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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.
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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Xenu loves you!
The planiverse was written by A. K. Dewdney, a prof a The University of Western Ontario. He was my thesis instructor and a very cool and intelligent guy. He wrote a column in Scientific American for a few years on computer and mathimatical puzzles and problems and is probably best known as the creator of Corewars. I highly suggest checking out some of his old columns and writings.
The difference between Canada and the USA is that in Canada healthcare is a right and gun ownership is a privilege.
My mom works in a bookstore and knows that i liked Flatland (i have read it twice), so she gave me the advanced reading copy of Flatterland to try.
While it starts off with some neat Terry Pratchet type humor and social satire, it quickly bogs down into nothing but math. While i am a big fan of quantum physics and the metaphysics of 'what is reality', i found this book to be too much math for my tastes. Too many examples and diagrams, all gone over and over and over until i couldn't take it any more and would jump ahead to the next mathematical theme. The humor at the beginning made me laugh out loud, but the rest of the humor was not to my liking and would have preferred he left that out.
I gave my copy to a math major and she loved it right away, couldn't keep her nose out of it. Maybe this would be good for a young student interested in starting into the math world, as the examples are explained from several points of view and are definitely not skimmed over lightly.
The author of the new book, Ian Stewart, is probably best known for his column "Mathematical Recreations" in Scientific American.
It is interesting to note that his predecessor in writing that column, A. K. ("Kee") Dewdney, also wrote a book (The Planiverse) inspired by Abott's Flatland.
- Tal Cohen
Here is a copy of flatland online from project gutenberg. Great fun to read.
I'm not sure it's fair to assume that Abbot was either. In fact, it doesn't seem unreasonable to believe that Abbot was intentionally commenting on / highlighting the (rampant) sexism and classism of his time.
just my $0.02 -- psykelus
i've compiled the book, including illustrations, into a newton book format. available here:
http://www.newtontraveler.com/books.html
- Entertaining Bits from the Ancient Kernel Tree
I have to agree with this poster. What matters in a scientific theory is not the formulation used, but what _predictions_ are made. Heaviside's equations are completely, absolutely identical in content to Maxwell's original formulation, and are MUCH more physically intuitive.
/. moderation.
A sad day for
Bob
Science, like Nature, must also be tamed, with a view turned towards its preservation.
Of course it's a joke. Everyone knows it's turtles all the way down.
Jerry Thorwayn is an author of a book called "Proffessor Ovilstar's Infinate Paradox", and it deals with all kinds of math theorums, as well as these flat land principals. You can see it here: www.ovilstar.net. He has written a whole book about this type of thing and inter-weaves romance and excitement into it. Kind of a sci-fi educational book :)
You're using "trivial" to mean "identity", or "Minkowski". I'm using it to mean "simple", that is, non-complicated, straightforward.
Granted, bad choice of words, but that's why I specified what I meant by trivial.
Dimensions are only orthogonal if the metric is trivial (i.e., diagonal).
The "metric" as I stated above is a 4-dimensional tensor (matrix, essentially) which (basically) provides the coefficients in the distance measure.
i.e., in 3-space, we have a distance measure of
ds^2 = dx^2 + dy^2 +dz^2
Here, the metric has a 1 in the dx-dx term, a 1 in the dy-dy term, and a 1 in the dz-dz term: in terms of a matrix, this would be just the three-dimensional unit matrix.
General relativity says that the metric is affected by the presence of matter and energy, so therefore, depending on the spacetime configuration, the dimensions may not be orthogonal. Near a black hole, this is actually distinctly not true - there is significant radial/temporal mixing in certain coordinate systems. Granted, you can always define a coordinate system with orthogonal coordinates.
In any case, you were mainly talking about special, rather than general, relativity here. The 4-dimensional metric being talked about is a Minkowski space - time is distinctly separate from any others, because in the Minkowski metric, we have
ds^2 = dx^2 +dy^2 +dz^2 - c^2 dt^2
note that time has a changed sign. We call this 3+1 spacetime.
All special relativity does is define exactly how you transform from one coordinate system to the next - in this case, via Lorentz boosts. Lorentz boosts in one direction have both a spatial boost and a temporal dilation, which is what you are talking about. It doesn't mean the coordinates aren't orthogonal - it just means that when you boost from one frame to a faster-moving frame, both the boost direction and the temporal direction are affected.
Short answer: you answered your question yourself - you said "rate of movement", but above you said "movement" - there's no reason to expect that "moving" is the same as "steady motion" - or, that a simple translation is the same as a velocity shift. In truth, it isn't.
