"Flatland" and Einstein′s Universe
On our Relation to the Temporal Dimension

by

Wolfgang Ruttkowski¹

In his "romance of many dimensions", Flatland (1885), Edwin A. Abbott² attempts to describe a two-dimensional world, whose inhabitants, flat themselves, can only move in a plane, neither upwards nor downwards. This description - as an exercise in consistency of visual imagination - goes far beyond the intellectual scope of children′s′ books. But that is not all: the narrator of the story, an inhabitant of Flatland, has dreams and visions of even more limited worlds, "Lineland" and "Pointland", in which the freedom of movement that "Flatland" affords seems immense if not inconceivable. In the end this narrator has a quasi-religious experience of a "higher world", one that enables him to rise out of the limitations of his drab existence in Flatland into a "new dimension", into "Spaceland", that is to say, into our world. The man from Flatland gets punished for his vision and at the end of this science-fiction-satire we see him imprisoned and silenced. This was not Einstein′s fate, who opened another dimension for us, though not a purely spacial one. It is tempting to extend the parallels and comparisons discussed in "Flatland" into Einstein′s universe³ and see, what this kind of "analogical phantasizing" will yield.

Without going further into the details of Abbott′s little book, we may summarize that inhabitants of Flatland cannot transcend their own two dimensions and, therefore, cannot survey them fully. They might have other ways of knowing about them, but they certainly cannot visually imagine them and, of course, not at all a third dimension. They also would not be able to describe a third dimension in their conventional language, since the concepts of their language are derived from their own world of daily experience⁴, witch does not reach into the "next" (third) dimension.

This cluster of limitations applying to the inhabitants of Flatland can - by analogy - be extended into all four dimensions known to us and to their imaginable inhabitants. To do this, we arrange the dimensions in an ascending order: A line is marked by points; a plane by lines; a three-dimensional space by planes; in Einstein′s space-time-dimension space is measured by time and vice versa. We distinguish (with Abbott) "Pointland", "Lineland", "Flatland", "Spaceland" and (additionally) "Einstein′s universe". The inhabitants of Pointland cannot move freely within a line, those of Lineland cannot move within a plane, those of Flatland cannot rise into space, those of Spaceland cannot move freely in time.

The last case, of course, marks our own situation: We live in time, we are aware of it and of its all-importance⁵. But we cannot move freely in it. We are caught in it like in an elevator, which does not stop, as Einstein would say. Time is our tyrant. It does not allow us to return to days gone by; and it is dragging us mercilessly into an unknown future. While being dragged this way, we age rapidly-and finally meet death.

By now we all know from modern science that we could escape this tyrant time only if we were capable of speed faster than light. If a space ship could carry us away at the speed of light, time would stand still for us. We would not age any longer. If our vehicle of transportation could travel faster than light, we would become younger on our trip. - But, horror after horror, at the return to our beloved planet: Nobody would recognize us any longer. Like in the archetypal myth of the man who went to sleep in a mountain (or under the sea⁶) our friends and family would have died long ago. Because of the enormous distances involved, our trip would have taken a long time (earth time!), and here time would have not stood still (or be reversed). We would return as strangers to an estranged world. Therefore, some might feel that it is a good thing that any normal object is forever confined (by the laws of relativity) to move at speeds slower than the speed of light. If it were otherwise, we could acquire divine powers.

What do we mean by saying we cannot "survey" time? - Since we cannot move at will into the past or future, we cannot truly know either one. We experienced only our own past, not that of others, and even the memory of our own past is always distorted by the present. We, who remember⁷our past, are different persons from our former selves, who experienced the past. The past itself has done this to us. It has changed us. Therefore, the past is sealed to our knowledge almost as hermetically as is the future. For the visitor from Spaceland everything in Flatland, which is considered by its inhabitants to be "solid" or "enclosed on four sides", lies open and exposed to his view, since he enjoys the advantage of rising over it into the third dimension. Here, he is able to move freely. In the same way, for the visitor from Einstein′s universe, who can move freely in the "fourth dimension", time, the past and the future would he exposed and open to inspection. Would this make him "all-knowing", in the way God is supposed to be all knowing? - It seems that someone, who can know anything that happened or will happen, still misses out on one aspect of life: He would not be able to look into the hearts of men. He could observe only external events; and only indirectly could he deduce motivation from the kind of action he could observe. This is what we often do in hindsight. But the stirrings of the human soul would be unknown to this visitor. Therefore, also in Einstein′s universe it would be a privilege to be allowed to "look into someone′s heart" and a special moment, when someone "opens his heart" to someone he loves.

[...]

1 I would like to thank the participants of Bukkyo Daigaku′s (Buddhist University′s) Tetsugakkai (Philosophical Circle), to whom this paper was presented on Febr. 6th 1991, for their lively discussion. Published in Acta Humanistica XX/2, Humanities Series No. 18 (Kyoto, March 1991) 280-295.

