This nOde last updated November 27th, 2004 and is permanently morphing...
(9 Ix (Jaguar) / 17 Keh (Red) - 74/260 - 184.108.40.206.14)
1. Land that varies little in elevation.
2. flatlands. A geographic area composed chiefly of land that varies little in elevation.
- flat´land´er noun
_Flatland : A Romance of Many Dimensions/Sphereland
: A Fantasy About Curved Spaces and an Expanding Universe_/2 Books in
1 Volume (Everyday Handbook)
by Edwin A. Abbott, Dionys Burger, Isaac Asimov
Paperback 2 Bks in 1 edition
HarperCollins (paper); ISBN: 0062732765 ; Dimensions (in inches): 0.87 x 7.99 x 5.33
Unless you're a mathematician, the chances of you reading any novels about geometry are probably slender. But if you read only two in your life, these are the ones. Taken together, they form a couple of accessible and charming explanations of geometry and physics for the curious non-mathematician. Flatland, which is also available under separate cover, was published in 1880 and imagines a two-dimensional world inhabited by sentient geometric shapes who think their planar world is all there is. But one Flatlander, a Square, discovers the existence of a third dimension and the limits of his world's assumptions about reality and comes to understand the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. The further mathematical fantasy, Sphereland, published 60 years later, revisits the world of Flatland in time to explore the mind-bending theories created by Albert Einstein, whose work so completely altered the scientific understanding of space, time, and matter. Among Einstein's many challenges to common sense were the ideas of curved space, an expanding universe and the fact that light does not travel in a straight line. Without use of the mathematical formulae that bar most non-scientists from an understanding of Einstein's theories, Sphereland gives lay readers ways to start comprehending these confusing but fundamental questions of our reality.
Over a hundred years ago, Edwin A. Abbott wrote a mathematical adventure set in a world on one plane, populated by a hierarchical society of regular geometrical figures--who think and speak and have all too human emotions. Since then _Flatland_ has fascinated generations of readers, becoming a perennial science-fiction favorite. By imagining the contact of beings from different dimensions, the author fully exploited the power of the analogy between the limitations of humans and those of his two-dimensional characters. A first-rate fictional guide to the concepts of relativity and multiple dimensions of space, the book also will appeal to those who are interested in computer graphics. This field, which literally makes higher dimensions seeable, has aroused a new interest in visualization. We can now manipulate objects in four dimensions and observe their three- dimensional slices tumbling on the computer screen. But how do we interpret these images? In his introduction to the volume, Thomas Banchoff points out that there is no better start on the problem of understanding higher-dimensional slicing phenomena than reading this classic novel of the Victorian era.
Parable of the Gemstone
To understand the intense controversy surrounding superstring theory, think of the following parable.
Imagine that, at the beginning of time, there was once a beautiful, glittering gemstone. Its perfect symmetries and harmonies were a sight to behold. However, it possessed a tiny flaw and became unstable, eventually exploding into thousands of tiny pieces. Imagine that the fragments of the gemstone rained down on a flat, two-dimensional world, called Flatland, where there lived a mythical race of beings called Flatlanders.
These Flatlanders were intrigued by the beauty of the fragments, which could be found scattered all over Flatland. The scientists of Flatland postulated that these fragments must have come from a crystal of unimaginable beauty that shattered in a titanic Big Bang. They then decided to embark upon a noble quest, to reassemble all these pieces of the gemstone.
After 2,000 years of labor by the finest minds of Flatland, they were finally able to fit many, but certainly not all, of the fragments together into two chunks. The first chunk was called the "quantum," and the second chunk was called "relativity."
Although they Flatlanders were rightfully proud of their progress, they were dismayed to find that these two chunks did not fit together. For half a century, the Flatlanders maneuvered these two chunks in all possible ways, and they still did not fit.
Finally, some of the younger, more rebellious scientists suggested a heretical solution: perhaps these two chunks could fit together if they were moved in the third dimension.
This immediatelyset off the greatest scientific controversy in years. The older scientists scoffed at this idea, because they didn't believe in the unseen third dimension. "What you can't measure doesn't exist," they declared.
Furthermore, even if the third dimension existed, one could calculate that the energy necessary to move the pieces up off Flatland would exceed all the energy available in Flatland. Thus, it was an untestable theory, the critics shouted.
However, the younger scientists were undaunted. Using pure mathematics, they could show that these two chunks fit together if they were rotated and moved in the third dimension. The younger scientists claimed that the problem was therefore theoretical, rather than experimental. If one could completely solve the equations of the third dimension, then one could, in principle, fit these two chunks completely together and resolve the problem once and for all.
We Are Not Smart Enough
That is also the conclusion of today's superstring enthusiasts, that the fundamental problem is theoretical, not practical. The true problem is to solve the theory completely, and then compare it with present-day experimental data. The problem, therefore, is not in building gigantic atom smashers; the problem is being clever enough to solve the theory.
Edward Witten, impressed by the vast new areas of mathematics opened up by the superstring theory, has said that the superstring theory represents "21th century physics that fell accidentally into the 20th century." This is because the superstring theory was discovered almost by accident. By the normal progression of science, we theoretical physicists might not have discovered the theory for another century.
The superstring theory may very well be 21st century physics, but the bottleneck has been that 21st century mathematics has not yet been discovered. In other words, although the string equations are perfectly well-defined, no one is smart enough to solve them.
This situation is not entirely new to the history of physics. When Newton first discovered the universal law of gravitation at the age of 23, he was unable to solve his equation because the mathematics of the 17th century was too primitive. He then labored over the next 20 years to develop a new mathematical formalism (calculus) which was powerful enough to solve his universal law of gravitation.
Similarly, the fundamental problem facing the superstring theory is theoretical. If we could only sharpen our analytical skills and develop more powerful mathematical tools, like Newton before us, perhaps we could solve the theory and end the controversy.
Ironically, the superstring equations stand before us in perfectly well-defined form, yet we are too primitive to understand why they work so well and too dim witted to solve them. The search for the theory of the universe is perhaps finally entering its last phase, awaiting the birth of a new mathematics powerful enough to solve it.
Imagine a child gazing at a TV set. The images and stories conveyed on the screen are easily understood by the child, yet the electronic wizardry inside the TV set is beyond the child's ken. We physicists are like this child, gazing in wonder at the mathematical sophistication and elegance of the superstring equations and awed by its power. However, like this child, we do not understand why the superstring theory works.
In conclusion, perhaps some of the readers will be inspired by this story to read every book in their libraries about the superstring theory. Perhaps some of the young readers of this article will be the ones to complete this quest for the Theory of the Universe, begun so many years ago by Einstein.
Michio Kaku - _Hyperspace_