Abbott, Edwin

Abbott, Edwin A. Flatland. Penguin Books, New York. 1998. 

Abbott, Edwin A. Flatland. Dover Publications, Inc., New York, 1952. (Original publication Seeley and Co., Ltd., London, 1884.)... 

Figure 2.2 Edwin Abbott Abbott s conception of Lineland with women as dots and the King as a line at center. The King can see only points.

As Thomas Banchoff points out in Beyond the Third Dimension, the first edition of Flatland appeared as only one thousand copies in November 1884, but since then interest and sales have dramatically increased. Edwin Abbott Abbott was not the first person to consider a 2-D universe inhabited by flat creatures, but he was the first to explore what it would mean for 2-D creatures to interact with a higher-dimensional world. Today computer graphic projections of 4-D objects bring us a step closer to higher-dimensional phenomena, but even the most brilliant mathematicians are often unable to grasp the fourth dimension just as the square protagonist of Flatland had trouble understanding the third dimension. 

The challenge of modern computer graphics fits right in with one of the chief aims of Edwin Abbott Abbott in the introduction of his time-... 

However, Edwin A. Abbott s fanciful two-dimensional world described in Flat-land is no more the world of molecules and chemical reactions than it was the world around us. While molecular topology is adequate to explain many aspects of chemical behavior, the evolution of quantitative models for structure-activity relations is unavoidably moving into the realm of three-dimensional (3D) structure. Modern computing enables rapid manipulation of 3D chemical structures, and it is leading the way for a proliferation of models for the quantification of electronic structure. For complex behavior of chemicals including physicochemical properties, reactivity, and biological activity, 3D structures are essential. 

And what does that mean In the 1920s Louis DeBroglie described electrons as both particles and waves because they have precise mass, go splat-splat-splat (or click-click-click ) into Geiger counters yet show interference like radio and light waves. It is one thing to say particle-waves and quite another to really picture them. Try it. Our problem is that electrons are outside of both our direct senses and experiences. As Bronowski notes, twentieth-century physics introduced abstraction and uncertainty and the need for what he describes as tolerance in modeling nature." The nineteenth-century satire Flatland by Shakespearean scholar Edwin A. Abbott illustrates our limitations. ... 

FLATLAND takes its name from the book FT.ATLAND A Romance of Many Dimensions written by Edwin A. Abbott in 1884. In his book, Abbott depicts his world through the eyes of 19th century Victorian satire, imagining a land of two dimensions. Likewise, the depiction of our three-dimensional world of chemistry in the two dimensions of the printed page is the aim of the FLATLAID system, developed by the author for use on a VAX computer operating under the VliS environment. 

The difficulty of a three-dimensional observer to envisage the effects of a rotation in four dimensions may be likened to the response of a two-dimensional being in the legendary Flatland of Edwin Abbott (1952) to a rotation in three dimensions. Unless the rotation axis lies perpendicular to the flat plane a rotating vector moves into the incomprehensible third dimension and appears to contract in two-dimensional projection. Seen from outside the contraction is compensated by an expansion (dilation) of the vector into the third dimension. 

In 1859, Edwin L. Drake began drilling for oil near Titusville, Pennsylvania. Almost immediately, Drake s well produced oil, and this success encouraged other oil drillers to set down wells. In 1860, the first refinery was built by William Abbott and William Barnsdall at Oil Creek. Their batch operation produced gasoline, naphtha, kerosene, and bottom residuum. 

Romance of Many Dimensions" by Edwin A. Abbott. While Abbott s work tries to introduce the reader to the concept of the multi-dimensional space, it chooses fewer dimensions than three as starting point. By doing so, Abbott came up with imaginary laws of nature that apply in one and two dimensions. Although these laws, which for instance explain how rain is experienced in two dimensions, are unrealistic, they impressively illustrate the mystery of lower dimensionalities. 

Prom Flatland A Romance of Many Dimensions by Edwin A. Abbott... 

---