2 Edwin A. Abbott (1838-1926) was a noted Shakespearean scholar whose hobby was the study of higher mathematics.

3 We use, of course, the term "Einstein′s Universe" in a metaphorical manner as a brief code word for our-rather generalized and vague-notions of those concepts of time-space, causality etc. that modern physics seems to have agreed on. As an introduction to Einstein′s universe, we might just as well use the author′s own "popular exposition": Albert Einstein (1879-1955): Relativity; The Special and General Theory (Transl. by Robert W. Lawson. 1964. In chapter XXXI, the reader will notice, that Abbott′s kind of analogical reasoning was not alien to Einstein himself.); and: A. E. und Leopold Infeld: Evolution der Physik von Newton bis zur Quantentheorie (1962). - In philosophy, a mere enumeration of authors (in alphabetical order) who have written book length treatises on the problem of time - during the last decades and in English, German or French alone - may attest to the prominence of this topic: J. W. De Bakker (1988), G. Berger (1964), H. Bergson (1889), S. M. Cahn (1967), Millie Capek, ed. (1976), T. Chapman (1982), Hedvig Conrad-Martius (1954), W. Cramer (1954), Richard R. M. Gale (1967, 1968), Werner Gent (1926-30), Adolf Grünbaum (2 1973), Hatano, Seiichi (1963), Martin Heidegger (1927), Steven Heine (1985), Paul Helm (1988), Ian Hinckfuss (1975), Edmund Husserl (1928), F. Kümmel (1962), J. R. Lucas (1973, 1984), A. March (1948), H. Meyerhoff (1955), J. Pucelle (31962), Y. Reenpää (1966), Hans Reichenbach (1924, 1928, 1956, 1958, 1971), John M. E. McTaggart (1934), Mark J. Temmer (1958), Bas van Fraassen (1970), Johannes Volkelt (1925), G. J. Whitrow (1961), G. H. von Wright (1968), Wolfgang Wieland (1956), Alfred North Whitehead (1929), Z. Zawirski (1936), Jiri Zeman (1971).-

4 Benjamin Lee Whorf is especially known as having pursued this idea, e.g. in: "An American Indian Model of the Universe." (ca. 1936) in: International Journal of American Linguistics, 16, 1950, pp. 67-72; also in: Language, Thought, and Reality (ed. John B. Carroll, 1956), -in German: Sprache, Denken, Wirklichkeit (transl. by Peter Krausser, 1963); see also Ekkehart Malotki: Hopi-Time; A Linguistic Analysis of the Temporal Concepts in the Hopi Language (1983), Reinhart Koselleck: Futures Past; On the Semantics of Historical Time (1985), -Henry Kucera and Karla Trnka: Time in Language; Temporal Adverbial Constructions in Czech. Russian and English (1975); - for the developmental aspect of our time concepts see Jean Piaget: The Child′s Conception of Time (transl. by A. J. Pommerans, 1969).

5 The evolution of various time concepts has been traced, in the history of ideas and in cultural anthropology, amongst others, by Harrison J. Cowan: Time and Its Measurements (1958), Stephen Jay Gould: Time′s Arrow Time′s Cycle; Myth and Metaphor in the Discovery of Geological Time (1987), Georges Gurvitch: The Spectrum of Social Time (La multiplicitie des temps sociaux, trans. by Myrtle Korenbaum, 1964), Charles Nordman: The Tyranny of Time (1925), Richard Broxton Onians: Origins of European Thought (1988), Ricardo J. Quinones: Renaissance Discovery of Time (1972), -Gustav Wendorff: Zeit und Kultur; Geschichte des Zeitbewusstseins in Europa (1980).- In literature, we can mention only very few, very different works, in which time is a central theme: Michael Ende′s "fairy tale-novel": Momo; Oder die seltsame Geschichte von den Zeitdieben und von dem Kind, das den Menschen die gestohlene Zeit zurückbrachte (1973), -Thomas Mann′s "Zeitroman": Der Zauberberg (engl.: The Magic Mountain, 1924) and his highly original essay "Lob der Vergänglichkeit." (in: Eckart, 21. Vol., 1952; comp. R. Thieberger: Der Begriff der Zeit bei Thomas Mann, 1952); Marcel Proust′s A la recherche du temps perdu (1913-27), and H(erbert) G(eorge) Wells′ utopia The Time Machine (1895).While the latter describes a "time-trip" up to approx. the year 800000, Inge Aichinger′s (b. 1920) short story "Spiegelgeschichte" (1954, Mirror Story) attempts the interesting experiment of letting narrated time run in reverse: A life story is being told backwards from its tragic ending to its hopeful beginnings.

6 In Europe, the story of Rip Van Winkle may serve as an exemple; in Japan the popular tale of Urashima Taro.

7 One of the central themes of Proust′s novel (see above).