The New Flatland

SilenceKit writes "The New York Times has a cool story today on a sequel to Flatland, the classic geometry/social satire which "it may be no exaggeration to say has been read by every self-respecting physicist, mathematician and science fiction writer." The new one, by Ian Stewart, is called "Flatterland" and is a tour of a century of strange geometry -- from fractals to "Minkowski space," whatever that is. The story (free registration required) is at the Times" I was loaned Flatland: A Romance Of Many Dimensions by one of my college profs - it's a great book, and this come from someone who really hated geometry (What bad high school teachers can do). It's still available on fatbrain - pretty good for a 19th century text about geometry, to still be in print.

Comments

Dr Rudolf von Bitte Rucker is better known as...

[Paul Crowley]

Rudy Rucker, author of the Software, Wetware, Freeware, Realware series. He later wrote a somewhat more accessible introduction to thinking about dimension called The Fourth Dimension and How to Get There which I recommend highly. Rudy Rucker is lots of fun and most things he gets involved with are cool - check out his list of works.
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Not quite the sequel

[AntiFreeze]

Actually, there have been two books already hailled as "sequels" to Edwin A. Abbot's Flatland.

The first is Sphereland, written in 1960 by Dionys Burger. The English translation I have has a forward by Isaac Asimov [cool little useless tidbit].

The second is Geometry, Relativity, and the Fourth Dimension, written by Rudolf v. B. Rucker in 1977. Aside from the <sarcasm>eloquent title</sarcasm> it follows in the same format as the previous two.

The following is part of the blurb from Sphereland:

This delightful fantasy by a distinguished Dutch mathematician both entertains and instructs in the multidimensional geometries of curved space and the expanding universe. Written in 1960 as a sequel to Edwin A. Aboot's Victorian satire, it is the story of a Hexagon, the brilliant grandson on Flatland's Square who in his lifetime is confronted with even greater dimensionality problems. In the process of solving them he corrects his grandfather on some points...

And Geomerty, Relativity, and the Fourth Dimension:

This is a highly readable, popular exposition of the fourth dimension and the structure of the universe. ... Find a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional world in terms of the fourth dimension. ...

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Oh Cut that crap out.

[efuseekay]

Never read Bearden's paper. From the OP, it's total crap.

(a) I can write Maxwell's equation in whatever form I like : quaternions, vectors, component by component (go read Gell-Mann's book to see how cumbersome that is) covariant-indice form, and (most beautifully) in differential forms. It expresses a bunch of coupled differential equations that's all.

(b) Maxwell's theory is a classical field theory. You can attach words like " unified ", "successful", and blah to it, and it's still a classical field theory. I don't understand what the heck the OP is rambling about "quartenions" blah. There is no point to be made. The use of "big words" and impressive looking references only serve to give the false impression that there is actually "something" there.
(FYI, we now have quantum field theory, where we promote variables to operators and then impose canonical quantization on it. Which, btw, is totally incompatible with general relativity).

I don't blame the OP for being ignorant about the finer points of physics (after all, it's a career choice which pays very little!). But the sad truth is that nowadays, there are so many "wannabes" like Bearden who writes crap and mislead the general public. The people should be careful about what they read.

Multiple Dimensions

[Alien54]

Before the advent of Relativity, Maxwell and others were very interested in the investigation of multiple dimensions. Math Geeks should search for quaternions, etc.

In 1873, Maxwell succeeded in uniting a couple hundred years of electrical and magnetic scientific observations into a comprehensive, overarching electromagnetic theory of light vibrations ... carried across space by this "incompressible and highly stressed universal aetheric fluid ..." Maxwell's mathematical basis for his triumphant unification of these two great mystery forces of 19th Century physics were "quaternions" -- a term invented (adopted would be a more precise description) in the 1840s by mathematician Sir William Rowan Hamilton, for "an ordered pair of complex numbers" (quaternion = four).

Complex numbers themselves, according to Hamilton's clarifications of long-mysterious terms such as "imaginary" and "real" numbers utilized in earlier definitions, were nothing more than "pairs of real numbers which are added or multiplied according to certain formal rules." In 1897, A.S. Hathaway formally extended Hamilton's ideas regarding quaternions as "sets of four real numbers" to the idea of four spatial dimensions, in a paper entitled "Quaternions as numbers of four-dimensional space," published in the Bulletin of the American Mathematical Society [4 (1887), 54-7]. It is obvious from Maxwell's own writings that, even before Hathaway's formalization, his choice of quaternions as mathematical operators for his electromagnetic theory was based on his belief that three-dimensional physical phenomena are dependent upon higher dimensional realities.

In a tragedy for science, after Maxwell's death, two other 19th Century "mathematical physicists" -- Oliver Heaviside and William Gibbs -- "streamlined" Maxwell's original equations down to four simple (if woefully incomplete!) expressions. Because Heaviside openly felt the quaternions were "an abomination" -- never fully understanding the linkage between the critical scalar and vector components in Maxwell's use of them to describe the potentials of empty space ("apples and oranges," he termed them) -- he eliminated over 200 quaternions from Maxwell's original theory in his attempted "simplification."

This means, of course, that the four surviving "classic" Maxwell's Equations -- which appear in every electrical and physics text the world over, as the underpinnings of all 20th Century electrical and electromagnetic engineering, from radio to radar, from television to computer science, if not inclusive of every "hard" science from physics to chemistry to astrophysics that deals with electromagnetic radiative processes -- never appeared in any original Maxwell' paper or treatise! They are, in fact--

"Heaviside's equations!"

You can check this out by read a highly revealing paper on the subject by another renowned British mathematical physicist of this century, Sir Edmund Whittaker, titled simply "Oliver Heaviside" (Bulletin of the Calcutta Mathematical Society, Vol. 20, 1928-29, p.202); or, another overview of Heaviside by Paul J. Nahin, "Oliver Heaviside: Sage in Solitude" (IEEE Press, New York, 1988, p.9, note 3.).

The end result was that physics lost its promising theoretical beginnings to becoming truly "hyperdimensional" physics ... over a century ago ... and all that that implies.

Lt. Col Thomas E. Bearden, retired army officer and physicist, has been perhaps the most vocal recent proponent for restoring integrity to the scientific and historical record regarding James Clerk Maxwell -- by widely promulgating his original equations; in a series of meticulously documented papers on the subject, going back at least 20 years, Bearden has carried on a relentless one-man research effort regarding what Maxwell really claimed. His painstaking, literally thousands of man-hours of original source documentation has led directly to the following, startling conclusion:

Maxwell's original theory is, in fact, the true, so-called "Holy Grail" of physics ... the first successful unified field theory in the history of Science ... a fact apparently completely unknown to the current proponents of "Kaluza-Klein," "Supergravity," and "Superstring" ideas ....

To investigate this further you should take a look at --

"Possible Whittaker Unification of Electromagnetics, General Relativity, and Quantum Mechanics,"
by T.E. Bearden
(Association of Distinguished American Scientists
2311 Big Cove Road, Huntsville, Alabama, 35801)

Note, NOT available at Amazon

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