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PLANIVERSE the PLANIVERSE Computer Contact with a Two-Dimensional World the PLANIVERSE the PLANIVERSE computer contact with a two-dimensional world A.K. OEWO NEY c Sp1ingcr Scicnce+Busincss Media, LLC o 2000, 1984 by Alcxamkr K. D~\\'dne)'. Originally p1Jbl'shed by Springer Science+Bus'ness Media New York in 2000 AII rights r~s~,,·ed. No pari of this pllblication ma)' b~ reprodllCed, storcd in:l r~tricl'al s)'stem, or tr:1I1smitted, in :111)' tO:Jr111 or b)" an)' Illcans, electronic, IllIThanÎC"al, photocop)'ing, r~cording, or oth~r\\'ise, ",ithollt the prior ",riuen permission ofthe pllblisher. Origin:llly Pllblished as A l'oseidon l'ress Book by I'ocket Books, A Dil'ision ofSimo!l & Schllster, Ine. rllblish~d in th~ United St.ltes b)' Coperniclls, 3n imprim ofSpringa·ValJg New York, Ine. First Coperniclls softcol'er edition, 2000. Coperniclls Springer.val.\1> New York, Ine. 175 Fifth A,·clulc Nc,," Yurk, NY 100 I O Libr"ry (,f COl'l>rcSS Cat;llogill g-in -Pllblic;ltiol' Data Dcwdnc)', A.K. Thc pbni,·ersc . computer COIlUU wi th ;l ("\,·o-dimcnsional world / A.K. De,,"dllc)'. p. "n. Indudcs bibliographkal refercllccs. 1. H)"perspacc. 1 Titk. QA699.D48 2000 530.1'42--<k21 99-42454 MallufuCllIrcd in thc Ullitcd Sutes of Amc,ia. l'rilllcd OII acid-fre c ]Mpe'. 987654321 ISBN 978-0-387-98916-7 ISBN 978-1-4613-0199-8 (eBook) DOI 10.1007/978-1-4613-0199-8 To I. Richard Lapidus, physicist and friend contents Preface to the Millennium Edition ix 2Dworld xiii 1 Arde 1 2 A House by the Sea 9 3 On Fiddib Har 23 4 Walking to Is Felblt 41 5 City Below Ground 59 6 The Trek 83 7 The Punizlan Institute 107 8 Traveling on the Wind 137 9 High on Dahl Radam 161 10 Drabk the Sharak of Okbra 185 11 Higher Dimensions 207 Ardean Science and Technology 217 Acknowledgments 241 preface to the millennium edition When The Planiverse first appeared 16 years ago, it caught more than a few readers off guard. The line between willing suspension of disbe- lief and innocent acceptance, if it exists at all, is a thin one. There were those who wanted to believe, despite the tongue-in-cheek subtext, that we had made contact with a two-dimensional world called Arde, a disk- shaped planet embedded in the skin of a vast, balloon-shaped space called the planiverse. It is tempting to imagine that those who believed, as well as those who suspended disbelief, did so because of a persuasive consistency in the cosmology and physics of this infinitesimally thin universe, and x preface to the millennium edition in its bizarre but oddly workable organisms. This was not just your run- of-the-mill universe fashioned out of the whole cloth of wish-driven imagination. The planiverse is a weirder place than that precisely be- cause so much of it was “worked out” by a virtual team of scientists and technologists. Reality, even the pseudoreality of such a place, is in- variably stranger than anything we merely dream up. The first step in understanding the Planiverse is to “get it.” This means understanding that two dimensions means two dimensions. If the surface of this page represents a small portion of the planiverse, the following wriggly line could be a piece of planiversal string. The two free ends cannot be knotted together. For that we would need an extra, third dimension that comes out of the page, so to speak. But give us some planiversal glue and we could attach one end to the other, trap- ping inside the loop of string anything that happened to be there when the glue set. The appendix to the present volume contains a more or less com- plete history of how the planiverse came into being. Briefly, after an ar- ticle about the planiverse appeared in Martin Gardner’s mathematical games column in Scientific American, thousands (not hundreds) of readers wrote in with enthusiastic suggestions. Among these were a number of professional scientists and engineers, as well as several knowl- edgable readers with sensible suggestions. We have woven these ideas into a seamless place, but a story was needed to make an engaging book. The story would take us on a tour of Arde, a disk-shaped planet that swims in planiversal space. From Foreword to finish, the tale was told with a straight face, written in the style of an academic whose literary opportunites are con- tinually overwhelmed by events. The story used that modern deus ex preface to the millennium edition xi machina, the computer. It was on their computer, after all, that a group of students happened to make first contact with the planiverse and its four-armed hero, Yendred, whose yen for “higher things” turned to dread