Hyperspace

With hyperspace (from the Greek hyper for "about") is generally referred to an extension of a conventional space , so a construction over transcends the existing room concept. In most cases, this is a higher-dimensional space that has additional degrees of freedom compared to a three-dimensional space . The specific meaning of the term, however, depends heavily on the respective context and can only be understood using the spatial term used there.

Origin of the term

The term hyperspace was first used in the second half of the 19th century, when abstract concepts of space emerged in mathematics that went beyond three-dimensional visual space . The beginning of the mathematical examination of such exotic spaces goes back to June 10, 1854, when Bernhard Riemann presented his radically new geometry of curved arbitrary-dimensional spaces in his habilitation lecture at the University of Göttingen . Based on or inspired by its use in mathematics, where it also represented a break with traditional ideas, the term also found its way into many other areas, such as literature , philosophy , psychology and physics . In an address to the American Mathematical Society in December 1897, mathematician Simon Newcomb summarized the fascination that the concept exerted well beyond mathematics in the following words:

"The introduction of what is now very generally called hyper-space, especially space of more than three dimensions, into mathematics has proved a stumbling block to more than one able philosopher."

"Introducing what is now commonly referred to as hyperspace - especially space with more than 3 dimensions - into math has proven to be a stumbling block for more than one able philosopher.)"

Use in math

In mathematics, the term was originally used for higher-dimensional Euclidean spaces with four or more dimensions. Later the term was also extended to other higher-dimensional spaces, which may be based on a space concept other than Euclidean.

In a completely independent conceptual formation, hyperspaces are constructed as structures over topological spaces in topology . The hyperspace of a space is understood to mean a space whose points are suitable subsets of and in which they can be embedded . This hyperspace concept was developed in 1914 by Felix Hausdorff in its basic features of set theory for metric spaces , it was expanded in 1922 by Leopold Vietoris to general topological spaces. ${\ displaystyle H (X)}$${\ displaystyle X}$${\ displaystyle X}$${\ displaystyle X}$

Use in physics

In physics, hyperspace is understood to be a physical space that has more than three dimensions and thus goes beyond our conventional three-dimensional conception of space. However, the term was originally rarely used in the scientific literature to designate higher-dimensional spaces, but initially coined in science fiction literature. After the physicist Michio Kaku then in 1994 a popular book about the theoretical physics entitled Hyperspace (English for hyperspace was published), the term has been increasingly used in the popular science and rarely also in specialized literature. Depending on the underlying physical theory, hyperspace has a number of dimensions between 4 ( general relativity theory ) and 11 ( M theory ).

Fictional use

Since Riemann's introduction of non-Euclidean geometries into mathematics, descriptions of “higher dimensions” have often found their way into art and literature. In particular, the interest in an additional spatial “ fourth dimension ” reached a peak between 1870 and 1920, hyperspaces and higher dimensions became a metaphor for the foreign and opaque. A literary classic that uses the fourth dimension as an allegory for the limitations of the human imagination is the short story Land of Land from 1884 by Edwin Abbott Abbott . But the term also appears in other authors such as Oscar Wilde , Marcel Proust , Fyodor Dostojewski and HG Wells . In addition, ideas of higher dimensions inspired works by musicians such as Alexander Scriabin , Edgar Varèse and George Antheil as well as painters such as Pablo Picasso and Marcel Duchamp and influenced the development of Cubism and Expressionism .

In contrast to other literature, in which the use of it declined sharply after the peak of interest around the turn of the century before last, the term hyperspace has become firmly established in science fiction . There it describes a medium through which spaceships can take “shortcuts” in order to circumvent the relativistically based impossibility of faster than light speeds. The term hyperspace (English for hyperspace) was introduced in science fiction in 1931 by John W. Campbell in the American magazine version of his novel Island of Space (in translation: Cosmic Cruise ).

Physical representation of hyperspace in art and literature

In the literature, hyperspace is mostly described as a parallel world with special properties in order to be able to use it as a plot device . In this hyperspace the real physical laws of nature mostly do not apply or only partially apply .

The alternatively used term warp space takes this image into account. Some authors describe an artificially created, limited phenomenon, for which they then often use the term space warp , which also appeared for the first time with Campbell. The image of a thread-like structured hyperspace is occasionally used - then mostly called slipstream -, for example in the television series Andromeda , where the authors were inspired by terms from string theory . However, the original term hyperspace is by far the most common. Although the hyperspace concept used in science fiction has no rational plausibility , since the 1950s at the latest it has become a common device to circumvent the limitations of real physics. Representations of higher dimensions, which place them at the center of the action and not just use them as an aid, are relatively rare. An example of this is the use in the series Babylon 5 , where hyperspace is a central plot element of the series and is pictured as a colored, cloud-like environment.

