Hyperspace (10 page)

Why ghosts, of course!

In the absence of any physical principle motivating the introduction of higher dimensions, the theory of the fourth dimension suddenly took an unexpected turn. We will now begin a strange but important detour in the history of hyperspace, examining its unexpected but profound impact on the arts and philosophy. This tour through popular culture will show how the mystics gave us clever ways in which to “visualize” higher-dimensional space.

The fourth dimension penetrated the public’s consciousness in 1877, when a scandalous trial in London gave it an international notoriety.

The London newspapers widely publicized the sensational claims and bizarre trial of psychic Henry Slade. The raucous proceedings drew in some of the most prominent physicists of the day. As a result of all the publicity, talk of the fourth dimension left the blackboards of abstract mathematicians and burst into polite society, turning up in dinner-table conversations throughout London. The “notorious fourth dimension” was now the talk of the town.

It all began, innocently enough, when Slade, a psychic from the United States, visited London and held seances with prominent townspeople. He was subsequently arrested for fraud and charged with “using subtle crafts and devices, by palmistry and otherwise,” to deceive his clients.
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Normally, this trial might have gone unnoticed. But London society was scandalized and amused when eminent physicists came to his defense, claiming that his psychic feats actually proved that he could summon spirits living in the fourth dimension. This scandal was fueled by the fact that Slade’s defenders were not ordinary British scientists, but rather some of the greatest physicists in the world. Many went on to win the Nobel Prize in physics.

Playing a leading role in stirring up this scandal was Johann Zollner, a professor of physics and astronomy at the University of Leipzig. It was Zollner who marshaled a galaxy of leading physicists to come to Slade’s defense.

That mystics could perform parlor tricks for the royal court and proper society, of course, was nothing new. For centuries, they had
claimed that they could summon spirits to read the writing within closed envelopes, pull objects from closed bottles, reseal broken match sticks, and intertwine rings. The strange twist to this trial was that leading scientists claimed these feats were possible by manipulating objects in the fourth dimension. In the process, they gave the public its first understanding of how to perform these miraculous feats via the fourth dimension.

Zollner enlisted the help of internationally prominent physicists who participated in the Society for Psychical Research and who even rose to lead the organization, including some of the most distinguished names of nineteenth-century physics: William Crookes, inventor of the cathode ray tube, which today is used in every television set and computer monitor in the world;
¹³
Wilhelm Weber, Gauss’s collaborator and the mentor of Riemann (today, the international unit of magnetism is officially named the “weber” after him); J. J. Thompson, who won the Nobel Prize in 1906 for the discovery of the electron; and Lord Rayleigh, recognized by historians as one of the greatest classical physicists of the late nineteenth century and winner of the Nobel Prize in physics in 1904.

Crookes, Weber, and Zollner, in particular, took a special interest in the work of Slade, who was eventually convicted of fraud by the court. However, he insisted that he could prove his innocence by duplicating his feats before a scientific body. Intrigued, Zollner took up the challenge. A number of controlled experiments were conducted in 1877 to test Slade’s ability to send objects through the fourth dimension. Several distinguished scientists were invited by Zollner to evaluate Slade’s abilities.

First, Slade was given two separate, unbroken wooden rings. Could he push one wooden ring past the other, so that they were intertwined without breaking? If Slade succeeded, Zollner wrote, it would “represent a miracle, that is, a phenomenon which our conceptions heretofore of physical and organic processes would be absolutely incompetent to explain.”
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Second, he was given the shell of a sea snail, which twisted either to the right or to the left. Could Slade transform a right-handed shell into a left-handed shell and vice versa?

Third, he was given a closed loop of rope made of dried animal gut. Could he make a knot in the circular rope without cutting it?

Slade was also given variations of these tests. For example, a rope was tied into a right-handed knot and its ends were sealed with wax and impressed with Zollner’s personal seal. Slade was asked to untie the knot, without breaking the wax seal, and retie the rope in a left-handed knot.
Since knots can always be untied in the fourth dimension, this feat should be easy for a fourth-dimensional person. Slade was also asked to remove the contents of a sealed bottle without breaking the bottle.

Could Slade demonstrate this astounding ability?

Today we realize that the manipulation of higher-dimensional space, as claimed by Slade, would require a technology far in advance of anything possible on this planet for the conceivable future. However, what is interesting about this notorious case is that Zollner correctly concluded that Slade’s feats of wizardry could be explained if one could somehow move objects through the fourth dimension. Thus for pedagogical reasons, the experiments of Zollner are compelling and worth discussing.

For example, in three dimensions, separate rings cannot be pushed through each other until they intertwine without breaking them. Similarly, closed, circular pieces of rope cannot be twisted into knots without cutting them. Any Boy or Girl Scout who has struggled with knots for his or her merit badges knows that knots in a circular loop of rope cannot be removed. However, in higher dimensions, knots are easily unraveled and rings can be intertwined. This is because there is “more room” in which to move ropes past each other and rings into each other. If the fourth dimension existed, ropes and rings could be lifted off our universe, intertwined, and then returned to our world. In fact, in the fourth dimension, knots can never remain tied. They can always be unraveled without cutting the rope. This feat is impossible in three dimensions, but trivial in the fourth. The third dimension, as it turns out, is the only dimension in which knots stay knotted. (The proof of this rather unexpected result is given in the notes.
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)

Similarly, in three dimensions it is impossible to convert a rigid left-handed object into a right-handed one. Humans are born with hearts on their left side, and no surgeon, no matter now skilled, can reverse human internal organs. This is possible (as first pointed out by mathematician August Möbius in 1827) only if we lift the body out of our universe, rotate it in the fourth dimension, and then reinsert it back into our universe. Two of these tricks are depicted in
Figure 2.8
; they can be performed only if objects can be moved in the fourth dimension.

