Flatland is a romance of people living in a two-dimensional world. In this story, one of the Flatlanders dared to explore a world below and a world above their flat “universe”.
But in The 4-D Doodler, a three-dimensioned being —like all of us— is pulled to a four-dimensioned world, but only a part of him goes to the fourth dimension; so he is trapped between the third and the fourth dimension.
The adventurers in both books are some kind of dimensional-travelers, but with the exception that here, the author —Ralph Waldeyer— points to the possibility that moving from one dimension toward another is not necessarily quantized. That is, it is possible to live in a n-dimension space and in a n+1-dimension space simultaneously, only that different “regions” of the body are not in the same dimension at the same time.
Waldeyer offers an interesting possibility that maybe Edwin Abbott —the author of Flatland— did not suspect: what if A. Square —the main character of Flatland— instead of being lifted to the Spaceland “in whole” was lifted just “a part” of him? This is exactly what happened to Professor Gault when Harper —his assistant— took a two dimensional paper cutout of him and “jacknifed” the paper cut placing him (by some sort of fourth dimension doodling) in the third and fourth dimension simultaneously.
“Do you believe, Professor Gault, that this four dimensional plane contains life-intelligent life?”
At the question, Gault laughed shortly. “You have been reading pseudoscience, Dr. Pillbot,” he twitted. “I realize that as a psychiatrist, you are interested in minds, in living beings, rather than in dimensional planes. But I fear you will find no minds to study in the fourth dimension. There aren’t any there!”
Professor Gault paused, peered from beneath bushy white brows out over the laboratory. To his near sighted eyes the blurred figure of Harper, his young assistant, seemed busily at work over his mathematical charts. Gault hoped sourly that the young man was actually working and not just drawing more of his absurd, senseless designs amidst the mathematical computations....
“Your proof,” Dr. Pillbot broke into his thoughts insistently, “is purely negative, Professor! How can you know there are no beings in the fourth dimension, unless you actually enter this realm, to see for yourself?”
Professor Gault stared at the fat, puffy face of his visitor, and snorted loudly.
“I am afraid, Pillbot, you do not comprehend the impossibility of such a passage. We can not possibly break from the confines of our three dimensional world. Here, let me explain by a simple illustration.”
Gault took up a book, held it so that a shadow fell onto the surface of the desk. “That shadow,” he said, “is two dimensional, has length and breadth, but no thickness. Now in order to enter the third dimension, our plane, the shadow would have to bulge out in some way, into the dimension of thickness an obvious impossibility. Similarly, we can not enter the fourth dimension. Do you see?”
“No!” retorted Pillbot with some heat. “In the first place, we are not two dimensional shadows, and---why, what is the matter?”
“I said if you will step over to this desk I will explain to you in elementary terms–very elementary and easy to understand–why you will never be able to study four dimensional beings–if any exist!” Gault’s voice was tinged with sarcasm.
Pillbot came over, followed by Harper, who was interested in any explanations about the fourth dimension–even elementary ones....
Gault, with a glint in his eye, pressed the paper figure flatly on the surface of Harper’s desk.
“This paper man, we will say, represents a two dimensional creature. We lay him flatly against the desk, which represents his world–Flatland, we mathematicians call it. Mr. Flatlander can’t see into our world. He can see only along the flat plane of his own world. To see us, for instance, he would have to look up, which is the third dimension, a direction inconceivable to him. Now, Doctor, are you beginning to understand why we can never see four dimensional beings?”
“You–you mean to say,” he quailed, “that we are under scrutiny by some Being of the fourth dimension?” “That’s it,��� replied Harper with a whinny. “I–I know it, I can feel it. It became aware of our three dimensional life in some way, and its attention is now concentrated on the laboratory!” He wrung his hands. “I just know something else terrible is going to happen!”
Download the whole story! It's a nice complement to Flatland!