Abbott’s Flatland

Charles Hinton studied mathematics at Oxford, married Mary Boole (one of the daughters of famous logician Geoge Boole), and then moved to the United States after being convicted of bigamy. He taught mathematics at Princeton University and the University of Minnesota. In 1907, Hinton published An Episode of Flatland (a work more scientific than Abbott s Flatland) in which 2-D creatures resided on the surface of a circular world called Astria. Gravity behaves as it does in our world, except that on the plane its force varies inversely with distance instead of with the square of distance. 

In Hinton s book, Astrians have only one eye, just as Abbott s Flatland creatures. (In principle, both authors could have given their creatures two eyes, each with 1-D retinas, to provide binocular vision.) To pass each other as they travel on the surface of Astria, the inhabitants must go under or over each other, like acrobats. All female Astrians are born facing west all males are born facing east. Astrians keep their orientation until they die because there is no way to flip over without being rotated in the third dimension. To kiss his son, an Astrian dad must hold the boy upside down (It s too bad that Astrians didn t have long necks that would permit them to tilt their heads backwards and upside down to see behind them.)... 

These results should affect the inhabitants of other dimensions. Surely, Abbott s Flatland creatures would have greater challenges than we do when communicating. In three dimensions, sounds get softer as we walk away, but in two dimensions, they get increasingly spread out in... 

A beginning has been made on the estimation of adsorbate concentrations from the isotherms of pure vapors, assuming that the adsorbate is ideal and follows an analog of Raoult s law [49, 74, 75]. Some systems follow such a law, such as ethane-propane-carbon black [26] and -butane-ethane-molecuiar sieves [29]. Others do not. Thus, in the case of benzene-n-heptane-silica gel, adsorbates deviate negatively from ideal solutions, whereas in the vapor-liquid equilibria for these hydrocarbons the deviation is positive [90]. An excellent review of the thermodynamics is available [97], including the concept of two-dimensional equations of state for the adsorbate layer, strongly reminiscent of Abbott s Flatland [1],... 

Right. Just as we build up a mental image of our 3-D world, the Flatlanders have many ways to understand and survive in their 2-D world. You pause. But Abbott s book doesn t only discuss 2-D worlds. It also discusses the square s visions of a 1-D world called Lineland. The square says ... 

It goes upsilon where the operating room doesn t even exist Similarly, a 4-D creature s 3-D retina can see all of your insides without breaking your skin. This assumes that light rays are reflected into the fourth dimension—we ll have to research that further. I ve memorized Abbott s nice description of a 2-D creature lifted out of Flatland and looking down into his 2-D world from a 3-D world ... 

The notion that molecules at a surface are in a two-dimensional state of matter is reminiscent of E. A. Abbott s science fiction classic, Flatland.Perusal of this book for quotations suitable for Chapters 6, 7, and 8 revealed other parallels also the color revolt and light scattering, "Attend to Your Configuration" and the shape of polymer molecules, and so on. Eventually, the objective of beginning each chapter with a quote from Flatland replaced the requirement that the passage cited have some actual connection with the contents of the chapter. As it ends up, the quotes are merely for fun Perhaps those who are not captivated by colloids and surfaces will at least enjoy this glimpse of Flatland. 

You open Flatland, searching for a particular page. Remember, in the nineteenth century women were considered much less able than men. I think Abbott was trying to show some of the society s prejudices, because later in the book a sphere visits Flatland and says It is not for me to classify human faculties according to merit. Yet many of the best and wisest of Spaceland think more of your despised Straight Lines than of your belauded Circles. ... 

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