Think about it this way. It's true, time and space are orthogonal. If I do a time translation (i.e., in my coordinate system I redefine t = t + t0) it doesn't affect the x, y, or z coordinates. Likewise for spatial coordinates.
But there's no a priori reason to expect that when you start talking about another frame of reference that is in constant motion with another that it shouldn't affect the other coordinates. After all, you're already mixing things: you have to talk about z = z0 + vt, for instance. Here, instead of the boost simply being z = z0 + vt, there's a Lorentz factor as well.
About 10 years ago, I ran across a book in a used book store that greatly reminded me of Flatland called "The Planiverse." It is not quite as mathematical as Flatland, but instead gets more into the biological-type details. The residents of the planiverse are not geometric shapes, but rather 2-dimensional organisms. The book explains complexities of their world (how do you have weather in a flat world, and how do you deal with water runoff?), their society (how would 2 dimensional paper, books, and libraries work?) and biology (if a flat organism has to eat, it cannot have a digestive track, otherwise it would be split into two pieces!).
/ o/qid=987870273/sr=8-1/ref=aps_sr_b_1_1/104-961239 4-9227167
I remember really enjoying it, but I admit I was sixteen years old at the time and have not picked up the book since. You can find it at the usual places: http://www.amazon.com/exec/obidos/ASIN/0387989161
-E
'Nuff said.
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"Of course, that's just my opinion. I could be wrong." --Dennis Miller
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:
And Geomerty, Relativity, and the Fourth Dimension:---
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"Of course, that's just my opinion. I could be wrong." --Dennis Miller
You can get that book for 90 cents on Amazon or anywhere else that sells dover thrift editions.
You can also get it for free online from Project Geutenberg
Any word on wether the new flatland will be sexist as hell? Reading the original was an interesting look into good old-school great chain of being type classism...
The nobitity are polygonal, with rank being determined by number of sides. Commoners are isocoles triangles, with acute angles at the low and equilaterals at the high end of the social spectrum. Women, whatever their rank, are lines.
I wonder how they are going to style the new one without being hopelessly sexist and classist while maintaining continuity...
+++ ATH0 +++
One thing that strikes me about flatland that I don't hear people talk about much is the stickingly effective way that Abott uses analogy to help deal with hard to grasp concepts.
Don't understand what you can do in 4 dimensional space? No problem; just analyze what you can do in 3D that someone in 2D can't. Simply extrapolate from there.
This book taught me about seeing reality from other's perspectives, about the power of analogy, and the value of approaching a problem starting from where the *other* person's viewpoints lie.
-pos
The truth is more important than the facts.
The truth is more important than the facts.
-Frank Lloyd Wright
Actually, you were educated stupid and evil by evil educators. Academia is a religious cult empowerment of self word. Not even a god can deny that I have squared the circle of a static Earth and cubed the Earth sphere by rotating it once to a dynamic Time or Life Cube. Only a false god or academically brainwashed indoctrinated mindless moron would deny that the Earth lacks the top and bottom, the front and back, and 2-sides physical dimensions of a Cube that spirals a 4-season quad helix around the Sun - creating a swirling of 4 simultaneous years as in a separately created year for each of 4 seasons. You do not have the "guts" to seek Time Cube "Truth".
beautiful!
your fan WDK - WKiernan@concentric.net
His nickname says it all ... "Trevor Goodchild" ... the evil-mad/scientist/doctor from Aeon Flux? :)
Free Techno/Jazz/DNB/MI Music by guys obsessed with monkeys!
I believe you score highly on the Crackpot Index
Mode (3) smart-aleck mode. Press * to return to main menu.
You could have at least said the the Maxwell theory of em fields was contradicted by the observation of particle phenomena (quanta). But you didn't, and even so that misses the point completely.
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When I said "classical field theory", that's what I meant. The quantum theory of EM is called "Quantum electrodynamics", and is part of "quantum field theory".
Apparent paradoxes are used as an argument to justify an irrational, dualistic interpretation of the theory.
If you mean the particle-wave duality, then it is not a paradox. Please do not confuse "not-intuitive" with "paradox". Quantum Field Theory is a hard subject to master, and it breaks down at some energy scales. But it is an excellent theory at low common day energy scales. QED predicts the fine structure constant to more than 10 decimal place, and no theory in this world is better than QED.
However, at a closer look one can find that any paradox arises only from an inconsistent physical concept or other errors in logic. Goedel proved that from a logical system which contains a contradiction, absolutely any proposition may be proven. With a consistent theoretical interpretation (in any branch of science) no paradox should occur at all.