Zollner sparked a storm of controversy when, publishing in both the
Quarterly Journal of Science
and
Transcendental Physics
, he claimed that Slade amazed his audiences with these “miraculous” feats during seances in the presence of distinguished scientists. (However, Slade also flunked some of the tests that were conducted under controlled conditions.)

Figure 2.8. The mystic Henry Slade claimed to be able to change right-handed snail shells into left-handed ones, and to remove objects from sealed bottles. These feats are impossible in three dimensions, but are trivial if one can move objects through the fourth dimension
.

Zollner’s spirited defense of Slade’s feats was sensationalized throughout London society. (In fact, this was actually one of several highly publicized incidents involving spiritualists and mediums in the late nineteenth century. Victorian England was apparently fascinated with the occult.) Scientists, as well as the general public, quickly took sides in the matter. Supporting Zollner’s claims was his circle of reputable scientists, including Weber and Crookes. These were not average scientists, but masters of the art of science and seasoned observers of experiment. They had spent a lifetime working with natural phenomena, and now before their eyes, Slade was performing feats that were possible only if spirits lived in the fourth dimension.

But detractors of Zollner pointed out that scientists, because they are trained to trust their senses, are the worst possible people to evaluate a magician. A magician is trained specifically to distract, deceive, and confuse those very senses. A scientist may carefully observe the magician’s right hand, but it is the left hand that secretly performs the trick. Critics also pointed out that only another magician is clever enough to detect the sleight-of-hand tricks of a fellow magician. Only a thief can catch a thief.

One particularly savage piece of criticism, published in the science quarterly magazine
Bedrock
, was made against two other prominent physicists, Sir W. F. Barrett and Sir Oliver Lodge, and their work on telepathy. The article was merciless:

It is not necessary either to regard the phenomena of so-called telepathy as inexplicable or to regard the mental condition of Sir W. F. Barrett and Sir Oliver Lodge as indistinguishable from idiocy. There is a third possibility.
The will to believe
has made them ready to accept evidence obtained under conditions which they would recognize to be unsound if they had been trained in experimental psychology.

Over a century later, precisely the same arguments, pro and con, would be used in the debate over the feats of the Israeli psychic Uri Geller, who convinced two reputable scientists at the Stanford Research Institute in California that he could bend keys by mental power alone and perform other miracles. (Commenting on this, some scientists have repeated a saying that dates back to the Romans: “Populus vult decipi, ergo decipiatur” [People want to be deceived, therefore let them be deceived].)

The passions raging within the British scientific community touched off a lively debate that quickly spread across the English Channel. Unfortunately, in the decades following Riemann’s death, scientists lost sight of his original goal, to simplify the laws of nature through higher dimensions. As a consequence, the theory of higher dimensions wandered into many interesting but questionable directions. This is an important lesson. Without a clear physical motivation or a guiding physical picture, pure mathematical concepts sometimes drift into speculation.

These decades were not a complete loss, however, because mathematicians and mystics like Charles Hinton would invent ingenious ways in which to “see” the fourth dimension. Eventually, the pervasive influence of the fourth dimension would come full circle and cross-pollinate the world of physics once again.

[T]he fourth dimension had become almost a household word by 1910…. Ranging from an ideal Platonic or Kantian reality—or even Heaven—the answer to all of the problems puzzling contemporary science, the fourth dimension could be all things to all people.

Linda Dalrymple Henderson

WITH the passions aroused by the trial of the “notorious Mr. Slade,” it was perhaps inevitable that the controversy would eventually spawn a best-selling novel.

In 1884, after a decade of acrimonious debate, clergyman Edwin Abbot, headmaster of the City of London School, wrote the surprisingly successful and enduring novel
Flatland: A Romance of Many Dimensions by a Square.
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Because of the intense public fascination with higher dimensions,
the book was an instant success in England, with nine successive reprintings by the year 1915, and editions too numerous to count today.

What was surprising about the novel
Flatland
was that Abbott, for the first time, used the controversy surrounding the fourth dimension as a vehicle for biting social criticism and satire. Abbot took a playful swipe at the rigid, pious individuals who refused to admit the possibility of other worlds. The “bookworms” of Gauss became the Flatlanders. The Boeotians whom Gauss so feared became the High Priests, who would persecute—with the vigor and impartiality of the Spanish Inquisition—anyone who dared mention the unseen third dimension.

Abbot’s
Flatland
is a thinly disguised criticism of the subtle bigotry and suffocating prejudice prevalent in Victorian England. The hero of the novel is Mr. Square, a conservative gentleman who lives in a socially stratified, two-dimensional land where everyone is a geometric object. Women, occupying the lowest rank in the social hierarchy, are mere lines, the nobility are polygons, while the High Priests are circles. The more sides people have, the higher their social rank.