Attempts in science fiction literature to illustrate hyperspace itself often describe a chaotic, confusing environment. Examples of such representations are the novels The Mapmakers (1955) by Frederik Pohl , Hyperspace (1959) by R. Lionel Fanthorpe , All the Traps of Earth (1960) by Clifford D. Simak , Timepiece (1968) by Brian N. Ball and A Different Light (1978) by Elizabeth A. Lynn . Occasionally, hyperspace has also been described as populated by exotic beings, such as in Christopher Grimm's 1959 novel Someone to Watch Over Me . The most widely known visualization of a fictional hyperspace comes from the Star Wars film series , which was released in theaters from 1977: Although the While the term only functions as a trick for the plot taken over from earlier science fiction works, the hyperspace concept finally entered pop culture thanks to the spectacular effects that illustrate the jump of the spaceships into hyperspace .

In addition to the visual representation as an optically visible parallel space, there is also the opposite concept of describing hyperspace as an abstract, invisible place. This representation is used, for example, in the works of Larry Niven ( Ringwelt ) or Michael McCollum ( Gibraltar Stars Trilogy ). Also in the television series and movies of the Star Trek franchise, where the term subspace is used for hyperspace. The subspace is only visualized in later series such as Voyager.

General

Hyperspace models of various well-known science fiction works

literature

mathematics

• Alejandro Illanes, Sam B. Nadler: Hyperspaces: Fundamentals and Recent Advances . CRC Press, 1999, ISBN 0-8247-1982-4 .
• Keith R. Wicks: Fractals and Hyperspaces. Springer, Berlin 1991, ISBN 0-387-54965-X .

Popular science

Fiction

Individual evidence

1. ^ Simon Newcomb : Philosophy of Hyper-Space . In: Science. January 7, 1898: Vol. 7. no. 158, pp. 1-7.
2. ^ Bernard V. Lightman: Victorian Science in Context . University of Chicago Press, 1997, ISBN 0-226-48111-5 , pp. 264 f.
3. ^ "Philosophy of Hyperspace" - Address by Simon Newcomb to the American Mathematical Society at Project Euclid
4. Steven Schwartzmann: The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English . MAA 1994, ISBN 0-88385-511-9 , p. 110 ( excerpt (Google) )
5. Eric W. Weisstein : hyperspace . In: MathWorld (English).
6. ^
7. ^ Felix Hausdorff, Egbert Brieskorn: Collected works . Springer, 2001, ISBN 3-540-42224-2 , p. 762 ff.
8. ^ A b Brian Stableford : Science Fact and Science Fiction: An Encyclopedia . CRC Press 2006, ISBN 0-415-97460-7 , p. 238ff
9. a b Michio Kaku: Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford Univ. Pr., 1994, ISBN 978-0-19-508514-3 , p. 21 ff.
10. ^ A b Definition in Brian M. Stableford : Historical Dictionary of Science Fiction Literature . Scarecrow Press, 2004, ISBN 0-8108-4938-0 , p. 168 ( excerpt (Google) )
11. Talking Spaceships and String Theory: Wolfe on 'Andromeda' Tech ( Memento from August 2, 2010 in the Internet Archive ) (English) - Interview with the co-producer of the television series Andromeda , RH Wolfe
12. ^ "The notion lacks rational plausibility, having no answer to Einsteinian objections" in Brian M. Stableford : Historical Dictionary of Science Fiction Literature . Scarecrow Press, 2004, ISBN 0-8108-4938-0 , p. 168 ( excerpt (Google) )
13. ^ Brian M. Stableford : Historical Dictionary of Science Fiction Literature . Scarecrow Press, 2004, ISBN 0-8108-4938-0 , p. 94 ( excerpt (Google) )
14. David Bassom: The A to Z Guide of Babylon 5 . 1996, ISBN 0-7522-0252-9 paragraph Hyperspace under letter H; Torsten Dewi: The Babylon 5 Universe . 1998, ISBN 3-89365-677-4
15. ^ Elisabeth Kraus, Carolin Auer: Simulacrum America: The USA and the Popular Media . Boydell & Brewer, 2000, ISBN 1-57113-187-6 , p. 126 ( excerpt (Google) ).
16. Larry Niven: Ringworld . 2008, ISBN 978-3-404-24238-2 , Chapter Five; Michael McCollum: Star Fire 2008, ISBN 978-3-453-52320-3 , chapter 29.