Since your previous statement is wrong, this is non-sequitur. There is no paradox in QED. Every undergrad physics student know E&M is not self-consistent. (Read Feynman's lectures on physics Vol 2 for a beautiful exposition. The book is aimed at freshmen, so you should be able to figure it out.)
"Quantum mechanics used only the Heaviside/ Gibbs externalized electromagnetics and completely missed Maxwell's internalized and ordered electromagnetics enfolded inside a structured scalar potential.Accordingly, QM [quantum mechanics] maintained its Gibbs statistics of quantum change, which is nonchaotic a priori. Quantum physicists by and large excluded Bohm's hidden variable theory, which conceivably could have offered the potential of engineering quantum change -- engineering physical reality itself.
This, I gathered, is the whole problem. Bearden's generous used of big-sounding words and rhetoric masked the fact that this is a lot of BS. So, let's see
"externalized/internalized" : what does this mean?! There is no such thing in physics or math. "QM maintained its Gibbs statistic charge, which is no-chaotic apriori" : What's a Gibbs statistic charge? What is "no-chaotic"?! "Charge" is a conserved quantity in a field theory, which means that it is some physical thing (like eg. electric charges) that you can measure and is constant in time provided that there is no "current" (eg. electric current) flow into the system.
I am too tired to say horrible things about the last sentence.
I am sorry if I sounded sarcastic. But please read some better books if you want to understand this stuff. A good place to start is "Feynman Lectures on Physics Vol 1-3". And forget about crap like Bearden's book.
As I said, physics is both financially and socially unrewarding. The price of admission into physics is many years of hard work and lots of frustration. But to be able to learn the stuff so that one can figure wonderful things out, and doing it correctly, is well-worth it. There is no short-cut to hard-core science.
Mode (3) smart-aleck mode. Press * to return to main menu.
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.
Mode (3) smart-aleck mode. Press * to return to main menu.
I have only flipped through the new book (though there was another one published some time back called Sphereland or something of the sort -- it was sort of "Mr Tomkins in Wonderland" rewritten for the Square's hexagonal grandson). So I can't really comment.
To those of you who haven't read the original, you should, if only to see how frightening the mores of late 19th century England really were. The culture of Flatland is one in which classism and sexism (and probably racism as well -- it's been a while since I read it) is hardcoded in the biology of its inhabitants. It doesn't put a great deal of effort into scientific logic (if you think about it, the Flatlanders basically live their lives floating in empty space), but its culture is vividly drawn.
Sadly, Edwin Abbott Abbott's writing style doesn't measure up to his imagination -- he's very heavy-handed, with every corner of the story steeped in the telltale narrative overload of Delivering a Message. You get a peculiar picture of a man who is either strongly pro-status quo or violently against it but either way resigned to the belief that things are ordained to be as they were in his time and could never change.
It's a peculiar little book -- I got my edition as a Dover Thrift Classic for a buck and I think it wound up in the custody of a high school theology teacher of mine (Catholic schooled and proud). I do recommend getting the cheapest printed version you can find; it's better with the pictures.
If you're interested in a more scientifically thought out book about a flat universe, you might want to check out The Planiverse by A.K. Dewdney -- it's a story based on some old Scientific American columns he did about what life would really be like in a flat universe. It's a rather more interesting book that probably more resembles Dragon's Egg by Robert Forward than it does Flatland and follows the story of a laboratory full of grad students and researchers as their computer somehow makes contact with a two-dimensional universe through an inhabitant by the name of Yendred who leaves his relatively civilized home on a spiritual quest. It's quite heavy on details (but isn't that the point?) and a much easier read than Abbott.
So now I guess I have to read two books...
/Brian
here at channel.nytimes.com as usual.
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Escher was the first MC and Giger invented the HR department.
If nothing changes (==moves) in spacetime, doesn't it mean the future has already been determined? Then there would be no need for causal relations either.
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Escher was the first MC and Giger invented the HR department.
If you find this stuff about higher dimensions interesting, take a look at this article. Merely an introduction, but it goes on further into new theories, including the idea that gravity might be aware of higher dimensions (whereas other forces are not).
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Escher was the first MC and Giger invented the HR department.
Time is often considered a fourth dimension, but what was meant in the book was spatial. Einstein's General Relativity predicts that space is curved near massive objects, and it takes a fourth spatial dimension to curve the three-dimensional fabric of space. In fact the theory involves time as one of the dimensions so the four-dimensional spacetime is curved in a fifth dimension. See my article for more.
