"William E. Emba"|
This short novel, originally published in the January 1931 ASTOUNDING,
and republished by Damon Knight in SCIENCE FICTION OF THE 30'S (1975),
involves a mathematical physicist whose theories get applied by an
experimentalist who gets trapped, along with his beautiful daughter,
in an alternate dimension. The theoretician must think out a rescue.
The story rolls in its simple-minded goshwowness, plotting, and
characterizations, of the traditional pushbutton sort. Mathematics
is mentioned frequently, including a nifty attempt to explain how
higher-dimensional rotations can be induced from below: one attaches
right-angled frames in tension, with the natural spring lengths
corresponding to the lengths they will have in the desired folding.
The simple-mindedness of the characterizations becomes comic, even
ridiculous, at times. Of mathematical interest is that the hero is so
handsome in his appearance, and drives such a sporty car, that various
characters are confused, and have a hard time believing he is the famed
mathematical genius who has been called in for the rescue. Even the
third-person narrator makes an effort to convince the reader that this
peculiar mixture of looks, hipness, and brains is in fact the truth.
The writing is socially dated and not all that imaginative. What's mathematically interesting is Leinster's descriptions of how nD beings can interact with an (n+1)st spatial dimension: how 2D beings can create a 3D right angle using springs, how 3D beings can use mirrors to see into "extra" dimensions, and how 3D beings can use magnets to create pathways to "extra" dimensional spaces. (I'm putting "extra" in quotes because of course this isn't correct lingo mathematically.) Also cool: Leinster uses time as a 4th dimension and so goes to a 5th dimension in order to get more spacial dimensions. However, sometimes the narrative implies that the 4th dimension is spacial, but no one is perfect.
There is a sequel to the Murray Leinster's "The Fifth Dimensional Catapult". The story is "The Fifth Dimension Tube", which appeared in Jan 1933 issue of Astounding Stories.
"Tube" is available for free download here.
"Catapult" is available for free download here
Hmmmm....Thanks to Vijay Fafat's link above to the Gutenberg.org copy of this story, I noticed that there is another story in the same issue of Astounding Stories with a brief but very nice description of the geometry. The Gate to Xoran by Hal K. Wells says:
Perhaps I should add a separate entry for that one. What do you think?
THAT gate is the one through the fourth dimension, for Xoran and your planet in a four-dimensional universe are almost touching each other in spite of the great distance separating them in a three-dimensional universe. We of Xoran, being three-dimensional creatures like you Earthlings, can not even exist on a four-dimensional plane. But we can, by the use of apparatus to open a Gate, pass through a thin sector of the fourth dimension and emerge in a far distant part of our three-dimensional universe.
“The situation of our two worlds,” Arlok continued, “is somewhat like that of two dots on opposite ends of a long strip of paper that is curved almost into a circle. To two-dimensional beings capable only of realizing and traveling along the two dimensions of the paper itself those dots might be many feet apart, yet in the third dimension straight across free space they might be separated by only the thousandth part of an inch. In order to take that short cut across the third dimension the two-dimensional creatures of the paper would have only to transform a small strip of the intervening space into a two-dimensional surface like their paper.
“They could, do this, of course, by the use of proper vibration-creating machinery, for all things in a material universe are merely a matter of vibration. We of Xoran plan to cross the barrier of the fourth dimension by creating a narrow strip of vibrations powerful enough to exactly match and nullify those of the fourth dimension itself. The result will be that this narrow strip will temporarily become an area of three dimensions only, an area over which we can safely pass from our world to yours.”