid. “Here in the Arizona desert, near the devil’s road, the Camino del Diablo, among the sullen buttes, sentineled by giant Saguaro cacti, in a trailer cooled by a humming box—there the exquisite toys marched and countermarched…”

    Noah also demonstrates to Lanson that this projection of mathematical manipulations on a larger reality is possible, by showing the same effects on a mica boulder outside Lanson’s home-trailer. Clearly, Noah has accessed some underlying mathematical stratum which he can manipulate…

    Which then leads us to the opening of the story itself… on how, in June 1955, 2 days after an earth rocket reached the moon, the moon started misbehaving - enlarging, shimmering, appearing to turn inside-out… Noah had set his clockwork on the rocket, though he denied this to Lanson repeatedly, leaving Lanson with the haunting thought about genius and eccentrics at the end of the story:

    “In fact, it might be as well to heed my friend Griffenhoek. It would be improper of him, it would be maniacal, to act against us. Still, perhaps we should try a little harder to make sense. Otherwise, someday… . Tick-tick-tick-tick…”

    The quality of writing is high and the author does not shirk away from details. There are many lines which are artistic. e.g. “Griffenhoek likes to insist that history is at best a thin gruel: forlorn nubbins of fact blobbing in a sea of conjecture.”. Highly recommended read.