when he finally encountered them. (One must not imagine that the name has anything to do with my own, even when spelled back- ward.) It surprised and worried the author that so many people believed the tale was factual. Subtext that should have implied a fantasy (albeit a highly detailed one) was missed by many. Even in 1984 the neotenic trends in western culture were well established. Naturally, the same people missed the allegorical content completely, that it was, in the words of Oxford humanist Graham Stewart, a “sufi story.” Such con- tent was superadded. The temptation of invoking the higher (third) di- mension as a symbol for the workings that undoubtedly lurk behind the manifest reality of our world was simply too great to resist. The story begins with the original preface, which follows. A.K. Dewdney January, 2000 2Dworld The following book, of which I am not so much author as compiler, originates with the being whose picture appears on the first page. His name is Yendred and he inhabits a two-dimensional space I call “the Planiverse.” The discovery of the Planiverse, a reality still not accepted by many people, makes an interesting story in itself. The purpose of this introduction is to tell it. The first contact was made at our university only a year ago. My students and I had been running a program called 2DWORLD, the result of several consecutive class projects carried from one term to the next. Originally designed to give students experience in scientific sim- xiv THE PLANIVERSE ulation and in large-scale programming projects, 2DWORLD soon took on a life of its own. It started as an attempt to model physics in two dimensions. For example, a simple two-dimensional object might well be disk-shaped and be composed of billions of two-dimensional atoms. It has a kind of mass (dependent on the type and number of atoms in it) and may move about in the two-dimensional space represented by this page. Unlike the page, this space has no thickness whatever and the disk is doomed to eternal confinement therein. We may further imagine that all objects in this space obey laws like those which prevail in our own space. Thus, if we give the disk a gentle push to the right, it will move to the right and continue moving to the right, sliding along at the same speed in a space which extends this page beyond your pres- ent location. Ultimately, within this imaginary plane, it will move far from the earth itself—unless of course, it encounters a similar object: Doing so, the objects meet and suffer what physicists call an “elas- tic collision.” Here we see the two objects at the precise instant of their greatest compression just before springing apart in opposite directions. In accordance with another well-known law in our own, three-dimen- sional universe, the two disks carry off between them exactly as much combined energy as they brought to the collision. Given their tracks, they 2Dworld xv had to collide. They could not have slipped sideways past one another. There is no room in two dimensions for that, there is no “sideways.” This sort of physical event is not difficult to represent on a com- puter graphics display terminal, nor is it difficult to write a program which creates all the behavior I have just described in the case of the two disks. Naturally, if there are to be atoms in the disks, there is con- siderably more work for the programmer to do and, when the program is running, considerably more work for the computer. But one can write this sort of program and actually view the results on a screen. The program called 2DWORLD started in a manner not unlike this. In the first term that the project was assigned, the students, under my direction, had incorporated not only a simple set of objects and laws governing momentum into 2DWORLD, but had extended it to a system of planets orbiting a single star. At the end of the first term, there was talk among the students of a particular planet which they called “Astria.” They wished to give it a surface geography and have beings called “Astrians” living on it. I nipped that ambition in the bud; the semester was nearly over and examinations would soon be upon them. That sort of detail was mere wishful thinking in any event and far beyond their programming abilities. Nevertheless, the 2DWORLD program was very clever and enjoyable to watch. I remember especially well the formation of something very like a galaxy from an inchoate mass of stars. Indeed, I counted the project a great success and con- gratulated myself on confining the dimensions of the physical space to two.
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