SPECULUM

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====== Ioan Couliano (TG:1-3) – Flatland ======

Let us suppose that we have a two-dimensional world, with two-dimensional inhabitants. They would be wholly unaware of the existence of the third dimension, and phenomena whose explanation is trivial in a three-dimensional world would be as many riddles to them, which only Flatland geniuses might be able to comprehend.

In 1916 Albert Einstein published one of those very few books that matter in human history, called The Special and General Theory of Relativity, for General Understanding. The German word is gemeinverständlich. To his friends, Einstein jokingly referred to it as gemeinunverständlich, “for general misunderstanding.”

The private Einstein was more correct than the public one. To the lay person who tries to figure out the consequences of Einstein’s theory, the ensuing worldview is mind-boggling. It is so remote from experience that it can in no way be represented without at least some explanation. Einstein himself gave that elsewhere, in cryptic words that say that imagination, dream, and vision, albeit disavowed by scholars, play a part that exceeds mere reasoning in scientific theories.

With a little historical background, one can follow some of Einstein’s references. To explain why we are not in a position to understand the world from inside out, he resorts to a rather famous fable: the fable of Flatland devised by a Shakespearean scholar, the Reverend Edwin Abbott Abbott, in the early 1880s. Let us suppose that we have a two-dimensional world, with two-dimensional inhabitants. They would be wholly unaware of the existence of the third dimension, and phenomena whose explanation is trivial in a three-dimensional world would be as many riddles to them, which only Flatland geniuses might be able to comprehend. Starting from this analogy, Einstein developed his view of the universe as being the hypersurface of a hypersphere. If five dimensions were enough for Einstein to make sense of the physical forces known to him, today physicists in search of a Grand Unified Theory (GUT) of the universe increase the number of dimensions to ten or eleven, seven of which are wrapped up in tiny particles. To give one striking example of the usefulness of this theory, we could just mention that electricity is explained as the result—or rather the reception—of four-dimensional gravity in our three-dimensional world.

Einstein’s view of the universe, as predicted, was “generally misunderstood.” Nevertheless it gave rise to a proliferation of methods of investigation that profoundly affected the humanities. We can say that, with a few exceptions—the most noteworthy being the biologist D’Arcy Wentworth Thompson—scholars were not usually establishing any direct filiation between their theories and the Einsteinian universe. Yet, when properly reinterpreted in their historical context, all these theories show astounding similarities. Today we call them cognitive; the Russian scholars, writers, and artists who in the 1920s began a whole movement that bore fruit in linguistics and literary theory called them formalism; they are better known from their French version, which spread under the name of “structuralism.”

No matter how apparently divergent their premises, all of these cognitive methods have one thing in common: They recognize a synchronic or systemic dimension to any historical phenomenon, and, in most cases, they reject our common views of history as meaningless. (In fact the word history is meaningless; it is what Gregory Bateson calls an explanatory principle—that is, a principle that, without explaining anything, simply states the limits of our knowledge.) In what follows, I will describe the essence of some of these methods. Yet I have to say from the outset that many of them are of little use to the historian, in so far as they fail in their attempt to integrate system and history, synchrony and diachrony.

The most extraordinary consequence of the Einsteinian space-time continuum for the historian of ideas is the existence of “ideal objects” which become understandable only when they are recognized as such in their own dimension. This may sound even more incomprehensible than Einstein’s universe. To make it understandable let us revert to Flatland, and suppose that the flat country is the surface of the soup in a dish. Let us suppose that the circles of oil on that surface are the intelligent inhabitants of Flatland. Obviously, being two-dimensional they can move in two directions only: left-right and forward-backward. The direction up-down is as meaningless to them as Would be a new direction to us, toward an unknown fourth dimension (the mathematician Rudy Rucker calls such a direction ana-kata). What they see of each other is a line, any space (such as a house or a bank) being closed to them by a line only. Yet, seeing them from a third direction of space, we can directly see their entrails, the interiors of their houses, and we could easily steal from their most well guarded bank safe. (As strange as it might seem, a being in a hypothetical fourth dimension of space would equally enjoy these advantages relative to us.)

Let us now suppose that I disturb all this flat world by starting to eat the soup with a spoon. How would a Soup lander experience the spoon?

He or she would be horrified by a strange phenomenon. First a rather short line, corresponding to the tip of the spoon, would appear in Soupland, which would increase as the spoon reaches for the bottom of the dish and would decrease again when the handle crosses the surface. Then, all of a sudden, a tremendous-soupquake would take place, and part of the world would be absorbed into nowhere. The disruption would continue for a while, as soup drips out of the spoon and crosses Soupland, then the situation would revert to normal.

To the Souplander, the spoon does not appear as a solid, vertical object, as it appears to us. Souplanders can experience the spoon only as a series of phenomena in time. It should not come as a surprise that life expectations are rather short in Soupland. Therefore it would take millions or billions of generations of Souplanders to make sense of the spoon phenomena. And it would take a genius of uncommon depth to make calculations that would show that the only way to put them together would be to postulate the existence of a superior dimension— the third—in which objects of an unknown sort exist. (Since they cannot possibly see us, even the most intelligent of the Souplanders would probably believe that the third dimension is just a mathematical fiction that serves only as a heuristic device.)

Similarly, we fail to understand what phenomena may be in space-time (and what “history” really means), especially when the objects of our inquiry are not tangible. Many do not even believe a “history of Ideas” to be possible, let alone a history that would not be mere summation but something having to do with “space-time”! Yet the novelty of the multifarious methods that belong to the cognitive approach was to show that ideas are synchronous. In other words, ideas form systems that can be envisaged as “ideal objects.” These ideal objects cross the surface of history called time as the spoon crosses Soupland, that is, in an apparently unpredictable sequence of temporal events.

As I indicated before, no matter how all cognitive methods treating historical phenomena (including ideal objects) synchronically have so far enriched our understanding of the past, it is legitimate to draw a line between those that failed to provide meaningful clues for the integration of synchrony and diachrony and those that did not shrug before this supreme test of our discipline. The century’s fascination with archetypes and repetition, formalism, structuralism, and “morphologies” of different kinds needs neither proof nor exposition here. Yet only a very few of the forebears of the cognitive approach could understand (and a great many of them would be as surprised to find out about this as their critics) that what had triggered their dissatisfaction with traditional methods was actually the new view of time implied in Einstein’s theory of general relativity.