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Escher was the first MC and Giger invented the HR department.
Why? You state this without proof. Well, then my counter claim is that the universe isn't even a sphere, its a tube, and there is only one of them. Now we have two unprovable claims that lead to different conclusions.
This shows why the universe must be Open
The open-ness or closed-ness of the universe has nothing to do with geometric theory.
This is a worthy long term destiny for us to aim for, and I urge that we start preparing now.
Okay, this is a troll, you got me.
this all reminds me of my tenth grade geometry teacher when he would take us on visits to flatland and planeland on the chalkboard. He would also often ask us to play touchy-feely with the triangles! Argh! The terrible memories are coming back...lets leave geometry IN THE TEXTBOOKS! Argh..just when i thought i had blocked those memories from my brain!
The anti-salmon
This also reminds me of a book (and website) a friend of mine made about adventures, romance and higher math. The website is at ovilstar.net and it has some really interesting music and pictures on the site...the book is pretty interesting, and so are the essays...it is a book about an adventurer (professer ovilstar) and of course math and romance...it all mixes together really well....right?
But really...check out ovilstar.net and buy the book (only 4.95 and it promotes the selling of books online)
The anti-salmon
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
Check out the Vinny the Vampire comic strip
"It is a greater offense to steal men's labor, than their clothes"
The Universe can be considered 5 dimensional. Imagine that the universe is a sphere, for a moment. When it started off at the big bang, it was a point. Then it quite literally blew up, like an expanding balloon. This was called inflation.
This is not the whole story, though. For inside the balloon is another ballon, and inside that one another. It is like an Onion, with all these different shells expanding outwards from the central fire of Creation. Extrapolate this to our 4 dimensional universe, and you can see that the Metaverse is 5 dimensional. There is some reason to believe that the metaverse will not be of infinite age, in which case there may be another 6th dimension of other metaverses constantly being created.
This shows why the universe must be Open - it cannot contract again because it would collide with the universe underneath us. Eventually, our universe will slough off the edge of the onion, and that will be the end of us.
Unless, that is, we start researching technologies to transverse the universes, and travel to the younger universes below us. Then eventually we can approach the everlasting point of creation at the nucleus of the onion.
This is a worthy long term destiny for us to aim for, and I urge that we start preparing now. Why bother with the petty details of day to day life - we should be thinking of the destiny of our race, our species, our Universe, and striving to make tommorrow ours.
I picked up this story today for a buck after reading the thread and was really suprised to find it more of a Victorian satire than an education on multi-dimensionality. Of course, I'm just finishing the first section now (which is presumably where most of the satire lies), so this will probably change. I read the reviews at amazon.com and was suprised at the ignorance of the reviewers. This is really blatent satire and it is rediculous to think otherwise, especially given the introduction (in the revised second edition). It is incredibly ironic to see women's rights advocates railing this book. Hell, I know next to nothing about Victorian-era England yet it was easy to pick up the social commmentary. I will say that mathematics have definitely improved somewhat in the last 120 years. The explanations are pretty simple and unneccesary for a modern reader (at least to the point I've reached).
The suggested price of the paperback is just a buck, so go to any of the horribly massive biblioplexes (borders, whatever) and it should be in the sci-fi section.
Your "onion" shells are the first part of the cosmology of his Culture universe. But in the 6th dimension the universe is a torus; and as the onion shells expand and then contract they circle this torus, arriving back at their point of creation without ever colliding with the universes behind them. So each universe is closed, but an infinite number of them are created and destroyed at the center of the torus.
Let's see, there is also an "energy grid" separating the universe-onion-shells which the Culture has not yet learned how to penetrate, though it comes in handy for powering faster-than-light spaceships.
For more info on this I suggest reading one of these books by Iain Banks:
The Player of Games
Consider Phlebas
Use of Weapons
Excession
There is also an online Banks fanzine called the Culture, and an online interview somewhere (do a search) where he explains this cosmology in great detail, and other items about the Culture which aren't explained fully in the books -- like how the characters get their names.
Brackets contain world's first nanosig, highly magnified:[.]
Q: Where do Flatlanders bury their dead? A: In a pine square.
Actually, that book by Rudy Rucker isn't much of a sequel to Flatland. Like almost all geometry books, it discusses the issue, but isn't framed in the Flatland world.
However, Rucker DID write a direct sequel. It is a short story called "Message found in a copy of Flatland" and you can find it in "Transreal!" which is an anthology of his writings (and one of the best damn SF books I know). Check it out, ISBN 1-878914-00-6